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## Mathematician's Watch

Can you figure them all out?

2. 6.9999999... = 7

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Originally Posted by spare part
...Can you figure them all out?
Without Google! Just a calculator (I cannot do natural logarithms in my head)

(spoiler - highlight to see)
ratio of the opposite side to the adjacent side for a right angled triangle where these side are 45 degrees apart is 1
square root of 4 is 2
11 is 3 in binary - not sure why they would round a number in a representation that is only allowing integers!
natural logarithm of 55 is 4.0073
good old Pythagorus - 3^2+4^2=25, square root of this is 5
3 factorial = 3x2x1 = 6
As Torsten says 6.999999..=7
16 / 2 = 8
3x3 = 9
g = 9.8 ~ 10
B is 11 in hexadecimal but the o has me stumped - Python/C start hex representations with 0x, FORTRAN starts it with z. The Octal representation of hex b is not 11, which was my other thought.
1100 is 12 in binary

(/spoiler)

So some confusion over 11. Others are not too obscure!

This would not be a watch to be trying to read first thing in the morning.

4. Originally Posted by Shaula
Without Google! Just a calculator (I cannot do natural logarithms in my head)

(spoiler - highlight to see)
11 is 3 in binary - not sure why they would round a number in a representation that is only allowing integers!
(/spoiler)

...
Erm.

(spoiler reply - highlight to see)
I'm not so sure about that for "Round(11)". For 12 they show "11002" - with the subscript to indicate base. They don't include that subscript in the "Round(11)". A mathematicians' watch should be consistent!

(Also, there's no reason why binary, which is just a base like any other, can only show integers. e.g. In decimal, 0.5 is one half. In binary, one half is 0.1, (i.e in binary, 0.1 + 0.1 = 1.0). Each digit is valued at base^position, with positions to the right of the decimal being -1, -2, ...; so the first decimal place in binary is 2^-1, which is one half, the next is 2^-2, which is one quarter, etc.)

... having said that, either way that particular number seems an integer, so the rounding is pointless anyway.

... ... and having said that, I've got no better answer for 3!

(/spoiler)
Last edited by pzkpfw; 2017-Apr-17 at 09:46 AM.

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Yeah, I wasn't sure about my number 3 either. But you know, putting down nothing for a question gets you no points in an exam! I should have added a note about that alongside mentioning my confusion on 11. Original version before I posted had 11 and 3 as ??.

You know I have never seen anyone use decimal points in binary representations! I'd have not even thought to do that. You live and learn.

Oh, wait wait wait....

(spoiler)
Is three meant to be round(pi) but the top of the symbol is cut off?
Last edited by Shaula; 2017-Apr-17 at 11:13 AM.

6. Originally Posted by Shaula
Oh, wait wait wait....

(spoiler)
Is three meant to be round(pi) but the top of the symbol is cut off?
Yes, the version of this watch I've seen (in the form of a large clock) made that typographically clear. I suspect the one in the picture is the product of a sequence of typeface changes and copying by people who didn't understand the original.

Grant Hutchison

7. Originally Posted by grant hutchison
Yes, the version of this watch I've seen (in the form of a large clock) made that typographically clear. I suspect the one in the picture is the product of a sequence of typeface changes and copying by people who didn't understand the original.

Why a mathematician would use g for ten is also suspect. Why not use that Round function again?

8. Originally Posted by Shaula
...
You know I have never seen anyone use decimal points in binary representations! I'd have not even thought to do that. You live and learn.
...
I believe that in that context, it's a "binary point" not a decimal point.

Why not "Int(pi symbol)" for three?

9. Here is a version of the same watchface (there are several different varieties), which shows something typographically interesting going on with the "11" symbol, too.

Spoiler: (Highlight this box to see the hidden message.)
`So I guess this started life as "0B", a two-digit representation of 11 in hex, and has mutated to "ob".`

Grant Hutchison
Last edited by grant hutchison; 2017-Apr-17 at 12:57 PM.

10. Originally Posted by grant hutchison
Here is a version of the same watchface (there are several different varieties), which shows something typographically interesting going on with the "11" symbol, too.

Spoiler: (Highlight this box to see the hidden message.)
`So I guess this started life as "0B", a two-digit representation of 11 in hex, and has mutated to "ob".`
Almost a capital pi, so that fits with the rounding thing, if your intent is to make fun of mathematics. I mean, make math fun.

11. Originally Posted by grapes
Almost a capital pi, so that fits with the rounding thing, if your intent is to make fun of mathematics. I mean, make math fun.
Well, on this occasion I was talking about the symbol that subsitutes for 11 on the watch dial.
But, yes, what looked like "11" in the OP watch's symbol for 3, is rendered "II" in the image I linked to. You can see how this typographical mutation has been taking place, slowly eroding sense into nonsense. The watch I linked to is evidently an earlier example from the evolutionary chain.

Grant Hutchison

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Originally Posted by grant hutchison
Here is a version of the same watchface (there are several different varieties), which shows something typographically interesting going on with the "11" symbol, too.
I still cannot find which language just uses 0 as a Hex prefix though. If they were really mathematicians it'd be the FORTRAN or R representation*!

*Z'B' / 'B'Z or 0xB I believe

13. Originally Posted by Shaula
I still cannot find which language just uses 0 as a Hex prefix though.
Not as a hex prefix - just a zero placeholder in a two-digit representation. Common enough to see Dec 11 as Hex 0B in ASCII tables. Here is one, for instance.

Grant Hutchison

14. I got stuck on g. What came into my head was 32.2.

15. Originally Posted by Torsten
6.9999999... = 7

No it isn't!

Yes it is!

...

16. This is also a mathematician's watch:

It is the whole numbers from one to twelve. I believe mathematicians use them too.

He replies that it was pretty close to the square root of 500,000 in base eight.
Last edited by DonM435; 2017-Apr-17 at 06:19 PM.

18. Originally Posted by DonM435
No it isn't!

Yes it is!

...
So long as no one accuses me of baiting.

Originally Posted by Swift
This is also a mathematician's watch:

It is the whole numbers from one to twelve. I believe mathematicians use them too.
That picture reminds me of a Timex commercial from the '70s. The ad has a man explaining why, whenever Timex shows a closeup of a watch face, the time is around 1:50. Two reasons; the hands nicely cradle the brand name, and because the commercials often aired in the evenings, say, around 10:00, they didn't want people saying, "Hey, that watch is wrong".

ETA: So I searched for the ad and didn't find it, but did see one where the time is about 9:40. That was one where a dolphin takes it for a swim. Hmmm, maybe meant for afternoon airing.
Last edited by Torsten; 2017-Apr-17 at 08:00 PM.

19. Originally Posted by DonM435
He replies that it was pretty close to the square root of 500,000 in base eight.
Then there's the true story about Srinavasa Ramanujan, and the taxi G.H. Hardy took when he visited him in hospital one day.
When Hardy remarked that the taxi number, 1729, was a rather boring number, Ramanujan immediately responded that it was actually very interesting, because it was the smallest number expressible as the sum of two cubes in two different ways (1³+12³ or 9³+10³).

Grant Hutchison

20. There's an urban legend that time is shown on clock faces as it is because it's the hour at which Abraham Lincoln died.

21. The person in the office next to me has the clock in the OP but in a more legible typography (white on green, like a chalkboard and the characters mimic the chalkboard.) He's head of engineering. I'm in accounting.

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It takes a lot to actually draw a clock:

Carl Duzen--who has a graduate degree in physics had to relearn how to draw a clock--and discovered why it is hard for folks with his condition to draw clocks--in that you have a "superposition of three types"

"There's the hours that are represented from 1 through 12, even though there are 24 hours in a day.But then, there's the second layer, which is the minutes. And a 1 represents not a 1 anymore, but 5 minutes. And a 2 represents 10. After that layer is the second hand, which is now measuring 1 through 60 seconds."

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I feel like I'm nerding all over the place for this and I haven't even done maths in years! Obviously I have, but not academically! Might end up trying to buy one for my friend who's just started his Maths PHD!

24. Originally Posted by publiusr
It takes a lot to actually draw a clock:

Carl Duzen--who has a graduate degree in physics had to relearn how to draw a clock--and discovered why it is hard for folks with his condition to draw clocks--in that you have a "superposition of three types"

"There's the hours that are represented from 1 through 12, even though there are 24 hours in a day.But then, there's the second layer, which is the minutes. And a 1 represents not a 1 anymore, but 5 minutes. And a 2 represents 10. After that layer is the second hand, which is now measuring 1 through 60 seconds."

I remember, as a kid, being annoyed with my alarm clock because it had tick marks dividing each hour into five parts (so that there would by 60 around the dial, for the minutes). As the alarm time was set with a single pointer, this meant that I could easily set the alarm for 6:12 or 6:24 or 6:36 ... but setting it to 6:15 or 6:30 involved guesswork. Indeed, I later found some clocks that divided the hours into quarters, minutes be damned.

25. I have two clocks in my classroom: one similar to the OP's, the other is set to UTC.

26. Originally Posted by Trebuchet
There's an urban legend that time is shown on clock faces as it is because it's the hour at which Abraham Lincoln died.
No, it's just marketing:
However 10 past 10 is thought to be a more "positive" time by brand experts, as it looks as if the face of the watch is smiling.Digital clocks are often sold at 12:08 for similar aesthetic reasons.

It is thought to be pleasing on the eye, with the increase in pixels "satisfying" the potential buyer.
This decidedly analogue answer hasn't always satisfied though, with some people believing there are more sinister forces at work.

A favourite conspiracy theory is that clocks show 10 past 10 because that is the exact time of Abraham Lincoln's death.
However, although he was shot at 10 past 10 in the evening, he died at around 7am the following morning.

27. Originally Posted by DonM435
I believe that in that context, it's a "binary point" not a decimal point.

Why not "Int(pi symbol)" for three?
The general term is radix point.

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