Is a mathematical zero impossible?

[O'Nero Samuel]

I'm not a mathematician, I'm a very close cousin, a physicist. I've been comparing the idea of a zero from the mathematicians' point of view and the physicists' point of view and find both somewhat incompatible. Maybe the term incompatible seem a little extreme, so allow me to use the term inconsistent. Here goes my argument;

Mathematically,

if you subtract 2 from 2 what would be left is nothing. This nothingness is what mathematicians call a zero.

Physically,

If you take away everything, from the largest of galaxies to the smallest of particles, eg gluons, photons, bosons, etc, what would be left? The philosopher would say nothing. The mathematician would say nothing implying a zero. But the physicist would say space. Now space is not really nothing, it is something. It has its intrinsic characteristics. It can bend, it can warp and can do a lot of thing that nothing can not do mathematically.

Now if mathematical nothingness and physical nothingness are inconsistent, where and how can we find symmetry? To cut a long story short, my conclusion is this;

A MATHEMATICALLY ABSOLUTE ZERO (NOTHINGNESS) IS IMPOSSIBLE.

Now please mind my use of words: "mathematically absolute" means a zero that is a zero in every transform. I wonder if this fact has been proven mathematically, or if this is just my hypothesis. Now, please don't be mistaken. I'm not talking about Curt Gödel's Incompleteness theorem: that is a totally different issue. If this hypothesis has been proven I'd be glad to get a reference to this proof - it would help save me a lot of time I'd spend to prove it mathematically and finish the physics I'm working on. I'd really appreciate the Ockham's riffle. But if there is not, then I guess the race can begin.

Finally, and most importantly, maybe I might just be talking nonsense, eh? Please do let me know. And tell me also what is wrong with this type of thinking.

[pears]

If you take away everything then you have to include space in that surely? Everything minus everything equals Nothing.

[mathematic]

Mathematics and physics are two different subjects.

Zero is a simple mathematical concept.

"Nothing" as a physical concept needs to be defined precisely. As the argument shows, it is not easy. It has nothing to do with the mathematical term "zero".

[studiot]

Actually. O'Nero your thoughts are not far from the truth.

 

There are in fact several key ideas or words that differ in mathematics and physics.

 

Are you familiar with set theory and the construction of the real numbers from elementary sets?

 

Informally mathematicians distinguish two versions of 'nothing'. Null and Zero.

 

Consider sets of numbers.

 

There is a set that has one member, a set that has two members, as set that has three members and so on.

 

That is {a} ; (a,b}; {a,b,c} and so on.

 

The letters a, b, c etc can stand for any number so b could be the number that solves the equation 2+2=b (ie 4)

 

a could be the number that solves the equation x + a = x for all numbers, x.

That is another name for zero. It must be a valid number since it solves an equation.

 

So the set {0} is a set that contains just one number zero.

 

But in additions to the sets above there is another set of numbers that has no members whasoever.

 

This is called the empty set or the null set {} and is different from {0}.

 

Does this help?

[harshgoel1975]

Question of "A MATHEMATICALLY ABSOLUTE ZERO (NOTHINGNESS)" is as big as question of origin of universe, as the definition given by Samuel , it seems not yet answered rather not possible or possible.

 

I tried to give the definition and origin of Zero and the physical significance in terms of philosophy

 

http://www.scribd.com/doc/173858063/Physical-Significance-of-Zero

 

May be it help to fuel your thoughts further,

Further on this topic, I would like to add that absolute zero is not possible for may other aspects as well, refer the below hypothesis which outline the concept.

 

http://www.scribd.com/doc/71594194/Harsh-s-Hyper-Thesis-of-Universe

 

Universe is infinite and there is no absolute zero.

[Thorham]

If I have five bucks, and I spend all of them, how many do I have left? Right, zero.

 

Really, how hard was that?

Edited August 2, 2014 by Thorham

[harshgoel1975]

If I have five bucks, and I spend all of them, how many do I have left? Right, zero.

Really, how hard was that?

 

I think this example is relative zero and not absolute...

Edited August 2, 2014 by harshgoel1975

[Thorham]

I think this example is relative zero and not absolute...

Relative to what? If you have three apples, and you give them away, you're left with exactly zero apples. Nothing relative about it, otherwise you would still have some amount of apples left relative to something, which is nonsense.

[harshgoel1975]

Relative to what? If you have three apples, and you give them away, you're left with exactly zero apples. Nothing relative about it, otherwise you would still have some amount of apples left relative to something, which is nonsense.

Agree, as the question here is "A MATHEMATICALLY ABSOLUTE ZERO (NOTHINGNESS) IS IMPOSSIBLE." so apple just change hand , what about ABSOLUTE ZERO, not with me not with anyone...

[O'Nero Samuel]

Relative to the fact that you have the ability to get more apples ( that would be a plus). This apple scenario sucks! I think Harshgoel1975 puts it all in a nut shell; that is an example of a relative zero. Now let me put this relative zero in a different perspective. For example we have four observers, A, B, C and D. A and B are moving at a speed of, say, Xm/s relative to observer C, whom we can assume to be stationary. The relative speed between A and B is zero. Although moving independently, the seem to each other not to be moving (in their frame, their relative speed to each other is a zero)relative to each other. But relative to to observer C, they are moving: and observer C measures a speed Xm/s for the same observation. In other words, a relative speed that was zero in A and B's frame is not zero in C's frame. To make the scenario more interesting, lets assume another observer D is moving with a speed of (X+dx)m/s. D gives an entirely different observation. Giving this example, can one assume that a zero is relative to the observer, and probably his methods of making these observations? If that is true, does this not now confirm my initial hypothesis?

Actually. O'Nero your thoughts are not far from the truth.

 

There are in fact several key ideas or words that differ in mathematics and physics.

 

Are you familiar with set theory and the construction of the real numbers from elementary sets?

 

Informally mathematicians distinguish two versions of 'nothing'. Null and Zero.

 

Consider sets of numbers.

 

There is a set that has one member, a set that has two members, as set that has three members and so on.

 

That is {a} ; (a,b}; {a,b,c} and so on.

 

The letters a, b, c etc can stand for any number so b could be the number that solves the equation 2+2=b (ie 4)

 

a could be the number that solves the equation x + a = x for all numbers, x.

That is another name for zero. It must be a valid number since it solves an equation.

 

So the set {0} is a set that contains just one number zero.

 

But in additions to the sets above there is another set of numbers that has no members whasoever.

 

This is called the empty set or the null set {} and is different from {0}.

 

Does this help?

There are several key ideas that differ in meaning between mathematics and physics? Now that, my friend I seem to find hard to swallow. Now i have a question:

DOES EVERY FORM OF MATHEMATICS DESCRIBE A PHYSICAL PHENOMENON, OR SOME JUST DESCRIBE ABSTRACT LOGICAL IDEAS THAT ARE NOT RELATED TO THE PHYSICAL DOMAINS OF LOGIC?

Now be very careful with the answer to the above question; for though it may seem relativistically simple to answer, its implications are quite far reaching. To give you a clue to what i mean, lets take the possibilities of the answer being "yes, all mathematics describes a physical phenomenon". Then this would be a direct contradiction your elegant conclusion that there are several key ideas that differs in mathematics and physics; for physics tries to describe all of the physical observable universe using mathematics as a tool for elegance and simplicity, so there should be an absolute symmetry between these two studies. Good thing is that it is this absolute symmetry that we have being enjoying as physicist in finding out everything we know so far about the universe. Without the appropriate mathematics, the physics cannot be described. That was why Einstein himself got stocked on his bid for the TOE: his conclusion, if I'm to paraphrase, was "...The derivation, from the equations, of conclusions which can be confronted with experience will require painstaking efforts and probably new mathematical methods.

Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved."

On the other hand, if your answer is "No, mathematics does not describe all physical phenomenon but sometimes some logical ideas that are not directly related to the physical domain of logic." Then my question for you would be what domain of logic does these mathematics describe. For every mathematician would agree with me that the beauty and elegance of mathematics, which every mathematician prides their life and reputation on, is the ability to describe a phenomenon with simplicity and eloquence. Then if an abstract mathematics is not describing the physical domain, then what is it describing?

 

Coming back to your description of a zero using the set theory, I think that was simple enough. The set theory describes multiplets and not necessarily the intrinsic manipulation of the elements of these multiplet. So the zero in the set could represent anything. For example, i can have a set such as;

A={a, b, 4, 3e, boy, &, apple, 0}

Now this set is a valid set. The above set means that somehow, from the point of view of the compiler, there seem to be something related with the elements of these sets. we cannot work with most of the elements of that set as a mathematical quantity. Now back to my initial argument.

 

I'm not talking about the zero in the form of a non interactive zero you just described.

Agree, as the question here is "A MATHEMATICALLY ABSOLUTE ZERO (NOTHINGNESS) IS IMPOSSIBLE." so apple just change hand , what about ABSOLUTE ZERO, not with me not with anyone...

Thanks with that statement! The apple didn't go into a zero, the apple just change hands. From your frame of reference, the apple is a zero, but from the person who collected the apple, there is the apple. The same apple. The zero of the apple is impossible.

[ajb]

Now i have a question:

DOES EVERY FORM OF MATHEMATICS DESCRIBE A PHYSICAL PHENOMENON, OR SOME JUST DESCRIBE ABSTRACT LOGICAL IDEAS THAT ARE NOT RELATED TO THE PHYSICAL DOMAINS OF LOGIC?

It is a question that has been asked before and so people have thought about this.

 

It seems to me that just about every known branch of mathematics can be used in physics somewhere, but this does not mean that every theorem or construction has been applied to physics.

 

However, other have suggeted a lot more than this. There is the mathematical universe hypothesis of Tegmark. It states that "Our external physical reality is a mathematical structure". According to Tegmark all mathematical structure are physically realised.

[studiot]

 

O'Nero

 

Coming back to your description of a zero using the set theory, I think that was simple enough. The set theory describes multiplets and not necessarily the intrinsic manipulation of the elements of these multiplet. So the zero in the set could represent anything. For example, i can have a set such as;

A={a, b, 4, 3e, boy, &, apple, 0}

Now this set is a valid set. The above set means that somehow, from the point of view of the compiler, there seem to be something related with the elements of these sets. we cannot work with most of the elements of that set as a mathematical quantity. Now back to my initial argument.

 

I'm not talking about the zero in the form of a non interactive zero you just described.

 

 

"For example, i can have a set such as; A={a, b, 4, 3e, boy, &, apple, 0}"

 

That much is true, but the rest is nonsense. The set you describe has negligable significance in Mathematics or Physics.

 

 

O'Nero

 

There are several key ideas that differ in meaning between mathematics and physics? Now that, my friend I seem to find hard to swallow.

 

Your mind appears closed to the offerings of others.

 

The word vector has at least four different meanings in Maths, Physics, Computing Science, and Biological Science.

 

Studiot

 

Are you familiar with set theory and the construction of the real numbers from elementary sets?

 

 

I offered you the beginnings of an informal discussion and asked a polite question to find out if it could be tightened up and made more formal.

 

You did not deign to answer.

 

How does this lead to fruitful discussion?

[O'Nero Samuel]

It is a question that has been asked before and so people have thought about this.

 

It seems to me that just about every known branch of mathematics can be used in physics somewhere, but this does not mean that every theorem or construction has been applied to physics.

 

However, other have suggeted a lot more than this. There is the mathematical universe hypothesis of Tegmark. It states that "Our external physical reality is a mathematical structure". According to Tegmark all mathematical structure are physically realised.

Thanks! That was a direct answer, it was really helpful. I'd look into the mathematical universe hypothesis of Tegmark.

 

"For example, i can have a set such as; A={a, b, 4, 3e, boy, &, apple, 0}"

 

That much is true, but the rest is nonsense. The set you describe has negligable significance in Mathematics or Physics.

 

 

Your mind appears closed to the offerings of others.

 

The word vector has at least four different meanings in Maths, Physics, Computing Science, and Biological Science.

 

 

I offered you the beginnings of an informal discussion and asked a polite question to find out if it could be tightened up and made more formal.

 

You did not deign to answer.

 

How does this lead to fruitful discussion?

This is a forum where possibilities should be discussed and correlated with currently established theories, and you have your way of sounding condescending. I understand the fact that some words in mathematics have different meanings when used in other fields of studies, physics one of them. I'm not talking about the names used to tag these ideas, I mean their apparent significance and ways of applications. Thanks though, i'd look into the question you asked.

I value the opinion of everyone in this forum, it has helped me in developing so many aspects of my theories, that is why i look forward to having more insigful opinion, and more so, criticism: i need them; but not condescension.

Edited August 2, 2014 by O'Nero Samuel

[studiot]

I was the only poster to acknowledge that you might have a point, even if not totally correct in formal mathematics.

It's not condescension.

 

It's the rules of this forum.

 

You have posted in maths, where we speculation and theories are not allowed.

There is another section for that called speculations, where the rules are more relaxed.

 

Further I asked a question and have since explained why I asked it. Again the rules are quite specific about promoters answering such questions.

 

The whole point of my question is to be able to offer a more detailed answer, because my brief, informal, comment on set theory contains the essence of the mathematical reason why your statement (why shouted in red - this is annoying to many, including myself)

 

 

A MATHEMATICALLY ABSOLUTE ZERO (NOTHINGNESS) IS IMPOSSIBLE.

 

is wrong.

 

The reason is simple, there are two mathematical versions of 'nothing', one of which corresponds to your statement above.

 

I had thought that you would be interested in discussing that further.

[Thorham]

Relative to the fact that you have the ability to get more apples ( that would be a plus)

That just means that the number of objects you can own is variable.

 

The apple didn't go into a zero, the apple just change hands. From your frame of reference, the apple is a zero, but from the person who collected the apple, there is the apple. The same apple. The zero of the apple is impossible.

It's about the number of apples that you own, not about there being zero apples. Numbers can be used to indicate quantities, and for some things, these numbers can be zero, such as the number of euros in your wallet, or the number of times you've climbed Mount Everest.

[O'Nero Samuel]

I was the only poster to acknowledge that you might have a point, even if not totally correct in formal mathematics.

It's not condescension.

 

It's the rules of this forum.

 

You have posted in maths, where we speculation and theories are not allowed.

There is another section for that called speculations, where the rules are more relaxed.

 

Further I asked a question and have since explained why I asked it. Again the rules are quite specific about promoters answering such questions.

 

The whole point of my question is to be able to offer a more detailed answer, because my brief, informal, comment on set theory contains the essence of the mathematical reason why your statement (why shouted in red - this is annoying to many, including myself)

 

 

is wrong.

 

The reason is simple, there are two mathematical versions of 'nothing', one of which corresponds to your statement above.

 

I had thought that you would be interested in discussing that further.

My apologies then, if I misunderstood your stand. You think my point is not totally correct in formal mathematics? What do you mean by formal mathematics. I was reading Von Neumann's "Mathematician", and he tried to describe, in two or more paragraphs maybe, the ambiguity and disconnectedness of "formal mathematics" (to steal your phrase) from the empirical sciences. Here is one of his paragraphs;

"There is a quite peculiar duplicity in the nature of mathematics. One has to realize this duplicity, to accept it, and to assimilate it into one's thinking on the subject. This double face is the face of mathematics, and I do not believe that any simplified, unitarian view of the thing is possible, without sacrificing the essence."

Could it be this two-facedness of mathematics that makes you think I might not be totally correct?

If you could only neglect the bold, CAPITALIZED SHOUTING IN RED format of the statement, you would see that I'm not speculating: I'm asking a question about zeros: its mathematical and empirical implications. Maybe Neumann was right all along. Mathematicians has to sacrifice the empiricism science and nature to grab hold of rigorous logic. Its very sad indeed.

Going by Neumanns' argument, I think the two-faced ambiguous nature of mathematics makes the brief, informal comment on set theory too blurry to grab empirically. I'd appreciate if you could elaborate.What are the two mathematical interpretations of a zero? Could you give a link or recommend a text that would help be see things in your point of view? And sure, I'd like to discuss the part of the zero that corresponds to my questions. I'd be exhilarated!

That just means that the number of objects you can own is variable.

 

 

It's about the number of apples that you own, not about there being zero apples. Numbers can be used to indicate quantities, and for some things, these numbers can be zero, such as the number of euros in your wallet, or the number of times you've climbed Mount Everest.

The zero you have been describing is one of the, so to speak, types of zero there is according to Studiot. I'm talking about an absolute zero. I wish I had better words with which to express myself. I blame this on mathematics though!

[ajb]

What are the two mathematical interpretations of a zero?

Zero can be rather abstractly understood in terms of ring theory. Loosley a ring is a set for which we have addition and multiplication with some natural conditions. In particular we have zero as the additive identity, that is a +0 = 0+a = 0 for all a in the ring. That is zero is the identity element of an abelian group where we write the multiplication as a +.

 

From the properties of the ring you can show that 0.a = a.0 =0. Here . is the binary operation of a monoid.

 

These are the two algebraic interpretations of a zero that I am aware of. There are other ways of understanding a zero in different contexts. I think the ring theory is the closest to what you need as the integers form a ring. A field is a commutative ring whose non-zero elements form an abelian group under multiplication. That is you have an inverse element for multiplication for all elements of the ring apart from zero. For example, the real numbers form a field.

 

In the contect of ring theory zero has a very specific meaning. In other contexts it may be not so clear, but zero is usually understood as the identity element of an abelian group (or maybe commutative monoid).

 

I'm talking about an absolute zero. I wish I had better words with which to express myself. I blame this on mathematics though!

Do we have a very clear mathematical notion of an absolute zero? It is not a term I have come across in this context.

 

Unless you are thinking of something more like a torsor for an addiive group? I.e. we don't fix the idenity. Loosley, "a torsor is a group that has forgtten its identity".

Edited August 4, 2014 by ajb

[studiot]

 

ajb

O'Nero Samuel, on 04 Aug 2014 - 3:02 PM, said:

What are the two mathematical interpretations of a zero?

 

ajb

Zero can be rather abstractly understood in terms of ring theory. Loosley a ring is a set for which we have addition and multiplication with some natural conditions. In particular we have zero as the additive identity, that is a +0 = 0+a = 0 for all a in the ring. That is zero is the identity element of an abelian group where we write the multiplication as a +.

 

From the properties of the ring you can show that 0.a = a.0 =0. Here . is the binary operation of a monoid.

 

These are the two algebraic interpretations of a zero that I am aware of.

 

The zero ajb describes above is a valid member of the set and is not, I think , the meaning that O'Nero ascribes by the use of the word 'nothingness' (post#5).

 

I think he is referring, not to a member of any set, but to the set which has no members ie the empty set.

[O'Nero Samuel]

Zero can be rather abstractly understood in terms of ring theory. Loosley a ring is a set for which we have addition and multiplication with some natural conditions. In particular we have zero as the additive identity, that is a +0 = 0+a = 0 for all a in the ring. That is zero is the identity element of an abelian group where we write the multiplication as a +.

 

From the properties of the ring you can show that 0.a = a.0 =0. Here . is the binary operation of a monoid.

 

These are the two algebraic interpretations of a zero that I am aware of. There are other ways of understanding a zero in different contexts. I think the ring theory is the closest to what you need as the integers form a ring. A field is a commutative ring whose non-zero elements form an abelian group under multiplication. That is you have an inverse element for multiplication for all elements of the ring apart from zero. For example, the real numbers form a field.

 

In the contect of ring theory zero has a very specific meaning. In other contexts it may be not so clear, but zero is usually understood as the identity element of an abelian group (or maybe commutative monoid).

 

 

Do we have a very clear mathematical notion of an absolute zero? It is not a term I have come across in this context.

 

Unless you are thinking of something more like a torsor for an addiive group? I.e. we don't fix the idenity. Loosley, "a torsor is a group that has forgtten its identity".

Thanks a lot. This is why I value this forum: when one thinks in isolation, he stands the chance to tend to lean more towards subjectivity when drawing conclusions from the empirical science. I think I'm beginning to understand the mathematical description of a zero. But, just not to be mistaken, would I be correct to say that the mathematical description of a zero is relative to the point of view from which the user (observer, maybe) makes his interpolations? And according to studiot, would i also be on track to say that a mathematical zero can either be an active element of a set, or an entirely null set? If so, then when the mathematicians use the word "zero" they are not talking about absolute nothingness described by philosophers using the word?

 

The zero ajb describes above is a valid member of the set and is not, I think , the meaning that O'Nero ascribes by the use of the word 'nothingness' (post#5).

 

I think he is referring, not to a member of any set, but to the set which has no members ie the empty set.

Going with these trend of thought, does it mean that every algebraic interpolations are done with respect to the group of the elements of the field in consideration? And, when two fields has elements that do not intersect the commutative interactions between the elements of these fields acts as a zeros when changing frame of reference?

And I think what I came looking for is in your last statement. From what i've gathered so far, numbers are interpolated with respect to the set they belong to, and a null set, allow me to use the phrase, "looks like" a zero. Is there any more information one can get out of a null set that is not relative to other sets that has element. And if I am to rephrase, is there anything mathematically described as a zero function?

[ajb]

would I be correct to say that the mathematical description of a zero is relative to the point of view from which the user (observer, maybe) makes his interpolations?

Everything in mathematics is like that, you need to define your terms carefully. This is why discussions of "zero" and "nothingness" tends to be rubbish.

 

And according to studiot, would i also be on track to say that a mathematical zero can either be an active element of a set, or an entirely null set?

You should make a distinction between nothing, that is the emply set, and the notion of zero, as the additive identity. This maybe the root of any confusion you have.

 

If so, then when the mathematicians use the word "zero" they are not talking about absolute nothingness described by philosophers using the word?

Right, they will make the distinction beteen zero and the emply set.

 

 

Going with these trend of thought, does it mean that every algebraic interpolations are done with respect to the group of the elements of the field in consideration?

You are using a lot of words here that have sepecific meaning in mathematics. I don't know what your question is.

 

 

And, when two fields has elements that do not intersect the commutative interactions between the elements of these fields acts as a zeros when changing frame of reference?

Again I do not understand. What has changing frame of reference go to do with the algebraic structure of fields? (Fields here in the algebraic use of the word)

 

And I think what I came looking for is in your last statement.

I gave you a very "hidden" definition of an affine space. This is almost a vector space but we have forgotten the origin. You can look a the difference of two vectors but not their sum. Mathematically the more general situation is that of a G-torsor for a group G.

 

From what i've gathered so far, numbers are interpolated with respect to the set they belong to, and a null set, allow me to use the phrase, "looks like" a zero. Is there any more information one can get out of a null set that is not relative to other sets that has element. And if I am to rephrase, is there anything mathematically described as a zero function?

The null set looks like zero in what respect? It looks like an identity with respect to union of sets?

 

The concept of the empty st is vital in axiomatic set theory. Maybe you can find some answers to you questions there.

 

A zero functon would be understood as a a function with output being constant and zero. You have to be careful with language here.

[O'Nero Samuel]

Everything in mathematics is like that, you need to define your terms carefully. This is why discussions of "zero" and "nothingness" tends to be rubbish.

 

 

You should make a distinction between nothing, that is the emply set, and the notion of zero, as the additive identity. This maybe the root of any confusion you have.

 

 

Right, they will make the distinction beteen zero and the emply set.

 

 

 

You are using a lot of words here that have sepecific meaning in mathematics. I don't know what your question is.

 

 

 

Again I do not understand. What has changing frame of reference go to do with the algebraic structure of fields? (Fields here in the algebraic use of the word)

 

 

I gave you a very "hidden" definition of an affine space. This is almost a vector space but we have forgotten the origin. You can look a the difference of two vectors but not their sum. Mathematically the more general situation is that of a G-torsor for a group G.

 

 

The null set looks like zero in what respect? It looks like an identity with respect to union of sets?

 

The concept of the empty st is vital in axiomatic set theory. Maybe you can find some answers to you questions there.

 

A zero functon would be understood as a a function with output being constant and zero. You have to be careful with language here.

Thanks for the references, I'm looking into them. I guess my use of mathematical term is obfuscating the ideas behind my questions. Now I'm getting a first hand experience of the conundrums facing the mathematician as described by Von Neumann in his "The mathematician".

[hoola]

it seems as though math theory allows self contained interaction between the constituents of math, while based upon the logic that underlies reality, and can describe objects, and being logical within the confines of math, do not always accurately portray every aspect of physical realities, although largely seem to. A question to me seems, what special things can math provide proof of that do not manifest in the real universe...? Infinites are sometimes needed in finite proofs, but that doesn't mean that infinities are real other than they exist as functional concepts within math itself. I don't think infinity exists outside the realm of the maths...Also the zero seems of similar property. In considerations of "zero", and the nature of the "why anything" question, how did things get started? If there was a void at the beginning, why should anything show up? I say because this void had a default minimum of information, of one "bit". That bit was manifest in the notion that there was a void....and one void only, not 2 or 27. So there was exactly "1 nothing". I refer to this 1 nothing as the virtual bit, or v-bit..I see the v-bit as the genesis model of informational modelling of the universe(s)...when everything is removed from space, then space itself is pulled out, a v-bit remains that cannot be reduced...so only can increase...(the one way arrow of time is an associated effect), and that single virtual bit increased into all this.....and is still increasing and explains the expansion.

Edited August 28, 2014 by hoola

[ajb]

A question to me seems, what special things can math provide proof of that do not manifest in the real universe...?

There are lots of results in mathematics for which it is not clear that there is any physical significance. For example we have the Poncare conjecturé which was proved by Grigori Perelman;

 

"Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere."

 

(Loosely, if it has all the properties of a 3-sphere then it is a 3-sphere)

 

I am not aware of any physics that uses this result. That is not to say that there is not any physics here, just that right now we don't see any physics.

[studiot]

I would like to add the note that the '3-sphere' ajb refers to is the hypersurface, not the hypersolid.

 

quote from wiki :

 

http://en.wikipedia.org/wiki/3-manifold

 

 

3-sphere[edit]

Main article: 3-sphere

A 3-sphere is a higher-dimensional analogue of a sphere. It consists of the set of points equidistant from a fixed central point in 4-dimensional Euclidean space. Just as an ordinary sphere (or 2-sphere) is a two-dimensional surface that forms the boundary of a ball in three dimensions, a 3-sphere is an object with three dimensions that forms the boundary of a ball in four dimensions.

 

Edited August 30, 2014 by studiot

[JonG]

There is another angle on the question of the number zero which I have found to be a bit arbitrary. It is stated in this Wikipedia article:

 

https://en.wikipedia.org/wiki/Empty_product

 

Quote:

The notion of an empty product is useful for the same reason that the number zero and the empty set are useful: while they seem to represent quite uninteresting notions, their existence allows for a much shorter mathematical presentation of many subjects.

 

This suggests that the idea of the number zero or the empty set can be convenient, or useful, but not necessarily meaningful. An example of an empty product is given as the factorial, 0! = 1.

 

Having noted that, the same article makes the statement:

 

Quote:

As another example, the fundamental theorem of arithmetic says that every positive integer can be written uniquely as a product of primes.

 

I'll leave it to others to find a flaw in that!

Edited October 11, 2014 by JonG