How long is a piece of string?

[jebus197]

Interesting documentary: http://www.youtube.com/watch?v=80jxKQP2V0Y...&playnext=1

Who knew that measuring a piece of string completely accurately could risk creating a black hole?

Have to love Seth Lloyd's mad professor laugh through most of the final parts though.

So what's your view, how long is a piece of string?

One thing I spotted that they missed out was [Heisenberg's] uncertainty, which should render all hope of measuring a piece of string accurately completely futile.

Hopefully if anyone ever seriously decided to attempt to undertake such a task they would stop before they realised this, in sufficient time to avoid destroying the Earth and all of it's inhabitants - and potentially all of the solar system too.

[Colin-uk Veteran]

Twice as long as half its length :shifty:

[jebus197]

So you might think. Watch the film and then try to answer again.

[Jason S. Global Moderator]

im on part 3/6. fascinating!

[primexx]

The length of the fractal is finite as the increase in length approaches 0.

[Xilo]

The length of the fractal is finite as the increase in length approaches 0.

Only in a realistic sense. In a mathematical sense, if you keep dividing a number, approaching 0 is infinitely long and you will never get there.

[primexx]

Only in a realistic sense. In a mathematical sense, if you keep dividing a number, approaching 0 is infinitely long and you will never get there.

huh?

[Xilo]

Say each iteration you divide the length by 4. You start at 1.

1: 1 * 0.25 = 0.25

2: 0.25 * 0.25 = 0.0625

3: 0.0625 * 0.25 = 0.015625

4: 0.015625 * 0.25 = 0.00390625

5: 0.00390625 * 0.25 = 0.0009765625

The values will get smaller and smaller with each division of 4. However, mathematically, it will never reach zero. The limit will approach 0, but it will never reach 0. Granted, the values will become negligible realistically very quickly but it won't have a finite length. It will, however, have a defined limit which isn't quite the same.

[yxz]

i love and hate quantum mechanics

[leesmithg]

The length is what it measures at.

[Xilo]

My coworker god a PHD in math and took quantum physics and now does programming. I've got into discussions with him similar to the videos. It's pretty interesting if you are able to wrap your head around it all.

[soumyasch]

One thing I spotted that they missed out was [Heisenberg's] uncertainty, which should render all hope of measuring a piece of string accurately completely futile.

They do. About 20 minutes before the end (Don't know which part of the YouTube videos that map to, I DVRed it off my STB]. After the prof with a thing for the stuffed animals asks the host to ponder over Schroedinger's cat.

[primexx]

Say each iteration you divide the length by 4. You start at 1.

1: 1 * 0.25 = 0.25

2: 0.25 * 0.25 = 0.0625

3: 0.0625 * 0.25 = 0.015625

4: 0.015625 * 0.25 = 0.00390625

5: 0.00390625 * 0.25 = 0.0009765625

The values will get smaller and smaller with each division of 4. However, mathematically, it will never reach zero. The limit will approach 0, but it will never reach 0. Granted, the values will become negligible realistically very quickly but it won't have a finite length. It will, however, have a defined limit which isn't quite the same.

how can it be infinite length if it can never be greater than a finite value?

[Xilo]

Because the length infinitely increases even it's an insignificant fraction of an amount. Like:

1.9

1.99

1.999

1.9999

1.99999

1.999999

This can can keep going for any number of 9s you add to the decimal but each one will be greater than the last. Hence, infinite length. By the way, there are 2 different definitions for infinite in the mathematical world. My coworker (math PHD) told me once, but I don't quite remember the specifics.

What you're thinking about is the limit which is a finite number.

This is where part of the dilemma of measuring the exact length comes in. If there's infinite amount of decimal places, it's impossible to measure precisely how long it really is. We can only get approximations.

Edited January 6, 2010 by Xilo

[McCordRm]

I seriously hate math.

[carmatic]

Because the length infinitely increases even it's an insignificant fraction of an amount. Like:

1.9

1.99

1.999

1.9999

1.99999

1.999999

This can can keep going for any number of 9s you add to the decimal but each one will be greater than the last.

but they will all be less than 2 ... and isnt there a rule where if you have a ... after the last 9 you write down, it basically gets rounded up to the next integer? so basically, 1.999... = 2

besides, i thought the whole point of the act of measuring something was to achieve an intended outcome, like calculating the trajectory of a rocket so it would go where you want it, and you only ever use as many decimal points as you need (or your measuring tools can give you)

i suppose that you will finally be satisfied when you can measure down to the last atom...

Edited January 6, 2010 by carmatic

[markwolfe Veteran]

but they will all be less than 2 ... and isnt there a rule where if you have a ... after the last 9 you write down, it basically gets rounded up to the next integer? so basically, 1.999... = 2

There are several proofs for 0.99999... = 1. And none of them involve giving up and rounding. :p

[carmatic]

There are several proofs for 0.99999... = 1. And none of them involve giving up and rounding. :p

well i guess the key word in my post is 'basically'

when you get into it, you dont actually 'round up' a term such as '0.999...' , but you can validly round up '0.999' without the elipses

[guruparan]

I am allergic to maths always :hmmm:

[jebus197]

You have to remember too that from a quantum mechanics perspective, since all of the molecules in the string exist as an infinite number of entangled pairs, that the string in effect could be considered infinitely long too.

This would require not only that you measure the lengths that you see, but also the lengths that you can't see. (Although experiment - and maths - is able to indirectly infer their existence).

It is only in the act of measurement itself that we are able to derive a definite length. (Although once more Heisenberg's uncertainty would once again cause our ability to do so to be somewhat limited).

Edited January 6, 2010 by jebus197

[DrewJW]

But can it run Crysis at full?

[LOC Veteran]

My head, it's burning!

[+M2Ys4U Subscriber¹]

Is this Alan Davies' program? If so, I really enjoyed watching that on the BBC a few months ago. Enlightening stuff.

[ecotrojan]

Easy

From the middle to the end then back again

[jebus197]

Easy

From the middle to the end then back again

Nope! Watch the show and read the comments and then try again.