October 8, 2010

An Invitation

Posted by Tom Leinster

It’s my birthday, so I’d like to invite you all to a café. Guess which one?

This invitation is especially for those standing outside the Café with their nose pressed against the window. Recently I wrote this:

There are lots of great mathematicians who read this blog (some of whom I know personally) but never contribute. I think in some cases this is because they set themselves very high standards for what a comment should be, so they hardly ever make one. That’s a shame, because then the rest of us don’t get a chance to hear their thoughts.

John replied:

For a long time I’ve tried to encourage these people to post to the $n$-Café by posting hasty, ill-thought-out, joke-filled and error-ridden comments. […]

So, while it’s great that most people post really interesting and well-thought-out stuff here, it’s even better when we relax enough to make a few mistakes, as we would in normal conversation.

Some people don’t like the idea of making mistakes in public. If you’re one of them, you can use a pseudonym. Personally, I prefer real names to pseudonyms, but I’d much prefer to see interesting comments under a pseudonym than not to see them at all. (The comment form also asks for your email address. You can use a fake one if you want, but it’s only visible to the Café hosts and administrator anyway.)

Some people might wonder about typesetting. It’s easy: just type in plain text, as you would in an email. If you want to get fancy and incorporate Latex, you can: e.g. see this worked example. But plain text is fine.

Come in, come in!

Posted at October 8, 2010 2:17 PM UTC

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Re: An Invitation

Happy Birthday, Tom!

I suppose I’m not in the target audience for the invitation, since I’m an occasional contributor here (and I’m sure I must have made some public mistakes here, too). In the spirit of commenting under real names, though, maybe I’ll own up to writing the email that John quoted anonymously here.

Posted by: Mark Meckes on October 8, 2010 4:12 PM | Permalink | Reply to this

Re: An Invitation

Thanks! I remember that email to John, and quite right you were too: he’s a lazy so-and-so.

Posted by: Tom Leinster on October 8, 2010 4:17 PM | Permalink | Reply to this

Re: An Invitation

Happy birthday Tom. Can I buy you a coffee?

Posted by: Simon Willerton on October 8, 2010 4:15 PM | Permalink | Reply to this

Re: An Invitation

Just had one, thanks. But could you solve this conjecture?

Posted by: Tom Leinster on October 8, 2010 4:19 PM | Permalink | Reply to this

Re: An Invitation

Happy Birthday Tom!

I find your work very beautiful!

You wrote:

“There are lots of great mathematicians who read this blog (some of whom I know personally) but never contribute. I think in some cases this is because they set themselves very high standards for what a comment should be, so they hardly ever make one. That’s a shame, because then the rest of us don’t get a chance to hear their thoughts.”

One way to have great mathematicians to visit the n-Café would be to have them interviewed. The interview could have two parts. First, a personal interview by a gentle interviewer. Like an interview by Charlie Rose. This is not as easy as it may seem. The quality of an interview depends very much on the interviewer. The interview itself could be private but posted later at the n-Café, where the general public would be invited ask questions in the presence of a moderator. The guest would be free to choose the questions he wants to answer. There could be one or two rounds of questions.

Posted by: André Joyal on October 8, 2010 6:54 PM | Permalink | Reply to this

Re: An Invitation

Thank you for your kind words, André; they mean a lot to me.

I like the interview idea. I guess you’ve seen that John has been doing some interviews over at Azimuth? With the two interviews he’s published so far (both with Nathan Urban), the interviewee has joined in the conversation at the blog. It seems to have worked well.

I’ve just been watching a few Charlie Rose clips. (I didn’t know who he was.) I see what you mean about the gentle style. For the last ten years at least, the British news media seem to have valued most a very aggressive style of interviewing that’s counterproductive as often as enlightening.

Posted by: Tom Leinster on October 8, 2010 10:50 PM | Permalink | Reply to this

Re: An Invitation

For the last ten years at least, the British news media seem to have valued most a very aggressive style of interviewing that’s counterproductive as often as enlightening.

Ah, the John Humphreys’ school of interviewing. Still, given that the usual interviewee is a UK politician, it’s not an unreasonable stance. Perhaps for these interviews it should be modelled more on Desert Island Discs - that often got very interesting answers but never seemed threatening (apart from the threat of being abandoned on a desert island).

Desert Island Theorems, anyone?

Posted by: Andrew Stacey on October 11, 2010 8:10 AM | Permalink | Reply to this

Re: An Invitation

For those who do not know, John Humphries is a BBC presenter on the program Today (weekday mornings from 6.30 to 9). On yesterday’s program there was the following news item : The great crime novelist P.D. James has been awarded a prize for journalism for her interview of the BBC’s director general last December. She was given the opportunity to edit the program for one day, and to choose what she wanted discussed and who she wanted to interview. She was very courteous and gentle in her interviewing technique, but was absolutely tenacious in demanding an answer. The interview is I think on You Tube. It shows how you don’t have to be aggressive to get results in an interview.

(I should add that P.D. James was born in 1920.)

Posted by: Tim Porter on October 12, 2010 7:39 AM | Permalink | Reply to this

Re: An Invitation

OOPS The spelling should be Humphrys, apparently.

Posted by: Tim Porter on October 12, 2010 7:47 AM | Permalink | Reply to this

Re: An Invitation

I’ve been doing a lot of interviews for the new This Week’s Finds: after Nathan Urban will come the climatologist Tim Palmer at Oxford, then the physicist Thomas Fischbacher will talk about agriculture, then Eliezer Yudkowsky will talk about rationality and ‘friendly artificial intelligence’ and many other things… and right now I’m interviewing David Ellerman, who has worked on category theory but spent most of his years on economics, and recently wrote a book on the difficulties of helping people.

It’s a huge amount of fun! I wish I’d thought of it earlier! Instead of trying to be entertaining, I can relax and let the person being interviewed be entertaining. I don’t need to pretend to be smart anymore; in fact it helps to pretend I’m dumb, because it helps the readers if I ask a lot of questions.

It’s also fun being interviewed, at least for anyone who likes showing off, or has an idea they’re eager to explain.

So, I think interviews are great, and I hope someone here tries some. I you do them in an email exchange, there’s no need to transcribe anything, and the interviewee gets to polish their remarks to come out sounding brilliant.

Posted by: John Baez on October 10, 2010 4:29 AM | Permalink | Reply to this

Re: An Invitation

Happy birthday, Tom. I guess that as a (very) occasional commenter here I too am not in the target audience for your post, but I like the welcoming attitude.

I don’t have anything like the understanding or expertise to comment on most of the posts, although if ever people want to consider symmetric monoidal categories which aren’t autonomous or compact or abelian (<cough>Ban</cough>) then I may feel moved to chime in…

Posted by: Yemon Choi on October 8, 2010 7:16 PM | Permalink | Reply to this

Re: An Invitation

Yemon, it’s great that you hang around here. There aren’t many analysts who do, as far as I know. And it was you who was first to answer David’s plaintive call:

Where can someone find a friendly functional analyst around here?

It’s funny about Ban. My impression is that once upon a time, it was an example commonly used in introductory category theory texts, but now, not so much. Perhaps category theory is taught earlier, or functional analysis later?

Posted by: Tom Leinster on October 8, 2010 11:26 PM | Permalink | Reply to this

Re: An Invitation

Conversely, I get the impression that back in the 1960s and 1970s people in functional analysis were keener on using the basic language of categories in their presentations than they are now. (See old books of Semadeni, and Cigler-Losert-Michor.) Perhaps someone like Fred Linton would know more about this?

This seems mildly paradoxical, given that in the trendier areas of functional analysis, the NCG paradigm/religion leads to people happily working with more interesting categorical tools.

(I don’t recall Ban being used as an example when I learned category theory, but I may just have forgotten; my notes never made it across the Atlantic and are now probably lying in a ditch just outside Newcastle…)

Posted by: Yemon Choi on October 9, 2010 12:05 AM | Permalink | Reply to this

Re: An Invitation

In his memorial comment for George Mackey, Lawvere writes of his PhD thesis that:

…the fact that the category of Banach spaces and continuous linear maps is fully embedded into a category of pairings of abstract vector spaces, together with the definition and use of “Mackey convergence” of a sequence in a “bornological” vector space were discovered there and have played a basic role in some form in nearly every book on functional analysis since. What is perhaps unfortunately not clarified in nearly every book on functional analysis, is that these concepts are intensely categorical in character and that further enlightenment would result if they were so clarified.

Posted by: David Corfield on October 15, 2010 8:57 AM | Permalink | Reply to this

Re: An Invitation

Interesting. I vaguely remember Lawvere sending that. Do you know a reference for what he’s talking about?

(I’m a bit sceptical about ‘nearly every book on functional analysis’; of the three books on functional analysis on my shelf, none has an index entry for either Mackey convergence or bornological space. But maybe his point is that their role is so hidden that they aren’t even always mentioned by name. Or maybe it was just a generous overstatement of the sort often found in comments of an obituarial nature.)

It’s an intriguing prospect, anyway, that there’s an ‘intensely categorical’ story hiding just out of view in standard expositions of functional analysis. If someone can point to a rigorous exposition of this story, or even a non-rigorous one, I’d like to see it.

Posted by: Tom Leinster on October 15, 2010 10:01 AM | Permalink | Reply to this

Re: An Invitation

The opening line of Topological *-autonomous categories by Michael Barr says

In [Mackey, 1945], Mackey introduced the category of pairs of vector spaces, equipped with a bilinear pairing into the ground field. It is likely that he viewed this abstract duality as a replacement for the topology. See also [Mackey, 1946], the review of the latter paper by Dieudonné as well as Dieudonné’s review of [Arens, 1947], for a clear expression of this point of view.

‘Mackey space’ and ‘Mackey topology’ both crop up.

Posted by: David Corfield on October 15, 2010 10:32 AM | Permalink | Reply to this

Re: An Invitation

David,

please collect that stuff on the Lab, if it’s not there yet.

Posted by: Urs Schreiber on October 15, 2010 11:02 AM | Permalink | Reply to this

Re: An Invitation

Thanks, David.

It is likely that he [Mackey] viewed this abstract duality as a replacement for the topology.

I find this especially interesting. Stone, also working in functional analysis and only a few years earlier, had taken the revolutionary step of introducing topology to algebraic contexts. Now Mackey is taking it away!

(Mackey isn’t taking away exactly what Stone put in. Still, there seems to be a playing-out of the classic back-and-forth between topological structures and the algebraic structures comprised of functions on them.)

The story of Stone’s idea(s) is told rather excitingly in the introduction to Peter Johnstone’s book Stone Spaces. Here are some snippets:

Stone’s second key idea was the introduction of topology. He observed that the set of prime ideals of a Boolean algebra can be made into a topological space in a natural way …

Now this was a really bold idea. Although the practitioners of abstract general topology […] had by the early thirties developed considerable expertise in the construction of spaces with particular properties, the motivation of the subject was still geometrical […] nobody had previously had the idea of applying these techniques to the study of spaces constructed from purely algebraic data such as a Boolean algebra.

Mackey’s idea also appeals to me for the following reason. One aspect of functional analysis that I’ve always found mysterious is the profusion of topologies: strong, weak, weak${}^*$, … (My immediate, childish reaction is ‘isn’t one of them just right?’ But apparently not.) I guess I’m not familiar with situations in which a single structure carries multiple nontrivial, useful, topologies, so I don’t know how to conceptualize it. Perhaps Mackey’s idea, as described by Barr in his opening paragraph, provides a different perspective.

Posted by: Tom Leinster on October 15, 2010 11:54 AM | Permalink | Reply to this

Re: An Invitation

My immediate, childish reaction is ‘isn’t one of them just right?’ But apparently not.

The correct response, of course, is ‘right for what?’

Posted by: Mark Meckes on October 15, 2010 4:03 PM | Permalink | Reply to this

Re: An Invitation

And I forgot the most striking Stone quote (1938), again from Johnstone’s book:

A cardinal principle of modern mathematical research may be stated as a maxim: “One must always topologize”.

Posted by: Tom Leinster on October 15, 2010 12:22 PM | Permalink | Reply to this

Re: An Invitation

Be wise, topologize!

Posted by: Todd Trimble on October 15, 2010 1:44 PM | Permalink | Reply to this

Re: An Invitation

I would love to know more about what one can say about Ban from a category-theoretic viewpoint.

Posted by: Mike Shulman on October 9, 2010 12:27 AM | Permalink | Reply to this

Re: An Invitation

And of course anything learnt about Banach spaces from a categorical viewpoint should be added to the nLab.

Oh, wait! There’s already a page with some of this on: algebraic theories in functional analysis. Woefully incomplete, of course.

Perhaps after the birthday celebrations, when the whisky [sic] has gotten everyone a little relaxed, someone could scrawl a little more on that page.

Posted by: Andrew Stacey on October 11, 2010 8:31 AM | Permalink | Reply to this

Re: An Invitation

Is there a “teaser-like” explanation of why you are interested in this topic?

Posted by: Tim van Beek on October 11, 2010 1:28 PM | Permalink | Reply to this

Re: An Invitation

There’s a little bit more about the category of Banach spaces over at the nLab article Banach space. Some cleanup of that article will be necessary because, for example, there is some vague suggestion that this category with its standard tensor product (the one adjoint to the standard internal hom on Banach spaces) is a category with duals, which is false as discussed in this MO exchange here.

Also there is the question of which categories the category of Banach spaces and short linear maps might be monadic over, if not $Set$. I think there was some discussion somewhere that it’s monadic over the category of metric spaces with basepoint and short maps.

Posted by: Todd Trimble on October 11, 2010 3:15 PM | Permalink | Reply to this

Re: An Invitation

That latter adjunction is quite interesting and seems to have been (re)discovered at least twice - I remember going to a talk by Godefroy on “free Lipschitz spaces” and being probably one of two people in the room to think to themselves, “ooh, he’s taking the counit of an adjunction”. I have no idea if it’s monadic or not, but that is just due to my ignorance and not to say that the question would be hard to figure out. Do you remember where you might have seen this, Todd?

Now that having a long-term job prevents me from using my usual excuse of “this is interesting, but I have to focus instead on things I can publish and hawk in the bazaar”… maybe I shall dig out a copy of Semadeni or similar and have a stab at expanding/sanding the nLab material. Especially now that Tom has laid on the flattery ;-)

Posted by: Yemon Choi on October 11, 2010 9:32 PM | Permalink | Reply to this

Re: An Invitation

I have no idea if it’s monadic or not, but that is just due to my ignorance and not to say that the question would be hard to figure out. Do you remember where you might have seen this, Todd?

I see it quoted in the preview (graciously supplied by Springer ;-) of this article:

• E.G. Manes, A pullback theorem for triples in a lattice fibering with applications to algebra and analysis, Algebra Universalis, Vol. 2, No. 1, pp. 7-17 (1972).

but I’ve not actually read that article.

Posted by: Todd Trimble on October 13, 2010 3:56 AM | Permalink | Reply to this

Re: An Invitation

Yemon’s got me bang to rights: I didn’t use Ban, the category of Banach spaces, as an example in the category theory course in Cambridge that I taught and he took. (Nor have I used it in subsequent courses, because the students wouldn’t know what it was.)

But Ban does appear as a recurring example in Borceux’s Handbook of Categorical Algebra. And it seems like Yemon is on top of its properties. Also, as Yemon says, Fred Linton knows a great deal about this: I’d guess that he’s the world expert.

Posted by: Tom Leinster on October 9, 2010 12:33 AM | Permalink | Reply to this

Re: An Invitation

It’s funny about Ban. My impression is that once upon a time, it was an example commonly used in introductory category theory texts, but now, not so much.

I can’t say about once upon a time, but I know Larry Moss is introducing folks to category theory with Jiří Adámek et al., which is fairly old now (1990;2004) but has a number of examples for Ban and Banb.

Posted by: wren ng thornton on October 9, 2010 2:28 AM | Permalink | Reply to this

Re: An Invitation

which is fairly old now (1990;2004)

Er, that would be my NLP/SMT heritage speaking where five years (let alone twenty) is antiquity. Perhaps not so appropriate for mathematics or category theory generally.

Posted by: wren ng thornton on October 9, 2010 2:33 AM | Permalink | Reply to this

Re: An Invitation

Happy Birthday, Tom!!

It was great talking with you in Lausanne last week.

As I did back when John was thinking about rational homotopy theory, I promise to comment if a subject comes up in which I feel competent and if I have something to say that I think others might find interesting. I do enjoy sitting quietly in a corner of the café and listening to others!

Posted by: Kathryn Hess on October 8, 2010 7:28 PM | Permalink | Reply to this

Re: An Invitation

Thanks—I very much enjoyed the trip to Lausanne too. As you know but the rest of the world doesn’t, I was there to take part in the thesis defence of Nicolas Michel. I’m hoping that one day soon, a version of his thesis (Categorical Foundations for $K$-Theory) will be available online, so that I can write something about it here.

Posted by: Tom Leinster on October 8, 2010 10:55 PM | Permalink | Reply to this

Re: An Invitation

Well clearly I’m not in the target audience since my comments tend to get deleted …

Posted by: Kea on October 8, 2010 8:21 PM | Permalink | Reply to this

Re: An Invitation

Not everyone who lurks here is a mathematician! Let alone a great one. So I consider it totally reasonable that I have nothing to add.

Posted by: Dan Carney on October 8, 2010 8:27 PM | Permalink | Reply to this

Re: An Invitation

Happy Birthday!

Viel Glück und viel Segen auf all’ deinen Wegen!

Input from my socialisation dictates that I ask “what gifts did you get?” and “how are you going to celebrate?”. Since I’m not invited you are supposed to answer the latter question with a version of “nothing fancy” :-)

JB said:

…as we would in normal conversation.

The problem is that in a normal conversation you know whom you are talking to, see their reactions and can react to that accordingly.

Switching from personal conversation to an online forum is similar to switching from telling stories to your children to writing children’s books, being a politician or stand-up comedian and making your first appearance on TV, from staging plays to making movies. You don’t know whom you are talking to, and some very nasty responses are a certainty. Some people succeed, some don’t, some never try. I think I know of a generalization of a theorem of Alfred Lord Tennyson that applies to the latter group:

“It’s better to have tried, and failed, than never to have tried at all!”.

P.S.: Just in case I have to provide some mathematics, any news of the Thompons’ group F and its amenability?

Posted by: Tim van Beek on October 8, 2010 9:18 PM | Permalink | Reply to this

Re: An Invitation

Among other things, a cartoon introduction to biology for kids, to help me as I dip my toes into mathematical biology. If I ever go to a biology conference, I plan to sit in the front row and read it ostentatiously. Sample fact: total weight of all bacteria $=$ 150 times total weight of humans.

“how are you going to celebrate”?

Nothing fancy.

any news of the Thompson’s group F and its amenability?

Not that I’ve heard. The two papers mentioned in Danny Calegari’s blog entry are still on the arXiv (yes it’s amenable; no it’s not). Neither has been withdrawn or updated since May 2009.

Posted by: Tom Leinster on October 8, 2010 11:11 PM | Permalink | Reply to this

Re: An Invitation

Happy Birthday Tom!

I guess I don’t fulfill any of the criteria to be in your target audience, since I’m not any kind of a mathematician, let alone a great one, but I merrily babble away anyway. (Not so much for a while, as I’ve been busy scribbling pictures instead, but now I feel a positive duty to start again.)

That said, I hate making mistakes, and feel guilty if I think I might be leading anybody else astray with my errors; but I figure, well, I’m going to make them anyway, so I might as well make them somewhere where other people can learn from them. No mobs have come after me yet …

Posted by: Tim Silverman on October 8, 2010 10:43 PM | Permalink | Reply to this

Re: An Invitation

Oops.

Dan wrote:

Not everyone who lurks here is a mathematician! Let alone a great one.

and Tim wrote:

I’m not any kind of a mathematician, let alone a great one

I didn’t mean to invite only those who regard themselves as great mathematicians… If you’re too cautious to comment, you’re probably not someone with that kind of self-image!

Posted by: Tom Leinster on October 8, 2010 11:00 PM | Permalink | Reply to this

Re: An Invitation

Yeah, saying “there are a lot of great mathematicians who read this blog” might scare away a lot of people who are on the brink of posting a comment. You get the image of Connes, and Serre, and Manin, and many more, all waking up in the morning, firing up their computer, and reading the silly thing you just wrote.

Posted by: John Baez on October 10, 2010 4:36 AM | Permalink | Reply to this

Re: An Invitation

Well, too late now.

What I really meant was “people with interesting things to say”. But “people” got turned into “mathematicians”, and “with interesting things to say” got turned into “great”.

Posted by: Tom Leinster on October 10, 2010 6:26 AM | Permalink | Reply to this

Re: An Invitation

Perhaps one should read Tom’s message as ‘great’ people, who are ‘mathematicians’ (although not ones who declare it in public -you know ‘closet mathematicians’ who enjoy a quite private solution of a maths problem or consider that a furtive look in the window here might be a fun thing to do as they are taking the dog for a walk.)

Seriously, well sort of, quite a few of us have met very interesting people who would never claim to be mathematicians but show considerable mathematical common sense and love the challenges mathematics poses. Some years ago when we still existed at Bangor, I took a pile of laminated (A4 size) cards with questions/puzzles of a mathematical nature to a regional science festival and was entranced to spend from 10 in the morning until about 4 in the afternoon watching people attempting to answer the puzzles, sometimes in self organised groups who were discussing the pros and cons of various attacks with energy and a lot of mathematical common sense. One man had to leave and asked me to explain the solution of one problem to his wife but not to reveal it to him. He wanted to continue thinking about the problem and not to have the solution revealed at that moment.

The puzzles were not ones on n-categories I should add, but problems on operational research. (Actually I have wondered if some of the ideas discussed here in the café might not one day have applications in OR. Any thoughts you lot!)

Because of this, I think that there are people who look in here who have a good knowledge of some areas of mathematics and could contribute from time to time. There are a lot who do that already and who make the café a very interesting place to hang out or to visit on that morning stroll to pick up today’s `news’.

Posted by: Tim Porter on October 10, 2010 7:21 AM | Permalink | Reply to this

Re: An Invitation

I guess we need to work a bit more on our advertising strategy.

But more importantly… happy birthday!

Posted by: John Baez on October 10, 2010 7:07 AM | Permalink | Reply to this

de-lurk versus colurk; Re: An Invitation

Each morning, with the first cup of coffee, I am prompted by Facebook to send “Happy Birthday” greetings to a fraction (less than 1/365) of my 1,355 Facebook “friends.”

I customize these messages with background that Facebook provides on what that individual’s interests are. For example, several people in yesterday’s wishes also got John Lennon quotations, if they’d listed the Beatles in the Music preferences.

Some of my “friends” are far better Mathematicians than I am (Neil J. A. Sloane, for instance), just as some of my “f2f friends” are far better Mathematicians than I am (for instance, earlier this week was a Math Department Tea for the new grad students and postdocs and instructors at Caltech).

Even deceased Mathematicians can be productive, as with posthumous collaborations by Erdos (co-authored papers that were only partly complete by the time he died, where the survivor or survivors finished and published later).

So I await with keen interest those, live or undead, whom this blog thread provokes to de-lurk.

Which reminds me – what would colurking be?

Posted by: Jonathan Vos Post on October 9, 2010 5:35 PM | Permalink | Reply to this

Don’t invite: make yourself attractive

There are lots of great mathematicians who read this blog (some of whom I know personally) but never contribute. I think in some cases this is because they set themselves very high standards for what a comment should be, so they hardly ever make one. That’s a shame, because then the rest of us don’t get a chance to hear their thoughts.

Experience shows that interesting people start sharing their thoughts when the discussion here gets interesting. The $n$Café did see various “great mathematicians” chime in here, whenever the discussion reached a certain point.

Interesting people tend to be busy. They don’t hang around in blogs just to socialize – and there are other places designed for that purpose anyway. They come if there is something interesting to be found. What is there to say in reply to “Come in, come in.”? Facebook also invites people to come in and say something .

To boost the $n$Café’s role as a place where intersting math (at all levels of sophistification) is exchanged by interesting people, it is important to keep it focused. If people get used to the fact that the $n$Café-thread in their RSS reader contains a high signal-to-noise ration with a high percentage of interesting math, they will take the time to look through it. And will comment when some discussion touches a point of interest to them. If however people get the impression that there is just random chat filling their RSS reader, they will stop looking through it for the gems.

So it seems to me there is little point in inviting people. Try to be attractive, and people will come by themselves.

Posted by: Urs Schreiber on October 10, 2010 1:47 PM | Permalink | Reply to this

Re: An Invitation

Belated Happy Birthday, Tom!

Your remarks remind me of a seminar organized by Steenrod:
A Small Seminar for Half-baked Topological Ideas’

no completed work to be discussed

Posted by: jim stasheff on October 10, 2010 2:56 PM | Permalink | Reply to this

Re: An Invitation

I’ve got to say that you lost me at “great mathematicians”. But I have decided that I am at least willing to put my hand up to being a “person”.

Still, I’m a fan of this place. Even though I understand a fairly small percentage of the posts, the ones I do - and the discussions which follow - are often fascinating. So hello, and happy birthday.

Posted by: Richard Elwes on October 13, 2010 7:56 AM | Permalink | Reply to this

Re: An Invitation

Hi Richard. Thanks for your wishes. It’s clear now that the “great mathematician” phrase was a mistake… but I can tell myself that when I encouraged people to make mistakes in public, I was leading by example.

I see you do lots of interesting public understanding of mathematics activities, to great acclaim. What’s next?

Posted by: Tom Leinster on October 13, 2010 8:04 PM | Permalink | Reply to this

Re: An Invitation

Thanks! Though I think “great acclaim” is pitching it rather strong… As for next, well I am waiting for my first book to appear (finally) in the next week or so, and meanwhile, well, I am sniffing about for a new project or two. I have a few semi-formed ideas, some of which may turn into something concrete in the fullness of time…

Posted by: Richard Elwes on October 14, 2010 5:07 PM | Permalink | Reply to this

Re: An Invitation

Congratulations! And in time for the Christmas market, I see. Good luck!

When I was in the final, painful stages of writing my own first (and only) book, I noticed that it was already available to preorder on Amazon. I had this delicious fantasy that if I preordered it myself, then it would arrive through my door fully-written, saving me from having to finish writing the blasted thing…

Posted by: Tom Leinster on October 15, 2010 6:03 AM | Permalink | Reply to this

Re: An Invitation

Well, first of all…Happy (late) Birthday to you, Tom!

I’m a fellow Libra and wanted to ask you if you are feeling “balanced”? (For you non-Libra’s…we carry the sign of the balance, or the scales).

I always tend to feel balanced when the sun is in the sign of Libra. Don’t know why or how it works, but it just does.

Since scales can be used in mathematics, I guess I qualify (in a long-shot kinda way) as a mathematician (don’t I?).

I’m not really a mathematician (in fact I just now learned how to spell “mathematician”, thanks to “Spell-Check”), unless you count the fact that I had to take Calculus as part of my B.S. in Business Administration.

Guess I’m just another one of your lurking, non-mathematician fans who likes to read about what I missed by not taking more math classes, as well as read what smart, witty people have to write about when not solving some problem that’s WAY over my head, lol.

I do have a challenge for you smart guys though:

Who can tell me where this line comes from:

“The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.”

Posted by: Daniel on October 13, 2010 6:00 PM | Permalink | Reply to this

Re: An Invitation

Thanks. Happy birthday to you too, some time about now.

Posted by: Tom Leinster on October 13, 2010 8:09 PM | Permalink | Reply to this

Re: An Invitation

lol, nice move on putting Google onto my quote, Tom!
That’s a pretty cool page there, btw.

Yeah my birthday was 09-27-1956. In the world of Numerology, that makes me a 3. 9+9+21=39 and 3+9=12 and 1+2=3. That’s as far as my number can be reduced to so that’s my birth number.

Posted by: Daniel on November 6, 2010 7:37 PM | Permalink | Reply to this

Re: An Invitation

Hello everybody! Happy birthday, Tom!

It seems I’m visiting this page more often and hope to contribute some things soon :)

Posted by: Matija Basic on October 13, 2010 9:49 PM | Permalink | Reply to this

Re: An Invitation

Happy birthday! (a bit late…)

As someone who is just starting to delve deeply into the world of math, and as someone who feels helplessly lost (but very excited… like someone drowning in a coral reef) with category theory, I haven’t had anything of any value to contribute… I may be a little less wary about posting in the future though. ;-)

Cheers.

Posted by: Cory on October 14, 2010 12:48 AM | Permalink | Reply to this

Re: An Invitation

John wrote: “Some people don’t like the idea of making mistakes in public.”

Many people don’t like the idea of wasting time on reading too many errors in private.

Posted by: Zoran Skoda on October 16, 2010 4:26 PM | Permalink | Reply to this

Re: An Invitation

I wrote that, not John. Were you deliberately making a mistake in public?

Anyway, I think that people who are really averse to reading errors should probably stick to refereed papers. Blogs have many of the advantages and disadvantages of real-life conversations. One such—both an advantage and a disadvantage—is that they involve the blind alleys, half-formed thoughts, guesses, mistakes, and corrections that are the authentic stuff of intellectual progress.

I agree with you that too many errors is a bad thing. Otherwise, of course, it wouldn’t be “too many”. There’s a balance to be struck. But academics are strongly conditioned against making mistakes in public, and I want to encourage people to worry less about that, and look more at the gains to be had from online collaboration and discussion.

As I said in the original post, I know several mathematicians who read this blog but rarely or never comment. There must be many others who I don’t happen to know. It’s up to them, of course, but in a way it’s a pity because lots of people would enjoy their contributions. My post was intended as gentle encouragement and a friendly welcome.

Posted by: Tom Leinster on October 16, 2010 5:32 PM | Permalink | Reply to this

Re: An Invitation

One of the things that has happened is that “in real life” public is a continuous variable: a discussion at coffee break is less public than a local seminar is less public than a talk at a conference etc. One of the problems is that on the internet everything is exactly as public as anything else that’s public.

I remember reading a story about Feynman at Los Alamos. People were already coming to him with problems and he’d go about excitedly claiming some solution, often jumping the gun and missing some important element of the problem. After further thought he’d often get to the correct answer. The others apparently came up with the rule “If Feynman says it three times then it’s true.” I wonder what the view would have been if, in addition to all his correct ideas, these things were as readily available to the world in general as his papers at the time.

Posted by: dave tweed on October 16, 2010 6:17 PM | Permalink | Reply to this

Re: An Invitation

I do not mean errors in the literal sense, but all the nonessential blast which comes with making joking as opposed to substance the center of things. For example, you now ask me if John said this or you said this and weather I was intentionally making mistake. You see the point is that it would be utterly stupid from me to divert the discussion to tricks on what who said. If such things are focus of discussion I choose another site to pay attention to.

Urs phrased nicely the same idea above. The substance has to be in the center of things, with his remark, at all levels of sophistication, but with good and focused intentions. It is useful to have mixture of questions which are both above and below our own level of understanding some question. In Moscow mathematical school which was in its golden years quite an ideal math environment, hi schoolers and academicians freely mixed in seminars and discussed in corridors. But they were all focused on math. Not movies, politics, beer, advertising, political correctness and snobism.

I find it distracting when I have to scroll through entries which do not have mathematical substance but rather yield to all-present commercial brainwashing and advertising like e.g. the star-trek discussion entry http://golem.ph.utexas.edu/category/2009/09/trivia_question.html. I am much less active in cafe than in nlab, precisely because of that dillusive component which is pretty present in some months. With all due respect to people who had good intention in creating what I perceive as distractive entries, distraction is distraction.

Posted by: Zoran Skoda on October 17, 2010 3:39 PM | Permalink | Reply to this

Re: An Invitation

I find it distracting when I have to scroll through entries which do not have mathematical substance but rather yield to all-present commercial brainwashing and advertising like e.g. the star-trek discussion entry

Sheesh. Lighten up!

Posted by: Todd Trimble on October 17, 2010 4:25 PM | Permalink | Reply to this

Re: An Invitation

I have another blog now, Zoran. So you don’t need to complain about my posting the occasional trivia question here anymore: that’s a thing of the past.

I can see there are disagreements about how ‘serious’ this blog should be. As my presence here diminishes, I hope I can safely leave the rest of you to sort that out. But it seems a purely technological solution could be possible: have posts labelled according to topic in some way that makes it easy for people to ignore topics they don’t like. Since I read posts and comments the old-fashioned way, by looking at the blog and going to topics I like, I’m already happy. But for people who (apparently) get notified by their RSS feed every time a comment shows up, surely there should be some high-tech way to achieve the same goal.

Posted by: John Baez on October 17, 2010 6:17 PM | Permalink | Reply to this

Re: An Invitation

John, as you know, I am very interested in your other/new blog. I wanted to recommend it to some of my acquiantances who do seriously environment issues, though I am deferring this as at the moment there is much technology and math still there, what may be distracting to them if they are primarily interested in ecology. The fact that I picked example of your distracting post is of course accidental, I went through old issues and found first such to exemplify it to Tom. Everybody wants you to stay very active here as well!

Posted by: Zoran Skoda on October 17, 2010 7:31 PM | Permalink | Reply to this

Re: An Invitation

http://portal.connect.znanost.org/content/view/3351

I also cite there the interesting discussion between Joyal and Baez. As the introduction to the linked post above is in Croatian, here is a translation of first few paragraphs:

Mathematical physicist John Baez after a phase in quantum gravity and a phase in applications of category theory, decided to attack the questions of survival of the planet Earth as we know it. These days, Baez started blog azimuth, wiki Azimuth Project and Azimuth Forum associated with the wiki with the purpose to learn what scientists (especially mathematicians and physicists as him) can do. Everybody is invited to contribute to the wiki. Wiki software is instiki, which can (if the browser can mathML, e.g. with plugin MathPlayer) present LaTeX formulae (in fact iTeX + Markdown code).

Baez says that the gravity theory can wait, but climate changes, polution and population growth do not wait so one has to take an iniciative. Though a beginner in this science, he has an advantage over many other scientists on the account his sharp reasoning and clear exposition.

Posted by: Zoran Skoda on October 17, 2010 7:52 PM | Permalink | Reply to this

Re: An Invitation

Thanks, Zoran — that’s very kind of you! It means a lot to me that you’re telling people about the Azimuth Project and occasionally contributing to my new blog. That’s where my heart is now.

Posted by: John Baez on October 18, 2010 5:53 AM | Permalink | Reply to this

Re: An Invitation

Zoran wrote:

I do not mean errors in the literal sense, but all the nonessential blast which comes with making joking as opposed to substance the center of things.

Ah, OK. That’s a totally different matter then, and it’s not at all what this post was about. I was addressing people who worry about making mathematical mistakes in public. It had nothing to do with joking around.

But now that you have raised the subject of joking around, I’ll say what I think. I agree with John: there’s a spectrum of tastes on how much of it there should be on this blog. I also agree with you that there has sometimes been too much, though it sounds like it bothers me less often than it bothers you.

I think the importance of jokes or non-serious comments in a blog such as this is sometimes underestimated. Every academic knows that disagreement over questions that should be purely academic—that any member of the public would regard as unbelievably obscure—can occasionally turn personal. This is particularly a danger on internet forums, where it’s hard to hear tone of voice. Having a few jokes, a little bit of light chat, can remind people that we’re all human beings, as well as mathematicians and physicists and philosophers and so on. It creates some shared human warmth. And that can help to stop disagreements turning sour.

So while I don’t want to see a lot of joking around here, I think that a small amount can actually have a beneficial effect.

Posted by: Tom Leinster on October 17, 2010 9:03 PM | Permalink | Reply to this

Re: An Invitation

That’s a good point, Tom. And even when the jokes and chitchat go on longer than I’m interested in, they usually just take one click in my RSS reader to skip over. That’s fewer clicks than it takes me to delete spam in Gmail. (-:

Posted by: Mike Shulman on October 17, 2010 9:36 PM | Permalink | Reply to this

Re: An Invitation

I agree, Tom. The problem I see in “joking” is not with a tone, where self-criticism, good spirit and wit are on beneficial side, but with lack of focus on intellectual things (here mathematical in particular) and allowing for political, personal, commercial etc. things to take on. As far as personal “insults” etc. true intellectual discussion never cares or is aimed about those. As Latin proverb says Non quis sed quid.

Posted by: Zoran Skoda on October 18, 2010 11:35 AM | Permalink | Reply to this

Re: An Invitation

John’s original newsgroup, spr, back when it was John’s, had both: an inviting and relaxed atmosphere with “shared human warmth” and at the same time a moderation system that would block any off-topic messages. Back then that was widely regarded as being the only way to run a sensible discussion group. Here on the blog we have many messages (like the one I am just writing) that would never have made it through spr moderation, simply because they were not on the technical topic.

It’s curious, but there are a bunch of (other) things the the usenet system had all sorted out and working well, which got thrown out of the window when people switched to blogs – and which maybe we need to re-establish piece by piece.

Posted by: Urs Schreiber on October 18, 2010 4:57 PM | Permalink | Reply to this

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