Science a GoGo's Home Page Forums General Discussion Not-Quite-Science Forum Is the Universe a mathematical construct?

Who says the age of miracles is passed.

I have not read this thread (it's a time thing) so this may be inappropriate.

I think it all comes down to what we mean by a mathematical construct.

If we mean that the Universe was designed on mathematical formulae, it is hard to see how that differs from religion (God bless it)

If we mean that mathematics is the best language we have found to describe our observations of the Universe, perhaps that makes good sense.

How is infinite time, or for that matter non-infinite time, a paradox? Time either is or isn't infinite. If it is infinite then it just means that there is no "start" to the universe. Within that time the universe AS WE KNOW IT would have had a start at the big bang, and will "end" when it fades out into entropy, assuming that we aren't living in a "big bounce" universe. But infinite time doesn't produce incompatible results. I have no idea whether time is infinite or not. Either way we don't understand just where the universe as we know it came from. There are some ideas, but none of them have been experimentally tested/verified. We're pretty sure there was a big bang, but we don't know if there was anything before that. Maybe before the big bang there was an infinitely long period of nothingness, just empty space. Looking into the future right now it appears that the universe will keep expanding essentially forever. But there isn't any paradox to that.

For an infinity with a start point, try the infinity of positive integers. They start with zero and go to infinity.

Bill Gill

Does this mean you subscribe to the view that infinity is just a big number?

Is there no distinction between "infinite" and "unbounded"?

Looks like I came back at just the right time!

That's an interesting concept, Bill.

I shall have to give the idea of infinite nothingness some more thought before commenting, but, surely, if the period before the BB was infinite, everything that could happen would have already happened, an infinite number of times, before the BB. These things would, of necessity, have included the BB; so there is a paradox.

No paradox. A big bang could have happened an infinite number of times before the one with which we are familiar. And after entropy washes our Big Bang out into the "nothingness" of the infinity of time again it can happen again and again. The in between times could just be filled with the quantum foam.

Notice that I am not saying that this does happen. I am saying that there is no particular paradox involved. It is just a fact that we don't understand the Big Bang and how the universe came about and/or where the it came from.

Bill Gill

But not a paradox if Brane theory (for example) happens to be correct.

Edit: Just saw your post (above), Bill G. Yes, that seems to be consistent with both L. Krauss' explanation of a universe from 'nothing' and with current observations re expansion of space.

Possibly this is correct if you are talking of mathematical infinities, but even Cantor talked of an "absolute infinity". This is the sort of concept I am talking about. Mathematically (according to Cantor) this "overarching" infinity does not exist, yet he was unable to dispense with it entirely.

If a BB has happened an infinite number of times, there can be no more to happen. There can be only one "absolute" infinity, and that is outside the realm of mathematics.



You are coming back to these questions, I hope?

looking back at my last post, two things strike me.

1. "Absolute infinity" is tautologous, but I use it in deference to Cantor, and to stress that I am not referring to mathematical "infinities".

2. As I think that infinity is not a number, I use the term "an infinite number of times" reluctantly. How can we claim that something happens an infinite number of times and still maintain that we are discussing science, which exalts the concept of proof?

Re infinity, we are discussing matters beyond the scope of scientific proof, and are firmly in the realm of philosophy. We can agree on that, can we not? I do find your arguments re infinity quite mind-bending, Bill S. I wish I could understand the problem that you evidently see. As I see it, either the universe has always existed in some way, shape or form, or else it was brought into being by an ineffable cause which itself has always existed (with one foot outside the experience of time, rather like photons perhaps). Personally, beyond the semantics, I don't distinguish a difference between those hypotheses. It seems that you reject both notions because they're beyond scientific proof - which, of course, they are. On the other hand, what kind of proof could be presented to show that there was no existence of any kind before a given moment?

The above isn't intended as negative criticism. I don't have answers, just opinions. I'm all ears, as they say.

Bill, you are getting off into philosophy again. I'm not much of a philosopher, so I don't worry about things you seem to be worrying about. As far as I am concerned infinity basically means that there is no beginning and no end. Of course that kind of disagrees with my reference above to the infinity of positive integers starting at zero, but when it comes to philosophy I just can't get all excited about that sort of thing.

Now I do feel kind of uneasy about the idea that the universe has no beginning and no end. Intuitively I expect everything to have a beginning and an end. At the same time I have a problem with what there was before the universe came into being. However, that doesn't affect my daily life and all of physics still works just fine, so I don't expect to wake up in the morning and find out the universe has disappeared. Therefore I don't worry about it.

Bill Gill

I would like to agree, but scientists and mathematicians frequently talk of this or that being infinite, or happening an infinite number of times, or, even worse, saying that something can become infinite, or stop being infinite. This is fine, as long as they make it clear that what they are talking about is the mathematically infinite, for which, in my opinion, a less confusing term would be “unbounded”.

Absolutely none! In fact, I suspect that the nearest one can come to proof/falsification in this matter is the seemingly logical argument that there can never have been a time when there was nothing, or there would be nothing now. One trouble with that is that there are many who want to question the nature of nothing.

Worrying is not my thing, Bill. In particular there are three things I never worry about:
Money; because I don’t have any to worry about.
Maths; because I don’t know enough to know what is worth worrying about.
Infinity; because it wouldn’t make any difference.

It was that sort of disagreement that started me thinking about the feasibility of the infinite series. When I find something that makes no sense to me I tend to keep at it until it makes sense. When I then find people who think differently I want to test my ideas, but that tends to test their patience.

Here's a related opinion.
Neil Turok: "I think maths is a miracle"
http://www.youtube.com/watch?feature=player_detailpage&v=3pGv91iaz7g

Bill Gill, you say, I say,Bill, you sayIn my opinion, the same is true of G~0~D. This is why I use a zero, 0 (a symbol of a no thing) here. Also, it is why I use the O (a symbol that includes everything) here. G~O~D is the all encompassing. But I hope you don't mind if there are those of us who honour philosophy as the mother of science and art. What then is your philosophy of Life--of body, mind and spirit? It seems to me that individual lives do end. So do cycles of days, weeks, months days, and so on.IMO, there was NO thing, G~0~D IMO, you, me, and others will eventually leave the cosmos made up of "things".

Bill Gill

A few more verses from the G~0~D-Spell according to St. Lindsay.

Correct that is a black or white answer.



Now you state the problem because the above was black and white.




And so you realize and state that BB is not a start if time is infinite




How you come to that conclusion from your above statements has completely got me.

DOES AN INFINITE LINE HAVE A START .... ANSWER NO ... NOT EVER IT DOESN'T HAVE BY DEFINITION

A ray does

http://mathworld.wolfram.com/Ray.html

=> In geometry, a ray is usually taken as a half-infinite line (also known as a half-line) with one of the two points A and B taken to be at infinity.

Talking about time being infinite in both directions is beyond stupid because it can't be or the "entire universe" couldn't exist ... here we are distinguishing the universe meaning beyond our universe as in everything that ever was and ever will be.




And that is the same situation as a Ray it's half infinite there are numbers outside the range which is all the negatives, so claiming it that range is infinite is completely wrong.

And there is the point I am trying to get you to understand that you people play word games with infinity without holding a truly strict definition on it.

To science and to me half infinite does not equal infinite and we will never agree it does ..... it is blatantly wrong.


Put bluntly time has to be a half infinite (starting at t=0) or a segement (starting at a and ending at b) ... the idea it is truly infinite is a direct paradox and totally absurd not even GOD can work that one because then GOD must have a GOD.

The concept that time must start is itself interesting because it leads directly to a question can time exist without space and vice versa ... think about GR carefully.

Incorrect, despite the upper case. It is you who are, inadvertently perhaps, playing with words, Orac. The description of a ray as half-infinite is merely a means to differentiate it from a line that extends to infinity in both directions. Infinity that has a beginning is nonetheless infinity.



No Orac, it's you who are completely wrong. The ray is not finite, and neither are the number of positive integers.


Despite the red text, you and science are, once again, not in agreement. As I've told you, the so-called half-infinite ray is in fact infinite. Has it occurred to you that there's no such thing as half of infinity, regardless of the nomenclature of convenience used by geometricians?

Complete garbage you can write a mathematical proof it ... it is dead simple it was done in the 18th century.


Here let me do it in layman terms for you.


Your and Bill's infinity is zero to positive infinity ... so I give you one number -1 is that in your range .... answer NO.

Therefore your infinity in not infinity of all numbers because I can give you a number outside the set.

Cantor showed in 1891 that by that statement alone you don't have an infinite set

http://en.wikipedia.org/wiki/Cantor's_theorem


Your infinity is the positive infinity, a half infinity or even the infinity of positive real numbers BUT IT IS NOT INFINITY OF ALL NUMBERS ... blabber all you like it simply isn't any child can see it isn't and you can prove it.

To claim so is beyond stupid and science, mathematics and I are in complete agreement no matter what your ridiculous claim.

If you have a start point you can't have an absolute infinity of anything geometric, mathematics or in physics because something exists outside the set UNLESS you truncate it.

The only way you can make your stupid infinity conform to an absolute infinity is by truncating the set by another rule .... in your case by discarding or ruling out negative numbers.

Infinite time must by definition run from minus infinity to positive infinity seconds if you put a start in then there exists a time which must be before the start and time is therefore not infinite because a time exists outside the set. If you want to have that definition you have a positive infinite time but that is really interesting.

To show you how interesting it gets lets use you definition of infinity (0 ... positive infinity) the interesting question it poses and I want you to think on is what physics would cause that ... you just established an arrow of time with absolutely no basis for doing it ... your basis as best we can make out is you don't like negative numbers.

I bring this up because there is some interesting stuff being done on this at the moment ... I will expand the experiments if we can get over the word play garbage.

Okay so if we can get you past the word play around infinity lets look at what the problem is.

Here is an experiment done by Anton Zeilinger yet again (we hate him )

http://arxiv.org/abs/1203.4834

For those not technical here is the layman explaination

http://scienceblogs.com/principles/2012/05/04/entangled-in-the-past-experime/


Now I want redewenur and Bill to think carefully what would happen in a universe that was guaranteed to only run forward because it had to start at t=0 and move forward to positive infinity.

I’ve just read (most of) page 1 of this thread, it seems to be largely a philosophical discussion, with a bit of maths thrown in. I read things like:

and I think, after all our discussions, could it be that Orac and I are on the same page?

All this stuff about infinite series, half-infinities and infinite time may be valid mathematically, but in reality, it is hard to see how they can make any sense at all.

What does seem to make sense is that, by definition, something that has an end is not infinite. We may not be able to assign a beginning, but it has an end, so it is finite. (No word play there, right?)

Physics, we are told, works just as well if we assign forward or backward directionality to time. If this is the case, something that has a beginning must also be seen as having an end if time is reversed. Here I refer to Orac’s link:

http://scienceblogs.com/principles/2012/05/04/entangled-in-the-past-experime/

for anyone who might think that reversed time is not a scientific concept. (still no word play, right?)

Since this thread seems to have developed into something of a free-for-all in terms of personal opinions; here is a suggestion for which I have no more scientific proof than has been used to support many of the opinions in this thread.

The cosmos, i.e. everything that is, has been or ever will be, is infinite.

Infinity and time are not the same thing. Infinity is not a big number, nor an immeasurable expanse of time. We cannot define in terms of physical or temporal extent.

Because infinity does not involve either time or measurable space, there can be no change in infinity. Everything just “is”.
Our universe appears to have come into being at the BB, and time and space came into existence at the same spacetime event.

Our Universe remains within the cosmos, eternal and unchanging. Change is just something we think we experience because we are limited to 4+1 dimensions. Think of the spider in Flatland.

Space and time have no relevance outside our Universe. They are simply the means by which we are able to make sense of our world. Without the illusions of time and space the Universe would not be a suitable place for rational beings to evolve; we would not be here.

Not for one moment am I claiming that this how reality is. There is no way I could know that. All I am saying is that it dispenses with paradoxes and seems to hang together reasonably logically.