How long is a piece of string?

[psionicinversion]

The string is as long as the thing that makes it so if you want know it's length ask the thing that made it :D

The string is as long as the thing that makes it so if you want know it's length ask the thing that made it :D

[Peter Griffin]

I wouldn't worry about the length of the string....unless of course you swallow it.

[primexx]

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.

never heard of this second definition of "infinite", but since the limit is the length of the string, how can the length be infinite? the length of the number describing the length may be infinite, as in an infinite amount of digits, and there may be an infinite amount of values added to the length, but that shouldn't make the total an infinite value.

[Xilo]

Take a look at this wiki page. Warning. Your brain might explode.

http://en.wikipedia.org/wiki/Infinity

This one describes the math behind the fractal and why it's infinite. Actually, my description wasn't quite right in regards to the actual fractal, but still a sort of infinite length.

http://stochastix.wordpress.com/2007/12/28...koch-snowflake/

Edited January 7, 2010 by Xilo

[PricklyPoo]

never heard of this second definition of "infinite", but since the limit is the length of the string

That is the problem, there is no way to define the "actual length / limit", as the more accuracy you try to obtain in measuring it, you end up measuring more and more material. Eventually you have to round off to get an estimate.

You can technically reach a limit though - the planck length. But like the video states, once you get to the atomic scale, the uncertainty principle ties in, ultimately preventing you from ever obtaining a "true" measure of length.

[qdave]

I seriously hate math.

yep its evil and hard...and yet everything is based on it.

[yxz]

yep its evil

:(

[primexx]

That is the problem, there is no way to define the "actual length / limit", as the more accuracy you try to obtain in measuring it, you end up measuring more and more material. Eventually you have to round off to get an estimate.

You can technically reach a limit though - the planck length. But like the video states, once you get to the atomic scale, the uncertainty principle ties in, ultimately preventing you from ever obtaining a "true" measure of length.

we were talking about the mathematical "limit" not the practical one.

but I think my original assumption was wrong. The increase in length doesn't diminish with each iteration.

Edited January 7, 2010 by primexx

[lamminium]

lol

This reminds me of Cantor's theorem. At the time of reading the proof, my head whirled a bit. @.@