Does Infinity exist in nature

[fredrik]

You can't measure zero, you can only measure "smaller than we can measure."

 

Are you sure? Maybe there is a tiny flake from a previous apple sitting in the bottom of the bowl that you just haven't noticed.

 

These comments relate to the point I tried to make as well.

 

As I think of it, each observer or subsystem of the universe interaction with another and has a complexity limit that constraints the amount of resolvable and distinguishable information it can encode.

 

It follows that there is a minimum amount of "evidence" that can be counted, and that hypotetically smaller fragments than this would be indistinguishable from zero TO THIS observer. The effect I would expec that the physical action of this observer is then invariant with respect to these hypotetical indistinguishable fragments. Ie. the systems responds as if they weren't there.

 

It's what I tried to say here:

Does the action of two interacting systems' date=' really reflect a continuum of distinguishable possibilities or not?

[/quote']

 

Is the full continuum physically distinguishable or not? If not, the action should somehow display - at it's fingerprints - that it's actually just responding to some discrete finite set that for the observer in question is indistinghuisalbe from the continuum.

 

But since it's easier to count states in a discrete set, the possible advantage of a reduced abstraction (provided we find it, as it should apply of physics) should be obvious.

 

To take analogy, consider a human. A second human assumes the first human acts rationally in compliance to it's expectations. Ie. poker game, she chooses to play her cards to optimize the expected outcome given the expectation of what cards the other players has. But then it is also evident in the action - as judged by the second observer - if the first observers acts as if he didn't see certain things. For example that she couldn't distinguish a zero risk from a small fractional risk. Since the rational action weighs in all risks, the action that doesn't account for the risk, is different and thus observable to a second observer.

 

This is a different way of thinking though, that is not standard in physics. Usually Sets of possibilities and states are treated as timeless uinversals. Perhaps that not quite right?

 

/Fredrik

[sr.vinay]

Infinity till date has been theoretical, for we do not know beyond what we see. As in, we've not built telescopes that can capture images beyond a few solar systems or galaxies. This being said, we don't know the exact boundaries, if any, that define the universe. This would make infinity just a theory. For there cannot be something infinite derived from things we've measured.

[manfred]

A related question is: can the universe be infinitely old?

 

Of course, if you believe the big bang is the absolute beginning, there being no predecessor event that caused the big bang - then you'll agree it has a finite age. Same if you believe in GOD. But some people propose that as an alternative to an eternal God, there is an eternal universe. The big bang could have been preceded by a big crunch, or the big bang was a 4 dimensional manifestation of a multidimensional entity. So in these types of scenarios, the universe (in the broadest sense: everything that exists) could be infinitely old.

 

But I argue that the universe cannot be infinitely old. If it were infinitely old, we would never arrive at TODAY. Imagine "today" to be represented by a man who is waiting in a line to check into a hotel (one with an infinite number of rooms, of course). The line in front of him is infinitely long (there are an infinite number of days before him). No matter how many people check in at the front of the queue, the queue remains infinitely long (infinity -1 is still infinity). Hence, we never reach today. Therefore the age of the universe can't be infinitely old.

[michel123456]

In this syllogism, TODAY happens when you reach the desk?

So it happens only once.

It doesn't work like that.

TODAY happens everyday.

[manfred]

In this syllogism, TODAY happens when you reach the desk?

So it happens only once.

It doesn't work like that.

TODAY happens everyday.

 

I realize "today" is a floating concept. Let me get more precise: I am breaking down time into discreet, measurable intervals and labelling them on a number line that stretches into the past (it also stretches into the future, but that is irrelevant).

 

Replace "today" with t=0. the prior discrete interval is t=-1, etc, stretching into the infinite past. The argument is irrespective of the length of the interval, but using "day" is intended to help us visualize.

 

Incidentally, this is just a variation of the Hilbert paradox.

[michel123456]

There are 2 ways to represent infinite.

_The first is to figure out a line extending infinitely on both sides. It is the base of the Hilbert paradox. It is an open configuration, with the limits somewhere far far away, that drives into counter intuitive situations.

It has been chosen by mathematicians for representing the numbers, and by many christian philosophs.

 

_The second is to figure out a circle, something that goes continuously all way round. It is a closed configuration that drives into very simple situations, sometimes intriguing but always explainable. It has been chosen by geometers thousands of years ago and by philosophs of antiquity that had no problem into representing a never ending universe, although their universe was much smaller than ours.

 

You could also remark that God in christianity is full of mysteries, and that any mystery arising from scientific knowledge, such as the infinite, is used as an argument for the existence of the almighty deity.

In ancient times, gods were also almighty, but they were not covered by any peplum of mystery. In the contrary, the gods were used as explanations, and their manifestation was each time associated to a very real phenomena.

In fact, there was more mystery in numbers than in deity.

[PaulS1950]

What, if any, is the difference between eternal and infinite.

Is it that eternity has no beginning and no end but the infinite can have either or both?

ie:

the infinite fractional number set between 1 and 2

[SunsetW]

Hi folks, what about facing two mirrors each other. I think it is a very clear example of infinity in Nature. Infinite image reflections are there no matter anyone see it or not, they just exist there I think, or maybe I am wrong? I know there is an issue with light diminishing effect (photone scattering in spacetime I think), but I am not sure that it is really relevant. Another issue is quantum apect of that phenomenon (Copenhagen interprtation, human consciousness relevance for measuring).

 

I also think that an evidence of infinity in Nature is very important for definitive classification of mathematics. If infinity is only a human construct then it is a serious threat, because whole mathematics could be just a human construct and the most we know could be wrong. On the other hand, if there is an evidence of infinity in Nature then mathematics could be a scheme of Universe or the language of God, because humans mathematically describe infinity (like black hole) even anyone didn't see it.

 

PS. Sorry for my English, it is not my mother language.

[manfred]

Hi folks, what about facing two mirrors each other. I think it is a very clear example of infinity in Nature. Infinite image reflections are there no matter anyone see it or not, ..."

The counter reflections are not infinite. Each is dimmer than the previous, because only a portion of the light is reflected each time. It eventually dims to nothing.

 

I also think that an evidence of infinity in Nature is very important for definitive classification of mathematics. If infinity is only a human construct then it is a serious threat, because whole mathematics could be just a human construct and the most we know could be wrong. On the other hand, if there is an evidence of infinity in Nature then mathematics could be a scheme of Universe or the language of God, because humans mathematically describe infinity (like black hole) even anyone didn't see it.

I believe infinity is a valid and useful mathematical concept, but it is an abstraction that doesn't map directly into reality.

 

For example: take one meter stick. In concrete terms, it can be divided into 100cm, 1000mm, 1,000,000 microns etc. In abstract terms, it can be said to consist of an infinite number of points. But a "point" is a concept of a dimensionless thing, which is not a real entity. You can't arrive at a point by successive division - there is always a finite length. You can't map points into reality, except in the mind. Nevertheless the concept of points, and of infinity, is useful because of the mathematical tools - such as calculus, which effectively utilizes these concepts. But it's an abstraction, not concretely real.

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Merged post follows:

Consecutive posts merged

What, if any, is the difference between eternal and infinite.

 

Infinite is a generic term that can apply to anything. Eternal refers to infinite time. Eternity usually refers to an infinite past and infinte future, but in some contexts may refer to only one direction (past or future).

 

the infinite fractional number set between 1 and 2

This is an abstraction. You cannot map the elements of this set into concrete reality.

[PaulS1950]

1 1/2, 1 1/3, 1 1/4, 1 1/5 ...

You mean like this? (I realize that this is an infinite set of fractional numbers > 1 and <= 1.5)

Edited May 23, 2010 by PaulS1950

[SunsetW]

Folks we have to find example of infinity not in mathematics (it surely exist there), but in Nature and it should be as soon as possible, because we are facing the most dangerous monster - infinity (if it is just a logical concept)! If infinity is only a human construct it is very possible that the whole mathematics is only a human construct (infinity is incorporated in many mathematical concepts like calculus), and it is more than likely that many physical theories are nothing but garbage. For example whole quantum mechanics is very good mathematical description of reality on small scale, but we could not be sure that everything is happening just like that. We could only be sure that mathematics is telling us that it should be just like that. What if mathematics is just a construct of human logic. Kurt Godel proofed very clearly that formal systems produced by human logic couldn't be very reliable. It sounds almost apocalyptic that large part of human knowledge about Nature could be wrong.

Edited May 24, 2010 by SunsetW

[michel123456]

Mathematics are a human construct. There is nothing to be afraid of. Mainly, most physicists remain perplexed by the fact that Mother Nature looks to be explainable through mathematics. It is source of astonishment.

[SunsetW]

The only thing by which someone has to be perplexed is Godel's conclusion about formal systems like physical theories and (I would say) whole mathematics are! By analogy with it, Schrodinger's equation is nothing but garbage, and even more because we couldn't properly see are its repercussions really true!

 

PS. I actually know that it is commonly known that infinity doesn't exist in the Nature (nobody has discovered it yet), but did You know that infinity is issue in mathematics for centuries? Mathematicians usually make distinction between potential and actual infinity. Potential infinity isn't a problem but actual infinity certainly is, and I don't think that it is ever properly solved. Real astonishment is that everything we know could be wrong, but we''ll wait and see what will LHC say! Many could be surprised! And that is why I respect one experimental physicist more than dozens mathematicians (my colleagues, sorry about that, you all know that I don't think that literary)!

Edited May 25, 2010 by SunsetW

[johnsmithy]

being new to this way of thinking , i accepted the mathematical term of infinity. I can somehow grasp it. It's man made you can always add 1 to every number and thats that. I find it absurd to think you can reach the end of that , even if writing down the longest number with a carbon pen you willl reach maybe a point when you run out carbon atoms in this universe.

Nature as we define it is what surrounds us, and latest big bang theory would say the universe has a begining. An accumulation of something that bursted into existence. For that i guess there could be a finite state of that something. I mean that accumulation can only generate that much of stuff therefor univese=finite. Mass has an end when it becomes energy , a something that can't be created ? yet as decades pass we still find smaller and smaller stuff that comes into the realm of quantum physics the fun part of science where it might or might not be there but for sure it is or not. Maybe it's just a matter of tools at hand . If you could define a limit to energy i could say there is 1 bit or no bit just as easy .

 

Even if we can find out what energy is , we still have a problem with the fact that it runs on a support called the fabric of space. Our finite universe which from what i ghater is finite since it has a begining and multiple ends, sits on the magical fabric of space time that can;t be probed but only deduced.

 

Thinking of it, even if we probe space-time and figure it out we would still have question what is beyond that, maybe our problem is that we can't understand limits.

For me fractals describe best what is nature and therefor the infinity , and the fact we are part of it somewhere lost in a recurrence.Ofcourse that doesn't mean we should relax in a tree and just eat fruits and wait for the end.

 

As for a previous post, maybe mother nature tries to explain itself trough us and other beings that are self aware.

Edited May 27, 2010 by johnsmithy

[SunsetW]

Amen

آمين

אָמֵן

 

P.S. It is not an infinite problem. For example many theoretical and mathematical physicist have their own theories and formal models of what will happen when two protons collide in LHC at energy of 7 TeV, and only an experimental physicist will know exactly what will happen just after she will do the experiment. The point is that I know just what I see! If I say something that I didn't see (for example fractal structure of Nature or the infinity in the black hole), it is only a speculation, or matter of faith, religion or whatever you want! This is what theoretical physicists and mathematicians do! They are people of faith!

 

P.P.S. By the way folks, I'm very excited about all opportunities of the Internet. Look at us, we each are sitting in far parts of the World, and discussing about infinity and other state-of-the-art issues of contemporary science. We could easily establish a virtual institute and even more write a book all together about infinity or a fundamental principle of Nature or something else more interesting. And these book would be an unrivalled state of the art of the issue because it would be written by many, and everybody knows that ten (wo)men know about something certainly better than one (wo)man, and a hundred (wo)men know better than ten! You know what I mean!

 

Thank God for the Internet and we could establish a virtual institute and write a book, I'm really not joking!

Edited May 27, 2010 by SunsetW

[HardonColluder]

I'd expect it to be impossible to prove infinite in nature . Infinite can be used as a different perspective on fractions . For example

If I space apart 2 points and then place an object halfway between the 2 points (1/2) , then I move it a quarter more , then another 8th , then a 16th and so on , halving the fraction each time , I can do this an infinate amount of times , moving forward each time , without ever reaching the end as I can only move in the space I defined in the beginning . The more I move forward the smaller I become and the more it takes to move forward (Just like attaining light speed) . If someone needed to make 100$ and I said 'I can give you 50$' , then he said 'Well now I need another 50$' , so I give him 25$ and so on , he'd be getter richer to infinite , whilst never attaining 100$ because we're just playing with fractions of 100 (As 100 is not a fraction of 100 , it's unattainable) . But don't think on it for too long - That way madness lies!!!

 

See http://en.wikipedia.org/wiki/Continuum_hypothesis

[manfred]

I'd expect it to be impossible to prove infinite in nature . Infinite can be used as a different perspective on fractions . For example

If I space apart 2 points and then place an object halfway between the 2 points (1/2) , then I move it a quarter more , then another 8th , then a 16th and so on , halving the fraction each time , I can do this an infinate amount of times , moving forward each time , without ever reaching the end as I can only move in the space I defined in the beginning . The more I move forward the smaller I become and the more it takes to move forward (Just like attaining light speed) . If someone needed to make 100$ and I said 'I can give you 50$' , then he said 'Well now I need another 50$' , so I give him 25$ and so on , he'd be getter richer to infinite , whilst never attaining 100$ because we're just playing with fractions of 100 (As 100 is not a fraction of 100 , it's unattainable) . But don't think on it for too long - That way madness lies!!!

 

See http://en.wikipedia.org/wiki/Continuum_hypothesis

 

Even in your example, infinity is just a concept - you can't really do anything an infinite number of times. Think about the act of actually doing it: after each act, your count will be finite. The use of infinity here is just a thought experiment; such thought experiments are useful in mathematics (such as determining limits - as you are doing here, or developing proofs by induction) - but does not map into reality.

[elas]

Well Does infinity exist in nature?

 

I have recently heard blackholes actually slowly die, they somehow radiate energy (I think in gravity waves).

 

Perhaps Black holes (not the event horizon, the "Actual Stuff") has a real size?

 

Also the bigbang seems to suggest our universe isnt endless, Just really really really big. So the universe Does not go for infinity.

 

Theres a Limited Speed, Mass/energy in the universe and Size.

If there is a limit on everything there is a limit on complexity.

 

Do we realy know of any instances in which infinity does exist, or have we created the concept?

 

Try to reverse the question, 'how can infinity not exist' that is to say if it were possible to travel through space in a straight line (no curvature) what could bring infinity to an end?

 

Is it not remarkable that 4000 years ago scholars in northen India were taught that infinity was an endless field of universes, 3000 years ago people were told (in the Book of Mary) that God created only seven of the many universes that exists (we are number 3), but we then quickly settled for one universe, but cannot explain how or why.

 

Lee Smolin (The Trouble With Physics) does mention that there is a minority in favour of an infinite number of real (i.e 3 dimensional) universes, but as he is writing on QT it is only mentioned in one sentence.

 

We seem to have lost our ability to think big, but mathematically the percentage of our universe occupied by one electron is greater than the percentage of infinity occupied by one universe; it is our insignificance in the big (i.e. infinite) picture that permits our existence: the universe is a mere pimple in infinity here today, gone tomorrow. Nothing is more natural.

Edited June 2, 2010 by elas

[Sisyphus]

Try to reverse the question, 'how can infinity not exist' that is to say if it were possible to travel through space in a straight line (no curvature) what could bring infinity to an end?

 

If you travel across the surface of the Earth in a straight line, you will never reach an edge. Nevertheless, the surface of the Earth is not infinite. There are geometries that allow the universe to be finite despite being unbounded.

 

3000 years ago people were told (in the Book of Mary) that God created only seven of the many universes that exists (we are number 3),

 

I've never heard of this, and I can't seem to find what you're speaking of. What is it?

 

but we then quickly settled for one universe,

 

Lee Smolin (The Trouble With Physics) does mention that there is a minority in favour of an infinite number of real (i.e 3 dimensional) universes,

 

It seems these two sentences are contradictory, no?

 

but cannot explain how or why.

 

Science deals with making testable predictions. Another universe, by definition, can have no measurable effect on us. Thus it is untestable and outside the realm of science. There are, however, interpretations of physical theories that posit other universes, but they are just that: speculative interpretations, that can never be shown true or false. But it's not like nobody talks about them.

 

it is our insignificance in the big (i.e. infinite) picture that permits our existence: the universe is a mere pimple in infinity here today, gone tomorrow. Nothing is more natural.

 

Prove it.

[gustard33]

Well Does infinity exist in nature?

 

Of course it exists. The concept we have invented is finity.And to those who say prove it - prove infinity doesnt exist.

[clemzzz]

Infinity doesNOT exist in Nature , the whole concept of infinity is FUN but utterly preposterous .

There is no such thing as a perfect circle , Pi goes on for ever (thus it's wrong ) For the perfect circle you would need space to be infinitely small. If pi did , actually come to an end after a finite number of decimal places ,then you'd probably solve so many questions in physics , but it doesn't. If it is truly infinite imagine the decimal digit getting stuck on an infinite number of sixes or an infinite combination of 123456789123456789 etc. etc. ( that doesn't truly make infinity preposterous but lets move on )

Forget the maths , lets imagine the famous chimp and type writer concept

So....you sit your chimp infront of a typewriter and give it infinite time (and paper/ink!) to type "random" characters , the idea goes that it will eventually type the complete works of shakespear . But surely ,every book ever written , and surely every book everwritten in every language possible with the typewriters character set. It starts to get crazy! How about every book ever written in every language ever written with just one typo and then every possible typo possible and so on. BUT here's why Infinity breaks down , what IF the chimp gets into a sequence of typing the complete works of shakespeare over and over and over in sequence , and simplified , what if the chimp just hits an infinite sequence of "a"s If this happens ( and it WILL ) then there's no chance and I mean absolutely no possibility what so ever of completing the infinite sequence of the complete works of shakespeare etc. IT fails in so many more ways.

 

And my Point:

If the infinity sign appears in an equation that is trying to define a natural process ,then it's wrong , it IS by definition , ludicrous.

GR is very very good , BUT it does not explain a black hole correctly

I hope in my lifetime , this problem is solved.

[ajb]

I guess that one should also point out that we do have divergent quantities for second order phase changes. A good example is the ferromagnetic transition, here the heat capacity diverges to infinity.

 

My understanding is generally if infinities occur then either we need "new physics" or a phase transition has occurred.

[AlphaSheeppig]

I may be wrong but I'm fairly certain that when an object moves faster than the speed of sound, the sound waves in front of the object are infinitely dense, so infinity does exist in nature.

 

Actually, in practice, the sound waves are distributed over a distance of around 10 μm... It is not a instantaneous change. The density is extremely large, but not infinite.

 

 

I guess that one should also point out that we do have divergent quantities for second order phase changes. A good example is the ferromagnetic transition, here the heat capacity diverges to infinity.

 

This is not a field that I know much about, but in most cases like this, some other principle that was negligible in the original theory becomes significant. Quantities often diverge, but in every case I've seen, there's some other principle that comes into play to stop it reaching infinity...

[HiggsBoson]

If anything can be divided infinitely, then infinity can exist.

[In2thedeth]

Well how about things like the Phi Cycle or Phi Vortex (Golden Ratio)? Fractals and such show the idea that this is a continuation both ways infinitely. These seem to show in many ways that infinity could and most likely does exist in nature.