Is Finitism a Key to Understanding the Infinity in Physics and Math?

[cam875]

I was reading the wiki on this and found it very interesting and would like to hear what established mathematicians and physicists think about this kind of philosophy.

Personally I believe that God(used in reference to the universe itself, am not religious) created infinity and man created finite numbers since the world we perceive is finite and that's how our brain organizes everything and keeps us going. Everything in our little lives is finite and it seems ignorant to think that the true reality of our universe is that mundane, I am not saying everything is infinite since I don't know the truth either but I think ignoring infinity is due to the fact that it just doesn't work nicely in mathematics and some are almost scared of its complexity since as humans we don't know of anything tangible that is infinite. Our perception of the truth is blinded by our primitive senses. We know what we perceive, and anything beyond that is coined theoretical.

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

 

[russ_watters]

Its just silly pseudophilosophical nonsense. If one believes in the God of the Bible, then he created everything.

If you're a scientist or mathematician, there is nothing special or different about infinity and there are most certainly everyday examples of infinity in action. The speed your car is traveling at is an instantaneous velocity that mathematically is over a time period of 1/x as x approaches infinity. If you fire a spacecraft out into space and it never hits anything, then it travels forever.

 

[cam875]

but technically we as humans don't observe infinity naturally considering how somebody can easily get by doing things purely on a finite scale and never having to think once about infinity. Thats probably what lead to that theory being created in the first place.

 

[Hurkyl]

I think ignoring infinity is due to the fact that it just doesn't work nicely in mathematics

Not only does infinity work nicely in mathematics, it often makes things work even more nicely!

Furthermore, many uses of infinity (or other infinite things) have no relation to what finitism is getting at. For example, although a finitist would reject the existence of most real numbers, they would definitely accept the extended real numbers \pm \infty.

 

[cam875]

so if i gave you an equation such as a = (bc)^2 or something and said solve for "a" where "b" = \infty and "c" = 3, would you be able to give me a real value that could be used to model things accurately?

 

[JoeDawg]

We know what we perceive, and anything beyond that is coined theoretical.

Well, yes, but that's because *it is* theoretical.
Math is about abstraction, its a model based on our primitive preceptions.
Infinity is an abstraction.
Infinity is only really useful in the context of math and when we apply math.
But that's prone to error, because our mathematical models are incomplete and prone to error.

We experience and then extrapolate.

Zero is another abstract idea.
Useful in math, but defining 'nothing' in a more mundane way is invariably nonsensical.

 

[WaveJumper]

Its just silly pseudophilosophical nonsense. If one believes in the God of the Bible, then he created everything.

If you're a scientist or mathematician, there is nothing special or different about infinity and there are most certainly everyday examples of infinity in action. The speed your car is traveling at is an instantaneous velocity that mathematically is over a time period of 1/x as x approaches infinity. If you fire a spacecraft out into space and it never hits anything, then it travels forever.

Wasn't it proved that cars, ships, etc. move in 4D rather than in 3D some 104 years ago? Or are you claiming the universe is everlasting?

 

[cam875]

in 1905 it was only special theory of relativity that was introduced by einstein. His formulation of tensors and all that in 4D didn't complete until I think 1916 with the general theory. And who knows maybe a knew theory will overcome relativity.

 

[Hurkyl]

Infinity is an abstraction.
Zero is another abstract idea.

One is just as abstract.

 

[JoeDawg]

One is just as abstract.

True, but its the loneliest number.

 

[Focus]

I think that there is no infinite in the universe. I don't think real numbers do reflect the real world and I would say the axiom of infinity is false. It is just more convenient to think of things as being infinite than to try to model them as finite.

Mind you when you talk about things like this, its all man made concepts, so it is a bit futile to say God made infinity because you have no way of really defining what infinity is.

 

[cam875]

infinity is much more difficult to visualize and grasp since it is not experienced normally by us than finite is, finite can be a lot nicer than infinite because geometry and things like that work nicely with real numbers instead of \infty.

 

[Hurkyl]

infinity is much more difficult to visualize and grasp since it is not experienced normally by us than finite is,

No, I'm pretty sure the reason you find it "much more difficult to visualize and grasp" is simply because you haven't learned it. It is typical that one grasps topics they've studied much better than topics they haven't studied.

finite can be a lot nicer than infinite because geometry and things like that work nicely with real numbers instead of \infty.

Actually, geometry was the primary example I had in mind when I said "things work better with infinity". Calculus is a lot simpler when you use the extended real numbers. The projective plane was an important milestone in classical geometry, and is indispensable when studying the geometry of polynomial equations.

 

[Pythagorean]

Its just silly pseudophilosophical nonsense. If one believes in the God of the Bible, then he created everything.

I think this is somewhat irrelevant, since the OP claims they are not religious, which would make the Christian God and the Bible irrelevant. It sounds more like he's a deist (Spinoza or einstein's god) than a theist, but this probably isn't too constructive to the theme of the thread.

If you're a scientist or mathematician, there is nothing special or different about infinity and there are most certainly everyday examples of infinity in action. The speed your car is traveling at is an instantaneous velocity that mathematically is over a time period of 1/x as x approaches infinity. If you fire a spacecraft out into space and it never hits anything, then it travels forever.

disclaimer: this is meant supplementally, not as an argument against as you haven't really addresses the point I'm about to make, but you've led me into it nicely.

I'm a scientist (if you consider a BS in Physics a scientist, maybe I need a PhD?) and I don't believe that infinite actually exists.

I've never explicitly seen infinity in nature, only in mathematics and theory. When you speak of a spacecraft traveling forever, is that really a conceivable event? I don't think it is. Reality is very harsh towards our ideals. That's not to say that a spaceship couldn't travel for millions of centuries, but this is still quite a few magnitudes away from infinity (an infinite amount of magnitudes!)

 

[cam875]

from what I have been told about calculus it is extremely accurate but not pure since you always can bring your second point closer and closer to the point your solving an instantaneous velocity for, so one person could have his two points with a separation of 0.01 for time(x axis) and another person could be even closer with 0.0001 separation but technically there is no end to how close you can bring the two points together and you can't come up with the true answer just an extremely accurate one. This is what someone told me that's taking it right now, so I am not sure if he's right or not.

 

[Pythagorean]

from what I have been told about calculus it is extremely accurate but not pure since you always can bring your second point closer and closer to the point your solving an instantaneous velocity for, so one person could have his two points with a separation of 0.01 for time(x axis) and another person could be even closer with 0.0001 separation but technically there is no end to how close you can bring the two points together and you can't come up with the true answer just an extremely accurate one. This is what someone told me that's taking it right now, so I am not sure if he's right or not.

That's definitely a working philosophy in the maths. As you get closer to 0, I believe the word is infinitesimal rather than infinite.

 

[cam875]

so they do accept that they will never get to the actual answer just an extremely extremely close answer?

 

[Pythagorean]

so they do accept that they will never get to the actual answer just an extremely extremely close answer?

yes, but this is quite fine. The most obvious, slap-stick case is carpentry. When we measure 2x4's in carpentry, we don't care if the tape droops a little bit or we're not perfectly straight (both will lead to an overshoot in the measurement) because the difference isn't significant enough to merit the concern of the accuracy since we wouldn't even be able to cut the 2x4's to the exact length we want; we didn't even really want an exact length, there's a nice distribution of lengths that will work for us, so the higher decimal points became pointless.

 

[Gear300]

so they do accept that they will never get to the actual answer just an extremely extremely close answer?

Exact answers and extremely close answers may not differ all too much at all.
1/3 = .333...
1/3 * 3 = 1
.333... * 3 = .999...

 

[Hurkyl]

That's definitely a working philosophy in the maths.

It's sort of a broken one, though. There is nothing inexact about things like real numbers, limits, or infinite series.

Learning how to use and manipulate approximations is one of the most important topics in calculus -- and if you can't tell approximations apart from things that aren't approximations, then you haven't really understood.

 

[Brilliant!]

I'm enjoying the irony here. If we think in finite terms because our primitive mind can't handle infinite, then it's logical to assume that we could be wrong about the existence of infinite all together. After all, infinite was something we realized, it wasn't implanted into us.

Let's just agree not to make foolish statements like "The Universe created this that and the other".

 

[Focus]

I'm enjoying the irony here. If we think in finite terms because our primitive mind can't handle infinite, then it's logical to assume that we could be wrong about the existence of infinite all together. After all, infinite was something we realized, it wasn't implanted into us.

Let's just agree not to make foolish statements like "The Universe created this that and the other".

What exactly do you mean by infinite? Can you give a concise definition?

 

[Brilliant!]

Are we playing the same fiddle, or are you serious? If you're serious, I can't see how my ability to describe or perceive infinite has something to do with anything. I'm only making a particular observation. If the argument is that we can't understand indefiniteness, and we therefore create a definite system that we can understand, then it is foolish to say something like "The universe created infinity". If the universe created anything, then we'd have to allow for the very large chance that what we call "infinity" isn't what it created, but what we mistakenly assume is what it created.

 

[Hurkyl]

Are we playing the same fiddle, or are you serious? If you're serious, I can't see how my ability to describe or perceive infinite has something to do with anything.

If you cannot give any sort of coherent description of "infinite", then how can you possibly make claims like "our primitive mind can't handle infinite"?

Knowing what everyone means when they use words is pretty much a prerequisite for any sort of meaningful conversation...


And since some people seem to have absolutely no trouble handling what they mean by the word "infinite", you cannot possibly both
(1) be correct
(2) mean what it looks like you mean

 

[Brilliant!]

If you cannot give any sort of coherent description of "infinite", then how can you possibly make claims like "our primitive mind can't handle infinite"?

Knowing what everyone means when they use words is pretty much a prerequisite for any sort of meaningful conversation...


And since some people seem to have absolutely no trouble handling what they mean by the word "infinite", you cannot possibly both
(1) be correct
(2) mean what it looks like you mean

What does it look like I mean? If you detect anything other than an attempt to point out the inconsistencies of the OP's line of thought you have it all wrong.

 

[Hurkyl]

What does it look like I mean?

It looked like you claimed that people cannot comperehend "infinite", which appears to directly contradict the empirical evidence of people who do not only understand it, but work with it on a daily basis!

 

[Pythagorean]

It's sort of a broken one, though. There is nothing inexact about things like real numbers, limits, or infinite series.

Learning how to use and manipulate approximations is one of the most important topics in calculus -- and if you can't tell approximations apart from things that aren't approximations, then you haven't really understood.

I'm assuming that when cam said:

...and you can't come up with the true answer just an extremely accurate one.

he was referring to when we make observations in reality, in which no infinity actually exists. At least, I don't know of any infinity being observed in reality. In mathematics, we have little problem finding that:

lim (n->inf) 1/n = 0

is the "true answer" because this operation is defined by it's own language (mathematics).

but in nature, where n is a really large number (n>>1) and not actually infinity, we approximate equations that are otherwise unsolvable (or even unmanageable if we're lazy and the terms are insignificant enough). We integrate over shapes and volumes as if they're made of infinitesimal material when they're actually made of discrete particles.

 

[Brilliant!]

It looked like you claimed that people cannot comperehend "infinite", which appears to directly contradict the empirical evidence of people who do not only understand it, but work with it on a daily basis!

It was the original poster who made that claim, I was only pointing out how ridiculous it is.

 

[Pythagorean]

It looked like you claimed that people cannot comperehend "infinite", which appears to directly contradict the empirical evidence of people who do not only understand it, but work with it on a daily basis!

I worked with it every day for a couple semesters and I still don't really comprehend what infinity is outside of mathematics. I don't see how that proves that they comprehend any "deeper meaning" of it, which is what I think most laymen are getting at.

 

[JoeDawg]

It looked like you claimed that people cannot comperehend "infinite", which appears to directly contradict the empirical evidence of people who do not only understand it, but work with it on a daily basis!

I drive a car everyday, but apart from knowing where the gashole is, I don't pretend to understand it.