## May 12, 2007

### People Who May or May Not Actually Exist

#### Posted by John Baez

There are a lot of important people we know little about. Some might not even exist!

A couple of years ago James Dolan and Toby Bartels played a game where they took a long list of famous people and estimated the probabilities that they really existed. I’m curious about your opinions.

To get the game rolling, I’ll give a list of name and my own estimates. I haven’t thought hard about these numbers — they’re just instant shoot-from-the-hip guesses. I haven’t even bothered defining what it means for one of these people to exist! I’m not claiming they did everything attributed to them — just enough to make them count as themselves, whatever that means.

(For example: did you know Homer didn’t write the Odyssey and Illiad? They were actually composed by another guy with the same name!)

Arguing about the existence of some of these people could lead to nasty quarrels. If you’re the slightest bit rude, I’ll delete your comment. What I really want, most of all, is lists of probabilities.

Here’s mine! Try your own hand at it…

Posted at May 12, 2007 7:13 PM UTC

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### Re: People Who May or May Not Actually Exist

I’ve long believed that Jim Dolan is the alter ego to whom John Baez assigns his more outrageous opinions, on e.g. capitalization.

Littlewood has a story in his Miscellany, of meeting someone who said “Oh, you really exist! I thought you were just a pseudonym that Hardy put on his weaker papers.” I give that person a 60%.

Posted by: Allen Knutson on May 12, 2007 9:03 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

More importantly, what probability do you give James Dolan?

Posted by: John Baez on May 12, 2007 9:34 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

There’s also the case of the (typically British) double-barrel-named people like Swinnerton-Dyer who people who only know the names of theorems/lemmas/conjectures, eg the Birch-Swinnerton-Dyer conjecture, believe to be multiple people. Equally, Birch deserves half the credit rather than the third he gets from naive dash counting.

Posted by: dave tweed on May 13, 2007 1:36 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Yes, I remember being very confused about Birch, Swinnerton, and Dyer (who I thought might have helped invent the Dyer–Lashof algebra).

And then there’s the Bernstein–Gelfand–Gelfand resolution, where it seems Bernstein slacked off and did only one-third of the work.

Posted by: John Baez on May 13, 2007 6:31 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

This is what the en-dash is for!

Posted by: James on May 13, 2007 10:40 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Yes: if Dave Tweed had deployed the en-dash and written Birch–Swinnerton-Dyer, there’d be no risk of confusion. (?)

Posted by: John Baez on May 13, 2007 10:51 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I think there should be a lot of good jokes involving various combinations of these people.

Like: “Osama bin Laden, Santa Claus and Pythagoras were sitting at a bar…”

Posted by: John Baez on May 12, 2007 9:45 PM | Permalink | Reply to this

### Bar none; Re: People Who May or May Not Actually Exist

Osama bin Laden, Santa Claus and Pythagoras walk into a bar

“So, what will you three bearded gentlement have?” asked the bartender.

“Nonalcoholic beer,” said Osama. “No chaser. I feel sorry for anyone who is chased all the time.”

“A glass of milk, and some cookies,” said Santa Claus. “Also, a pencil and paper. I’m making a list…”

“I’ll have a bowl of chili,” said Pythagoras. “But only if it has no beans in it.”

The bartender serves them all. He hands them each a bill. They all look at each others’ bills. “Hey,” says Pythagoras, pointing at Osama and Santa. “How come mine is equal to the sum of those two squares’?”

Posted by: Jonathan Vos Post on May 12, 2007 10:32 PM | Permalink | Reply to this

### Re: Bar none; Re: People Who May or May Not Actually Exist

<Muffled laughter in the stalls; catcalls, peanuts etc from the gallery>

That was quick!

OK, Nicolas Bourbaki and Pythagoras are sitting next to each other on a plane …

Posted by: Tim Silverman on May 12, 2007 10:55 PM | Permalink | Reply to this

### Re: Bar none; Re: People Who May or May Not Actually Exist

… and Nicolas Bourbaki says, in a French accent, with a voice that sounds curiously like several voices in a choir: “shouldn’t that be ‘SETTING next to each other?’”

Posted by: Jonathan Vos Post on May 12, 2007 11:32 PM | Permalink | Reply to this

### Re: Bar none; Re: People Who May or May Not Actually Exist

Bourbaki and Pythagoras are sitting next to each other on a plane. Their food arrives and they kind of look at it in dismay, and poke at it with their plastic forks.

“Numbers,” says Pythagoras. “It’s all made of numbers.”

They each take a mouthful.

“Like sand,” said Pythagoras. “Dry, very dry.”

“That’s good,” says Bourbaki. “I like my food very, very dry.” He takes another mouthful. “This, on this other hand, is disgustingly sloppy. If I have to eat one more mouthful, I’ll puke. I’ll puke it up! In fact, I’ll puke it the whole length of the cabin and through the cockpit door!” And he points down the length of the plane.

“Don’t exaggerate,” says Pythagoras.

“Why not?” says Bourbaki. “This is a hyperbolic plane.”

Posted by: Tim Silverman on May 13, 2007 10:31 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I don’t really know what it means for a lot of these people to have existed. Does 5% mean there was a real person who did 5% of what the legendary figure is said to have done? Or that there’s a 5% chance that there was anybody at all that did any of it? Or that there’s a 5% chance that the current legend has a continuous history of retellings back to a completely different legend which mentioned the name of a real person?

Adam—0%. I don’t even know what it would mean for “Adam” to be real.

Gilgamesh—5%. I guess there might possibly have been a real king by that name, though the entire legend seems purely fictional.

Huang di—0%. I guess I should put him in the same category as Gilgamesh, but the time till the earliest evidence seems longer.

Moses—I suppose 30% seems vaguely reasonable for some possible core of reality at the centre of the legends.

Zoroaster—an author for the oldest part of the Avesta? Well, someone must have written it, so that would put him at 100%. I don’t know enough about Zoroastrian tradition (to put it mildly) to comment intelligently on legends.

Samson—0%. Everything about story this has the ring of folktale.

Hercules—0%. He’s pure mythology. He’s a god, his attributes and name are ultimately Babylonian. No way is he real.

Theseus—0%. Purely mythological.

Odysseus—0%. Local trickster god.

Agamemnon—5%. I can’t rule out the possibility that there was a real person of that name at the base of some of the legends.

Helen of Troy—0%. I suppose it’s conceiveable, that if Agamemnon existed, he may have had a brother who may have had a wife, but I don’t think that’s enough of a connection.

Homer—difficult. Do we count the author of the Iliad and the author of the Odyssey separately? It seems unlikely to me that they don’t each have single core authors, notwithstanding later additions and developments, so maybe 90% for each author separately, 20% for both together. But for all I know, maybe a Homer scholar could dismantle the narratives completely.

Buddha—as a core of the legend? 99%. As actor in all the legends? 0%

Lao Tzu—hmm. That some of the legends and philosophy trace back to a real person of some such name? 90%. That the Tao Te Ching was all written by him? 0%

Chuang Tzu—I’ll go with your 80%. I know very little about him.

Confucius—99%. He seems too well-authenticated to be unreal.

Pythagoras—99%. Though I don’t believe he had a golden thigh or slept for several years in a cave in Thrace.

Socrates—100%. It would just be bizarre for him to be a combined fiction of Plato, Xenophon and Aristophanes …

Plato—100%. How would one arrange for the disappearance of Plato? Who would write the dialogues?

Jesus—98%. I don’t believe in the miracles, and his entire infancy seems to be obviously a fabrication, but that there really was a provincial reformist who told parables and founded a sect that became the Christians?—that seems pretty likely. I’ve heard the suggestion that he started life as the fictional center of a short set of moralising essays—kind of like Job—but the incidents of his life don’t seem to have the right kind of poetic or novelising feel to them, despite the obvious echoes and duplicates of incidents from earlier literature.

Mary Magdalene—uh, duh, I suppose 50% will do.

Paul the Apostle—100%. Yes, it’s theoretically possible he’s a construct, but it seems pretty far fetched.

Muhammad—100%. I won’t vouch for the authenticity of every hadith, and no doubt there’s a lot of legend in early Muslim historiography, but I don’t see how you could eliminate Muhammad and still have history turn out the way it did.

Brunhilde—0%. She just screams “mythological”.

King Arthur—0%. Well, OK, I suppose there may have been some historical figure of post-Roman Britain who got mixed up with the legendary figure, but I don’t think that counts.

Morgan le Fay—0%.

Robin Hood—0%. Pure folktale.

Shakespeare—100%. Too much historical evidence. And someone wrote the plays and poetry. And it sure wasn’t Francis Bacon—it’s not like we’re short of samples of Bacon’s writing.

Santa Claus—0%. Unless you mean the historical St Nicholas, whom I place more credence in …

Johnny Appleseed—I guess 100%, but I’d automatically discount large quantities of legendary stories …

Paul Bunyan—maybe, not being American, I’m missing something, but I don’t see how I could possibly assign him more than 0%.

Zorro—0%. I’m not sure at what point exactly the joke began here, so I’ll just press on further into the swamp …

Jack the Ripper—99%. I suppose he could just be a statistical fluke …

Nicholas Bourbaki—100%. I take it you mean the French general …

I seem to be much more certain than you! That makes me nervous. Maybe I just don’t know enough …

Posted by: Tim Silverman on May 12, 2007 10:48 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Tim Silverman said,

I don’t really know what it means for a lot of these people to have existed. Does 5% mean there was a real person who did 5% of what the legendary figure is said to have done? Or that there’s a 5% chance that there was anybody at all that did any of it? Or that there’s a 5% chance that the current legend has a continuous history of retellings back to a completely different legend which mentioned the name of a real person?

Adam, Helen of Troy and Thomas Bayes walk into a bar…

Posted by: Blake Stacey on May 13, 2007 12:17 AM | Permalink | Reply to this

### Helen remembers; Re: People Who May or May Not Actually Exist

Bayes: “What are the chances that you’re real and the most beautiful woman in the world?”

Helen: “To you, zero. Get lost!”

On “Helen Remembers the Stork Club”

commentary on “Helen Remembers the Stork Club,” by Esther M. Friesner
(The Magazine of Fantasy and Science Fiction, Nov 2005) a finalist for the Nebula Awards which were announced 12 May 2007by SFWA (Science Fiction Writers of America).

“… Why the fascination with Helen? Buy my Muse a drink and ask her. I’ve always been one to want to know the backstory on certain characters, and when there’s no satisfactory backstory out there, I make one up. It amuses me and keeps me off the streets and out of the pool halls. Maybe I felt sorry for Helen, the Most Beautiful Woman in the World. Can we talk about pressure? Maybe I forgot all about the fact that she’s only a mythological figure and so doesn’t need to have a Before, just a Now. Maybe I wanted to give her more of a story than being just another pretty face. Yes, just another pretty face that caused a ten-year war, destroyed a major city, and when it was all over, got her husband to take her back by dropping her robe off her shoulders in the great-grandmomma of all Spartan Queens Gone Wild videos, but still—!…”

http://sfwa.org/pressbook/SFWAPR/070512-SFWA-NebulaAwards.html#Writers

Posted by: Jonathan Vos Post on May 20, 2007 4:48 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Tim Silverman wrote:

I don’t really know what it means for a lot of these people to have existed.

True, it’s a real head-scratcher. Not only don’t we know if they existed, we’re not even sure what it would mean for them to have existed! Their very definitions are so fuzzed-out that any method of making them precise seems hopelessly arbitrary. It’s a problem of identity that makes the philosophers’ puzzle about Hesperus and Phosphorus (the Evening Star and Morning Star) look like a piece of cake.

It’s fascinating how much of human culture involves mysterious figures like this. It’s an inevitable consequence of oral traditions, I guess. Here’s a nice example of a historian trying to grapple with this:

Among other interesting things, he writes:

Many different theories are available as to the ‘identity’ of Arthur and some brief methodological notes will be found here regarding the making of such identifications. While these theories are interesting, they fail to address fully one important question — was there a historical post-Roman Arthur? Many books, articles and web-pages simply make the a priori assumption that there has to be a historical figure behind the Arthurian legends. Such an assumption is totally unjustified. As anyone at all familiar with medieval literature in general will know, the historicisation of non-historical/mythical personages — often through association with some important event of the past — is not in any way an unusual occurrence. Some examples of this that will probably particularly interest readers of this article are Hengest and Horsa, who were Kentish totemic horse-gods historicised by the 8th-century with an important role in the 5th-century Anglo-Saxon conquest of eastern Britain (see Turville-Petre, 1953-7; Ward, 1969; Brooks, 1989; Yorke, 1993); Merlin (Welsh Myrddin), who was an eponymous founder-figure derived from the place-name Caer-fyrddin and historicised with the deeds of one Lailoken (see Jarman, 1991); and the Norse demigod Sigurd/Siegfried who was historicised by being associated with a famous historical battle between the Huns and the Burgundians dated 437 AD, in the Nibelungenlied (Thomas, 1995, p.390). Given this, no a priori judgements can be made as to whether a figure is, in origin, historical, mythical or fictional — each individual case must (and can only) be decided by a close examination of all the relevant material. When we have figures such as Arthur being portrayed as historical we are therefore, on a very basic level, looking at either a historical figure or a legendary figure who became historicised, with neither explanation enjoying priority on a priori grounds — it must be recognised that one can only say that there has to have been a historical Arthur once all the material has been evaluated and this has been shown to be the case; there is no possible justification for simply assuming this.

[…]

With regards to the whole question of historicity and historicisation, it has been suggested that, rather than ask whether there is any justification for postulating a historical Arthur, we should ask whether any candidate fits the ‘facts’ — certainly the undertaking of such an exercise is very beneficial but it probably doesn’t actually show anything, at least with regards to historicity. To take an example, several people have suggested, over the years, that Ambrosius is Arthur on the basis of Historia Brittonum Chapter 56. However, what they see can be one of two things — either they are seeing the ‘truth’, that Ambrosius was Arthur, or they are seeing a partial truth, that the portrayal of Arthur in these sources was based on Ambrosius but that this is a secondary development of a folkloric Arthur; in a sense Ambrosius was Arthur but not in the sense that most people would mean when seeking an answer to this question. How does one get away from this? The only way I can see is by adopting the above methodology, by asking what justification there is for postulating a historical Arthur. Indeed, it should further be pointed out that there are certain dangers in looking for characters who ‘fit the facts’ — to take the example of Chapter 56 of the Historia Brittonum once more, with sufficient ‘imagination’ and linguistic gymnastics, as has been noted, the list of battles in this Chapter can be made to fit just about any locality one can think of and as such these theories are mutually cancelling and methodologically indefensible — thus Collingwood (1929) succeeded in ‘discovering’ all the battles in the south-east, which happily fitted his theory that Arthur only fought the Jutes; Anscombe (1904) ‘found’ that all the battles were fought in the Midlands; and Skene (1868, I, pp.52-8) ‘discovered’ that all the battles could be identified with places in Scotland! The above methodological considerations hold whether one is looking at models for historicisation or ‘Arthurian originals’ — a vast literature has been generated, both online and offline, by the search for historical characters who ‘fit the facts’ but the simple truth of the matter is that the vast majority of these efforts are methodologically indefensible. While internally consistent, these theories are all mutually cancelling, explain only a tiny portion of the legend, if any of it, and an almost infinite number of such identifications can be made (especially when a shot of ‘ingenuity’ is added to the mix), all impossible to disprove but equally nearly all invalid.

But, I’m glad all these subtleties didn’t stop you from going through the list and giving them probabilities!

I seem to be much more certain than you! That makes me nervous.

Yes, you seem quite confident about assigning events a 0% or 100% probability. Are you often shocked by things not working out the way you expect?

I would not be terribly shocked if, say, there turned out to be a war between Trojans and Greeks that started from a marriage gone sour involving a beautiful woman named Helen… and if that happened, I might feel fine saying “Helen of Troy existed”. So, I wouldn’t assign this a 0% probability, they way you did.

Similarly for a lot of the other legendary characters.

Maybe I just don’t know enough…

Maybe you know too much! Isn’t that what causes people to assign 0% or 100% probabilities to lots of events?

Or, maybe you just know more than I do.

Posted by: John Baez on May 13, 2007 1:43 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Forget about the meaning of existence. I don’t even know what probability means here! I mean, what is the space out of which you’re choosing your samples?

What is the probability that the 10^10th prime number ends in a 3? The 100th? The 2nd? The 1st?

I think I remember hearing about a question in analytic number theory where someone gave a probabilistic argument that a (well defined, non-probabilistic) statement X is true, and then someone else came along and gave a more refined probabilistic argument that X is false. If it weren’t for the fact that we’re not that much smarter than each other, you could imagine this going on forever.

(I’m not trying to spoil any fun here. I just think these questions are also fun.)

Posted by: James on May 13, 2007 2:32 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I would most naturally represent the space here as the set of ways the world might be, according to the person who is doing the estimating. Of course, they don’t have those ways fully represented mentally, so they may be incomplete and/or inconsistent, which allows them to include non-extreme probabilities about facts we know to have a decidable truth-value, necessarily (like the primality of 1936628496623860273650372660673620483).

As for these probabilistic arguments, because of the nature of the probabilities, I’d hope that the arguments given are Bayesian! In which case they’ll depend on the priors, and I don’t know where those will come from.

Posted by: Kenny Easwaran on May 13, 2007 4:42 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Ah, we’re never far from philosophy! Agreeing with Kenny, we’d be looking at a Bayesian interpretation of probability theory here. Then there’s no reason to exclude mathematical propositions as things about which one can assign a probability. (See chapter 5 of my book.)

A good way to think of things is in terms of lotteries. What does John mean by assigning 50% to Lao Tsu? First of all, take as your measuring kit tickets which if you win give you £100, where winning occurs if you spin a two-coloured wheel of fortune and red occurs. Different wheels have different amounts of the circle painted red from 0 to 360 degrees.

Now John would seem to be just as happy with a ticket which will give him the money if Lao Tsu existed, as he would with a ticket based on 180 degrees of red. He would prefer the Lao Tsu ticket to one based on 170 degrees of red, but favour a 190 degree ticket.

You can imagine how many degrees of red corresponds to your belief in the Riemann Hypothesis - 359.99 degrees perhaps?

Of course, we have to specify the outcome precisely enough for the lottery comparison to make sense. We have to know what it is to say that Lao Tsu existed. Is it enough that someone, perhaps with a different name, shared specified features ? What if someone named Lao Tsu lived around that time but didn’t do anything very like the historical figure? These things have to be decided.

Posted by: David Corfield on May 13, 2007 12:56 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

OK, good. I still can’t imagine myself (yet!) in an actual situation where John’s set up could make sense, but as David suggested, here’s one where my question about the probability that the 10^10th prime ends in a 3 could make some sense. It’s a bit long-winded, but I want to make sure two things hold: (a) that I’m the only human involved, and (b) that this could work in the actual world, unlike an attempt to figure out what I think the probability that the number of angels that can dance on the head of a pin is less than 100 is.

Suppose we have a computer that can determine in a bounded amount of time whether the n-th prime number ends in a 3 for n up to a fixed number N larger than 10^10. (If N=10^11, I bet is easily doable with current technology). Let’s also assume I’m completely confident (by reading the code, say) that the computer does what it’s supposed to. Now suppose we play a game in which we flip coins to generate random numbers n in the range 1 to N, and for each n, I am given the choice of either

1. betting that the n-th prime number ends in a 3, or
2. betting that a spin of the two-coloured wheel (with x% red) will end up red.

Let’s also say that I have only some small amount of time like 10 seconds to make my choice. (Even further, let’s say that if I lose the bet, I’ll lose something very small, like one bean, whereas if I win the bet, I’ll win something very nice, like one Get Out of Committee Meeting Free card. So I do really want to play as much as possible.)

If the number n comes up and if after 10 seconds of thought, I’m indifferent between 1 and 2 (with an x%-red wheel), then I will now happily say that I think the probability that the n-th prime number ends in a 3 is x%. For example if n=10^10, I’m indifferent with 25% red (the asymptotic value, by the Chebotarev Density Theorem). If n=2, I’m indifferent with 100% red.

Or, I’m almost happy to say that. I’d prefer to say I’m x% *confident* with 10 seconds of effort that the last digit of the n-th prime is 3. This eliminates the word probability altogether and makes it clear that it’s really a statement about me, not about prime numbers. For instance if n=100 comes up, I won’t be able to figure out in 10 seconds anything about the last digit of the 100th prime, so I’ll just stick with 25%. But maybe someone really good at arithmetic could actually figure it out, and their confidence would be either 0% or 100%.

OK, but I still can’t imagine such a game about the previous existence of currently non-existent people. Suppose some guy at a carnival propositions me with a game where he picks a historical figure from some list, I have a choice between 1 and 2 as above. But before I agree to play (this guy is going to charge me many beans), I would insist on his giving me some kind of proof of the existence or non-existence of the person whenever he claims I lose. But it’s completely impossible to have proof of the previous non-existence of a currently non-existent person. So if he claims he has proof either way, it must be proof of the existence. And so I should always say I’m 100% confident that each historical figure existed. Thus ruining the game.

Now you see why I wanted to remove all other people from the set up of the first game. If someone challenges you to such a game, they probably know more than you. Before I asked my question, I had thought about two-player games with prime numbers, but rejected them all for this reason.

So, now that David has answered my first question, can anyone make up a game that can actually work to test our confidence in the existence of historical figures?

And it must pass the dancing angels test!

Posted by: James on May 14, 2007 2:24 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

There are big problems for the betting interpretation of credence (aka confidence, or subjective probability). I’m very confident that the Goldbach conjecture is true, but I’m not willing to stake much on it, because I think it’s unlikely that anyone will ever be in a position to settle the bet. (Or if we add a magical device that settles the bet for us automatically, then I’ll be willing to bet a lot on things that I’m very uncertain of, like Woodin’s Omega conjecture, just to have the device settle the conjecture.)

And of course, with real people doing the betting, I get very skeptical when people try to offer me bets that are favorable from my point of view.

In the end, I don’t think either of these objections is fatal to the idea of some notion of confidence that satisfies the Kolmogorov axioms (whether or not you think it should be called “probability”). We can’t get a behavioristically acceptable notion like this perhaps, but behaviorism is long dead anyway.

Posted by: Kenny Easwaran on May 15, 2007 5:42 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Kenny wrote:

There are big problems for the betting interpretation of credence (aka confidence, or subjective probability).

Indeed, if we let people freely decide what bets they want to take, they might not take certain bets even if they feel the expected winnings for these bets are positive!

This is obviously true if we allow people to behave ‘irrationally’. For example, I might refuse to take a bet even if I’m sure I’ll win it, simply because I’m in a bad mood.

But, it can even be true for ‘rational’ agents. For example, if I’m a diabetic and I need $50 to buy my insulin for next month, I’d quite rationally refuse a bet that gives me a 50% of losing that$50, and a 50% chance of winning \$1000.

In fact, it’s quite common for ‘rational’ people to be financially conservative in this way. Crudely speaking, this is because our happiness is not a linear function of our wealth.

I’m putting ‘rational’ in quotes because the whole topic of what counts as rational behavior is a lot more complicated than classical economics wants to admit. For a good introduction, try:

• Amartya Sen, Rationality and Freedom, The Belknap Press, Cambridge, Massachusetts, 2002.

I also try to avoid saying things ‘our happiness is not a linear function of our wealth’, since this assumes we have some useful numerical way to measure happiness, which is something I don’t believe.

But anyway…

I’m very confident that the Goldbach conjecture is true, but I’m not willing to stake much on it, because I think it’s unlikely that anyone will ever be in a position to settle the bet.

That’s a very strange attitude — I might even say its irrational! Why be scared of taking bets that nobody will be in a position to settle? They can’t hurt you.

But, I don’t claim to know the gold standard for rationality. Maybe you just want to keep your life simple and avoid having lots of unsettled bets!

But in any event: using the bets someone will take as a method of defining their subjective probabilities is indeed fraught with peril, since it drags us into the murky realms of economics and rational behavior, which are if anything even more mysterious than the definition of ‘probability’.

These days I’m often satisfied to take probability as a fundamental concept, not defining it in terms of other concepts, but instead stating rules for reasoning with it. I don’t claim this gets to the bottom of what ‘probability’ means; it’s a way of sidestepping that question.

I can imagine a certain idealized rational agent whose goal is maximizing their expected wealth, who will therefore take bets or refused them based on a calculation of their expected values computed using subjective probabilities. I sometimes find this handy even though it’s idealized. I sometimes like to imagine acting like such a person.

So, here’s what I mean when I say stuff like “the probability of Moses existing is 30%.”

I imagine rationally playing a game with small stakes of money, or chips, where my goal is to maximize my expected winnings.

I imagine the game involves placing bets on whether Moses exists. Various possible odds are given, and I get to either take or refuse each bet.

I imagine that these bets will be settled by a historian who is able to go out and do the research necessary to decide if Moses exists.

Perhaps we need to equip this historian with a ‘history viewing machine’ that lets them review the whole history of the world.

We also need to give them a definition of what it means for Moses to exist! This is pretty complicated, but for starters I’m willing to go along with the standard picture.

Finally, I pick my probability for the existence of Moses in a way that I feel will maximize my expected winnings.

I agree that all this is pretty complicated and contrafactual!!!

Luckily this game has served its real purpose, which is to trigger a bunch of discussions about history, philosophy, ‘existence’, and ‘probability’.

Posted by: John Baez on May 15, 2007 9:22 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

You might think twice about betting on the truth of the Goldbach conjecture at generous odds even if you think it’s likely, if the conditions of the bet require it to be settled as soon as truth or falsity is established. You may well consider that, if it’s false, a counterexample will appear far more quickly than a proof would if it is true.

There’s a curious effect resembling this which occurs in a situation with three people. Each is given a black or white hat whose colour they don’t know. They simultaneously see the other two hats and have to decide whether to come forward to take a bet on whether all hats are the same colour. Anyone who comes forward is entered into a lottery to see who is given the bet.

You have to factor into your calculation the fact that if you’re the only one stepping forward, which will happen if you have an odd hat, you’re certain to get the (bad) ticket. Whereas if all of you step forward you only have a 1 in 3 chance of winning the (good) ticket.

Posted by: David Corfield on May 15, 2007 10:13 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I don’t really know what it means for a lot of these people to have existed. Does 5% mean there was a real person who did 5% of what the legendary figure is said to have done? Or that there’s a 5% chance that there was anybody at all that did any of it? Or that there’s a 5% chance that the current legend has a continuous history of retellings back to a completely different legend which mentioned the name of a real person?

Fortunately, philosophers have written about this, just as much as the morning/evening star! The standard discussion of this starts in the same Frege article (On Sense and Reference), and reaches a breakthrough with Kripke’s book Naming and Necessity.

Suffice it to say, the standard picture these days allows for these people to have existed without doing any of the things listed (and even for the possibility of those things having been done by someone else of the same name!) The picture says that we should trace the usage of our name historically, figuring out the sources from which we got the name “Plato”, for instance, and seeing where those sources got their name (which was very often different, being in Greek for instance, or using a different nickname), and so on, until we either reach a real person, or someone blatantly making something up about a name they had never heard before, or if it was just an accidental combination of stories about different people that were accidentally stuck together. In the first case we’d say the person exists (even if the stories all turned out to be lies about this person - say Gilgamesh sitting around one day telling his grandkids about all the troubles he went through). In the second case we’d say the person doesn’t exist (even if, by some bizarre coincidence, someone else had done lots of similar things and no one ever noticed). In the third case, it’s hard to say.

Of course, there are more philosophical subtleties than that. But it allows me to give a very high probability to Moses having existed, even though I find it exceedingly unlikely that anyone did even half of what’s attributed to him.

Posted by: Kenny Easwaran on May 13, 2007 4:36 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Kenny Easwaran said:

… the standard picture these days …

How can there be a standard picture?!

As far as I can tell, there are two main ingredients people use in judging identity: continuous existence and close resemblance. If they’re both clearly present, people feel comfortable saying two things are the same; if they’re both clearly absent, people feel comfortable saying they’re different; and if one’s present and the other’s absent, or if they’re both present in a very weak, tenuous form, then people disagree and give contradictory answers.

I don’t see how philosophers could “discover” that one of these criteria is right and the other is wrong, or determine exactly how tenuous a connection may be before it ceases to be a connection. That would be like discovering the one “correct” way to cook an egg, or the exact moment at which a soft-boiled egg becomes a hard-boiled egg!

Dang. Now I remember why I got tired of philosophy.

(This wasn’t personally directed at you, Kenny. I can believe you’re correctly reporting the facts, and everything. But it leaves me speechless with astonishment.)

Posted by: Tim Silverman on May 13, 2007 12:55 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

John Baez wrote:

It’s fascinating how much of human culture involves mysterious figures like this. It’s an inevitable consequence of oral traditions, I guess.

I’ve long been fascinated by the way legends form. When I was a kid, I just found it baffling that people would just make stuff up. Why would they do that? But then I got used to it, and caught myself kinda doing the same thing—“improving” anecdotes about real events as though they were pieces of fiction. So I struggle to avoid this, but it’s really difficult. Ernst Gombrich talks about this sort of thing a lot, in his essays on the history of art: the pull that artists experience towards ideal form and away from realism, so that even attempts to straightforwardly represent the truth are shaped by previous stereotyped examples, and the desire to tidy things up.

Something along these lines particularly stuck in my mind, a few years ago, in the Notes and Queries section of The Guardian newspaper, where readers could write in with questions and other readers could write in to answer them. Someone asked about the invention of marmite, and got three separate and incompatible replies, with circumstantial details, etc, like family history and everything (“my grandfather invented it, and this is how it happened”). So what was happening? Several men who told their children tall stories—maybe not even expecting them to believe them? Multiple independent invention? People exaggerating their walk-on roles in one important event? Who knows? And if we have several confused founder myths about a simple industrial product, only a hundred years old … what hope for the origins of Judaism, or the Greeks, or mathematics?

When archaeologists and treasure-hunters first uncovered the remains of the Myceneans, and oblique Hittite references to them, they were quite happy to associate the ancient people and artifacts with figures from legend. But a later generation of historians found that everything was more complex than people thought at first—the way it always is—and that earlier historians had fallen prey to the illusion that Everyone who Lived in the Past was Famous. (Because, hey, everyone we know about is famous.) (This sort of thing shows up in the sometimes startling differences between the 2nd and 3rd editions of the Cambridge Ancient History.)

Way back when sophisticated Greeks no longer really believed in their religion, but weren’t quite sure what to make of it, Euhemerus thought that all mythological accounts went back to historical events, and all “gods” were really kings or other famous persons; perhaps he was influenced by the fashion for deification among kings of the Alexandrian period (starting with Alexander himself). But we know that can’t be right, from seeing how religious mythology gets created.

Yes, you seem quite confident about assigning events a 0% or 100% probability. Are you often shocked by things not working out the way you expect?

Not as often as you might think … but maybe I’m just not easily enough shocked, even when I’m greatly surprised!

I would not be terribly shocked if, say, there turned out to be a war between Trojans and Greeks that started from a marriage gone sour involving a beautiful woman named Helen … and if that happened, I might feel fine saying “Helen of Troy existed”. So, I wouldn’t assign this a 0% probability, they way you did.

Well, here’s a difference in what we mean by “Helen of Troy”. It wouldn’t surprise me at all if there were several wars on the coast of ancient Anatolia, in which Greeks and Trojans found themselves on opposite sides; in one or more of them, it is possible a woman might have been invoked as a casus belli. But that wouldn’t make me say “Helen of Troy was real”. For me, Helen of Troy is too intimately bound up with Leda and the Swan, twins hatched from an egg, the Most Beautiful Woman in the World, the Fall of the House of Atreus, etc. So, for me, the “real” Helen of Troy is irreducibly mythological. A possible association with a real woman couldn’t make her a real person herself. So we aren’t disagreeing about probability here, we’re disagreeing about the meaning of the phrase “Helen of Troy”!

A better case might be Confucius. I agree it’s theoretically possible that somehow—by finding a huge cache of manuscripts in a cave, or something—the historical existence of Confucius might be demolished. I guess I can imagine being able to reconstruct the entire textual history of all the legends and records, taking him back to a mixture of folk heroes and a variety of historical figures of different times and places, so that the “real” Confucius dissolves.

Since I can easily imagine how this could happen, I suppose I “ought” to assign him a much lower probability of existing. But that just feels wrong! After all, this evidence doesn’t actually exist—I just imagined it! So, unless it turns up, I’ll continue to believe in Confucius.

Maybe you know too much! Isn’t that what causes people to assign 0% or 100% probabilities to lots of events?

Surely it’s the other way round—“The more you know, the more you realise you don’t know”!

Though I really don’t know how you can doubt the existence of Plato, or suspect the reality of Zorro. How about the real existence of the characters in soaps, which some of their viewers seem to believe in, at least partly, at some level?

Belief is a funny thing.

Posted by: Tim Silverman on May 13, 2007 12:46 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Johnny Appleseed was real enough. He was a business man named John Chapman, and there’s no shortage of newspaper articles and public records to confirm his existence.

There’s been some mythologizing though. Chapman wasn’t an itinerant seed-dropper. Planted orchards, left them in the care of managers, and returned later to collect his due.

Posted by: A.J. on May 13, 2007 3:40 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Sure you say that this “John Chapman” existed, but how do I know you’re not part of the same conspiracy that planted those articles to perpetuate the myth?

Myself, I give 95% confidence in Joshua Abraham Norton I, Emperor of the United States of America, Protector of Mexico.

Posted by: John Armstrong on May 13, 2007 6:18 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

What level of confidence do you have in his new clothes?

Posted by: Jeffrey Morton on May 13, 2007 7:03 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

No no,

I’m part of the “Ebenezer Butterick was real” conspiracy. The John Chapman folks are a different outfit.

Posted by: A.J. on May 13, 2007 7:44 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Tim wrote:

Plato — 100%. How would one arrange for the disappearance of Plato? Who would write the dialogues?

James Dolan responds:

isn’t this a bit like “how would one arrange for the disappearance of dr watson?”?

Posted by: John Baez on May 19, 2007 2:37 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Amusing, but … I don’t think Plato actually appears in any of his dialogues. Or maybe briefly once or something.

And who founded the academy? Who taught Aristotle? Were those all different people?

Posted by: Tim Silverman on May 19, 2007 3:28 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Well, bourbaki is only 100% if you are talking about the painting, representing general charles bourbaki instead of nicholas bourbaki…

Better give one hundred points/cent points to St Nicholas ;) at least his remains are conserved, a rigorous proof of existence according to catholic axioms :D

Anyone who really 100% believes that John Baez really exists and writes a weblog while being born long ago in the pre electronic age (1961)??? ;)

Posted by: lauret on May 12, 2007 11:48 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I’m still getting used to the fact that a growing number of people seem to believe that my own existence is a hoax. People, that is, who know me via the blogosphere, and are skeptical.

See, for instance, the responses on Digg to:

http://www.digg.com/programming/Greatest_Nerd_of_All_Times_Jonathan_Vos_Post

By the way, there is some support for the notion that “Robin Hood” — rather than being purely fictional — was an Anglicization of the mythic version of the actual William Wallace (Braveheart).

In an old-fashioned mimeographed fanzine, APA-L, in the early 1980s, I’d coined the term and concept of “anti-solipsism.” And anti-solipsist tells people: “You exist, but I do not.” A natural idea to one who toys with duality…

Surely there’s an n-categorical generalization of this…

Posted by: Jonathan Vos Post on May 13, 2007 12:26 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

So an anti-solipsist is someone who agrees with a solipsist?

Posted by: John Baez on May 13, 2007 2:00 AM | Permalink | Reply to this

### And He Built a Twisted House; Re: People Who May or May Not Actually Exist

Exactly. The solispsist and antisolipsist differ in the zeroth order in whether or not they assert their own existence, but agree at the first order, and hence the antisolipsist agrees with the solipsist. In the solipsist’s model, there is only one being, and so for the solipsist to agree with the antisolipsist is medeled by the solipsist as his agreeing with himself. The solipsist insists that the symmetry mapping the solipsist to the antisolipsist and vice versa is a trivial symmetry, having one element.

What A in universe A believes in Logic A about B in universe B with Logic B can be consistently modeled by a C in universe C with Logic C, using the proper construction of “imaginary logic” — which has been discussed in previous threads, and generalizes Kripke using Model Theory.

This is relevant in the context of you assigning zero probability to the existence of someone who might very well assign the same probability to you.

Don Quixote met someone who claimed to be Cervantes. Robert Heinlein, in the under-rated The Number of the Beast (6^(6^6)) has a bar at which different versions of the protagonist argue with each other.

Borges, in “Tlön, Uqbar, Orbis Tertius” points out the dangers of mapping what you a priori believe to be the nonexistent, when the level of existence is subject to on-the-fly revision.

This all cries out for n-categorification, as does the theory of recursive narrative. One can, for inistance, have a twisted structure of mutually referential narratives…

Certain ur-stories are the fixed points of story-transformations. Myths may be chaotic attractors in the space of iteratively mapped narratives. Greg Egan and Ursuula K. LeGuin emphasize the dynamic role of the narrator. The roll of adding machine paper of the original manuscript of “On the Road” becomes a Möbius strip in “Finnegan’s Wake.” This, of course, makes Greg Egan’s existence suspect, since his last name is the last 4 letters of “Finnegan.”

By the way, speaking of British and Australian writers, I should mention that King Arthur existed, but was actually Scottish:

http://www.magicdragon.com/Wallace/arthur.html

The computer screen, Ted Nelson emphasized, should NOT be used to model a sheet of paper. It can be a nonorientable manifold, an exotic manifold, or something quite different.

This narrative incorporates by reference an Alexander’s Horned Sphere doubly covered by an uncountable novel.

Posted by: Jonathan Vos Post on May 13, 2007 2:47 AM | Permalink | Reply to this

### Re: And He Built a Twisted House; Re: People Who May or May Not Actually Exist

Wouldn’t the anti-solipsist and the solipsist only agree in the toy universe containing only those two? It seems to me that the true anti-solipsist would say that everybody except herself exists.

That is, among Solomon the Solipsist, Annie the Anti-Solipsist, and Oscar the Other Guy:
Solomon believes that Solomon exists while Annie and Oscar do not.
Annie believes that Solomon and Oscar exist, while Annie herself does not.
Oscar is only there as window dressing for the example.

Posted by: John Armstrong on May 13, 2007 6:18 AM | Permalink | Reply to this

### Re: And He Built a Twisted House; Re: People Who May or May Not Actually Exist

“…the true anti-solipsist would say that everybody except herself exists.”

I’m pretty sure that this is the way I defined it in the ancient APA-L. I said something like: “You all exist, only I do not.”

I have no idea who keeps these archived, where printed at LASFS headquarters in Hollywood. Tom Digby, noted science fiction poet, was active in APA-L then, and might remember. He was important in the San Francisco worldcon, and still lives in (I think) California.

Tom Digby published a wonderful poem once with creatures from the first few Planck-times after the big bang, world weary, sure they were the last civilization; and creatures a googol years from now sure that they were the first self-aware beings. Cosmic irony. In some sense anticipating the current silly “Boltzmann Brains” debate.

Posted by: Jonathan Vos Post on May 13, 2007 6:50 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Jonathan Vos Post wrote:

By the way, speaking of British and Australian writers, I should mention that King Arthur existed, but was actually Scottish:

http://www.magicdragon.com/Wallace/arthur.html

Since the second piece of evidence adduced for this theory is

Merlin’s grave is near the River Tweed”

I hope you’ll forgive me joining Thomas Green in his skepticism. It’s sort of like saying “Osama bin Laden is hiding out at the North Pole! I have it straight from Santa!”

Mind you, Merlin was one of the inspirations for The Wizard. Merlin is a cool guy.

His only imperfection is that he lacks the property of existence.

Posted by: John Baez on May 13, 2007 7:16 AM | Permalink | Reply to this

### 100 Most Infleuntial; Re: People Who May or May Not Actually Exist

“The Ontological Proof of the Existence of God, and a Lemma on the Existence of Magic”, Aquinas, St.Thomas, and Ambrosius, Merlin, Summa Theologiae et Magicae, Rome: Leonine ed., vols. 4-12, 1888-1906. English translation, London: Eyre and Spottiswoode, 1964-73.

Have I mentioned my Group Theoretic axiomatization of Magic, in my novel manuscript “Axiomatic Magic” – which has Feynman and John Conway as characters?

I will try to come up with probabilities, but, today being Mother’s Day, I’d promised to drive my wife to Las Vegas for a 3-day vacation. Don’t know if the resort has (affordable) internet access. But if not, then in ~3.5 days.

The 100: A Ranking Of The Most Influential Persons In History (Paperback)
by Michael H. Hart

My wife and I got this as a gift from the President of the university where my wife is Physics professor. We’ve read and re-read it. It addresses the issue of existence, and influence, and explains the ranking methodology. Guess whom they rank #1? How many scientists and Mathematicians make the Top 100? A must read!

Posted by: Jonathan Vos Post on May 13, 2007 3:58 PM | Permalink | Reply to this

### Re: 100 Most Infleuntial; Re: People Who May or May Not Actually Exist

I remember reading that book (or at least, another book with very similar title and ambition) when I was young. I found it quite fascinating, and it was also the first place I heard anything about the controversy over who Shakespeare was.

Posted by: Kenny Easwaran on May 15, 2007 5:49 AM | Permalink | Reply to this

### Merlinomics; Re: People Who May or May Not Actually Exist

I liked that Hilbert Space Wizard scenario, with composition and tensor diagrams.

By the way, I did the rewrite for Steve Barnes of the most popular episode ever of The Wizard (TV series), a short-lived 1980s CBS television series. I solved an apparent violation of Asimov’s laws when a robot had apparently been caught red-handed (literally) in a murder.

Does Merlin work in Reverse Time, Dual Space-Time, does Feynman path integrals faster than anyone else using quantum computing, and are fireballs toy models of the Big Bang?

Does his wizards’s hat have finite or infinite content? Did he go the the same school as Dumbledore, the Wizrad Michael Scott, Gandalf, or any of the people in:

http://en.wikipedia.org/wiki/Wizards

What is the dimensionality of his wand?

Is a crystal ball actually a hypersphere, or exotic 7-dimensional Milnor hypersphere?

And what, again, is the probability that he existed: greater or lesser than King Arthur?

Posted by: Jonathan Vos Post on May 13, 2007 6:32 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Would you prefer “co-solipsist”?

Posted by: Jeffrey Morton on May 13, 2007 2:51 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Since we’re drifting a bit off-topic into general identity questions, I’ll just mention something some may find amusing: I’m learning to live with the fact that if you look up “David Tweed” on wikipedia you get an australian who (being legally careful what I say) at least engages in sharp financial practice and has been taken to court several times. So far, this sort of thing is bound to happen with some name.

However, what’s really surreal is that he wasn’t born with the name David Tweed but David Tschernitz and changed his name because he thought it sounded better for his dubious financial strategies. (There’s actually a genuine australian financial journalist called David Tweed who guided the choice of name Tschernitz switched to capitalise on the confusion; he’s suffered far more than me from the association.) Those who read New Scientist when it talked endlessly about nominative determinism will be wondering if there’s a variant: are there names that “sound” perfect for various careers, and does that indicate I should start working in finance?

So I wish the probability that the name “David Tweed” as a label for Tschernitz exists is 0 :-)

Posted by: dave tweed on May 13, 2007 10:44 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I like the fact that the only ones with actual photographs are Santa Claus, Zorro, and Nicolas Bourbaki.

I don’t like how most of you posting comments are too lazy to estimate probabilities on any of these people existing.

Posted by: John Baez on May 13, 2007 4:35 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

John Baez, I’m sorry to be noncompliant with your request. But I’ve spent scores of hours as a teacher of History of Science and Sociology discussing with students “founder myths”, the extent of estimated historicity of Christ, Moses, Mohammed (once cannot do the last in the Islamic world these days). I coincidently spent 2 hours on the Caltech campus earlier in the week discussing Christianity 1.0 (Apostles and Nazarenes), 2.0, and 3.0 (Council of Nicea) with someone (every religion begins as a cult; not every cult becomes a religion; what accounts for high fitness of some; why did Mitt Romney cite “Battlefield Earth” as a favorite novel; slaughter of the nazarenes, etc.). These are deep topics. I also spent hundreds, maybe thousands of hours making such determinations in each of over 20 centuries on my Chronology:

http://magicdragon.com/UltimateSF/timeline.html

Almost every “person” (Real or Reel or novelistic) you mention is discussed therein. I thought it better to give others a chance to play the game, after my thoughful (not flippant) references to Robin Hood and King Arthur, and not be a windbag.

Posted by: Jonathan Vos Post on May 13, 2007 7:02 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

It must be annoying to be asked to distill your expertise down to a simple numerical estimate of the probability that someone deserving to be considered Jesus, Moses, or Mohammed actually existed…

… but could you give it a shot?

Posted by: John Baez on May 13, 2007 7:26 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

For now, I tentatively assign (for the subset you mention) and an important predecessor:

Jesus: 90%

Mohammed: 92%

Moses: 50%

Abraham: 20%

Posted by: Jonathan Vos Post on May 13, 2007 4:02 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

A remark about Avraham: his original name was Avram (Avraham is obtained by the addition of a single letter symbolizing God) which means “Great Father” in Hebrew. Now, it would be rather strange if someone actually named his child “Exalted Father”, no? The Wikipedia suggests an alternative interpretation: “my father is exalted”, but it sounds like a dubious coincidence. It appears to me that this strongly suggests Avraham was not a real person. It also leads me to speculate that Avraham’s inventor actually wanted us to know Avraham wasn’t real: otherwise why he/she called him that? Surely there must be someone who invented monotheistic faith (after Akhenaten, though who knows, maybe actually inspired by him!), but I doubt it was someone called “Avraham”.

All that said, I’d give Avraham 1%

Posted by: Squark on May 14, 2007 6:32 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Just because he probably didn’t have that name doesn’t necessarily mean he probably didn’t exist! Would you say that Abraham didn’t exist if there really was some patriarch who was an ancestor to the people mentioned in the Bible that did exist, and who almost sacrificed his son in the relevant way, and was the basis of the stories, except with his name changed to make him sound greater?

Posted by: Kenny Easwaran on May 15, 2007 5:54 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Using this logic, we can conclude that Ataturk (whose name means “Father of the Turks”) does not exist. This will certainly complicate making sense of Turkish history.

Posted by: Walt on May 15, 2007 4:45 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Since the Greek myths are one of the few areas I’ve read enough about, here’s my probabilities for those (adding Iphigenia and Aeneas to highlight the full range of roles in the stories):

Odysseus (Ulysses): 45% like Agamemnon, may have been important enough figure for his name to graft onto the story. His role in events unlikely enough that he’s still more likely to be a literary creation.

Agamemnon: 70% hyper-important characters get grafted onto the names of real people

Iphigenia (daughter who Agamemnon sacrificed (disputed!) to get a favourable wind to Troy): 30% may possibly have existed, but the role she needs to fulfill in the narrative seems so unlikely she’s probably a literary creation

Helen of Troy: 37% possibly existed, but I doubt her beauty was sufficient to be the real basis for a war; more like an ancient version of WMD :-) .

Aeneas (Trojan who escaped giving the bloodline leading to founders of Rome in the “franchise reboot” story The Aeneid): 15% he’s very likely a “politically needed creation”; may just about have existed as a name grafted onto story.

Homer: 75% very likely but not as important as literary history suggest.

Posted by: dave tweed on May 13, 2007 11:23 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Thanks listing those probabilities, Dave! There are a lot more legendary Greek characters I could have listed (and a lot more biblical ones, too). Thanks for tackling some.

It seems Odysseus has the biggest spread so far: you say 45%, I say 30%, and Tim confidently asserts 0%. But, I think Tim has a different approach to ‘existence’.

I think most scholars agree that the Odyssey and Illiad were orally composed by a bunch of local bards, ever since Milman Parry went to Yugoslavia. But there could have still been an important ‘Homer’.

On a different subject: no offense intended, but I think ‘Tweed’ is a perfect name for a seedy character. It’s probably because of all those stories about Boss Tweed and the Tweed Ring. Your namesake the broker David Tweed is just burnishing the family reputation! I like the quote from his girlfriend’s dad:

If people have got shares and they have no idea what to do with them, then maybe they are better off without them.

Tweed wouldn’t be a good name for a violent criminal. But for a superficially respectable yet fundamentally corrupt white-collar criminal — the kind who wears a suit, obviously — it’s perfect.

If you don’t like this, you might consider changing your name… to, say, ‘Tschernitz’.

Posted by: John Baez on May 13, 2007 8:42 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I think most scholars agree that the Odyssey and Illiad were orally composed by a bunch of local bards

I have recently read Literacy and Orality in Ancient Greece by Rosalind Thomas. Perhaps this work is the most recent systematic study on this matter. It is quite readable and balanced. But from I have read, the issue you mention is not really settled.

Christine

Posted by: Christine on May 14, 2007 4:47 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Oh, interesting! Thanks for the update.

Posted by: John Baez on May 14, 2007 7:30 PM | Permalink | Reply to this

### some physics, …

Here are some more to validate. What’s the chance the following “exist”:

* Schrodinger’s cat

* An Everettian in another world than this one

* A smart Everettian in another world than this one

* A man on the moon

* A man on the moon and on earth in superposition (this one you can actually calculate provided you guessed the previous one correctly)

* A string theoretician in the year 2100

Cheers, Bob.

Posted by: bob on May 13, 2007 12:45 PM | Permalink | Reply to this

### Re: some physics, …

* A string theoretician in the year 2100

100%. The Technological Singularity will happen before then, you see, and the post-Singularity transhumans will have arbitrarily large amounts of computer power at their disposal. Historians among them will certainly be interested in string theory: if string theory gives anything useful, they’ll want to know how a useful description of reality came to be. Contrariwise, if string theory goes belly-up, they’ll want to know why so many people worked so hard on it for so long! Therefore, string theorists are destined to be resurrected within the simulation.

By the same “logic”, we can conclude that in the year 2100, Helen of Troy will without doubt have existed, because if she did not it would be necessary to create her. In the future, programmers will have the ability to do so (cf. The Woman in the Red Dress).

Posted by: Blake Stacey on May 13, 2007 4:28 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Tim wrote:

How can there be a standard picture?!

As far as I can tell, there are two main ingredients people use in judging identity: continuous existence and close resemblance. If they’re both clearly present, people feel comfortable saying two things are the same; if they’re both clearly absent, people feel comfortable saying they’re different; and if one’s present and the other’s absent, or if they’re both present in a very weak, tenuous form, then people disagree and give contradictory answers.

I don’t see how philosophers could “discover” that one of these criteria is right and the other is wrong, or determine exactly how tenuous a connection may be before it ceases to be a connection.

I think philosophers actually can make progress on these issues — but their progress may be closer to ‘establishing handy conventions’ than ‘discovering the truth’.

For example, consider the word ‘or’. Does it mean ‘exclusive or’ or ‘logical disjunction’? In natural language there’s no real answer to this question: it means some messy mixture of the two, which we sort out by context. But in technical discussions, it really pays to establish a convention — say, that it means logical disjunction. Otherwise, mathematicians and logicians would eternally be having arguments. I’d say “You’re committing the fallacy of affirming a disjunct!” and you’d say “No, you doofus, I’m just using ‘or’ differently than you!”

I’m sure you have no objection to occasionally establishing handy conventions like this.

The problem seems to be that when people do this, it’s rarely clear what’s going on. To what extent are we choosing arbitrary conventions, to what extent are we discovering facts about ordinary language, and to what extent are we discovering other facts about the world?

I think there are reasons it’s rarely clear. One is that we don’t want our conventions to be completely arbitrary, far removed from ordinary usage. Otherwise we’d feel no qualms about defining ‘or’ to mean something like… ‘and’!

So, we’re trying to ‘regiment’ ordinary language without distorting it more than necessary.

I can imagine historians getting really tired of arguments about what it means for historical/legendary characters to ‘exist’. I can imagine philosophers getting involved, trying to help them choose some handy conventions. And, I can imagine them settling on what Kenny called the standard picture.

But, I hope that in doing so they realized that to some extent they were regimenting ordinary language, not simply ‘discovering what it means to exist’. On that I agree with you.

Anyway, I think I’ve been using that standard picture without knowing it! This may account for some of our disagreements about the probability that Paul Bunyan and Zorro exist.

(Enough of the philosophical preamble! Let’s talk about something serious, like Paul Bunyan and Zorro!)

When I wonder whether Paul Bunyan existed, I implicitly follow the recipe Kenny outlined:

Suffice it to say, the standard picture these days allows for these people to have existed without doing any of the things listed (and even for the possibility of those things having been done by someone else of the same name!) The picture says that we should trace the usage of our name historically, figuring out the sources from which we got the name “Plato”, for instance, and seeing where those sources got their name (which was very often different, being in Greek for instance, or using a different nickname), and so on, until we either reach a real person, or someone blatantly making something up about a name they had never heard before, or if it was just an accidental combination of stories about different people that were accidentally stuck together. In the first case we’d say the person exists (even if the stories all turned out to be lies about this person — say Gilgamesh sitting around one day telling his grandkids about all the troubles he went through). In the second case we’d say the person doesn’t exist (even if, by some bizarre coincidence, someone else had done lots of similar things and no one ever noticed). In the third case, it’s hard to say.

So, I’d say ‘Paul Bunyan exists’ if we could in principle track back the legends of Paul Bunyan, through a trail of ever exaggerated retellings, back to some actual guy. I wouldn’t demand that this guy was a lumberjack so tall that his footprints formed the lakes in Minnesota, nor that he owned a giant blue ox named Babe that was 42 axe handles high.

Nor would I demand that it took 17 storks to carry the infant Paul Bunyan to his home… nor that he dug the Grand Canyon by dragging his axe behind him.

As of now, it seems the Bunyan legends go back to James MacGillivray, an newspaper reporter who collected lumberjack tales for an article for the Oscoda Press in 1906. Could these tales, or many of these tales, ultimately emanate from stories about an actual guy? I don’t know — but I gave it a 5% chance.

Next, Zorro.

Before reading the Wikipedia article on Zorro, I guessed a 2% chance that the Zorro legend traced back to some actual guy… maybe Zoroaster. (Just kidding.)

Zorro (often called “El Zorro” in early stories) was created in 1919 by pulp writer Johnston McCulley, and first made his appearance in The Curse of Capistrano, serialized in the pulp magazine All-Story Weekly.

But, maybe the authors of this article didn’t know that McCulley got the inspiration for Zorro from a historical figure. It’s only Wikipedia, after all. So, I’ll downgrade his odds of existence to 1%…

…but not Zero!

I should add that I threw in Santa Claus, Paul Bunyan, Zorro and Nicolas Bourbaki in part for normalization purposes: I wanted the cast of characters to include people who almost certainly didn’t exist, as well as some who almost certainly did. If one of you guys told me there’s a 100% chance that King Arthur existed, I’d find it very helpful to discover you also think there’s an 80% chance that Zorro existed.

Posted by: John Baez on May 13, 2007 8:21 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I wrote:

I don’t see how philosophers could “discover” that one of these criteria is right and the other is wrong …

and John replied:

I think philosophers actually can make progress on these issues—but their progress may be closer to ‘establishing handy conventions’ than ‘discovering the truth’.

I do agree with this—and more. If your problem is that you know a lot, but are hopelessly confused about how it all fits together, then a philosopher may be exactly what you need! And once you understand what the underlying concepts and distinctions are, you can pick conventions for your terminology.

John next wrote:

For example, consider the word ‘or’. Does it mean ‘exclusive or’ or ‘logical disjunction’? In natural language there’s no real answer to this question: it means some messy mixture of the two, which we sort out by context.

I’m not sure if this is an oblique reference to the clarification of the meaning of “or” by pragmatics which I’ll briefly describe for the benefit of everyone who isn’t familiar with it:

The standard story here, which really does claim to get at the truth, is that the literal meaning of “or” is (unambiguously) logical disjunction, but Grice’s Maxim of Quantity (“Be informative”) says that if the speaker knows that there’s actually a conjunction involved (it’s not just one or the other, it’s both), they should say “and”. So the listener can reason: “If it was both, they’d know it was both (I know that from context); and if they knew it was both, they’d say ‘and’; but they said ‘or’, so it wasn’t both.” So a logical disjunctive is pragmatically interpreted as an exclusive or, although this can be overridden if, for instance, the context tells you that the speaker wouldn’t know if it was really both.

I’m sure you have no objection to occasionally establishing handy conventions like this.

No, but, as you say below, it’s important to understand that it is a convention, and that there are alternatives, and to have terminology for them too.

Anyway, I think I’ve been using that standard picture without knowing it!

That would explain some of those percentages! Looking back over some of the things I said, it looks as though I rank “close resemblance” much higher than you!

Which partly explains why I’m so unhappy with the “standard story”. They’ve kidnapped my intuitions!

Posted by: Tim Silverman on May 13, 2007 10:51 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

So you all know by now that philosophers have debated for many years whether reference works via description (‘Socrates’ means ‘Athenian philosopher, teacher of Plato, who was condemned to death,…) or via baptism (chain of uses of name to refer to an individual connecting back to an original baptism).

Often these days these debates are ‘illuminated’ by examples using the language of possible worlds, a sign that modality is coming into play. ‘Was Socrates necessarily a philosopher?’. Yes, via description, in all possible worlds he was. No, via baptism, possible worlds a whisker away from ours exist in which the counterpart of Socrates was a poet.

What this trip into possible worlds tends to do, however, is to distract us from the political nature of naming. Here’s an extract from a post of mine about Alasdair MacIntyre on this theme.

MacIntyre poses the problem of someone in Ireland in 1700 who is able to inhabit both the community of indigenous Irish, and also the English community of plantation owners. To one group it must speak of Doire Colmcille - St. Columba’s oak grove - which “names - embodies a communal intention of naming - a place with a continuous identity ever since it became in fact St. Columba’s oak grove in 546”. To the other it refers to Londonderry which “names a settlement made only in the seventeenth century and is a name whose use presupposes the legitimacy of that settlement and of the English language to name it”. Londonderry was a plantation enforced on the Irish population by the English with the foreign concept of individual property rights - “what is from one point of view an original act of acquisition, of what had so far belonged to nobody and therefore of what remained available to become only now someone’s private property, will be from the other point of view the illegitimate seizure of what had so far belonged to nobody because it is what cannot ever be made into private property - for example, common land.”

MacIntyre remarks “In some sense all philosophy is political philosophy”.

Posted by: David Corfield on May 14, 2007 8:32 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I can’t even attempt to assign probabilities to some of those names, so I’ve taken the liberty of changing the rules somewhat, and also adding some names which John unaccountably overlooked.

Adam: legendary. But Science Acknowledges that one “Eve” existed Quite Some Time Ago, and she lived in Africa. As a matter of fact, science tells us that all men are women who underwent a sex change. I saw it on NOVA, so it must be true. Nyah, nyah— General Patton was a girl!

Gilgamesh: legendary, possibly inspired by historical characters.

Huang Ti: haven’t the foggiest.

Moshe: 5%. Funny thing, this “name” derives from the Egyptian “msh” (possibly pronounced in spoken Middle Egyptian something like “mosh”), which as a verb means “to be born, to be created”. The root “msh” appears in such kingly names as Rameses, Thutmose, and Ahmose.

Egyptologists agree that no one born in Egypt could possibly have actually been named “Mosh”— that doesn’t even make sense as a name, since it begs the question (answered by other Egyptian names incorporating this root): “born to WHOM? made by WHOM?” Some suggest “mosh” was a nickname, that the original name was longer. Or perhaps that’s just what the neighborhood kids called him: they say he was a foundling, so “born for (noman)” might have seemed appropriate. Kids can be so mean…

In monumental script, “mes” can be represented by several different glyphs, one of which is rather explicit: a squatting woman giving birth. By the way, I can’t believe humans are still doing that— the ones who remained women, I mean. Letting something grow inside of you, feeding off your blood— that’s disgusting! This paragraph has been brought to you on behalf of ten year olds everywhere.

The sign probably intended here is more abstract, resembling a trident but thought to represent the rafters of a “great hall”. As far as I know, only two names which are still in common use derive from ancient Egyptian roots. The other is “Susannah”.

Moroni: 0.001%. Things made up in school one day, as they say in Wikipedia. None of Joseph Smith’s tale has the least iota of plausibility, taking account of archeological and linguistic evidence.

Xenu: notation fails me.

I credit to Walt Pohl the suggestion that all religious scriptures began as a joke that took a serious turn.

Speaking of DNA evidence, the huge popularity of evening entertainment like “CSI” demonstrate that, while humans are certainly not losing their fear of death, increasingly they prefer to obliquely confront this fear through “scientific drama” rather than scriptural stories. So I figure it’s safe to slaughter some sacred cows, all in the spirit of family fun. I mean, the Church of Scientology is known for its boisterous sense of humor, right? Zowie! Jump the couch!

Samson: legendary. All communities in all ages have traditions of strongmen.

Hercules: the same.

Theseus: legendary, but possibly based on a historical person (compare Billy the Kid). All communities in all ages have told tales of adventurers.

Odysseus: legendary; all communities in all ages have traditions of wily tricksters. In our time we tell tales of a fabulist called Nabokov. Curiously enough, Nabokov is said to have lived in Ithaca. See what I mean?

Agamemnon: composite of earlier oral traditions concerning various historical chieftans. Too bad he wound up Just Another Dead Guy on 48 Hours Mystery. Agamemnon for President! Anatolia, here we come!

Helen of Troy: all communities in all ages have traditions of great beauties. In our time we speak of Marilyn. NASA insiders insist that the first named road on the Moon will be called Mulholland Drive. The key is indigo.

Homer: composite of bards who sang and improved early versions of the “Homeric” epics.

Gautama Buddha: 100%. I know someone who met him in Crown Heights. Disappeared under mysterious circumstances on the night of July 13, 1977, hasn’t been heard from since. Reportedly sought by the FBI for questioning in the Jimmy Hoffa case.

Lao Tzu: 50% sounds about right.

Zhuangzi: not a clue.

Confucius: 80%.

Pythagoras: 50%. Possibly the fictional alter ego of a writer whose name is lost to history: Mel Brooks.

Socrates: 70%. Just because Plato told dozens of memorable stories about thim doesn’t prove he existed. I believe Chaucer existed because he was not only a prominent citizen well attested in the written record, we even have autographs. But show me the warrant for the execution of Socrates!

Plato: 90%. Show me a deed with the name of “Plato the philosopher”.

Yeshua: 40%, but if any such person ever existed (at best, there exists only brief and ambiguous historical attestations in contemporary writings), he was only a minor agitator/terrorist associate (to the Romans— that fellow Iscariot being the reputed terrorist with whom Yeshua associated) or a spiritual leader (to a handful of followers) or the kind of pamphleteer you cross the street to avoid (to modern urbanites). Scholars agree that the character of this person, if he existed at all, was completely “reinterpreted” by later writers, particularly Paul.

Mary Magdelene: legendary. All communities in all ages have had their harlots with a heart of gold.

Paul the Apostle: 95%. His letters are too obviously the work of a highly disturbed individual to be historical fictions. Actually, he creeps me out. Let’s change the subject.

Mohammed: 90% sounds about right. He fought and won battles, after all — people don’t lie about serious stuff like that, although details can be changed. C.f. the Battle of Megiddo. You can’t believe everything you read on some temple wall. What, you think Tjaneni was going to write anything suggesting that Thutmose was caught napping in his tent? That, but for the grace of the Gods, things could have taken a very nasty turn? I think not — he knew from whence he got his bread and beer.

Brynhildr: legendary, but possibly a composite of oral traditions about earlier historical figures.

King Arthur: ditto. I have read books on this tired subject and despite valiant efforts by some authors, there has never been the slightest historical evidence for such a person.

Morgaine: ditto.

Robin Hood: ditto. All communities in all ages have had their trickster legends.

Shakespeare: 80%. I’ve seen deeds and wills involving a prominent citizen in a minor town by that name. But show me the autograph manuscript of a play or a poem.

Santa Claus: legendary.

Jonathan van Post: 0%. Sure, he exists, but I happen to know he’s an advance scout for the Mucoid Invasion from Gliese 581. Keep your pod repellent handy. I have Yogi Berra on speed dial — I figure he’s the one I want negotiate with any aliens.

Chris Hillman: at the event of writing, I’ll grant the existence, but I utterly reject the “person”. But I could be wrong, so I’ll give it 3%.

James Kibo Parry: 100%. He posts, in utterly inimitable style, therefore he exists. Duh!

Posted by: Chris Hillman on May 14, 2007 5:17 AM | Permalink | Reply to this

### Did Yogi Berra exist? Re: People Who May or May Not Actually Exist

Although I’ve seen Yogi Berra play for the Yankees, and later manage, and you think you’ve seen him on TV, his existence may be pegged at less than 100% because of evidence as below.

“I have Yogi Berra on speed dial – I figure he’s the one I want negotiate with any aliens.”

Given that Yogi Berra said:

“When you get to a fork in the road, take it.”

he clearly believed in the many-worlds interpretation of Quantum Mechanics.

Since he said:

“It gets late early out there.”

he clearly operated in something other than Newtonian Time, not necessarily Minkowski space.

This is supported by his saying:

“When asked what time it is, he said ‘You mean right now?’”

and supported by his saying:

“Prediction is very hard, especially about the future.”

As to the underlying combinatorics:

“Pair up by threes.”

As to the underlying Probability Theory:

“Ninety percent of the game is mental, the other half is physical.”

and in conclusion:

“Half the lies they tell about me aren’t true.” and “I never said half the things I said.”

REFERENCES:

Yogi Berra, Dave Kaplan, “When You Come to a Fork in the Road, Take It! Inspiration and Wisdom from One of Baseball’s Greatest Heroes”, 2001 ISBN 0786867752 (hardcover)

Wikipedia, Yogiisms.

Posted by: Jonathan Vos Post on May 18, 2007 11:15 PM | Permalink | Reply to this

### Re: Did Yogi Berra exist? Re: People Who May or May Not Actually Exist

“When you get to a fork in the road, take it.”

There’s actually an interesting story behind this one. Yogi used to live on a street that ended in a loop. His house was at the far side of the loop, about equal distances in both directions from where the road split. It really didn’t matter which direction you went, thus: “when you come to the fork in the road…”

Posted by: John Armstrong on May 19, 2007 12:41 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

When I was at university, I shared a flat with two guys. One night, I don’t know how, one of them and I got into a discussion about whether Moses existed. The other guy apparently wasn’t impressed by the topic and started improvising a song on guitar with a what-is-the-meaning-of-it-all theme. The chorus was simply “Did Moses exist?” repeated a few times. The only verse I remember was:

Did he carry the Torah
From high above
Or is it just Charlton Heston
I’m thinking of?

He’s now a representation theorist.

Posted by: James on May 14, 2007 2:35 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Besides actual existence there is also an issue of multiplicity of existence:

* More paintings are attributed to Rubens than one man could have ever produced in his life.

* On the other hand, there is the case of two copies of the same painting being made by two different Breugels .

* One thing which is certain is that there is of course more than one John Baez producing all these writings!

Posted by: bob on May 14, 2007 5:34 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Fairly resilient (that is, it would take a lot of evidence to shift my probability)
Moses: 50
Hercules: 5
Theseus: 10
Odysseus: 20
Agamemnon: 60
Helen: 30
Homer: 50
Buddha: 90
Confucius: 95
Pythagoras: 90
Socrates: 70 (I would have put this lower, but an earlier comment mentioned that Plato’s not the only one that talks about him)
Plato: 95
Jesus: 95
Paul: 95
Mohammed: 99
Arthur: 20
Morgan le Fay: 15
Robin Hood: 40
Shakespeare: 100
Santa Claus: 0
Johnny Appleseed: 100
Paul Bunyan: 1
Zorro: 0
Jack the Ripper: 90 (this is coincidentally one of the examples Kripke discusses many times in Naming and Necessity)
Nicolas Bourbaki: 0

Fairly unresilient (that is, some very slight evidence could shift my probability here greatly)
Gilgamesh: 10
Huang Ti: ??
Zoroaster: 80
Samson: 10
Lao Tzu: 90
Chuang Tzu: 95
Mary Magdalene: 80
Brunnhilde: 10 (I was only familiar from Wagner - her existence in Icelandic sagas might increase my probability here)

Posted by: Kenny Easwaran on May 15, 2007 6:16 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

This is fun! I include only those I have enough knowledge of to give something that is not a complete and utter guess:

Moses: 60% (in the bare sense of an early leader of the Hebrews, without assuming the truth of most elements of the story)
Samson: 20% (likely folktale, but may be an historical figure in the background)
Heracles: 20% (ditto)
Thesseus: 20%
Odysseus: 40%
Agamemnon: 50%
Helen: 20%
(I think there likely was a Toyan War, and if there was a main Greek commander it might have been Agamemnon. Helen is probably an embellishment)
Homer: 40%
Buddha: 85%
Pythagoras: 85% (Though most things believed about him are false, I think there was very likely a real man who originated the stories. He is too recent to be fully legendary IMO.)
Socrates: 97%
Plato: 100%
Jesus: 92%
Paul: 96%
Muhammed: 92%
Arthur: 60%
Morgaine: 10%
Robin Hood: 70% (in the sense of a real outlaw and his band as starting point for stories; he almost certainly did not live in times of King Richard or have a wife called Marian)
Shakespeare: 100%
Santa Claus: 0%
Zorro: 0.2%
Jack the Ripper: 90%
Bourbaki: 0%

Posted by: Alejandro on May 15, 2007 5:21 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I love this post! And some reactions are so funny. Here are my probabilities for the persons I can make a reasonable estimate of…

Moses: 30%
Samson: 10%
Heracles: 30%
Odysseus: 30%
Helen: 30%
Homer: 60%
Buddha: 85%
Confucius: 85%
Pythagoras: 95%
Socrates: 99%
Plato: 99%
Jesus: 99%
Mary Magdelene: 50%
Paul: 50%
Muhammed: 99%
Arthur: 20%
Robin Hood: 55%
Shakespeare: 99%
Santa Claus: 0% (he is based on the archbishop of Mira though - so that would be a 99%)
Zorro: 10%
Jack the Ripper: 99%
Bourbaki: either 100% or 0%

May I request a joke starting with “Pythagoras visits his doctor…”?

Posted by: Ionica on May 15, 2007 5:47 PM | Permalink | Reply to this

### Pythagoras visits a doctor; Re: People Who May or May Not Actually Exist

The idea of vegetarianism stretches back at least to Pythagoras who lived some 2,600 years ago. Pythagoras believed that the soul was immortal and inhabited someone else’s body after death. The soul itself was a spark of the divine, literally a bit of god. It followed that all life was related and all life was sacred. That idea not only led to vegetarianism but also to political ideas about human society: egalitarian, democratic, individualistic, libertarian ideas. These were radical, even revolutionary ideas. They were seen as subversive both to state and church. And in the early Christian era they were driven underground. Reincarnation is about automorphisms on the set of souls.

SO:

Pythagoras visits a doctor.

Pythagoras: My feet hurt. My teeth hurt.

Doctor: Maybe it’s because of your vegetarian diet?

Pythagoras: In a sense. When I eat carrots and radishes and the like, the sum of the squares of my two feet are related by the roots.

There’s a joke in there somehere, struggling to get out.

Posted by: Jonathan Vos Post on May 21, 2007 7:08 PM | Permalink | Reply to this

### Re: Pythagoras visits a doctor; Re: People Who May or May Not Actually Exist

struggling.. struggling..

Just put the poor thing out of its misery already.

Posted by: John Armstrong on May 21, 2007 7:43 PM | Permalink | Reply to this

### Re: Pythagoras visits a doctor; Re: People Who May or May Not Actually Exist

Reincarnation is about automorphisms on the set of souls.

yes, the abstract commandment “do unto others as you would have them do unto you” becomes more concrete when you find out that they’re you.

Posted by: james dolan on May 22, 2007 1:05 AM | Permalink | Reply to this

### Re: Pythagoras visits a doctor; Re: People Who May or May Not Actually Exist

Right. IF souls could be destroyed, then partial reincarnation would be an endomorphism. Who reincarnates as whom would be diagrammed as a directed acyclic graph, or (with cyclical time) a digraph.

But, for those who believe that souls exist, they typically believe that souls are immortal.

C. S. Lewis wrote about this probolem: Angels are immortal. Thus God cannot kill an angel. BUT, can God cause an angel to have never been created? Can God change the past?

C. S. Lewis concluded that God could (i.e. omnipotence is transcendent at above the 4-D manifold of “block time”) but chooses not to – for aesthetic reasons.

Some of this discussion (i.e. did Adam exist?) are similarly theological.

But much can be solved by Theomathematics and Theophysics.

Posted by: Jonathan Vos Post on May 23, 2007 5:02 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Those of you who assign a nonvanishing probability to the existence of “Adam”: what exactly is it you think has a nonvanishing probability to have existed?

Posted by: urs on May 15, 2007 6:04 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Since I gave Adam’s existence a 2% probability, I should probably say what I meant by ‘Adam exists’.

Since I buy the standard picture, I’d say ‘Adam exists’ if we could go back to earlier and earlier versions of the Torah, and find that the earliest ones can be traced back to oral histories which could then be traced back to the true story of some important ancestor who had a family roughly resembling Adam’s family in the Bible. Preferably one called ‘Adam’.

I agree that it might be awfully hard to decide what counts as ‘roughly resembling’ in this case!

By the sentence ‘Adam existed’, I would not mean that with a history viewing machine we could see a scene like this:

Posted by: John Baez on May 15, 2007 9:56 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Perhaps we can forego the exclusion from Eden, but without a little detail like ‘he had one son who killed another’, we’re left with a man who had a wife and (roughly) three sons, and who did some important things which got him talked about. Stories of what he did were passed down along a continuous chain but may have been altered so much that nothing true about what he did found its way into any written text.

Posted by: David Corfield on May 15, 2007 10:24 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

we’re left with a man who had a wife and (roughly) three sons

Kudos on remembering Seth (which many Christians do not). On the other hand, “The days of Adam after he became the father of Seth were eight hundred years; and he had other sons and daughters.” (Gen 5:4). So “rough” has to be very rough.

Also, how much credence are we to give the “fact” that “all the days that Adam lived were nine hundred and thirty years”?

One important thing he did that was talked about I’m willing to concede without skepticism, though: “and he died.”

Posted by: John Armstrong on May 16, 2007 12:29 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Perhaps we can forego the exclusion from Eden,

All right, now I see your point of view.

On the other hand, I always found most everything of the story involving Adam a nice example of something of obvious allegorical nature. A deep message in simple pictures. Like in a dream.

The creation from soil – while I certainly don’t believe it literally, I do think it does express some true feeling one may have about one’s existence, which is true in its way. Especially for people in a heavily agricultural society.

The life in paradise and the exclusion from it: every psychonalyst worth his or her money recognized childhood and adolescence. And I guess this may be childhood of a single person just as well as childhood of a species.

Then, offspring fighting each other and propagating “evil” in the world. Well. It’s hard not to trace that back to some real event or other, and thus make it a universal story.

So, for me, 0% for Adam in the standard picture, but a 90% true story in the sense that dreams can be true.

Posted by: urs on May 16, 2007 10:26 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I’d put Socrates at about 99.9%; reading Plato’s Apology, many of Socrates’ arguments are rather weak, and quite transparent, too. So much so that I can easily believe the text recounts an actual event, rather than a made-up legend to tell of visionary greatness.

On the other hand, I feel at risk of succumbing to “Wag the Dog”-inspired fears for historians to come; e.g. the most direct evidence I have ever seen that George Bush exists/is a real person is in the form of short video clips from TV. I might have to rate him around 85%.

Posted by: jesse on May 16, 2007 6:59 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

“For example: did you know Homer didnt write the Odyssey and Illiad? They were actually composed by another guy with the same name!)”

I think that a little research will show that almost all the great works of fiction were actually written by someone with the same name as the author.

Posted by: Andy on May 16, 2007 2:59 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Same shoe size, too, which is something people don’t often mention.

Posted by: Tim Silverman on May 16, 2007 3:06 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Belatedly having read this, I was struck by the ‘into a bar’ jokes. I’m now reading ‘Plato and a platypus go into a bar’.
It’s a hoot, all the jokes being an excuse to discuss philosophy - or vice versa!

Used copies available from Amazon.

Posted by: jim stasheff on June 11, 2007 3:06 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

There’s an article (here) in the New York Times about some philosopher who thinks there’s 20% chance that our universe is a computer simulation being run in another universe.

Now, to all those who cavalierly assigned probabilities to existence of historical figures, what do *you* think is the probability that our universe is a simulation?

Come on. Don’t be shy.

Posted by: James on August 15, 2007 7:40 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

There’s an article in the New York Times about some philosopher who thinks there’s 20% chance that our universe is a computer simulation being run in another universe.

In pondering this, take a moment to contemplate the magnitude of all the acts of human depravity, and all the suffering through natural causes, that the history of humanity (and other life on this planet) has entailed. Start with the Holocaust if you like, or maybe just yesterday’s car bombing in Iraq which killed 200 and injured 200 more. Give due weight (i.e. none) to all the lame excuses theologians have come up with over the centuries for the Problem of Evil. And now imagine a being able to simulate a whole universe (or at least a whole planet), but either so depraved or so incompetent as to cause or allow all that needless suffering. Every rape, every murder, every massacre. Every child dying of malaria, every famine, every plague.

Whatever the probability of this (which I believe is low by most reasonable measures – unless you want to assert a cosmology in which everything computable happens with certainty), it’s one of the most depressing scenarios I can imagine. If I was curious about my ancestors, I would find a better way to reason about them than to recreate all the suffering that I’d been lucky enough to escape myself.

Posted by: Greg Egan on August 15, 2007 1:00 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I have to disagree here. There’s no reason to draw the conclusion that the simulation (if it is such) is “depraved or incompetent” from the existence of evil.

As I see it, it’s entirely possible that any system so complex must by necessity include these “negative” effects. A common thread in the theory of consciousness is that any system complex enough to capture “thinking” must also be subject to irrational emotions, or even insanity. Evil may well be a similar epiphenomenon of society that can’t be so neatly excised.

Posted by: John Armstrong on August 15, 2007 1:41 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Absolutely. And if we are being simulated, surely it’s likely that it’s not just us in the simulation, but the whole universe — in which case, the creators have probably just plugged in some laws of the universe and pressed ‘go’ on their ubercomputer, and are busily studying data on large-scale cosmic structure. Why should they care about the behaviour of, or even notice the existence of, small-scale, self-replicating structures that happen to arise along the way, let alone decide not to do the experiment in the first place out of ‘compassion’ for them?

After all, there hasn’t been much moral outrage over the Conway’s Game of Life here on Earth! I don’t really see that this is any different.

Posted by: Jamie Vicary on August 15, 2007 2:37 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Creating life as an accidental side-effect falls into the “spectacularly incompetent” category (though given the necessary technological and intellectual context, I would also call it depraved indifference).

But it’s also not what Bostrom is asserting; his claim (most of the time, he has a few variations) is that the descendants of people much like us are simulating us deliberately, because they’re curious to know about their ancestors’ history, but are (apparently) too stupid and lazy to figure things out any other way, and too morally bankrupt to care about the consequences.

Posted by: Greg Egan on August 15, 2007 3:32 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Humans simulating humans: I entirely agree.

But otherwise, to use the descriptives “depraved indifference” or “spectacular incompetence” assumes a huge amount about those ‘entities’ in control of the simulation — why should our limited emotional responses mean any more to them than those of ants do to us? Not to say that there is nothing morally wrong with killing an ant, but I would consider “depraved” too strong an adjective for that situation.

You also assume that those operating the simulation would have the capability to perform the extraordinarily complex task of analysing the emotional response of every living being which happens to come into existence in the immense simulated universe, deciding when their ‘suffering’ becomes ‘too great’, and intervening in a huge number of small ways to alleviate any individual problems which arise. It’s quite reasonable to suppose that this is simply infeasible given the technology employed to perform the simulation: playing out a fixed, simple set of fundamental laws is one thing, but executing a hideously complex and subjective analysis of the moral component of the simulation is quite another again.

If this is the case — if microscopic intervention, in the style of miracles, is simply not possible — then the decision to be taken by the Ethics Committee deciding whether to fund this particular piece of computational physics is: would these simulated beings prefer to be simulated faithfully, according to an unempathetic set of laws which will take no account of their happiness, to the alternative of not being simulated at all?

There’s another possibility: perhaps the controlling entities evolve their universe in small time-steps of, say, 10,000 years of simulated time, perform post-analysis of the results, and erase anything that happened which was particularly ‘cruel’ before continuing. That’s quite consistent with our experience of the universe, although perhaps not much consolation, since the cruelty was simulated in the first place (Transition Dreams, and all that!).

Posted by: Jamie Vicary on August 15, 2007 4:19 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I accept that the possibilities become less offensive once you move away from Bostrom’s ancestor simulations, but I still think that any technologically sophisticated civilisation could probably do better than you suggest. At the very least, I think anyone capable of simulating, say, the volume of the solar system down to the femtometre scale would also be smart enough to be capable of ensuring that no life arose if they didn’t actually want any life. Detecting the emotional state of alien beings would certainly be harder, but once you accept that these beings were probably created deliberately rather than being unnoticed side-effects, it seems quite reasonable that their state of mind would be the subject of a great deal of careful analysis. It’s certainly not inconceivable that some dim and inconsiderate beings will somehow get their hands on computers with 10^60 or so times the power of current desktops, but this is, I think, mercifully very distant from Bostrom’s claim that it’s almost a mathematical certainty that we are living in a simulation.

the decision to be taken by the Ethics Committee deciding whether to fund this particular piece of computational physics is: would these simulated beings prefer to be simulated faithfully, according to an unempathetic set of laws which will take no account of their happiness, to the alternative of not being simulated at all?

Almost everyone who actually exists would prefer to exist – even with a very high level of suffering, but that doesn’t mean that prior to their existence we should take that likely preference into account. “X probably won’t beg me to kill him” is setting the bar extremely low, when there’s no pressing reason for X to be brought into existence at all.

Posted by: Greg Egan on August 15, 2007 5:40 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Greg wrote:

[Bostrom’s] claim (most of the time, he has a few variations) is that the descendants of people much like us are simulating us deliberately, because they’re curious to know about their ancestors’ history, but are (apparently) too stupid and lazy to figure things out any other way, and too morally bankrupt to care about the consequences.

Does Bostrom think it’s possible for future versions of us to simulate history in detail given data obtained in the future? Does he know or care about things like quantum mechanics and classical chaos, which make this implausible?

In other words:

Does he imagine that someday future historians will simulate history and find out on which days Hitler shaved his mustache? Or will these future historians be content to simulate a large class of worlds vaguely similar to our own?

I could read his stuff, but since you’ve already wasted some time doing that…

Posted by: John Baez on August 16, 2007 2:30 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

John wrote:

Does Bostrom think it’s possible for future versions of us to simulate history in detail given data obtained in the future? Does he know or care about things like quantum mechanics and classical chaos, which make this implausible?

I’ve never seen him claim that the simulators would expect to be recovering their history in detail.

I think the idea is more along the lines of generic curiosity about the past, historical “what if?” experiments, etc. There’s a long, long tradition of SF in which people find that their world is really some kind of “history experiment” in which battles, real or metaphorical, are being re-staged in order to try to learn something about the past. I can see why this idea resonates with people, but I remain hopeful that future historians would (as well as being swayed by the moral considerations) find far better – and far cheaper and more computationally efficient – tools.

Posted by: Greg Egan on August 16, 2007 3:03 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

It’s certainly arguable that a capacity for evil and a capacity for suffering are inevitable consequences of a certain level of intelligence.

But … so what? This tells us that banishing all evil and suffering from the world is a utopian fantasy, but it doesn’t come close to telling us that the history of our species approximates any reasonable lower bound. (Voltaire has already given an appropriate retort to the notion that we live in the best of all possible worlds.) It tells us that evolution banishes the theological Problem of Evil; given that we are conscious, and arose by random processes indifferent to moral outcomes, our deeply unpleasant history and partly unpleasant nature should not surprise us, or make us believe in some evil supernatural force.

But Bostrom’s hypothetical simulating being was under no compulsion to simulate us at all, let alone simulate processes in which such unpleasantness might have been anticipated (by anyone who wasn’t incompetent), let alone decline to intervene when they saw how badly things were going. If our universe is some kind of experiment (or one of the “ancestor simulations” that Bostrom keeps banging on about), it is a consequence either of depraved indifference, downright sadism, or spectacular incompetence.

If I announced “Tomorrow, I am going to create a world in my computer in which X million conscious beings will suffer and die, in exactly the manner that our ancestors did … but hey, I’ll get to answer some fascinating questions about history”, then I hope someone would come and drag me off to the International Court of Justice and charge me with crimes against humanity. Because if Hitler deserved to go there, and Pol Pot and Stalin deserved to go there, how can anyone who knowingly enabled all of their crimes, and worse, not deserve the same?

Posted by: Greg Egan on August 15, 2007 3:16 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

John Armstrong wrote:

As I see it, it’s entirely possible that any system so complex must by necessity include these “negative” effects.

There’s a great story by Stanislaw Lem in which a bunch of mathematicians prove theorems to this effect. I think it’s in his collection Imaginary Magnitudes, which is one of my favorite SF books of all time. It’s a collection of reviews of nonexistent books.

(Hmm, or maybe it’s in A Perfect Vacuum.)

Posted by: John Baez on August 16, 2007 11:53 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I don’t really follow the idea of “maybe our universe is a simulation” (I am not really sure what it is supposed to mean), but suppose I did:

we (you know: “we”) keep rats, monkeys and other obviously sensitive beings in artificial “simulations” of habitats, only to test precisely in which way they will suffer (until finally being killed) from the harm being done to them in these experiments.

Why would anyone hesitate to do this and much more in a computer simulation?

But actually, this comment of mine just indicates that I may not understand the idea of “the world around me being a computer simulation”.

My problem is, I don’t even understand what it means for the world around me not to be a computer simulation! ;-)

Posted by: Urs Schreiber on August 15, 2007 2:16 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Yada yada yada. I want numbers. I’m talking -1-categories. Y’all didn’t make so many qualifications before. (Or maybe you all did. But somebody gave numbers before.)

Just to get started, more or less than 50%? (Or for the topos die-hards, more than 49% or less than 51%?)

Posted by: James on August 15, 2007 2:38 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

For what is worth, my opinion is here.

Posted by: Christine Dantas on August 15, 2007 5:58 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

OK, I’ll give a number: 0%

If one of my ancestors is simulating me in a computer then I’m not sure how they could be my descendent. They are the descendent of some other computational process that they are simulating. I am still me, and I live in the universe I can observe.

David Chalmers has a fun little essay on the philosophy of the Matrix that is relevant to this whole discussion.

Posted by: Rolfe Schmidt on August 16, 2007 1:18 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

we (you know: “we”) keep rats, monkeys and other obviously sensitive beings in artificial “simulations” of habitats, only to test precisely in which way they will suffer (until finally being killed) from the harm being done to them in these experiments.

Why would anyone hesitate to do this and much more in a computer simulation?

Given current trends in community attitudes to these matters, which do you honestly think is most likely?

(A) 100 years from now, experiments on living vertebrates will be illegal in most of the world, with physiological computer simulations (of a nature that precludes the simulations themselves experiencing consciousness) taking their place; or

(B) 100 years from now, we will clone Homo erectus and Neanderthals and entertain ourselves by watching them club each other to death?

It’s easy to give flippant answers along the lines of “Looking at reality TV, it’s (B) for sure!”, but I’m curious as to whether people are really that pessimistic, or whether they’re actually just unable to take Bostrom’s hypothesis seriously even as an ontological proposition … and hence debating the moral aspects of it seems as silly as crying for all the people who get crushed to death in a Godzilla movie.

Posted by: Greg Egan on August 15, 2007 4:48 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

A), certainly. No doubt. I agree.

But I feel unsure as to what this implies for the question at hand. Indeed, I still feel unsure about what exactly that question means, as I don’t know what “conciousness inside a computer program” is, and the like.

But never mind me, I will just go back to lurking here.

Posted by: Urs Schreiber on August 15, 2007 5:01 PM | Permalink | Reply to this

### Bostrom boggles Blogs; Re: People Who May or May Not Actually Exist

In yesterday’s New York Times section on Science, John Tierney discussed an argument allegedly by Nick Bostrom, director of the Future of Humanity Institute at the University of Oxford, that our existence could be nothing more than a computer simulation being run by posthumanists.

Dr. Bostrom assumes that technological advances could produce a computer with more processing power than all the brains in the world, and that advanced humans, or ‘posthumans,’ could run “ancestor simulations” of their evolutionary history by creating virtual worlds inhabited by virtual people with fully developed virtual nervous systems.

Some computer experts have projected, based on trends in processing power, that we will have such a computer by the middle of this century, but it doesn’t matter for Dr. Bostrom’s argument whether it takes 50 years or 5 million years. If civilization survived long enough to reach that stage, and if the posthumans were to run lots of simulations for research purposes or entertainment, then the number of virtual ancestors they created would be vastly greater than the number of real ancestors.

The article includes links to four others related to Bostrom’s argument, and there’s a lengthy discussion going on at the TierneyLab blog.

On the latter blog, which already had 300 or more comments, I posted a grumble something akin to:

It’s an ongoing outrage that Nick Bostrom gets any credit for precisely the argument that I published years before him.

I was the first to publish a scientific article on the likelihood that we are indeed simulated by positron-electron entities at least a googol years from what humans think is the present, in the magazine Quantum Science Fiction (which published both fact and fiction).

Years later, Nick Bostrom got great publicity by rediscovering my argument, and claiming that he was the first to publish.

It is widely believed by Physicists, yet neither proven nor unanimous, that the universe is a quantum computer.

Richard Feynman had this in mind (and discussed it with me) when he became the great-grandfather of Quantum Computing. There were some revisions in his original proposal, but still wide agreement with his assertion that the universe computes it own next state by real-time integration.

I’ve thought about that since he and I were at Caltech together 1968-73. Before I graduated, I gave Post’s corollary to Feynman: “The universe is the smallest (least action) computer that can compute or simulate the future of the entire universe.”

I stated then and still believe that we could be nested as a simulation inside a larger universe, which could in turn be nested as a simulation inside a larger universe.

I specifically suggested that we (me and the readers of the essay) were likely to be embedded in a simulation by a far far future electron-positron civilization (citing Freeman Dyson’s physics theories of the deep future).

I was the first to put this in print, at: “Human Destiny and the End of Time” [Quantum, No.39, Winter 1991/1992, Thrust Publications, 8217 Langport Terrace, Gaithersburg, MD 20877; ISSN 0198-6686].

Professor Gregory Benford acknowledged to me that he drew on this theory in his novels of the galactic core (whole sentences in his novels, even paragraphs, in italics, were from his notes while he read my essay, many sentences and phrases of mine were used with permission for poetic and cosmological value), and then years later philosopher Nick Bostrom (director of the Future of Humanity Institute at Oxford University) rediscovered what I’d published first, and did a better job than I at getting mainstream PR on it.

The germ of the idea was in science fiction even before me and Feynman. “The Matrix” and “The 13th Floor” popularized the idea further.

You might also ask Dr. G. David Brin why Brin dropped out of a publishing project with Dr. Bostrom, or why the founders of the Transhumanist movement disavow Dr. Bostrom.

For instance:

In the July 24, 1978 issue of The New Yorker, Stanislaw Lem published “Review of ‘Non Serviam.’” The abstract in the New Yorker catalogue reads as follows:

A fictional book by a fictional scientist named James Dobb documenting his research in personetics, a science described as an offshoot of the cybernetics and psychonics of the 80s, crossbred with applied intelletronics. In lay terms, it is the artificial production of intelligent beings. These personoids live in a computer, in a purely mathematical world. They have no bodies, only souls. They have been programmed for language. The science has split into 2 schools. The American school at MIT aims at giving personoids a sex life. Dobb represents the English school, the behaviorists of personetics, who observe without interfering. Our minutes correspond to whole eons in the computer, making it possible to watch the emergence of a personoid history. In the 8th generation the notion of a Creator appaears. Personoids divide into godlies (believers in God) and ungodlies (atheists). In their discussions, recorded by Dobb, they prove logically that if there is a God, they don’t owe him anything. Hence the title of the book, “I am not serving.” The personoids have the same relationship to Dobb as persons do to God. When he disconnects the computer, he will bring the world to an end.

Posted by: Jonathan Vos Post on August 15, 2007 8:20 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Jonathan vos Post wrote:

It’s an ongoing outrage that Nick Bostrom gets any credit for precisely the argument that I published years before him.

You should be glad you’re not getting pegged as somebody who seriously advocates this version of Intelligent Design. Notoriety is cheap. The hard part is coming up with really useful ideas.

Posted by: John Baez on August 16, 2007 3:53 PM | Permalink | Reply to this

### Meta-Universes That May or May Not Actually Exist

If the simulation is good enough, it doesn’t make a bloody bit of difference if our universe is being simulated. If it’s not… well, go ahead and do experiments to check for bugs and bit errors! Until you find something, I don’t give a damn about this issue.

This ‘simulation’ idea is just one of many scenarios that drastically modify our ontology with only negligible changes in what it predicts about what we experience. The Boltzmann brain and multiverse scenarios are also currently fashionable. But, their popularity is dwarfed by the earlier popularity of deism.

I haven’t undertaken a complete catalogue of such scenarios — they seem limited only by our imagination and taste. So, I won’t dignify an individual scenario by guessing a probability that it’s correct!

However, I would argue that if the probability we’re being simulated is some number $0 \le p \le 1$, the probability that we’re being simulated by a civilization that’s itself being simulated is at least $p^2$.

Of course it could be more, up to $p$, since knowing that we’re being simulated would raise the plausibility of the whole simulation scenario. (I’m being a Bayesian here, so the probabilities are subjective.)

Continuing this argument, the probability that we’re in an $n$-fold tower of simulations is somewhere between $p^n$ and $p$.

Of course, the same argument works for towers in which our universe is created by a god who inhabits a meta-universe that was created by meta-god, etcetera.

Mixed towers are also possible. For example, our universe could have been created by an omnipotent deity that’s being simulated on a computer run by a mad scientist who’s a character in an online role-playing game!

Anyone want to estimate probabilities for that?

Posted by: John Baez on August 16, 2007 10:47 AM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

I am evidently lacking the ability imagining being simulated.

Let’s see: do we agree that, by Church-Turing, any computer program I can in principle let “run” simply by taking pencil, eraser and paper (huge amounts of pencil, eraser and paper, possibly, but still finite amounts) and do the precise steps the program asks me to do, using the paper as my storage memory (including registers etc.)?

Now, imagine me sitting there busily scribbling away on sheets of paper, thus processing the computer program which you think simulates some “conscious” being - or even entire civilizations of conscious and suffering beings.

Would you want me to stop writing 0s and 1s onto paper? Do you think that this process of writing 0s and 1s to paper, following a certain (however complicated) rule, may induce suffering on “simulated conscious beings” (except, actually, on me – the computer processor – in this scenario ;-)?

Posted by: Urs Schreiber on August 16, 2007 11:35 AM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

Urs wrote:

Doesn’t it require a bit of magical thinking to believe that whatever this machine does (internally) has to be subjected to International Law?

The question of whether simulated consciousness is still “really conscious” is already famously vexing. The question “should laws in this world apply to simulated worlds within ours?” raises extra issues. I don’t think it clarifies anything.

Vaguely similar questions are already important. People are arguing about rape and pedophilia in virtual reality.

Clearly a major issue here is the nontrivial interaction between our world and the simulated world!

Your question is more like this: “Should one be tried in our world for simulating a world in which evil occurs, even if that evil does not spill out into ours?

I don’t know — and to be honest, I don’t really care very much.

Posted by: John Baez on August 16, 2007 12:54 PM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

Urs, I’m not sure how much you’re just teasing us by saying you don’t understand these ideas, but at the risk of telling you things you already know, the basic idea here is just one of isomorphism.

It’s probably fairly uncontroversial to claim that if someone found a perfect isomorphism between one description, System A, of all the physical fields in our universe, and another description, System B, then we could never hope to tell which description was true. And I think everyone would agree that if conscious beings could exist in System A, they would also, necessarily, exist in System B.

What one branch of the philosophy of consciousness is concerned with is whether something less than a perfect isomorphism can, nevertheless, preserve various aspects of consciousness. If $H\subset A$ describes a conscious organism in system A, and there is some map $\phi: H\to B$ that does not strictly preserve all the physically meaningful structures on A, what kind of properties of $\phi$ might still imply that $\phi(H)$ experiences consciousness? And, furthermore, when (if ever) can we say that the experience of $\phi(H)$ is essentially “the same conscious experience” as that of H?

I’ve been very vague about the kind of structures A and B are supposed to be, but you can fill in your favourite models of physics. It’s also hard for a non-expert like me to say much about the formal properties of $\phi$ that various people speculate might suffice in order for $\phi(H)$ to be conscious, but I hope you can accept that it’s not absurd to wonder if $\phi$ really must be an isomorphism.

Of course, we would usually be concerned with the case where B=A, i.e. we want to know when we can map conscious beings H in our own universe into other structures in the same universe, with maps that are not isomorphisms of all of physics, without losing various properties of H.

In your example of following an algorithm involving binary numbers, using pencil and paper, what you’re really discussing is a class of theories of AI in which every $\phi$ can be factored through the set of all Turing machines (or some equivalent structure).

Posted by: Greg Egan on August 16, 2007 1:56 PM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

Urs writes:

Now, imagine me sitting there busily scribbling away on sheets of paper, thus processing the computer program which you think simulates some “conscious” being - or even entire civilizations of conscious and suffering beings.

Do you think that this process of writing 0s and 1s to paper, following a certain (however complicated) rule, may induce suffering on “simulated conscious beings”.

Sure! But I don’t mind if you call it “simulated suffering”.

Would you want me to stop writing 0s and 1s onto paper?

No, go ahead — I’d enjoy a few years to catch up on reading your old blog entries.

Posted by: John Baez on August 16, 2007 11:51 AM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

Okay, but only if Greg Egan isn’t watching, because he says he’d drag me to the International Court of Justice and find me (who is just scribbling zeros and ones, remember) guilty of deeds worse than those of Hitler, Stalin and Pol Pot together.

Would you stop him? If not, how can you seriously believe that, as you said

If the simulation is good enough, it doesn’t make a bloody bit of difference if our universe is being simulated.

?

I am really confused about this. Scale current desktops by a factor $10^{60}$ and it’s still equivalent to a universal Turing machine (with finite memory resources).

Doesn’t it require a bit of magical thinking to believe that whatever this machine does (internally) has to be subjected to International Law? (I know you didn’t say that, Greg did. I am just being intentionally provocative.)

Worse, maybe: Suppose I have a PENTIUM $10^{60}$ here on my desk. And it’s running.

Now, how do I decide if it is currently simulating a universe full of suffering people (we are beginning to sound like people in a buddhistr seminar, to some extent ;-). Isn’t that maybe even undecidable?

If not, when does the suffering start? Suppose the program simulates that universe not serially, but in the fashion of wheather forecasts or of jpeg rendering: first assembling a rough global approximation over the full time interval, then gradually refining that.

If I run the program for five minutes and then pull the plug, am I already bound for the International Court? Or do I have to wait for the screen to show a button:

Computation finished. Hit “Contiunue” to proceed to doomsday.

I’d consider all these questions as being rethoric. But given all the comments I have seen here, I am not so sure anymore.

Posted by: Urs Schreiber on August 16, 2007 12:12 PM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

I’ll pass on the metaphysics, but I do think it is interesting to ask what consciousness is. I feel like it would be a stretch to call an entity in your pencil-and-paper Turing machine conscious. Still, I’m afraid of saying that consciousness is something out of reach of a universal computer when the world looks like it can be simulated pretty well.

In any case, I’m pretty sure you are right that any simulator of our universe won’t be serial. What frame of reference would it use to define seriality?

Posted by: Rolfe Schmidt on August 16, 2007 2:59 PM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

I doubt the Turing framework will be at all adequate to support thinking we’d want to call conscious. At the very least, I should have thought we’d need to have grasped concurrency.

For one view on progress here, see Abramsky’s Information, Processes and Games:

In Concurrency Theory, the computational processes themselves become the objects of study; concurrent systems are executed for the behaviour they produce, rather than to compute some prespecified function. What function does the Internet compute? In this setting, even such corner-stones of computation as Turing’s analysis of computability do not provide all the answers. For all its conceptual depth, Turing’s analysis of computability was still calibrated using familiar mathematical objects: which functions or numbers are computable? When we enter the vast range of possibilities for the behaviour of computational systems in general, the whole issue of what it means for a concurrent formalism to be expressively complete must be re-examined. There is in fact no generally accepted form of Church-Turing thesis for concurrency; and no widely accepted candidate for a universally expressive formalism. Instead, there are a huge range of concurrency formalisms, embodying a host of computational features. (p. 15)

A good question that - “What function does the Internet compute?”

Posted by: David Corfield on August 16, 2007 4:13 PM | Permalink | Reply to this

### What is Baseball computing? Re: Meta-Universes That May or May Not Actually Exist

Every Major League baseball game has an embedded sequence of balls and strikes. In one at-bat, three strikes is an out, and four balls is a walk, whichever comes first. I’m not considering foul balls, which are strikes the first two times but never count as third strike (except for caught foul tips after 2 strikes). So its elementary but nontrivial that there are 64 valid at-bat sequences of balls and strikes, which means that a binary number applies to each at bat. So every game has an embedded sequence of binary-coded integers.

My friend Dr. George Hockney, a Quantum-Computing, General Relativity, and Lattice physics guy at JPL, asked me when I demonstrated this: What integer function is being computed by Major League Baseball?

This is not entirely silly. The Web shows chaotic dynamics, and we don’t know if it’s primarily because of the queueing theory and topology of the Web, or the nongaussian distribution of log-in times, or nongaussian distribution of web page sizes, or because people are the source of the chaos for some other cause.

Posted by: Jonathan Vos Post on August 16, 2007 9:31 PM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

Thanks for that link, David. I haven’t read the paper yet so I’m probably missing quite a bit still.

A Turing machine could compute the state of a set of interacting processes as a function of time – Urs’ gradually refined approximation of the universe would do something like this.

But in this case, the interaction never “happens”, only the results of the interactions are computed. So if consciousness entails interaction between concurrent processes (sounds reasonable to me), then I don’t think that Urs will need to go to jail for running his Turing machine.

I’m glad, that didn’t seem fair.

Posted by: Rolfe Schmidt on August 16, 2007 11:24 PM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

David wrote:

I doubt the Turing framework will be at all adequate to support thinking we’d want to call conscious. At the very least, I should have thought we’d need to have grasped concurrency.

I imagine we’re a long way from getting to the bottom of this, but it’s worth noting just how bizarre the consequences of either alternative would be.

Some people intuitively recoil from the notion that a serial computation with pencil and paper could result in conscious experience. Putting aside the fact that if we didn’t know about subatomic physics, our intuition would probably recoil equally from the notion that interacting quark and lepton fields can result in conscious experience, what does it imply if a single Turing machine that models my brain down to a subatomic level does not give rise to conscious experience?

If what’s missing is concurrency, then “how much” concurrency is crucial? If I simulate my brain with $10^6$ Turing machines running simultaneously and exchanging information, does that give rise to conscious experience? Or do I need one per neuron? One per atom? One per subatomic particle?

How can any of this affect any aspect of my thoughts, when there is no information present in the multiple-Turing-machine case that is not present in the single-Turing-machine case? How can the detailed spatial and temporal arrangement of information give rise to differences in subjective experience without giving rise to any difference in the information itself – and certainly not in any aspect of my behaviour?

How is it that the single-Turing-machine me and the multi-Turing-machine me would give identical answers to any question about their state of mind, but the first is completely lacking consciousness? And if this is the case, does the magic kick in gradually, or does it happen at a sharply defined point? Is the $10^10$-Turing-machine-brain an inhuman zombie whose calculations can never really matter, while the $10^10+1$-Turing-machine-brain is a feeling, thinking being that deserves our compassion and legal protection?

Of course if you don’t think that any number of Turing machines will suffice, and that the particular material nature of our brains is what’s crucial, then there are different thought experiments that give rise to some equally weird prospects. Nobody (I hope) would deny that an originally deaf or blind person with prosthetic sense organs was conscious, but just how far up the optic nerve can you start replacing damaged tissue with electronics before you rob someone of their humanity? Is it OK to torture me if my whole visual cortex is prosthetic, or do you need to replace … I don’t know, maybe my limbic system?

As I said, I think we’re a long way from getting to the bottom of this, but anyone who thinks it’s unbelievable for a serial computation (whether in silicon or pencil and paper) to feel something, should be aware that the alternative is at least equally strange.

Posted by: Greg Egan on August 17, 2007 1:54 AM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

It’s not the question of the material which constitutes us - I have no problem with our being made of a bunch of chemicals. What I doubt is that artificial intelligence will be possible without first finding a much better language, or languages, to describe thinking and action and how they are supported by the material constitution of the thinking acting entity. I very much doubt that the terms provided by Turing machine theory take us very far. Concurrency theory may perhaps take us a step further. But witness the problems already faced here. e.g., the next thing Abramsky writes:

Another question which ramifies alarmingly in this context is what is the right notion of behavioural equivalence of processes. Again, a large number of candidates have arisen. Experts use what seems most appropriate for their purpose; it is not even plausible that a single notion will gain general acceptance as “the right one”.

The only examples we have encountered of entities capable of thought are embodied actors dynamically interacting with the world and other actors. If this were my field, I’d look first to human and animal intelligence. Some interesting philosophical work is being done, such as Shaun Gallagher’s ‘How the body shapes the mind’. Of course, we must recognise the danger of starting out from such a restricted class of entities.

A idea occurred to me for a SF story while writing this. Imagine you are transplanted to an identical world but where your body/mind runs 10/100/1000 times faster/slower than the rest of the world. Think of the difficulty of being coupled differently to your environment. I guess it must have been done already.

Posted by: David Corfield on August 17, 2007 10:26 AM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

David wrote:

A idea occurred to me for a SF story while writing this. Imagine you are transplanted to an identical world but where your body/mind runs 10/100/1000 times faster/slower than the rest of the world. Think of the difficulty of being coupled differently to your environment. I guess it must have been done already.

There was a short story, whose title and author escapes me, in which criminals were punished by having their mental processes drastically slowed down, so they were at the mercy of the normal-speed people around them.

What I doubt is that artificial intelligence will be possible without first finding a much better language, or languages, to describe thinking and action and how they are supported by the material constitution of the thinking acting entity. I very much doubt that the terms provided by Turing machine theory take us very far.

Well, I’m certainly not suggesting that the Turing machine formalism is a particularly useful one for understanding the kind of information flows that underpin thoughts and actions; there are sure to be vastly better languages for describing what’s going on. But that in itself need not have any bearing on whether a Turing machine can create subjective experience. I expect that quantum field theory is also a pretty useless language for coming to grips with human and artificial intelligence, but that doesn’t stop quantum fields from giving rise to subjective experience.

Posted by: Greg Egan on August 17, 2007 11:21 AM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

There is a lovely story by H. G. Wells, The New Accelerator, in which the narrator has his mental processes first dramatically speeded up and then dramatically slowed down.

Posted by: Robin on August 17, 2007 12:44 PM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

Possibly even long before it comes to the issue of conciousness, we should realize that we are generally still lacking a decent understanding of “emergent phenomena”.

Most of us have grown accustomed to the possibility that there might be a set of fundamental (or at least “effectively fundamental”) laws governing the world around us on small scales.

On the other hand, it always deserves to be emphasized that there are lots of problem with deriving from such fundamental laws – even after they have correctly been identified – the complex behaviour they give rise to.

The QFT of the standard model of particle physics is pretty well understood. Still, deriving “bound states” from that remains a challenge. We cannot even satisfactorily derive the emergence of the existence of protons and neutrons from that of quarks!

And from there on it only gets worse. Exponentially worse, I’d say. We can satisfactorily derive the inner working of chemistry from quantum mechanics only for the simplest of atoms and molecules. Supercomputers are crunching away on computing properties of slightly more complex compounds. But things like protein folding are still far out of reach.

It continues this way. Even with the genetic code deciphered, even with the genome of a bunch of species catalogued, we have pretty much no idea what shapes, in detail, an organism as complex as a worm.

As we increase in scale this way, away from the “fundamental laws” of particle physics (for definiteness) we see more and more complex phenomena emerging from these simple laws. And increasingly so.

At some point, we might imagine, that conciousness arises as something close to the topmost level of complexity we perceive (or are able to imagine). Maybe after we pass through some kind of sonic barrier of emergent complexity. But given that we don’t even truly understand how a proton emerges from QCD, it might be just plain premature to try to say anything definite about whether and how conciousness might arise in this or that approximation to reality.

It may be fun to ponder. But I see little basis for anything but wild speculation here.

Posted by: Urs Schreiber on August 17, 2007 11:26 AM | Permalink | Reply to this

### Re: Meta-Universes That May or May Not Actually Exist

David wrote:

A idea occurred to me for a SF story while writing this. Imagine you are transplanted to an identical world but where your body/mind runs 10/100/1000 times faster/slower than the rest of the world. Think of the difficulty of being coupled differently to your environment. I guess it must have been done already.

Greg Egan has modestly refrained from mentioning Permutation City, his own meditation on the theme of simulation and ‘different couplings to ones environment’. Some of the characters run much slower than ordinary humans — and that’s the least of it. If you haven’t read this, David, you really should. I think you’d enjoy it a lot.

Posted by: John Baez on August 17, 2007 12:21 PM | Permalink | Reply to this

### Finite or Infinite? Re: Meta-Universes That May or May Not Actually Exist

The probability argument seems to implicitly require the universe (ours or the one we’re hypothetically embedded in) to be finite. There are more subtle measure theory concerns if at some point the cosmos tower is infinite. Up to isomorphisms, the tower could be a tree.

At which point the problem is Harary Reconstruction Theorem. Reconstruction is obviously FALSE for infinite graphs. So restrict the problem to finite cases.

Consider an infinite tree with an infinite vertex degree at each vertex and (to make this simple) “infinite” means countably infinite.

The infinite bag of subtrees are each the same as the tree from which we started.

But, hello! From an infinite set of infinite trees with an infinite vertex degree at each vertex, I can’t tell if I started with one tree, or an infinite forest of trees.

Posted by: Jonathan Vos Post on August 16, 2007 2:07 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

IMHO, Nature is obviously concurrent… Whether it is fundamentally concurrent is another story. If true, all phenomena that we observe would be an emergent result from such a fundamental concurrency…

Posted by: Christine Dantas on August 17, 2007 4:08 PM | Permalink | Reply to this

### Nature fundamentally concurrent?; Re: People Who May or May Not Actually Exist

Is Nature fundamentally concurrent? Wonderful question!

This is why “experimental metaphysics”, the issues of Nonlocality and Nonrealism are imporant in Quantum Mechnics.

Greg Egan has indeed added new depth and sophistication to the Consciousness Simulation conundrum, many times over. I believe that Ulam and von Neumann would be delighted with what Greg Egan has done to explore the ramifications of smart cellular automata.

MINDSCAN, A novel by Robert J. Sawyer

Tor Books Lead Science-Fiction Hardcover, April 2005
ISBN 0-765-31107-0

Tor Books Lead Science-Fiction Paperback, January 2006
ISBN 0-765-34975-2

“An exciting crowd pleaser. Richly informed by current interdisciplinary research in the burgeoning field of consciousness studies, and alive with provocative speculation of its own, Mindscan is a heady brew of hard SF, blended with enough comedy, romance, and adventure to appeal to a wider audience, as well.” [SFRA Review]

I particularly like the subplot where the AI resulting from scanning the mind of the protagonist exists in several versions. One version thinks that it is immortal. It has the same runing speed and subjective time rate as the original human, but draws different conclusions about its future, and in a nice stylistic trick, gradually begins speaking in longer and longer sentences, longer and longer paragraphs.

There is also the wonderful emergent consciousness distributedly embedded in the interactions of a pond ecology in the wonderful novel Heaven, By Ian Stewart and Jack Cohen, Warner Aspect. Hardcover, May 2004. Ian Stewart is, of course, a Mathematician and Math popularizer of great esteem, and Jack Cohen a brilliant and highly collegial evolutionary biologist. My son has bought multiple copies of this book, in harcover, to lend and give away to friends. Highly recommended.

Posted by: Jonathan Vos Post on August 17, 2007 5:37 PM | Permalink | Reply to this

### Physical limits of inference; Re: People Who May or May Not Actually Exist

Sorry, it wasn’t until after my previous post that I noticed the fascinating paper posted today, which is relevant to the Cosmic Simulation matter AND to the roots of learning algorithm threads.

Fri, 17 Aug 07

arXiv:0708.1362
Title: Physical limits of inference
Authors: David H. Wolpert
Comments: 36 pages, 2007 CNLS conference on unconventional computation
Subjects: Statistical Mechanics (cond-mat.stat-mech); Computational Complexity (cs.CC); Information Theory (cs.IT); General Relativity and Quantum Cosmology (gr-qc)

We show that physical devices that perform observation, prediction, or recollection share a mathematical structure. We call devices with that structure “inference devices”. We present existence and impossibility results for inference devices. These results hold independent of the precise physical laws of our universe. The impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted. Alternatively, they can be viewed as a non-quantum mechanical “uncertainty principle”. The mathematics of inference devices is related to the theory of Turing Machines (TM’s), e.g., some impossibility results for inference devices are related to the Halting theorem for TM’s. Furthermore, one can define an analog of Universal TM’s (UTM’s) for inference devices, which we call “strong inference devices”. We use strong inference devices to define the “inference complexity” of an inference task, which is analogous to the Kolmogorov complexity of a string. A task-independent bound is derived on the difference in inference complexity of an inference task performed with two different inference devices. This is analogous to the “encoding” bound on the difference in Kolmogorov complexity of a string between two UTM’s. However whereas the Kolmogorov complexity of a string is arbitrary up to specification of the UTM, there is no such arbitrariness in the inference complexity of an inference task. We informally discuss philosophical implications of these results, e.g., for whether the universe “is” a TM. We also derive some graph-theoretic properties governing sets of multiple inference devices. Next we extend the framework to address physical devices used for control, and then to address probabilistic inference.

Posted by: Jonathan Vos Post on August 17, 2007 7:28 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Well, I can’t deny that I’m a little disappointed. As far as I can tell (though I confess I haven’t read every recent comment here), I only got two responses to my question of what people think the probability $P$ is that our universe is a simulation:

Rolfe Schmidt said $P=0$ if the simulation is also required to be run by one of his ancestors.

John Baez said there exists a positive integer $n$ and a real number $p$ between 0 and 1 such that $P=p^n$.

My own feelings on the matter are basically the same as with the question of whether Moses existed. I can imagine someone coming up with evidence that convinces us that Moses existed, or that our universe is a simulation, or that Gods exist, but I can’t imagine how anyone could ever hope to prove the contrary. So I’m not really sure what it means to speak of the probability of such a thing. I’m imaging some kind of betting game or something.

A couple of months ago, when this thread was going strong, I tried for a few minutes to think of some completely unanswerable questions, like What is the probability that some given Turing machine $X$ halts. But with every example I came up with, I could actually imagine someone coming up with some reasonable probabilistic statement. But then I saw the question of simulated universes in the New York Times, and it seemed like the ultimate in ridiculous things to assign probabilities to, so I thought I’d test how willing the people here were to do it.

To everyone’s credit, no one gave an actual answer. But now I have a new question—what is it that makes you willing to assign a probability to the existence of Moses, but not to our universe being a simulation?

Posted by: James on August 18, 2007 5:01 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

James wrote:

what is it that makes you willing to assign a probability to the existence of Moses, but not to our universe being a simulation?

I tried to make my reason clear: it’s because I want to encourage people to think about the former question, and discourage them from thinking about the latter question.

Why do I want to discourage them from thinking about the latter question? I explained that too.

Posted by: John Baez on August 18, 2007 9:29 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Here someone who managed to exist and exist not simultaniously, acc. to the way of his teaching.

Posted by: Thomas Riepe on January 12, 2008 6:39 PM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

Winston Churchill didn’t really exist, say teens

(I wouldn’t bet anything on the reliability of the survey quoted, but still it’s amusing.)

Posted by: Greg Egan on February 4, 2008 4:16 AM | Permalink | Reply to this

### Re: People Who May or May Not Actually Exist

I know, this is five years old, but I had a new thought: