# Mind problem

1. Jul 18, 2010

### maritz

Take a long stick, lets say close to infinity, meaning infinity-0.000001, and ignore all the classical physics acting upon this stick, mount this stick on a rotation bar on earth and let it expand into the univers, now install a sensor at each point along this stick, and a person at the end of the stick somewhere in the univers, now rotate this stick 30 degrees on earth in the fastest time possible. the stick does not bend, break, burn or freeze, never.

what will the result felt by the person on the end, and that of the sensor measuring the if the stick bends or not.
And if the results of general relativity were ignored, will this experiment produce a person travelling faster than the speed of light.

JM Maritz

2. Jul 18, 2010

### Staff: Mentor

Well, yes, if you ignore the rules of physis, you can break the rules of physics in your mind. But is that really a useful thing to think about?

3. Jul 18, 2010

### yossell

sure
no problemo

okey-doke

got it

consider it done

yup

gotcha

(a) undefined, (b) undefined, (c) undefined.

4. Jul 18, 2010

### xlines

There is your problem: relativity places limits on maximal "stiffness" of your stick and your 30° twist travels along the stick at finite speed.

5. Jul 18, 2010

### mathman

The fastest time possible will be limited by the velocity at the other end of the stick, being less than the speed of light.

6. Jul 18, 2010

### yuiop

If we ignore all classical physics and all the results of General Relativity (and for good measure we might as well ignore all Special Relativity as well) then anything is possible and it is possible that this experiment will produce a person travelling at faster than the speed of light and it is also possible that the Moon is towed around the Earth by invisible pink unicorns too. Unfortunately the universe we are in is not like this. Special Relativity excludes the possibility of an infinitely rigid rod, so in this universe, your experiment can not produce person with superluminal motion (the rod bends).

On a mathematical nit-picky note, infinity-0.000001 = infinity and infinity plus/minus (any real number) = infinity.

Last edited: Jul 18, 2010
7. Jul 19, 2010

### Austin0

Are you sure they aren't blue unicorns???

On infinity:............I would completely agree with your definition on "common sense" or physical grounds but is it neccessarioly a mathematical definition??

Where infinity(set of all integers) + (some) real numbers = not infinity but transinfinity

WHere some real numbers =(transinfinite set of all real numbers) - (the infinite set of all positive integers).............????

8. Jul 19, 2010

### matheinste

Look up cardinality. It may help you with the concept of infinite numbers and how they behave and different degrees of infinity. Its as strange and as interesting as Relativity but probably easier to grasp.

Matheinste.

9. Jul 19, 2010

### Austin0

Hi I am fairly familiar with cardinality and Cantors ideas. WHile I also found them interesting in the end I thought them somewhat absurd given that infinity is inconceivable by the human mind in the first place and so is completely indefinable.
AS for countability. It created a picture in my mind of two mathematicians ,one counting integers and one counting reals, sitting there for as long as it takes; meaning relative eternities.

As for the diagonal proof. I failed to see how it improved on the obvious truth that between any two positive integers there must be an infinity of positive reals.
But that just MHO

10. Jul 19, 2010

### Austin0

PS
Having given myself many headaches and vertigo from thinking about infinity I always assumed Cantors trips to the funny farm were a consequence of getting too far into it.

But this just MHO

11. Jul 19, 2010

### matheinste

The obvious truth is less obvious when you look closely. Your statement above makes a lot of hidden assumptions. This also applies to learning relativity, the obvious is not always true.

Matheinste.

12. Jul 19, 2010

### yossell

Hey - *your* human mind perhaps :tongue:

Wha---? It is, like, *so* definable

Tip: Forget your mind's pictures, focus on the definition.

Mainly it improves on it by showing that, in a very precise sense, there can be different sizes of infinity, and that the size of the set of real numbers is strictly larger than the size of the set of integers, yea, even though both sets are infinite.

In short, though matheinste said it better: it rocks!

13. Jul 19, 2010

### matheinste

That tip also applies to anyone struggling with tensors, as I found out after many wasted hours trying to visualize them.

Matheinste.

14. Jul 19, 2010

### ExecNight

Your example is interesting, what if the stick is only 600.000 kms long not infinite minus 1(No idea what that means).

So when i move the stick, the other end would feel the force instantly, and that force being felt instantly is FTL by itself. But this is of course considering the stick don't get bend :)

And unfortunatly it will be so that pretty much gets us to nowhere at all.

15. Jul 19, 2010

### Austin0

I am sure you are right . Most statements by everyone contain a host of hidden assumptions.

I would be curious to hear your view on what you see of mine in this particular case????

16. Jul 19, 2010

### Austin0

.......... I was essentially joking. I would not seriously question a mathematicians
pleasure in the cleverness of the proof or their validity within the abstract realm of mathematics.

17. Jul 19, 2010

### yossell

yeah, me too - apart from the last two paragraphs

18. Jul 19, 2010

### matheinste

You are assuming that the cardinality of the positive reals is greater than the cardinality of the positive integers. That is not very well put mathematically because we are talking degrees of infinity and need another symbology for this maybe. Yossell is better informed than me on mathematics.

Matheinste.

19. Jul 19, 2010

### Gib Z

By definition we can compare Cardinalities of sets comparatively by proving if there exist bijections from one set to another. We can prove there is no bijection from the positive integers to the positive reals, and so the latter set has a greater cardinality. There exist symbols for these cardinalities, which we call Cardinals, but they are not required for this.

20. Jul 20, 2010

### Austin0

Maybe I could share the joke if I knew which last two paragraphs you are refering to??

No comeback for the blue unicorn???