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Jumper · Posted 09 Apr 2012, 12:51 #1

No, not a reference to the excellent Jimmy Jones and his wonderful 1960 pop record. Nor anything marsala chicken-based. It's this week's maths problem (well, geometry really). Yet another thing one ought to know by now but continues to puzzle.

I have an Art Deco clock on my mantelpiece, a present from a loved one (see, someone does after all). Pic below shows numbers 11,12,1, and 5,6,7, all very close together. Then 2,3,4, and 8,9,10, much further apart. Now, Einstein has it that time elapsed reduces with velocity. In other words as you accelerate, time actually speeds up. Why, therefore, do the hands keep that same rate of travel and stick to the right time if they have further to travel? What does Euclyd have to say?
I mean, next time I poke the fire (no ribaldry please) I don't want to end up in another....plac..e.

PaulT · Posted 09 Apr 2012, 13:45 #2

If you were to draw lines from the centre to the centre of each number you would find that each line was 30 degrees from its neighbour. The reason why the distance from each changes is because they are not in a circle.

RichardGarner · Posted 09 Apr 2012, 14:43 #3

mmm Deco, it makes my bakelite one seem a bit plane!!! It's all about angles and squashing/stretching a circle, if a number was too close not only would it be rubbish at keeping time it probably wouldn't look right

Dave · Posted 09 Apr 2012, 14:49 #4

As Paul says...

If you drew the biggest circle you could within confines of the five straight edges, you could put the numbers on equidistant, just like on a regular clockface!

I like the question though! It's a bit like thinking about the speed of a point just a few inches from the centre of a roundabout, as opposed to edge - although the thing is spinning at an equal rpm at both points, the inside is travelling a lot slower than the outside, simply as it has less distance to cover

Jumper · Posted 09 Apr 2012, 15:03 #5

Yes... almost as confusing as Gravity (don't know why I gave that a capital - hardly seems important enough). Good analogy, tell that to the soldier at the outside end of a 40-man file doing a sharp left wheel. Squashing/stretching a circle and ending up with an ellipse? Given MGR liking of elliptical dials, wouldn't my dashboard clock look nifty with a similar face?

By the way, just spotted a howler (of my own I hasten to add). Anyone else?

Dave · Posted 09 Apr 2012, 15:10 #6

That'll be Euclid then!

(or, Ticker Ticker Timex?)

No, Euclid, our kid!

Jumper · Posted 09 Apr 2012, 15:39 #7

Er, no Dave, sorry! Got the guy right but I spelled his name wrong - thought he was Welsh (on the distaff side of course). I though he was the Geometry professor to the Greek gods? Shame he wasn't an economist really.
There's a much bigger embarrassment lurking,at least I think so.

Dave · Posted 09 Apr 2012, 17:18 #8

Fair enough - spelling I can do, but Welsh/Greek Geometry Professors....

geesmith · Posted 10 Apr 2012, 23:48 #9

It's a marvelous piece...

...I'm still trying to work out how they get the hands to go longer? Won't they be the same size at certain times? Amazing what the Welsh can do.

I suspect the guy that designed it liked the afternoons to go quickly, finished work at five and went straight to the pub for a couple of hours.

Jumper · Posted 11 Apr 2012, 11:04 #10

geesmith wrote:It's a marvelous piece...

...I'm still trying to work out how they get the hands to go longer? Won't they be the same size at certain times? Amazing what the Welsh can do.

I suspect the guy that designed it liked the afternoons to go quickly, finished work at five and went straight to the pub for a couple of hours.

They don't go longer. They could only go longer if excessive speed caused centrifugal force to exert a disproportionate load on the tips (rather like the cruise control module on a R-R I once had). In fact, they go quicker.
After studying replies, I have come to the conclusion that the clock shows the correct GMT twice every day. Of course, if I then wind it up......

Jumper · Posted 11 Apr 2012, 11:10 #11

PaulT wrote:If you were to draw lines from the centre to the centre of each number you would find that each line was 30 degrees from its neighbour. The reason why the distance from each changes is because they are not in a circle.

Paul, might it be concentric circles?

geesmith · Posted 11 Apr 2012, 17:45 #12

Jumper wrote:
PaulT wrote:If you were to draw lines from the centre to the centre of each number you would find that each line was 30 degrees from its neighbour. The reason why the distance from each changes is because they are not in a circle.

Paul, might it be concentric circles?

In my previous reply I was lengthening the arms as they passed the horizontal to simply go along with another previous statement to do with time and acceleration....

Rather than plot it in CAD software I'm going to guess at 6 concentric circles without applying any effort or reasoning to my suggestion.

Not winding it does simplify matters.

Jumper · Posted 11 Apr 2012, 18:49 #13

In my previous reply I was lengthening the arms as they passed the horizontal to simply go along with another previous statement to do with time and acceleration....

Rather than plot it in CAD software I'm going to guess at 6 concentric circles without applying any effort or reasoning to my suggestion.

Just to back that up with forensic detailed data, and of course in the interests of science, I've just had my sliding pencil box out - the one with Dan Dare and the Mekon fighting all over it - and solved it.
The big hand of course doesn't reach the 3 and the 9, but does reach 12 and 6. Therefore, whislt the hands maintain one true circle, the numbers are on concentric circles - all having the same centre. Not nearly so profound as I had hoped.
Does your first sentence above indicate you think you may have rumbled the 'howler'?

geesmith · Posted 11 Apr 2012, 21:01 #14

My sentence above implied that if the tips of the hands could maintain a fixed distance from the numbers this would require an acceleration and deceleration of the tips to maintain accurate time. As this is not the case then Einstein probably didn't need to be quoted, particularly as it wasn't wound up.

So yes, that was my stab at the blooper. The hands of a fixed length would hopefully maintain a fixed speed, dependant of course on the type of escapement as the minute hand will be subjected to stops and starts which in turn would require deceleration and acceleration which would actually be greater than the acceleration/deceleration previously described, albeit for shorter distances/periods.

This takes into account the wonderful little timepiece appears too small to utilise a liquid displacement as described by the Greek engineer Philo of Brum.

Am I wrong?

Jumper · Posted 11 Apr 2012, 22:20 #15

Wow, that is sooooo close! Seems churlish not to follow up, so a pm follows. Wouldn't want to spoil others' fun.

geesmith · Posted 12 Apr 2012, 01:03 #16

I also wouldn't want to spoil others fun (I would really but..)

However, and barely related, if we could figure out a way to get an object to move at 150 million metres a second .... and make two of them, then run one along the top of the other BuzzLightyear's your uncle. Theoretically the top one would have infinite mass and be two dimensional and using infinite energy to get there, but it would be slightly faster than the speed of light and wouldn't it be a laugh. I can't see anything being faster than the speed of light myself, possibly dependant on where I'm standing and how quick witted I am.
Oh for just one more than infinite captain.

Nice old Art Deco clock though for all it's conundrums.

Jumper · Posted 12 Apr 2012, 11:36 #17

If the object were faster than the speed of light , surely you would not be able to see it and you would not know if it got there. As you say, you can't see anything being faster than the S.of L.
Also, if you were in front of it, as it approached, you wouldn't see it coming and you wouldn't last very long.
Finally, if your two speeding objects were travelling parallel to each other, would they ever converge? If they have mass, infinite or otherwise, then they would presumably have gravity and eventually either collide in a star nursery or orbit each other (?).

Dave · Posted 12 Apr 2012, 11:50 #18

Here's another thought....

If you had a car that could travel at the speed of light, would there be any point having headlights?

Jumper · Posted 12 Apr 2012, 12:48 #19

I suppose there will now be loads of replies extolling the frugality of the diesel engine. Mind you, in such a car there may have been a redesign of the dashboard clock. Further, I calculate that the time elapsed between turning the switch and the current reaching the xenons you would have travelled a fair distance. You probably wouldn't need the headlights anyway.

geesmith · Posted 12 Apr 2012, 15:32 #20

Do they make flat xenons? ..capable of withstanding infinite mass? I'll ask in Halfords..

Einstein only discussed the possibility of achieving light speed, he did say it was beyond our abilities to contemplate anything beyond that. Well Dave the photons in the headlight beams would travel at twice the speed of light (good job I have a scientific calculator)if the bulbs survived. I think the hardest part of this theory is making the bulbs.

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