Science & Mathematics Infinity

[Mean Muggin]

This discussion always has and always will make me very confused and angry!
Just to bring this back down to stupid-person level (ie me) - Woah!!! This thread really hurts my brain! If I could know one thing before I die, it would be whether or not the universe if finite or infinite.

I think that it is a concept which will never be solved, as neither answer is logical or makes any sense (not to me anyway!); The universe either goes on forever - impossible, or it ends somewhere - impossible.

If anyone on here reads my post and finds that it is extremely stupid an ill-informed, feel free to explain your concept/s to me (in a dumbed-down way!). Or you could get angry and reply with some sort of moderately abusive post, in which case I will not return after that


Anyway, sorry about that, continue on

Same here. If I was smart enough I would be doing astro physics, but I'll have to be content with being an accountant.

Can some one verify for us laymans that the law of relativity is based on what ever the subject is compared against? That's my understanding. So why is it such a spanner in the works in the whole finite / infinite debate?

Also, is Stephen Hawkings book written in a way so the layman can understand it?

 

[Moonwatcher]

'A Brief History of Time' is reasonable for the layman. Reading it whilst at highschool on occasions I had to just accept that he knew what he was talking about and move on. If you decide to read it I suggest if you don't understand a concept just keep pushing on and it will become clearer to you.

This thread has been a good read.

 

[Moonwatcher]

Conceded. I use 'Order' in the classical sense, more as the counterpoint to disorder (or entropy).

Science writers all the time relate entropy and disorder as the same thing. I did to when I began to read the thread. However I had a google of entropy vs evolution and found the main sticking point people had was this eroneous belief that disorder and entropy are the same thing. People see dna as an ordered structure for example and believe that this means the entropy is really low, but as Bomber has said the same ordered structure can increase its entropy( or that of it's immediate suroundings) without losing order. The second law of Thermodynamics is the law of increasing entropy not increasing disorder, as the dna strand illustrates.

 

[Mean Muggin]

http://goldennumber.net/universe.htm

New findings in 2003 reveal that the shape of the Universe is a Dodecahedron based on Phi
In October 2001, NASA began collecting data with the Wilkinson Microwave Anisotropy Probe (WMAP) on cosmic background radiation. Like visible light from distant stars and galaxies, cosmic background radiation allows scientists to peer into the past to the time when the universe was in its infancy. Density fluctuations in this radiation can also tell scientists much about the physical nature of space.

NASA released the first WMAP cosmic background radiation data in February of 2003. In October 2003, a team including French cosmologists and Jeffrey Weeks, a freelance mathematician and recipient of a MacArthur Fellowship or "genius award," used this data to develop a model for the shape of the universe.

The study analyzed a variety of different models for the universe, including finite vs. infinite, flat, negatively curved (saddle-shaped), positively curved (spherical) space and a torus (cylindric). The study revealed that the math adds up if the universe is finite and shaped like a dodecahedron

What's the opinion on this?

 

[Moonwatcher]

Quite amazing if true. I can't imagine the universe having vertices (corners) and straight edges. All the forces that I can think of are central or say have some sort of smooth curve to them like Magnetic fields.

Edit : symmetry is the word I'm looking for. Although a dodecahedron has symmetry it does not look the same from all angles.

 

[Wally Carter]

http://goldennumber.net/universe.htm



What's the opinion on this?

That's a fairly old article.

I would wait for the outcomes from the WISE satellite.

http://www.scientificamerican.com/article.cfm?id=wise-infrared-satellite

 

[evo]

In my view, most people struggle with the concept of infinity and how it fits with the picture of the universe because they are primarily thinking in physical terms. They are using the wrong tool. Science instead of philosophy.

Moreover they haven't thought enough about the nature of existence and what we mean when we use that term/concept "to exist".

It's fairly hard to grasp but this dude explains it quite well IMO..

[YOUTUBE]-gBLXJsDnII[/YOUTUBE]





The problem is thinking the Big Bang was the 'begining'; it wasn't - it couldn't be. There can be no beginning or a time when no-thing existed. It is a logical impossibility.

Alan Watts putting it another way..

[YOUTUBE]dLrMVous0Ac[/YOUTUBE]

 

[mdc]

In my view, most people struggle with the concept of infinity and how it fits with the picture of the universe because they are primarily thinking in physical terms. They are using the wrong tool. Science instead of philosophy.

Infinity is perfectly well-defined in mathematics, particularly post-Cantor. Badiou has it the right way round in using the mathematical definitions of infinity to inform philosophical thought.

Moreover they haven't thought enough about the nature of existence and what we mean when we use that term/concept "to exist".

One needs to tread very carefully in using logic to explain physics. Or best not tread at all.

Logic assumes a deterministic world view, which is plainly false.

 

[evo]

Infinity is perfectly well-defined in mathematics, particularly post-Cantor

That's true. But I don't think Mathematics is the right tool for this particular job.

Badiou has it the right way round in using the mathematical definitions of infinity to inform philosophical thought.


One needs to tread very carefully in using logic to explain physics. Or best not tread at all.

I'm not trying to explain physics. As I said in my opening sentence if you are thinking about 'the universe' in physical terms you are buggered from the outset (in my opinion)

Logic assumes a deterministic world view, which is plainly false.

Well I most fervently disagree.

Determinism is the one 'truism' in reality in my philosophical opinion. On what grounds is determinsim "plainly false", I'm genuinely interested. Are you going to argue from Satre?

 

[Wally Carter]

This thread has suddenly taken on the odor of Patchouli.

 

[BomberGal]

People see dna as an ordered structure for example and believe that this means the entropy is really high, but as Bomber has said the same ordered structure can reduce its entropy( or that of it's immediate suroundings) without loosing order.

Just in case you got confused, it's the other way around. (The formation of ordered structures can increase entropy, though of the whole system.)

Chemically, entropy = spontaneity (however fast or slow).

BTW, Malifice - I was just doing a quick read of something and it's worth pointing out something I missed earlier of yours - entropy cannot increase in an isolated system. Not the same as a closed system. I don't think it changes your point, it's just a technical thing.

 

[mdc]

Well I most fervently disagree.

Determinism is the one 'truism' in reality in my philosophical opinion. On what grounds is determinsim "plainly false", I'm genuinely interested. Are you going to argue from Satre?

I'm arguing simply on the basis of inherent physical uncertainties.

Take the two-slit experiment (here, if needed). If you attempt to observe an electron as its being shot out to tell me what it is (or what it's not), you change its properties. If you do not observe it, you can tell me nothing more than its properties in probabilistic terms. Uncertainty, on the quantum level, is a basic physical property. This isn't a failing on the part of our measuring devices, or our inability to account for certain variables. That uncertainty is inherent to the electron.

 

[Moonwatcher]

Just in case you got confused, it's the other way around. (The formation of ordered structures can increase entropy, though of the whole system.

Ah yes, I knew what I meant honest.

EDIT: In fact I'll change it now.

 

[sen entertainment bloke]

Everyone is pretty much on the wrong path.

 

[Moonwatcher]

I await enlightenment

 

[sen entertainment bloke]

I await enlightenment

You sort of have to work out how it all fits together for your self. Self enlightment is what you want.

Basically, though, infinity is an impossibilty. The same as zero is.

 

[evo]

I'm arguing simply on the basis of inherent physical uncertainties.

Take the two-slit experiment (here, if needed). If you attempt to observe an electron as its being shot out to tell me what it is (or what it's not), you change its properties. If you do not observe it, you can tell me nothing more than its properties in probabilistic terms. Uncertainty, on the quantum level, is a basic physical property. This isn't a failing on the part of our measuring devices, or our inability to account for certain variables. That uncertainty is inherent to the electron.

A few things about that:

1. I gather you are reasonably well read in ontology and epistemology. Do you not see a weakness in appealing to science to demonstrate determinism is "plainly false"? ie using empiricism to demonstrate non-causality, or acausality.

2. What does "Plainly false" even mean in a non-determinisitc world? And particularly in a world where the basic tennet of logic - the rule on non-contradiction isn't being applied.

3. On top of that most theoretical phycicist don't assert that QM has demonstrated that determinsim is false despite many and repeated claims in the media to the contrary. They (rightly) believe their role is to "shut up and calculate" and leave metaphysical arguments to philosophers.

4. "uncertain" does not mean the same thing as undetermined, or non-determined.

5. Even if they were asserting that, as BG rightly pointed out QM is still not a complete theory at least in regards toapplying it to the 'real world'..

Richard Feynman once said, "if you think you understand quantum mechanics, you don't understand quantum mechanics".

so one has to be very careful employing it to make absolute claims about reality.

 

[evo]

Basically, though, infinity is an impossibilty.

Perhaps in a mathematical sense it is but I don't agree with this in an ultimate see.The Totality, all that is, the All, utterly everything, or whatever else you would like to call it, is infinite by definition.

There is nothing other then "It".

That is why A=A is a very handy tool for thinking about reality.

 

[mdc]

1. I gather you are reasonably well read in ontology and epistemology. Do you not see a weakness in appealing to science to demonstrate determinism is "plainly false"? ie using empiricism to demonstrate non-causality, or acausality.

It's a little stroner than empricism. We can be quite rigorous mathematically, in describing Heisenberg uncertainty principle, for example.

So to answer your question, appealing to empiricism is dangerous, certainly. Appealing to mathematics, no.

2. What does "Plainly false" even mean in a non-determinisitc world? And particularly in a world where the basic tennet of logic - the rule on non-contradiction isn't being applied.

This isn't so, as long as you're willing to accept that things can be described probabilistically.

3. On top of that most theoretical phycicist don't assert that QM has demonstrated that determinsim is false despite many and repeated claims in the media to the contrary. They (rightly) believe their role is to "shut up and calculate" and leave metaphysical arguments to philosophers.

That's a disconnect I personally despise. That's not to say physicists have some sort of duty to wax philosophical, but rather that without minds that are willing to look at both, the potential of either is greatly limited.

Specialisation is one of the hidden cancers of modernity.

4. "uncertain" does not mean the same thing as undetermined, or non-determined.

In any good deterministic world, we should be able to play the following time machine game.

Go to t=0, record.
Go to t=1, observe.
Recreate t=0, predict t=1.

In our world, this fails.

5. Even if they were asserting that, as BG rightly pointed out QM is still not a complete theory at least in regards toapplying it to the 'real world'..

That's a rather vague statement. There are still open questions in physics which involve QM, of course, but the theory is sufficiently robust that one needn't worry that basic results like the uncertainty principle will suddenly be disproven.

Perhaps in a mathematical sense it is

The guy's spouting rubbish. It's perfectly well defined in a mathematical sense.

 

[evo]

Thanks for a considered reply.

It's a little stroner than empricism. We can be quite rigorous mathematically, in describing Heisenberg uncertainty principle, for example.

So to answer your question, appealing to empiricism is dangerous, certainly. Appealing to mathematics, no.

Mathematics relies on

1. logic
2. determinism. That is effectively what the equals sign means.

On the one hand, you are dismissing logic because it is obviously false due to it relying on determinism, while at the same same time appealing to mathematics as a good guide to reality. No wonder you like post modernism.

Mathematics is modelled upon deductive logic. If X is true and Y is true then Z follows... 1+ 2 = 3... determinism writ large.

This isn't so, as long as you're willing to accept that things can be described probabilistically.

Again, what does 'false' mean in a probabilistic world?

That's a disconnect I personally despise. That's not to say physicists have some sort of duty to wax philosophical, but rather that without minds that are willing to look at both, the potential of either is greatly limited.

Specialisation is one of the hidden cancers of modernity.

*shrugs* It is (good) theoretical physicists who declare it. I happen to agree.

The problem is not really the physicist themselves BTW, it is the laymen who (mis)interpret what they are saying ; and worse , guys like Deepak Chopra who think it gives them carte blanche license to make any sort of ludicrous claim about reality.

In any good deterministic world, we should be able to play the following time machine game.

Go to t=0, record.
Go to t=1, observe.
Recreate t=0, predict t=1.

In our world, this fails.

1. This is too narrow a definition of determinism.
2. In our world it doesn't 'fail'. We don't know all the inputs, ie it is uncertain. The electrons state is indeterminant rather than undetermined.
3. Determinism's only real claim is that everything is caused; that there are no acausal events. Even in this "probabilistic world" it still requires an observer, right? An observer is a cause.

That's a rather vague statement. There are still open questions in physics which involve QM, of course, but the theory is sufficiently robust that one needn't worry that basic results like the uncertainty principle will suddenly be disproven.

1. Why is physics "true" of reality?
2. the principle itself is not the problem. It is the misapplication of what is saying when mapped upon the 'real world' is what can be the problem.

The guy's spouting rubbish. It's perfectly well defined in a mathematical sense.

For the 3rd time, I'm fine with it in a mathematical sense I'm interested in the metaphysical sense, though -I know the OP asked it as a science/maths question - I'm just adding my 2 cents to this question from a philosophical one.

Maths is useless unless we know how to apply it to reality, or able to put it in perspective.

 

[sen entertainment bloke]

Perhaps in a mathematical sense it is but I don't agree with this in an ultimate see.The Totality, all that is, the All, utterly everything, or whatever else you would like to call it, is infinite by definition.

There is nothing other then "It".

That is why A=A is a very handy tool for thinking about reality.

Just not to sure which wire you have crossed. Probably trapped yourself with loose defining.

If everything is accounted for (your All) for, everything is not infinite. It is finite. Infinity is impossible.

If you want to go a little deeper, infinity is evolving.

 

[mdc]

Mathematics is modelled upon deductive logic. If X is true and Y is true then Z follows... 1+ 2 = 3... determinism writ large.

Let me reverse this.

I.e. to say, take the integer 3. Now I ask you, "3 is the sum of which two integers?". There are, of course, infinitely many pairs that are correct. If we attach the question to a temporal frame, and ask someone to announce to us at t=1 a pair whose sum is 3, this is something akin to the probabilistic model.

I.e. if X is the set satisfying my question, then;
at t=0 X = {a,b | a+b=3}, for all a,b in the integers.
at t=1 X = some specific pair of integers.

Only keeping in mind that the "announcer" will pick a truly random pair.

Again, what does 'false' mean in a probabilistic world?

Should be clear from the above.

The problem is not really the physicist themselves BTW, it is the laymen who (mis)interpret what they are saying ; and worse , guys like Deepak Chopra who think it gives them carte blanche license to make any sort of ludicrous claim about reality.

Fair enough. And you are right that most physicists are quite happy to be worker bees. I have a major in theoretical physics from UoM, and in all the classes I took, the only prof to express an interest in "what it all means" was a guest lecturer visiting from the Netherlands, iirc.

1. This is too narrow a definition of determinism.
2. In our world it doesn't 'fail'. We don't know all the inputs, ie it is uncertain. The electrons state is indeterminant rather than undetermined.
3. Determinism's only real claim is that everything is caused; that there are no acausal events. Even in this "probabilistic world" it still requires an observer, right? An observer is a cause.

1. What is your wider definition?
2. Not only is it undetermined, it is undeterminable.
3. That would answer 1, I guess. If that's your definition, then we don't disagree on much of anything. I am down with causility. I am not down with re-traceable or pre-determined causility.

1. Why is physics "true" of reality?

I think you'd agree this is far too big a question for BF to-and-fro. Let's leave it.

Maths is useless unless we know how to apply it to reality, or able to put it in perspective.

I repeat my fervent recommendation to read Badiou's take on it all.

 

[evo]

Let me reverse this.

I.e. to say, take the integer 3. Now I ask you, "3 is the sum of which two integers?". There are, of course, infinitely many pairs that are correct. If we attach the question to a temporal frame, and ask someone to announce to us at t=1 a pair whose sum is 3, this is something akin to the probabilistic model.

I.e. if X is the set satisfying my question, then;
at t=0 X = {a,b | a+b=3}, for all a,b in the integers.
at t=1 X = some specific pair of integers.

Only keeping in mind that the "announcer" will pick a truly random pair.

The probabilistic model is a logical proofing. Can you still not see the irony of employing logic to demonstrate that logic is false?

That is why I asked you in the opening missive if you were going to argue from Satre, or some other existentialist or phenomenologist. That would at least make sense.

3. That would answer 1, I guess.

Yes 3 is really explaining what i meant by one

If that's your definition, then we don't disagree on much of anything. I am down with causility.

I suspect you are not totally down with it, however.

I am not down with re-traceable or pre-determined causility.

If causallity is not pre-determined would you care to speculate what this "uncaused cause" is that is affecting reality? Does God really play dice? Can shit just happen?

"retraceability" is meaningless to me, anyway- the only thing that ever meaningfully exists is "now". The cat of Schroedinger fame is either alive or it isn't.

I think you'd agree this is far too big a question for BF to-and-fro. Let's leave it.

Yes, fair enough.

I repeat my fervent recommendation to read Badiou's take on it all.

hmmm , well I think he may be half right here.....

Badiou's philosophy draws two major implications from this prohibition. Firstly, it secures the inexistence of the 'one': there cannot be a grand overarching set, and thus it is fallacious to conceive of a grand cosmos, a whole Nature, or a Being of God. Badiou is therefore — against Cantor, from whom he draws heavily — staunchly atheist.

The whole Nature/ being of God/ "All" at the same time exists and doesn't exist. It is at the same time finite and infinite (to adress SEB's objection)

 

[Mean Muggin]

Just not to sure which wire you have crossed. Probably trapped yourself with loose defining.

If everything is accounted for (your All) for, everything is not infinite. It is finite. Infinity is impossible.

If you want to go a little deeper, infinity is evolving.

So you can account for everything in the universe? Finity is impossible, aswell as infinity. Hence this whole debate, which whilst very entertaining, is basically pointless as none of us will ever know the truth...whilst we are alive anyway.

 

[mdc]

Can you still not see the irony of employing logic to demonstrate that logic is false?

My statement was that it's best not to use logic to draw physical conclusions. That's a fair hike away from "logic is false".

so in your view "shit can just happen"?

Again, no. I believe in causality. I do not believe the linear, romanticist causality otherwise known as determinism.

According to wiki the term is "probablistic causation". The first line of the article is precisely what I was talking about earlier in terms of the game that we cannot play at the quantum level that is required for determinism:

Interpreting causation as a deterministic relation means that if A causes B, then A must always be followed by B

None of the above even remotely suggests that B "can just happen".