Can math truly describe our universe and it's phsical being?

[liquidanubis3]

My mom proposed to me her concept of why she doesn't believe in String Theory and other abstract ideas shown through math. She says that in a mathematical reality that it is physically possible to make movement but mathematically it is impossible. This she explains is because when you take two points in space such as say two integers , 1 and 2, it is mathematically impossible to ever reach that second point due to the infitesimal changes in x over time. She says that you never truly reach that 2nd point because there is always some time in infinity that you are occupying trying to reach your destination. I was wondering if anyone has an argument to that theory or some kind of rebuttal that would show her that yes, at the moment we cannot explain everything with math but I believe this theory of he's to be flawed, I just can't determine where and why it is so.

 

[russ_watters]

That's Zeno's paradox: http://en.wikipedia.org/wiki/Zeno's_paradoxes

IMO, it's a pretty weak dilema* and it isn't true that it mathematically prohibits movement. That would be a pretty severe flaw in our physics/math if that were true!

*It is an ancient dilema, proposed and solved thousands of years ago, before physics was even born!

Aristotle (384 BCE−322 BCE) remarked that as the distance decreases, the time needed to cover those distances also decreases, so that the time needed also becomes increasingly small.[11]

 

[xxChrisxx]

There is a very very simple way to practically prove this wrong. What she is saying is that motion isn't possible so:

1. Pick two points in space; say where you are standing and across the room.
2. Walk there.

You've just proved that you can reach an end point from a starting point.

She is unlikely to be convinced because her problem is most likely scale, you can point out that this is the same as saying it's possible to walk to the fridge to get some food, but totally impossible to walk to the shops.

It's possible to move from point A to point B nomatter what the distance inbetween, the mechanics ar ethe same. You move a set distance in a set time. (assuming no acceleration).

 

[vanesch]

To continue to what Russ said, Zeno's "paradox" comes about confusing the *number of terms* and their *sum*. It is not because you can mentally cut a certain procedure in an infinity of steps ("reaching halfway to destiny"), that the SUM of that infinitude of steps must diverge. The total time taken by this infinity of steps is the sum of the times of the individual steps, and that can very well be finite. This is studied in calculus: the convergence of series.

The apparent paradox comes about because we have difficulties imagining performing "an infinitude of tasks" in a finite amount of time, but for a body in motion, if the "task" is to cover a certain distance, the time it takes will be smaller the smaller is the distance. The sum of all these times will simply be the time it takes for the object to go from A to B, no matter in how many pieces we cut that "task".

 

[dx]

I doubt your mom has enough knowledge and understanding of physics to judge the validity of a physics research program, and assuming she does is one of the best ways to become a crackpot. Also, string theory is not the only scientific area where abstract math is used. Math is the language in which all physics is formulated, including all the physics that has already been tested to great accuracy and opon which all of our technology is based.

 

[jimzarry]

The other posts describe the answer to your question. Another way you could pose the questions is: is it possible to divide time into infinitely small segments? I think I have read that time and space are granular in the same way that energy is. Otherwise, quantum fluctuations result in infinite mass/energy from transient particles winking in and out of existence, in the same way that radiation from a black body has to be in discrete packets, or the radiation at an infinite number frequencies results in an infinite amount of energy raditated. I don't really have a handle on this but would appreciate somebody smarter than me addressing the question. Is time granular or infinitely divisible?

 

[Academic]

There are plenty of phenomenon in the universe that math has been utterly unable to describe, complex emergent phenomenon - like consciousness. It is unknown if we can ever invent mathematics to describe such complexities. Physicists usually assume everything can be reduced but for now that remains merely an assumption.

 

[James Leighe]

Energy is not granular as far as I know. As for time's infinite divisibility, probably, but since we cannot get a clock that measures time in smaller intervals that some limit (well below infinite precision) I don't see how it matters. But like the first guy said, all these issues are non issues to anyone with even an extremely feeble grasp on the math involved. Using math, we can describe motion with ridiculous accuracy.

Next time your mom says that all the theories can't work because you can't move (which you can, obviously) mention how those same theories are so ridiculously accurate to this day nothing has been observed to contradict QM at a small scale and GR on a large scale. Using QM we can predict with astonishing accuracy things like the magnetic moment of the electron and using GR we can deduce everything down to black holes and many of their properties.

I doubt these theories would have been quite so successful (read, all of physics pretty much would not exist) if you couldn't even describe motion with math.

 

[vanesch]

Physicists usually assume everything can be reduced but for now that remains merely an assumption.

That's a misunderstanding of what physicists assume (although some probably do), based upon a lot of buzz these last decades concerning "theories of everything". Most physical theories have a "scope of action", and the assumption is that the theory is good enough within that scope of action. Trying to predict consciousness within general relativity is - apart maybe for some very weird quirks by some theorists - not a common thing to do in physics (although it is always fun to speculate, why not, after all...).

It is true that some physicists take as a *working assumption* (you have to start somewhere) that the *observable universe* is *describable* by a totally consistent mathematical theory. However, *working theories* never need such a thing. They only need the assumption that the phenomena covered by their scope are *well enough* described by a (hopefully consistent) mathematical theory.

So making the leap from "physicists go a bit far in assuming that everything is part of a mathematical theory" to "maths are essentially useless to do physics", is a few bridges too far.

 

[ZapperZ]

There are plenty of phenomenon in the universe that math has been utterly unable to describe, complex emergent phenomenon - like consciousness. It is unknown if we can ever invent mathematics to describe such complexities. Physicists usually assume everything can be reduced but for now that remains merely an assumption.

Er.. just because something is an emergent phenomenon has nothing to do with the issue of whether or not mathematics can be used. Superconductivity is an emergent phenomenon. Have you looked at the BCS theory? Thermodynamics is a collective phenomenon. It has a well-defined mathematics associated with it.

Maybe it is another good time to make a repeated reference to Wigner's classic article on this.

http://nedwww.ipac.caltech.edu/level5/March02/Wigner/Wigner.html

Zz.

 

[mikelepore]

Your mom just picked a bad example, because this supposed paradox was already resolved by the time the idea of the limit was developed in the 17th century. Although it's a bad choice of an example, I think her main point, which is valid, is this: The set of things that really exist and the set of ideas that are free from mathematical contradictions are not the same thing. Easy enough to show: mathematics provides for me to own twenty million dollars, in the form of five bank accounts, each of which contains four million dollars. The math checks out perfectly, but that doesn't mean the situation is real. Therefore, the next time someone argues that some new idea about the structure of the universe is being verified because no mathematical inconsistencies have been found in the idea, we should say, "So what?" We can form mathematical descriptions of wormholes, time travel, eleven dimensional space, and much more, and then what is the total evidence of their reality? None whatsoever. It is equally realistic to speak of magical fairies.