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May 7, 2009

Odd Currency Puzzle

Posted by John Baez

Sorry to be posting so much light, frothy stuff lately — but since it’s an odd day, I can’t resist another puzzle.

What’s the oddest currency ever used in America?

Of course this is a subjective question, so I’d be interested to hear your opinion…

… but my own favorite candidate is the 19\frac{1}{9} dollar bill used in colonial Maryland:

A total of 57,000 bills of this sort were issued in 1767, 1770 and 1774. The dent in the upper left corner was deliberate: ‘indented’ bills were used to fight against counterfeiting, which was rampant at the time. Another trick was inserting deliberate typos, like the colon after “Annapolis”. Note also that this note is hand-signed, with a hand-written serial number! Back then, being treasurer was hard work.

You might argue that the 29\frac{2}{9} dollar bill was even odder…

… but I’d have to disagree: it’s oddly evener!

I thank Robert Schlesinger for tipping me off about the existence of these odd fractional bills. The above pictures come from the following delightful history, where you can also see a 4 dollar bill, a 6 dollar bill, a 13\frac{1}{3} dollar bill, and so on:

On the other hand, if you just find big bills odd, maybe you’ll go with the biggest American bill ever released — this orange $100,000 dollar bill:

The $10,000 dollar bill was also a bit odd, since it was decorated with the face of a guy most people have never heard of. Who?

Posted at May 7, 2009 7:34 PM UTC

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Re: Odd Currency Puzzle

The $10,000 dollar bill was also a bit odd, since it was decorated with the face of a guy who was never President! Who?

What’s so odd about that? The same is true of the $10 and $100 bills.

Posted by: Mark Meckes on May 7, 2009 9:50 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Good point. I guess I shoulda said “a guy nobody has heard of”.

In fact, I’m so embarrassed by this that I’m going to use my superpowers to rewrite my blog entry. But I’ll leave this here so everyone knows what a dope I am.

Posted by: John Baez on May 7, 2009 10:03 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Actually, I think most people who have even the most casual acquaintance with American currency will have at least seen the name of this guy. That’s another pretty big hint I guess.

Posted by: Todd Trimble on May 8, 2009 12:33 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

I know the answer to John's final question without checking the Internet (or other external reference), but I don't want to spoil anything.

Let's just say that it's more like the $10-dollar bill than the $100-dollar bill.

Posted by: Toby Bartels on May 7, 2009 10:04 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Are you another SCOTUS geek, or just a currency wonk? Either way, this time I don’t have to chase down any answers.

Posted by: John Armstrong on May 7, 2009 10:19 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

I tend to think of him in his like-the-$10-bill aspect.

Still, there aren't many people who are like the guy on the $10 bill and of interest to SCOTUS geeks, so this all amounts to a pretty big clue.

Posted by: Toby Bartels on May 7, 2009 10:24 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

(Man, I even missed the biggest clue at first! Now I feel like somebody should just delete my last two comments, since they detract from the cleverness of yours.)

Posted by: Toby Bartels on May 7, 2009 10:27 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

I thought the Brits were weird for using 1.05 pounds as a unit of currency. But I think 1/9 of a dollar beats that.

Just in case you don’t know what 1.05 pounds is called, I’ll not mention it so you can have fun guessing.

Posted by: Dan Piponi on May 7, 2009 10:33 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

£1.05 is more fowl than odd.

Posted by: Toby Bartels on May 7, 2009 11:22 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Just in case you don’t know what 1.05 pounds is called, I’ll not mention it so you can have fun guessing.

“A pound and a shilling”

Posted by: John Armstrong on May 7, 2009 11:32 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

That’s not ONE unit of currency
but I think that describes a single coin
whose name I’ll probably get wrong: a sovereign?

and has everyone figured out why 1/9 was reasonable?

Posted by: jim stasheff on May 8, 2009 1:27 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

Well, they’re not to be confused with gerbils, either.

Posted by: some guy on the street on May 8, 2009 12:33 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

Dan Piponi writes:

Just in case you don’t know what 1.05 pounds is called, I’ll not mention it so you can have fun guessing.

That’s interesting! I guessed it. But I hadn’t known that coin was worth 1.05 pounds. It reminds me of how a perch equals 16.5 feet!

Jim Stasheff wrote:

I think that describes a single coin whose name I’ll probably get wrong: a sovereign?

No… a sovereign was always worth a pound, I believe. The answer to Dan’s puzzle is not any of these:

Gold coins:

Five-sovereign piece, equal to five pounds.

Two-sovereign piece, equal to two pounds.

One-sovereign piece, equal to one pound.

Half-sovereign piece, equal to half-a-pound.

Silver coins:

A crown, or five-shilling piece, equal to one fourth of a sovereign.

Double-florin, or four-shilling piece, equal to one-fifth of a sovereign.

Half-a-crown, or two shillings and sixpence, equal to one-eighth of a sovereign.

Florin, or two-shilling piece, equal to onetenth of a sovereign.

Shilling piece, equal to one-twentieth of a sovereign.

Sixpenny piece, one-half of a shilling.

Threepenny piece, one-half of a sixpence.

Bronze coins:

Penny, equal to one-twelfth of a shilling.

Halfpenny, equal to one-half of a penny.

Farthing, one-fourth of a penny.

Anyone who gets tired of the obscure clues that clever folks are providing can get the answer to Dan’s puzzle here.

Jim Stasheff wrote:

and has everyone figured out why 1/9 was reasonable?

I think the above table of British coins is enough for anyone to crack this puzzle. Look at the 19\frac{1}{9} dollar bill in my blog entry and see how much a dollar was worth in British currency. Then use the table to figure out how many British pence a dollar was worth. At this point 19\frac{1}{9} of a dollar starts sounding like a reasonable amount of money!

Posted by: John Baez on May 8, 2009 5:08 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

At this point 1/9 of a dollar starts sounding like a reasonable amount of money!

I imagine anything sounds reasonable after you spend enough time on L.s.d.

Posted by: John Armstrong on May 8, 2009 6:09 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

I was told, and didn’t follow-up to check, that a 16.5 foot rod (or perch) was the standard length of an implement carried to urge on a team of two oxen.

Posted by: Scott Carter on May 8, 2009 3:09 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Scott wrote:

I was told, and didn’t follow-up to check, that a 16.5 foot rod (or perch) was the standard length of an implement carried to urge on a team of two oxen.

If you had clicked on the link to perch that I gave, you wouldn’t be feeling so guilty about never having gotten to the bottom of this.

For those not in the know:

The ‘perch’ or ‘rod’ still plays a hidden role in the American system of units — it’s the reason why the number of feet in a mile is evenly divisible by 16.5:

5280=16.5×3205280 = 16.5 \times 320

There are 4 rods per chain, 10 chains per furlong, and 8 furlongs per mile:

320=4×10×8 320 = 4 \times 10 \times 8

So, the big puzzle is why there are 16.5 feet per rod!

You cannot rest easy until you know more.

Posted by: John Baez on May 8, 2009 4:35 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Back in the good old days of the above currency and the notorious 11s test (for 11 year olds) there was an IQ type question: name the next term in the sequence:

1/4 1/2 1 3 6 12 24 …

I delighted in posing it to my classes when ever I had an excuse for discussing what IQ tests measure (of course the measure IQ and do it quite well -= any relation to intelligence is purely coincidental or at least culturally determined)

I would lead them on supplying an additional terms
and then`berate’ them that it was a standard question for 11 year olds.

Of course, they didn’t do much better with 1 5 10 25

Posted by: jim stasheff on May 8, 2009 3:18 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Just in case you don’t know what 1.05 pounds is called, I’ll not mention it so you can have fun guessing.

A g…a is a pound including tip, right? A 5% tip sounds rather little.

Posted by: Thomas Larsson on May 8, 2009 6:24 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

Odd day? Sounds a little odd to me. Anyway, it’s not. Still got a couple of months to go before that date comes around.

Unless it’s another of those US quirks, like celebrating pi-day in March rather than on the 31st of April as they do in civilised countries (it’s a public holiday in Norway).

Posted by: Andrew Stacey on May 7, 2009 10:37 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

But there are only 30 days in April! May day is a wonderful holiday, but I don’t think you can call it pi day.

Posted by: David Speyer on May 7, 2009 11:09 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

I try to encourage year/month/day. It has two advantages over the two more common orderings: the digits come in order of their significance, so it’s better for computers; and it’s neither of the other two systems, so you don’t have to worry about misinterpretation, especially if you use a four-digit year. Does anyone know which countries have this ordering as their standard?

Posted by: James on May 7, 2009 11:19 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Wikipedia is your friend:

  • Used internationally in some contexts as the ISO 8601 standard
  • Albania (more references indicate use of dd/mm/yyyy)
  • Canada (yyyy-mm-dd, government all-numeric standard)
  • China, People’s Republic of (yyyy-mm-dd or yyyy年m月d日 with no leading zeroes)
  • China, Republic of; same as China, P.R. except year might be represented using ROC era system: 民國95年12月30日.
  • Denmark (The format dd-mm-yy(yy) is the traditional Danish date format. The international format yyyy-mm-dd or yyyymmdd is also accepted. There are no preferences, although the traditional format is the most widely used. The formats dd.’monthname’ yyyy and in handwriting d/m/yy are also acceptable.)
  • Europe
  • Hong Kong (yyyy年m月d日 with no leading zeroes; and dd/mm/yyyy for English)
  • Hungary (yyyy.mm.dd and traditionally the number of the month is sometimes written in Roman numerals)
  • Iran (yyyy/mm/dd in Persian Calendar system (“yy/m/d” is a common alternative), yyyy-mm-dd in Gregorian Calendar system)
  • Japan, often in the form yyyy年mm月dd日; sometimes Japanese era year is used, e.g. 平成18年12月30日.
  • Korea (yyyy년 mm월 dd일; yyyy/mm/dd also used)
  • Latvia (But often dd.mm.yyyy. is used)
  • Lithuania (yyyy-mm-dd)
  • Macau (same as Hong Kong)
  • Mongolia (yyyy.mm.dd)
  • Nepal (also see Nepal Sambat which is also in use)
  • Norway
  • Singapore (Chinese representation: yyyy年m月d日, no leading zeroes)
  • Slovenia
  • South Africa (yyyy/mm/dd; “d/m/yy” is a common alternative)
  • Spain (Basque: yyyy.mm.dd)
  • Sweden (national standard format)
Posted by: John Armstrong on May 7, 2009 11:38 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

As John's comment shows, year-month-day is the legal standard in many places, including the world as a whole. But I think that it's used commonly only in Asia.

I do use it myself, however, and I helped to establish it on the nLab's page of latest changes.

Posted by: Toby Bartels on May 8, 2009 12:19 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

Speaking of odd or curious days: there was once a little article in the American Mathematical Monthly on the date November 30, 1999. Seems pretty prosaic, but anyone who was born on that day can play a little parlor trick where she can tell you instantly how many years, months, and days old she is. How?

Posted by: Todd Trimble on May 8, 2009 1:13 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

Mod 2000, the date of birth is 0000/00/00.

Posted by: James on May 8, 2009 4:28 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

I don’t get it.

Posted by: Mike Stay on May 8, 2009 11:24 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

I don’t get it.

Today is 2009-05-08, so she is 9 years, 5 months, and 8 days old.

Posted by: Toby Bartels on May 9, 2009 12:22 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

There are some very high-denomination British banknotes, but not in circulation.

Some Scottish and Northern Irish banks are allowed to print their own currency, but the currency they print must be backed up in sterling from the Bank of England.

Thus when the Royal Bank of Scotland arranges to print more money, a lorry is sent from London to Edinburgh with some 10^6 pound notes, or maybe even occasionally a 10^8 pound note.

Posted by: James Cranch on May 8, 2009 12:39 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Thanks to the recent economic crisis, the Fed plans to outdo the Royal Bank of Scotland and start printing these:

Posted by: John Baez on May 8, 2009 4:51 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

That last bill was just a joke, but this one was sadly real:

In February 2009, Zimbabwe’s currency was renormalized: a trillion dollars was redefined to be a dollar.

Posted by: John Baez on May 8, 2009 5:06 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

I’ve been using Zimbabwean inflation to create problems for my college algebra classes about working with exponentials and logarithms. They’ve finally surpassed the record set by the Hungarian pengő.

Posted by: John Armstrong on May 8, 2009 5:26 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Thus when the Royal Bank of Scotland arranges to print more money, a lorry is sent from London to Edinburgh with some 10^6 pound notes, or maybe even occasionally a 10^8 pound note.

I feel like that ought to be a joke, but I'm not sure. They do know that modern money is fictitious, and that it's just as valid to keep track of credits and debits in a computer database, right?

Posted by: Toby Bartels on May 8, 2009 6:08 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Since no one could ever steal and spend a 10^6 pound note, they might as well send them via the post.

Posted by: Tom on May 8, 2009 11:49 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Since no one could ever steal and spend a 10^6 pound note, […]

That's the premise behind a short story by Mark Twain.

Posted by: Toby Bartels on May 9, 2009 12:20 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

I was having fun imagining a children’s cartoon where some criminal mastermind breaks into the lorry, steals a £1,000,000 note, and then runs down the street waving it gleefully while chased by a crowd of bobbies.

Posted by: John Baez on May 9, 2009 4:50 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

There’s two separate issues there I think. My understanding is that from the point of its creation the Bank of England engaged in fractional reserve lending without sufficient reserves for the money not to be “fictitious to some degree”, it’s only the degree that has changed. Then there’s the issue that the pieces of paper called banknotes have special legal status (different from, say, a contract or other form of accounting). British banknotes still have the wording “I promise to pay the bearer on the sum of” whereas I don’t find that on American banknotes only that it is valid for payment of all debts (this being law in the UK but not printed on the note anywhere), so I’m not sure if there’s a theoretical difference in what the pieces of paper might signify. Of course, in practice I’m sure that the circumstances in which any difference mattered would be so extreme that laws would be unreliable anyway. But the British legal position still currently accords different recognition to a banknote than to a ledger entry for the same amount.

Incidentally, this issue that having the actual piece of paper which has legal status is different from being able to show that you own that piece of paper is apparently turning up in the area of US mortgage foreclosures: apparently some companies which bought parcels of mortgage debt either don’t have or can’t in practice actually find the original mortgage papers for individual mortgages and judges are refusing to begin foreclosure proceedings without them.

Posted by: bane on May 9, 2009 4:54 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Fractional reserve banking is one thing, but modern fiat currency is ultimately backed by nothing at all. Given that, it seems odd not to just have the Bank of England (or whoever starts the process) simply authorise the Bank of Scotland to issue whatever amount rather than to bother to send anything physical. It's not like, if there were a run on the Bank of Scotland, that the bank could then present the note to the Bank of England for payment. What would they pay in that was any different from what the Bank of Scotland issued itself?

British banknotes still have the wording “I promise to pay the bearer on the sum of”

That seems very odd, indeed! If this is a note issued by the Bank of England (just to keep things simple), then what currency are they promising to pay in? It's not as if coins are made of precious metals; they're worth a little bit as scrap but are otherwise also backed by nothing at all.

whereas I don’t find that on American banknotes only that it is valid for payment of all debts (this being law in the UK but not printed on the note anywhere)

Such laws (along with the state's acceptance of a given currency as payment of taxes) are what ultimately gives modern currency value in practice.


Actually, looking things up a bit on Wikipedia, I may have found the answer to one of my questions above. Scottish banknotes are different from English ones after all, in that this law does not apply to them!; that is, they are not ‘legal tender’. So in principal, if you go to a restaurant in Scotland and try to pay with a Scottish banknote, then they could refuse and (since English banknotes aren't legal tender in Scotland either) you would legally be at fault if you had no coins (although apparently there is a Scottish law about accepting ‘any reasonable offer’ that would save you).

This explains why the Scottish bank needs the English note, although I still don't understand why they need to physically transfer possession of it. (Can’t the Scottish bank just have a safety deposit box in London?) But to remove the physical existence of the note entirely would require a change in the law; although it's probably silly not to change the law, I gather that Scottish nationalism has something to do with it.

Links: http://en.wikipedia.org/wiki/Banknotes_of_the_pound_sterling#Scotland_and_Northern_Ireland, http://en.wikipedia.org/wiki/Banknotes_of_the_pound_sterling#The_question_of_legal_tender.

Posted by: Toby Bartels on May 11, 2009 3:35 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

Thanks to Toby for clearing up some of my imprecision in the use of “British” and “UK” in my repsonse. When I lived in Scotland I both looked this stuff up (although obviously in practice it doesn’t ever matter) but also learned how easy it is to automatically say British when one really means English.


Toby asked “This explains why the Scottish bank needs the English note, although I still dont understand why they need to physically transfer possession of it. (Cant the Scottish bank just have a safety deposit box in London?)”


Keeping important pieces of paper underlying the independent Scottish currency issuing banks (there’s not, to my understanding, THE Bank of Scotland in the sense of the privileged Bank of England, there are several small banks that have the right to issue their own bank notes) down south in London? That’ll raise some people’s hackles.

Seriously, I think that falls more under the category of “making that change might add new complaints for Scottish nationalists, and keeping things the current way costs almost nothing”. The UK / England / Scotland decomposition has enough genuinely hard issues that the UK hasn’t resolved to maximal satisfaction for all parties that adding new points of contention is really avoided :-)

Posted by: bane on May 11, 2009 12:51 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Keeping important pieces of paper underlying the independent Scottish currency issuing banks (there’s not, to my understanding, THE Bank of Scotland in the sense of the privileged Bank of England, there are several small banks that have the right to issue their own bank notes) down south in London? That’ll raise some people’s hackles.

You may notice a subtle shift before and after the horizontal rule that indicates when I did some research; I shifted from ‘the Bank of Scotland’ to ‘the Scottish bank’. There is a ‘Bank of Scotland’, which was originally a national bank but now seems more like the Bank of America (founded in 1904 in San Francisco as the Bank of Italy!) than the Bank of England; that and two others (the Royal Bank of Scotland and the Clydesdale Bank) are the Scottish banks that are authorised to issue their own banknotes.

Seriously, I think that falls more under the category of “making that change might add new complaints for Scottish nationalists, and keeping things the current way costs almost nothing”. The UK / England / Scotland decomposition has enough genuinely hard issues that the UK hasn’t resolved to maximal satisfaction for all parties that adding new points of contention is really avoided :-)

So Scottish nationalism explains the whole thing!

Posted by: Toby Bartels on May 11, 2009 5:49 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

Toby wrote:

I feel like that ought to be a joke, but I’m not sure.

Apparently it’s not a joke: the million-pound note is called a “Giant”, while the 100-million-pound note is called a “Titan”.

Posted by: John Baez on May 9, 2009 5:15 PM | Permalink | Reply to this

Re: Odd Currency Puzzle

I think our regular own dollar is pretty darn odd all by itself. Here are three of its biggest oddities:

1) It’s designed to be both a medium of exchange and a store of value at the same time which are contradictory functions, i.e. if we hold on to our dollars to store some value for later, then there’s no currency to circulate as a medium of exchange!

2) It is an informational token that is shoe-horned into acting like something of value in and of itself. This is way freaky odd. We are put into the mind-frame of thinking that the informational tokens are just as valuable as the wealth flow they facilitate, by virtue of their scarce (or unscarce as in the case of Zimbabwe) issuance.

3) It is issued on the basis of interest bearing debt, which has the side-effect that the money supply is forced to expand exponentially by logical necessity if debtors are to be able to locate the money to pay off the principal plus the interest of those debts. That is, there is never as much money in existence as there is debt plus interest, so when the interest comes due somebody else had better have taken out more debt to feed back into paying off the original debt’s interest. To me it’s extremely odd to base a monetary system on a Ponzi scheme, but that’s what we’ve done!

Posted by: Eric Harris-Braun on May 17, 2009 1:23 PM | Permalink | Reply to this

Odd Dimension Puzzle

INTERESTING HISTORY LESSON
On Railroad Tracks.
*

*This is fascinating and true.
Be sure to read the final paragraph; your understanding of it will
depend on the earlier part of the content.

The US standard railroad gauge (distance between the rails) is 4 feet,
8.5 inches. That’s an exceedingly odd number.

Why was that gauge used? Because that’s the way they built them
in England and English expatriates built the US railroads.

Why did the English build them like that? Because the first rail lines
were built by the same people who built the pre-railroad tramways and
that’s the gauge they used.

Why did ‘they’ use that gauge then? Because the people who built the
tramways used the same jigs and tools that they used for building
wagons, which used that wheel spacing.

Why did the wagons have that particular odd wheel spacing? Well, if they
tried to use any other spacing, the wagon wheels would break on some of
the old, long distance roads in England, because that’s the spacing of
the wheel ruts.

So who built those old rutted roads? Imperial Rome built the first long
distance roads in Europe (and England ) for their legions. The roads
have been used ever since.

And the ruts in the roads? Roman war chariots formed the initial ruts,
which everyone else had to match for fear of destroying their wagon
wheels. Since the chariots were made for Imperial Rome, they were all
alike in the matter of wheel spacing. Therefore the United
States standard railroad gauge of 4 feet, 8.5 inches is derived from the
original specifications for an Imperial Roman war chariot…
Bureaucracies live forever.

So the next time you are handed a specification/procedure/process and
wonder ‘What horse’s ass came up with it?’, you may be exactly right.
Imperial Roman army chariots were made just wide enough to accommodate
the rear ends of two war horses. (Two horse’s asses.) Now, the twist to
the story:

When you see a Space Shuttle sitting on its launch pad, there are two
big booster rockets attached to the sides of the main fuel tank. These
are solid rocket boosters, or SRB’s. The SRB’s are made by Thiokol at
their factory in Utah . The engineers who designed the SRB’s would have
preferred to make them a bit fatter, but the SRB’s had to be shipped by
train from the factory to the launch site. The railroad line from the
factory happens to run through a tunnel in the mountains, and the SRB’s
had to fit through that tunnel. The tunnel is slightly wider than the
railroad track and the railroad track, as you now know, is about as wide
as two horses’ behinds. **

So, a major Space Shuttle design feature of what is arguably the world’s
most advanced transportation system was determined over two thousand
years ago by the width of a horse’s ass. And you thought being a horse’s
ass wasn’t important? Ancient horse’s asses control almost everything…
and CURRENT Horses Asses are controlling everything else.*

Posted by: jim stasheff on May 21, 2009 3:26 PM | Permalink | Reply to this

Re: Odd Dimension Puzzle

For an interesting opposite to “we’re stuck with mistakes forever”, consider
railway development in Spain and Europe. I particularly like the bit where Portugal chose the same gauge as Spain and then rounded it to a unit common in Portugal, thus yielding a different gauge to than the original Spanish choice. (It doesn’t say if this was enough to actually render the Spanish trains unable to run on Portuguese tracks or not.) I guess the message extends to “and when things do get changed, you’ll get all the bad things about incompatibility whilst completely missing the benefits that could have been acheived by a change”.

Posted by: bane on May 21, 2009 4:14 PM | Permalink | Reply to this

Re: Odd Dimension Puzzle

There were quite a number of competing gauges on early British railways. Carriage makers and cartwrights were perfectly capable of making vehicles of different widths. Moreover, it’s rather unlikely that ruts in the road would force axle widths to an accuracy of less than half an inch. Also, roads need to be maintained, and if you can fill in potholes, you can fill in ruts.

It is true that it is quite likely not a coincidence that the standard gauge of railways is somewhat related to the width of a carthorse, since steam railways were preceded by horse-drawn railways in mines. But of course this only settles the gauge approximately (horse rail gauges varied from 4 to 5 feet), and still fails to deal with some widespread broad gauges (over 7 ft in the case of Brunel’s GWR) and narrow gauges (sometimes little more than 3 ft—or even 2 ft in a mining railway mentioned in Agricola’s De Re Metallica, although obviously this is not suitable for passenger transport).

It’s also perhaps worth mentioning that by the late Middle Ages, carthorses were already considerably larger than Roman chariot horses, and they continued to grow.

Lots of useful information in Wikipedia s.v. Rail Gauge, from which I gleaned some of this info; also discussed in Snopes.

Posted by: Tim Silverman on May 21, 2009 5:18 PM | Permalink | Reply to this

Re: Odd Dimension Puzzle

Judging by the Wiki article cited, it may be apochryphal that the change in gauge at the Russian border with ??? was to prevent military trains from crossing the border easily.

Posted by: jim stasheff on May 21, 2009 10:11 PM | Permalink | Reply to this

Re: Odd Dimension Puzzle

Jim wrote:

Judging by the Wiki article cited, it may be apocryphal that the change in gauge at the Russian border with ??? was to prevent military trains from crossing the border easily.

You can’t really affect transport just by a gauge transformation. But did you read the article on Russian gauge? It says that in Russia:

George Washington Whistler was invited as a foreign expert to assist in railroad construction. He was a proponent of a wider gauge and his efforts helped in lobbying the new standard. It is quite likely that an “invasion” argument (alleging that it is easier to adapt trains to narrow gauge than to broad gauge) was used in lobbying the project since military was closely supervising the construction; however, it is highly unlikely that such an argument was made by Melnikov during the actual selection process. Nazi Germany suffered such problems with their supply lines during World War II as a result of the break-of-gauge.

I’d heard of gauge-fixing and symmetry-breaking, but not break-of-gauge!

Posted by: John Baez on May 22, 2009 5:03 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

Jumping back to the original topic, there’s also the U.S. three cent piece if you’re looking for “odd” currency.

Posted by: mensley on May 29, 2009 2:15 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

This is the basis for another classic currency puzzle:

Which two of the following coins were never officially produced by the U.S. Mint?:

  • the penny,
  • the two-cent piece,
  • the three-cent piece,
  • the nickel,
  • the dime,
  • the quarter dollar,
  • the half dollar,
  • the dollar.

Answer: the penny and the nickel, which are ‘officially’ the one-cent piece and the five-cent piece.

The common decimal units of currency are the dollar, the dime, the cent, and the mill; the value of a U.S. coin is always given in terms of these. The penny (old or new) is a unit of British currency, and nickel is a metal; to use these as names of U.S. coins is a colloqiualism. (There are also cases where ‘penny’ is a reasonable translation of a term in another language, such as ‘pfennig’ or ‘denarius’, for a non-British coin.)

You can object to this puzzle on the grounds that ‘penny’ and ‘nickel’, in that context, clearly refer to the coins commonly called by those names. And the U.S. Mint did (and does) produce them, whatever it may have chosen to call them. But there it is: it's a classic puzzle. Fool your friends, and then tell them about the two-cent piece (and other obsolete denominations).

Posted by: Toby Bartels on May 30, 2009 8:07 AM | Permalink | Reply to this

Re: Odd Currency Puzzle

Mensley wrote:

Jumping back to the original topic, there’s also the U.S. three cent piece if you’re looking for “odd” currency.

Cool! These days people call it a ‘trime’:

Posted by: John Baez on May 30, 2009 10:58 PM | Permalink | Reply to this

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