no such thing as "infinity" in the real world (split)

[cladking]

No. It's not "infinitely complex" because there is no such thing as "infinity" in the real world.

 

It's far more complex than "infinitely complex" anyway. The odds of any given event occuring are effectively less than the reciprocal of infinity. If you ever think they are greater than you're looking at too large a scale or too short a time frame.

 

Maybe I'll just log back out again for a few months now.

[cladking]

 

 

Proof?

 

If you had a machine capable of infinite speed you could go to London and back in a moment. You could go anywhere in a moment including the ends of the universe.

 

"Infinity" is a mathematical construct that can't exist in reality. For all practical purposes the exceedly complex nature of reality is far greater than infinity anyway. A butterfly flaps its wings in China and causes galaxies to collide.

 

We can't predict the outcome of a single atomic collision yet a virtually infinite number of such collisions take place on a virtually infintesimal time scale which in aggregate determine not only our reality but the reality of colliding galaxies in the far future.

[Strange]

"Infinity" is a mathematical construct that can't exist in reality.

 

It is possible the universe is infinite. So by your logic it can't exist.

And just repeating the same assertion is nor proof or even evidence.

[cladking]

 

It is possible the universe is infinite. So by your logic it can't exist.

And just repeating the same assertion is nor proof or even evidence.

 

Sure. And it's possible that subatomic particals can bounce off of one another in an infinity of different angles. But in the real world there aren't an infinite number of resistances for a variable pot. Resistance at any setting is determined by the interface of the two conductors. The number of different resistances is exceedinly high and the changes over time are exceeding complex but it is not infinite.

 

You say there are an infinite number of numbers but again the real world doesn't work this way. Of what value is a number so large that the there is no means to record it even with a device the size of the known universe? For all practical purposes a number so large it can't be recorded on a single disc doesn't really exist. How do you manipulate this number and what would be its purpose?

 

You might draw a circle and claim it has an infinite number of sides but when you look at it under magnification it doesn't look like a circle at all.

 

There's nothing that's infinite in the real world for practical purposes unless you choose to view it that way.

[swansont]

!

Moderator Note

Split from http://www.scienceforums.net/topic/94289-physics-and-the-universe/

 

No. It's not "infinitely complex" because there is no such thing as "infinity" in the real world.

 

 

So what? The concept of infinity exists — there's even a symbol for it: ∞

 

The conversation was about complexity, which is also a concept. Not a part of the "real world". So your dubious claim is moot.

[Strange]

There's nothing that's infinite in the real world for practical purposes unless you choose to view it that way.

 

Repeating a baseless assertion three times doesn't magically make it true. Unless you have some evidence for your claim, you might just have to concede that you don't know.

You say there are an infinite number of numbers but again the real world doesn't work this way. Of what value is a number so large that the there is no means to record it even with a device the size of the known universe? For all practical purposes a number so large it can't be recorded on a single disc doesn't really exist. How do you manipulate this number and what would be its purpose?

 

It is very simple to define and represent numbers that are so large that, by your definition, they don't exist. Which suggests that your definition is wrong. (Go on, ask me if I am surprised.)

[studiot]

 

How do you manipulate this number and what would be its purpose?

 

If a number is large but not transfinite it will follow the rules for finite numbers, however big it might be.

 

So , for instance, given any integer, however large, I can easily make an even number from it (guaranteed).

 

If the number is transfinite then you can follow one of the schemes of rules for the manipulation of such numbers. There is more than one available and they are all different from the schemes for the manipulation of finite numbers.

[cladking]

 

 

 

 

So what? The concept of infinity exists — there's even a symbol for it: ∞

 

The conversation was about complexity, which is also a concept. Not a part of the "real world". So your dubious claim is moot.

 

As a concept or as a construct "infinity" exists but there is no referent for it in the entire universe.

 

If there were a referent for it then we can imagine a world that is in all ways identical to our world except there was no Abraham Lincoln. Where there was a Lincoln there instead a void. This is obviously an impossibility. No such world can exist.

 

How can people concieve of "infinity" but not notice the impossibly enormous odds against all actual events? What are the odds that somebody would enter exactly this post at exactly this time? What are the odds as determined by all human knowledge in 1890? What are the odds I'd type "hhdejlggfllk" to try tomake a point? There are a million ways to try to make this exact same point in this exact same thread but I typed "hhdejlggfllk".

 

When I started this post I had no idea where it was headed.

 

So what are the odds?

 

If a number is large but not transfinite it will follow the rules for finite numbers, however big it might be.

 

So , for instance, given any integer, however large, I can easily make an even number from it (guaranteed).

 

If the number is transfinite then you can follow one of the schemes of rules for the manipulation of such numbers. There is more than one available and they are all different from the schemes for the manipulation of finite numbers.

 

I once had an idea for a computer language that led me to compute how many monkeys and typewriters you'd need to get a readable copy of War and Peace in one attempt. It's ~ 4.2 X 10 ^ 805,999. But what are the odds that it would be written exactly as it exists before it was even begun?

 

All things are intimately connected. How would the world be different today if it had a different ending or the author had achieved more brevity? As you go back in time things have more impact on the present. If you physically could kill a butterfly in the Jurassic how would things be different today?

 

A number has no meaning except as it's being used correctly in an equation. What value is a number like ((((((((10 ^ 10) ^10) ^ 10) ^ 10) ^ 10) ^ 10) ^10) ^ 10)unless it can be applied to something? Yet this number (while easily divisible by 2 or 10) is, no doubt, far too small to express the odds against reality itself.

[Acme]

...

"Infinity" is a mathematical construct that can't exist in reality. For all practical purposes the exceedly complex nature of reality is far greater than infinity anyway. A butterfly flaps its wings in China and causes galaxies to collide.

 

We can't predict the outcome of a single atomic collision yet a virtually infinite number of such collisions take place on a virtually infintesimal time scale which in aggregate determine not only our reality but the reality of colliding galaxies in the far future.

First you declare infinity can't exist in reality, then you go on to give examples of infinity existing in reality. Here we go again with no limit to the ensuing absurdities...

[Mordred]

Man this thread has gotten infinetely foolish. Cladking your assertions make absolutely no sense.

 

 

In point of detail great care is taken to avoid problems that lead to infinite values.

 

In QFT for example.

 

"Take a field and assign a coordinate at every point in that region."

 

If you don't place a limit of measurement scale you end up with an infinite number of coordinates.

 

Much like you can devide a metre in half then devide the two halfs again.

 

No matter how many times you devide each section by 1/2 you will never have any section reach zero.

 

There are thousands of examples where infinity can occur,

Edited April 4, 2016 by Mordred

[swansont]

As a concept or as a construct "infinity" exists but there is no referent for it in the entire universe.

 

Again avoiding or missing the point. It was being applied to a concept, so a physical example doesn't need to exist.

[cladking]

Again avoiding or missing the point. It was being applied to a concept, so a physical example doesn't need to exist.

 

It's not my contention that the word "infinity" doesn't exist. Merely that it probably has no referent. We wouldn't have the word "zebra" if there was nothing that looked like a striped horse. The only referent for "infinity" is in the construct which is math.

First you declare infinity can't exist in reality, then you go on to give examples of infinity existing in reality. Here we go again with no limit to the ensuing absurdities...

 

The odds against something never becomne infinite or nothing could happen. The odds against everything are simply enormous on a universal scale.

 

No matter how many times you devide each section by 1/2 you will never have any section reach zero.

 

 

 

You can't divide anything by two more than several times in the real word. If you cut a two by four in half a few times there will be nothing but sawdust for the last piece.

 

Try folding a piece of paper eight times.

My comment is very much being taken out of context by being split off and I agree with Mordred that this discussion may be infinitely foolish. I have nothing to gain from pursuing it.

 

I had said that the world is "far more complex than "infinitely complex" anyway. The odds of any given event occuring are effectively less than the reciprocal of infinity. If you ever think they are greater than you're looking at too large a scale or too short a time frame."

 

I meant this to say virtually nothing is really possible yet everything exists anyway and people take the existence of infinity to mean everything is possible and everything (even worlds without a Lincoln) exists. This is about perspective and this discussion is turning it into something more akin to semantics. The reality is that there is no world without Lincoln and there's probably no referent for "infinity" in the real world where we all exist.

[Strange]

 

It's not my contention that the word "infinity" doesn't exist. Merely that it probably has no referent.

 

But, of course, you don't know that. It is just your personal opinion. Please stop stating it as if it were a fact.

[studiot]

cladking

How do you manipulate this number and what would be its purpose?

 

studiot

If a number is large but not transfinite it will follow the rules for finite numbers, however big it might be.

 

So , for instance, given any integer, however large, I can easily make an even number from it (guaranteed).

 

If the number is transfinite then you can follow one of the schemes of rules for the manipulation of such numbers. There is more than one available and they are all different from the schemes for the manipulation of finite numbers.

 

cladking

I once had an idea for a computer language that led me to compute how many monkeys and typewriters you'd need to get a readable copy of War and Peace in one attempt. It's ~ 4.2 X 10 ^ 805,999. But what are the odds that it would be written exactly as it exists before it was even begun?

 

All things are intimately connected. How would the world be different today if it had a different ending or the author had achieved more brevity? As you go back in time things have more impact on the present. If you physically could kill a butterfly in the Jurassic how would things be different today?

 

A number has no meaning except as it's being used correctly in an equation. What value is a number like ((((((((10 ^ 10) ^10) ^ 10) ^ 10) ^ 10) ^ 10) ^10) ^ 10)unless it can be applied to something? Yet this number (while easily divisible by 2 or 10) is, no doubt, far too small to express the odds against reality itself.

 

 

 

The whole point of this thread appears to be that you wish to demonstrate the truth of its title.

 

Unfortunately the title is imprecise since it employs imprecise words such as reality and existence.

Existence in particular has a specific meaning in mathematics, which does not directly correlate with our ideas of reality, physical or otherwise.

 

But you also asked a specific question of a mathematical nature, which seemed to me to question whether infinity could be handled mathematically and I gave a specific answer.

 

My answer, as does your reply quoted above, showed that it most definitely can.

 

So if you want to you can handle very large numbers or infinity mathematically.

 

We are agreed.

 

 

 

[swansont]

It's not my contention that the word "infinity" doesn't exist. Merely that it probably has no referent.

Again missing the point.

 

We wouldn't have the word "zebra" if there was nothing that looked like a striped horse.

Right. Because we don't have words like "dragon", "unicorn" or "yeti" or any number of made-up animals in my D&D books or sci-fi/fantasy literature.

[Strange]

A number has no meaning except as it's being used correctly in an equation. What value is a number like ((((((((10 ^ 10) ^10) ^ 10) ^ 10) ^ 10) ^ 10) ^10) ^ 10)unless it can be applied to something?

 

Of course every number has meaning (or several meanings, for example depending whether you treat it as an ordinal or cardinal).

 

Perhaps what you mean is that a number has no value or meaning to us unless it has a practical application. That is a rather narrow view, but even in that context there are numbers far larger than the one you have invented which do have a use.

 

There is also an ingenious proof that there are no uninteresting numbers!

 

Yet this number (while easily divisible by 2 or 10) is, no doubt, far too small to express the odds against reality itself.

 

Which raises a couple of points:

1. How have you calcuated (or estimated) the odds against reality? (Naively, I would have assumed it was 0)

2. So you have found a meaning (odds against reality) for a very large number of the sort you say is meaningless.

[cladking]

 

Which raises a couple of points:

1. How have you calcuated (or estimated) the odds against reality? (Naively, I would have assumed it was 0)

2. So you have found a meaning (odds against reality) for a very large number of the sort you say is meaningless.

 

You know the odds against tossing a coin 10 times and getting all heads are 1: 2 ^10 or one in 1024.

 

We all know we're really going to get something like H/ T/ H/ H/ T/ H/ H/ T/ T/ H.

 

What we don't really think about is that the odds against getting this are exactly 1: 1024 as well. Throw a coin about 10240 times and you'll see the proof of this.

 

Reality isn't always pretty but it's always exceedingly improbable. A butterfly flaps its wings in China and New Orleans goes under water seven days later. A billion years later and two galaxies collide. This is the nature of reality.

 

I couldn't begin to estimate the odds against any event. A ball rolls toward the edge of a table and it's safe to say it will end up on the floor but this is very short sighted thinking. It is short term and large scale. Try predicting something important like which butterfly in China you have to affect to save a city. Try predicting the effect of a reflection on the underside of a water lilly a million years later.

 

Man doesn't know even the tiniest fraction enough to quantify the odds against the outcome of the universe within many trillions of orders of magnitude. Any other belief is mere hubris. How am I supposed toguess the odds against any given outcome?

 

These are great questions though. These are questions we'd all do well to ponder.

 

 

 

 

The whole point of this thread appears to be that you wish to demonstrate the truth of its title.

 

...

 

We are agreed.

 

 

 

Such irony.

 

Of course you're right on all counts.

 

However, I aver that the reason science exists at all in any guise is to understand reality; nature itself. We carefully exclude the concept of reality because we are well aware that it is different for each of us.

 

But the question remains whether "infinity" exists or not. It can't be shown by experiment yet it is widely believed anyway.

 

Why do we believe in something that can't be shown to exist scientifically?

 

 

Of course the answer is simple enough but it can't be shown logically, scientifically, or practically.

 

The problem isn't "science" but rather our understanding of it. It is a metaphysical inconsistency as viewed from most perspectives. There are other perspectives equally logical and equally "scientific".

[Delta1212]

 

You know the odds against tossing a coin 10 times and getting all heads are 1: 2 ^10 or one in 1024.

 

We all know we're really going to get something like H/ T/ H/ H/ T/ H/ H/ T/ T/ H.

 

What we don't really think about is that the odds against getting this are exactly 1: 1024 as well. Throw a coin about 10240 times and you'll see the proof of this.

 

Who is the "we" in this sentence? Because I'm fairly sure you're currently taking to exactly the kind of people who do think about that fairly regularly.

 

As far as infinity existing, I suppose it depends on what you mean by "existing." The concept of infinity certainly exists. It definitely has an existence as a mathematical tool. There are relationships in nature that appear to be accurately described by methods that involve infinities.

 

Whether it has any "real" existence outside of a tool that we came up with to help us describe aspects of nature, I don't know. But I can say the same thing about the number 2.

[Strange]

Cladking is very fond of telling us what we think.

[studiot]

 

cladking

What we don't really think about is that the odds against getting this are exactly 1: 1024 as well. Throw a coin about 10240 times and you'll see the proof of this.

 

 

Good thinking +1

 

I take it you are now willing to acknowledge that the abtract can have real existence as Delta1212 says

,

So we are definitely agreed that the abstract mathematical concept of infinity has real existence for us to work on.

 

cladking

I aver that the reason science exists at all in any guise

 

As a matter of interest here is another (mathematical) definition of infinity, (due to Cantor)

 

Consider the counting numbers 1,2,3,4.......

 

For each one I can write the square of the number underneath

 

1,2,3, 4.....

 

1,4,9,16....

 

Now look again carefully.

 

Every square is also a counting number, but the list of squares does not include all the counting numbers.

So the set of all the squares is only a part of the set of all the counting numbers.

 

But I have put these sets in one-to-one correspondence so they must have the same number of members.

 

This is the basis of Cantor's definition of infinite as something that can be put into one-to-one corresponcence with a part of itself.

It is a very powerful concept that finds application in formal logic and mathematics and pleasing because it does not require the concept of 'anything carrying on forever and never finishing'

 

 

Edited April 20, 2016 by studiot

[Strange]

Good thinking +1

 

I'm not sure that it is a sign of "good thinking" to tell us something we all know on the basis that we don't know it.

 

You know the odds against tossing a coin 10 times and getting all heads are 1: 2 ^10 or one in 1024.

 

We all know we're really going to get something like H/ T/ H/ H/ T/ H/ H/ T/ T/ H.

 

What we don't really think about is that the odds against getting this are exactly 1: 1024 as well.

 

...

 

I couldn't begin to estimate the odds against any event.

 

And yet you have just done it.

 

This is just more incoherent nonsense.

 

 

But the question remains whether "infinity" exists or not. It can't be shown by experiment yet it is widely believed anyway.

 

It can't be shown by experiment that it doesn't exist either, and yet that is also widely believed. People are odd that way.

 

Why do we believe in something that can't be shown to exist scientifically?

 

You can find any number of people insisting that it is impossible for the universe to be infinite and others that it is impossible for it to be finite. Next time one of those idiots pops up, maybe you can ask them. (I put it down to ignorance, myself. So it is, potentially, curable.)

[studiot]

 

Strange

I'm not sure that it is a sign of "good thinking" to tell us something we all know on the basis that we don't know it.

 

 

"Pour encourager les autres"

Edited April 20, 2016 by studiot

[cladking]

"I couldn't begin to estimate the odds against any event."

 

 

And yet you have just done it.

 

 

 

You flipping a coin 10,240 times and logging the outcome to compare with statistical probability is in no way an "event". Indeed, I predict it will never become an event because for numerous reasons you'll never do it. In the real world coin tosses aren't entirely random anyway since there are factors that can confound the results such as that most coins are more aerodynamic when falling obverse down. This means the way the coin is flipped affects the results.

 

It can't be shown by experiment that it doesn't exist either, and yet that is also widely believed.

 

 

Reality isn't determined by consensus.

 

So who do you know who doesn't "believe" in infinity?

 

Experiment shows lots of big numbers but no infinity. Avogadro can compute chemical reactions even as subtle as dissolving salt in the ocean but the numbers are always finite in the real world.

 

 

But I have put these sets in one-to-one correspondence so they must have the same number of members.

 

This is the basis of Cantor's definition of infinite as something that can be put into one-to-one corresponcence with a part of itself.

 

 

 

 

Why use only counting numbers? You can square even the infinite number of numbers between 1 and 1.00000001 or between any two points no matter how close. You don't have to multiply a number by itself.

 

There are no limits to the things you can do with math but there are severe limitations to what you can do in the real world. Despite the impossibility of getting any given pattern in the results of flipping a coin 10/ 10,240/ 10,240 times you will still unique pattern every time. Despite not knowing which butterfly in China caused it there will still be a storm in ten days.

 

The storm is real. The butterfly is real. That numbers exist that extend infinitely with a one to one correspondance to a subset of itselt is not real.

 

People can't seem to see the incredible complexity of reality because they are blinded by the concept that there are an infinite number of points between any two points. As the rules that govern this complexity are discovered many more orders of magnitude of complexity will be overlaid on it. But the number can never become infinite because everything exists and events still unfold.

[Strange]

"I couldn't begin to estimate the odds against any event."

 

You flipping a coin 10,240 times and logging the outcome to compare with statistical probability is in no way an "event". Indeed, I predict it will never become an event because for numerous reasons you'll never do it.

 

Whether I or anyone else will do it is not the point. It could be done and the odds could be calculated. And in fact you have done it. Despite your claims it is impossible and you couldn't do it.

 

Reality isn't determined by consensus.

 

So what was your point in saying it is "widely believed"? Is it relevant that you believe it is not infinite, but not relevant that others believe it is? When we have no evidence either way.

 

So who do you know who doesn't "believe" in infinity?

 

The person who started this thread, perhaps.

[studiot]

 

cladking

Why use only counting numbers? You can square even the infinite number of numbers between 1 and 1.00000001 or between any two points no matter how close. You don't have to multiply a number by itself.

 

There are no limits to the things you can do with math but there are severe limitations to what you can do in the real world. Despite the impossibility of getting any given pattern in the results of flipping a coin 10/ 10,240/ 10,240 times you will still unique pattern every time. Despite not knowing which butterfly in China caused it there will still be a storm in ten days.

 

The storm is real. The butterfly is real. That numbers exist that extend infinitely with a one to one correspondance to a subset of itselt is not real.

 

People can't seem to see the incredible complexity of reality because they are blinded by the concept that there are an infinite number of points between any two points. As the rules that govern this complexity are discovered many more orders of magnitude of complexity will be overlaid on it. But the number can never become infinite because everything exists and events still unfold.

 

 

Sigh.

 

You seem to have gone into not listening mode again.

 

 

Why use only counting numbers?

 

Because some wag will then say

 

 

People can't seem to see the incredible complexity of reality because they are blinded by the concept that there are an infinite number of points between any two points

 

You use counting numbers because there is nothing between them - guaranteed they have no liasons dangereuse.