Sunday 9 September 2007

Infinity and The Singularity- Limits to Our Conceptualisation?

Regular readers will know that I have a theory on how the universe works in physical terms, parts of which have been the subject of posts here.

I'm not going to beat about the bush- parts of this post will get quite abstract, parts very theoretical, and parts will seem quite wild in the assertions I put forward.
However, I hope those of you who follow what I am saying see the logic of the proposition and all it's bizarre implications.

The problem relates to flaws in our understanding of the universe itself.

A while back, I came to the conclusion that the expansion of the universe could be explained in simple terms; it is the first and simplest way to acheive the ultimate aim of the universe, it's own demise.
By expanding, it creates space, it stretches out the gaps between the crest of waves, ultimately reducing all energy to zero point. Red Shift is the primordial dynamic of the universe in action- thinning out the energy.

In other words, at the start, the space is Zero, at the end the energy is Zero.

But here comes the problem. At the start, all the energy proceeds from the same place.
The same mathematical point- a singularity, a point in spacetime where all the laws of physics (except those of thermodynamics) break down.
Or do they?

You see, conventional physics has no option but to ascribe the wave function at this singularity an infinite value.
By implication, therefore, heat death can never come, it would take infinite time to reach heat death.

This cannot be true.

Here is the crux of the problem- in a finite universe, no real calculation can ever yield the result 'infinity'.

The problem is deeper than we realise.
Firstly, it cannot be true that the laws of physics 'break down' at a singularity.
It cannot be true that the universe will go on forever.

It is our laws of mathematics which have not accounted for a necessary limitation, which makes them incapable of explaining a number that has not been acknowledged.

Because mathematics tells us that there is only one number you can divide one by and reach zero.
That number is infinity.
Problem. Big Problem.

Because the universe shows us that there must be a REAL quantity, a REAL number, which IS the last of all numbers, beyond which, in our universe there ARE no more numbers.
Otherwise the laws of physics could not work. There are only a finite amount of quantities. One day, SOMETHING (The Universe) will be NOTHING.

Therefore, there is a real number which when one is divided by it, WILL yield zero as the answer.
The opposite of Nothing is not Infinity, it is Everything.
The Everything number.
It is so far beyond our conception, that for us, in our lives, it might as well be infinity, but it isn't.

In the same way, we know that in practical geometry two parallel lines never meet, but in the universe as a whole they not only can, they must.

We need to understand what mathematics is.
Its roots are purely empirical- we know from practical experience that 2+2=4
In fact the only numbers we can really visualise are the lower end of the scale, the rest we conceptualise by the concept of bases- 84 is 8x10+4.
84 is a real number. Such a quanitity can exist.
Not all numbers can.

Negative numbers, for example, are an accounting tool.
They exist on balance sheets, but if calculations involving real quantities yield them as answers, the answer is wrong.
There are never going to be -12 cans of beer in your fridge.

Pi is a ratio. It's not a real number, because it doesn't make sense. It is our way of expressing numerically a relationship- that between diameter and circumference, that can never be expressed in real terms, you couldn't make a genuinely perfect circle using real matter. The numbers just don't pan out.
The fact is we are trying to impose a human idea of a geometrical truth, when it doesn't entirely work.
The same is true of the square route of two.
We are just expecting too much to get a sensible answer.

The fact we try, and the fact we give expression to our attempt in a way we can link to the rest of the conceptual system we have designed for dealing with quantities, is a sign of our amazing ability to conceptualise.

But we shouldn't lose sight of empirical reality.

Infinity is an imaginary number. Imaginary numbers are numbers mathematicians use to explain concepts that defy expression.
For example, the square root of -9.
3 squared=9
-3 squared=9

So what therefore is the square root of -9?
Here come imaginary numbers.
Mostly, imaginary numbers serve simply to allow advanced mathematicians to explore the limits of our conceptualisation.
In no case can a REAL calculation, yield an answer that is an imaginary number.
Except when we come to look at our scale of numbers. Because our scale of numbers starts with real numbers, and ends in imaginary ones.
We know, deep down, this cannot be a true expresion of reality, it bothers us.
It has driven mathematicians mad.

Because up there in the higher reaches of quantities, is the ultimate quanitity.
When you multiply the total amount of variables existent in our universe, there will be a quantity beyond which no real calculation in the real universe will ever go.

The Omega number.
Now yes, this has scary consequences. Infinity squared= Infinity. We are comfortable with that.
But to accept that there exists a REAL quantity, which when multiplied by itself, yield itself, exactly like a mirror image of Zero, only it is EVERYTHING, is mindblowing.

Because long before we reach that number, the ways quantities compute, must behave differently to what we assume.
Because the number twenty places below Everything, when multiplied by itself, can't yield a result higher than Everything.

At some point, everything we assume about multiplying and dividing, must follow different rules, ones we don't know yet, because we don't know where the rules change- I can't begin to conceive the point where the rules would change, but it must be beyond a centillion, on purely conceptual grounds.

But thus must be so. For mathematics is the study of quantitive relationships in the real universe, a finite universe, with a finite number of possibilities. One day, all those possibilities will have been exhausted.

Ultimately, when we look at the equation 2+2=4, we need to remember the proviso;
In this universe.


Anonymous said...

I love the title of this post. I must say that you are deep beyond words. I can appreciate that. I really think you should be teaching at Cambridge or at least Oxford?

Anonymous said...

You mentioned maths and it was all over for me!

Anonymous said...

Perhaps at some point the universe will hit the finite like ocean waves on the beach and move back on its self and start all over again.

Anonymous said...

Hello, Me be Scary Monster.
Betty Boob Hug said that Me might like this place, so here Me is scrolling around and taking a look.

Quite the interesting post. Me enjoyed the concise way you handled such a gordian problem.

You have stated that some numbers live in the world of the abstract (negatives) yet one might say that all numbers, like words and language as well, are representative therefore they all belong to the realm of abstract thought. A menu is not a meal.

If at the start, space be zero than where did all the 'star stuff' come from?
Just thinking about this kinda stuff leads me down a road with so many forks and branches in it that me tiny pea-sized brain gets all discombobulated.

The Monster. STOMPS!

Good crushing and stomping here.

Anonymous said...

Space is not 'nothing' and nor is time. There are relations with other dimensions yet to be fully understood so ...

isn't this jumping the gun a bit ?

Anonymous said...

Alexys- I'm merely trying to comprehend the nature of reality, the finer points of which are very disconcerting.
I don't pretend to any more knowledge than anyone else who has studied (on an amateur basis) these points and wrestled with the issues raised.

Onyx Stone and Two Wolves are worth checking out for thoughts on the Universe as well.

Jenny- Don't worry, I am a poor mathematician in practice. You will be relieved to hear, tonight's issues are more socially relevant.

Goldennib- I really cannot truly comprehend how this will affect reality. My intuition is that it means that the rate of change starts to operate differently- but we are dealing at a point so far in the future, that all this is very hypothetical. My intuition tells me there must be some correlation between the total amount of energy vibrations (particles) and the total amount of Planck Ticks that pass in the history of the universe.
The Everything number, logically must be the total amount of energy vibrations x the total amount of possible options. Nothing can ever exceed that- that IS everything.

Scary M- They are all absracts- As I say, if it has more than one digit, it is a reprsentation. The diffeence is what they represent. 32 represents a quantity that can exist.
-32 represents a quantity that doesn't exist, but you need to remembr to deduct from one that does later in time (an accounting tool).
The square root of a minus number exists in no way, shape or form.

Where did all the stuff come from?

OK, my view;
In the begining an energy quanta appeared at a mathematical point.
By existing, it became subject to the operation of the Laws of Thermodynamics.
All else, literally, is history :)

E-K- Yes, multidimensional space, is fascinating to conceptualise, have you ever messed around with the idea of the hypperrcube?
The implications of extra dimensions are fascinating because of the way that space- or more than that hyperspace- or 11 dimensions something way beyond that in complexity, beyond the range of our narrow brains understanding- could fit together- we are talking about shapes that can have significantly more faces than points- and more.
Maybe this isn't theory- but reality.

Jumping the gun?
Of course.
Why not?

Anonymous said...

Good Lord!

I am with you so far...

Anonymous said...

I'm afraid Mutley is way ahead of me. I got seriously lost after "Infinity and The Singularity- Limits to Our Conceptualisation?"

Anonymous said...

Crushed should be my name today. You lost me totally and sent me running. But I'll be back.

Anonymous said...

Crushed, you would make an excellent teacher! I'm with Jenny when it comes to maths but even I can see that this is one of your best posts.

Anonymous said...

"Jumping the gun"

To say that our destiny is to 'space out'.

I dunno about that - I reeeally don't.

The fabric of space itself appears to have energy in it.

Anonymous said...

Mutley- If you are, great, if not, have another read, it IS hard to get your head round, I struggled until I realised that bizarre it sounds, there is a definite logic to what I'm suggesting.

Stan- I did warn at the start, that this post might be a bit esoteric and abstract.
The problem is when we get the nuts and bolts of how the universe works, we have to deal with 'counter-intuitives', realities which seem to go against our very narrow experience of it.

The best example is Space being finite, but limitless. A lot of people have real problems with that.

jmb- I apologise. Trust me, that really IS the most abstract I'll get.
Well, I suppose I can't predict future ideas I might have.

Welshcakes- Believe it or not, I'm actually a very poor mathematician, at least by academic standards- I actually graduated in an arts subject.

Oddly, I think you appreciate the empirical basis of mathematics best, if like me, you have no real aptitude for the subject- it just becomes an extension of applied logic, wheras these savants seem to see it as something which reality is a pale imitation of.
But numbers are a property of existence, not pre-existant.

Anonymous said...

E-K- The energy is pushing it apart. It is something, it is the fabric of reality the universe creates to dissipate itself, composed of every dead planck unit, every energy partcles leaves behind.

Anonymous said...

Another view:

Models are idols.

Numbers didn't exist till we applied them.

This thing we do with our brains, this ascription of values to the things we observe, these maths... they are intrinsic... to US!

Attempting to predict, quantify, explain and understand is what we, as humans, do.

We are innate survivalists, each of us having come from, without exception, a complete, unbroken line of 100% successfully procreative ancestors, through time immemorial.

As such, we seek

security --> familiarity --> patterns --> order

...and even, I daresay all too often,

---> stasis.

And we find these things, or create them. (We are tool-makers as well, after all.) But in a sense, our brains are often smarter than WE are; the "patterns" or "order" we see are, in fact, projections of our own characteristics, which we then recognize but perhaps misapprehend the source. It's subtly anthropomorphic.

Case in point: nature doesn't quantify. To believe that nature peeks at every Planck tick, balances her ledgers, and sees to it that each and every event has exactly the correct result, with no energy being created or destroyed, is as absurd as Jehovah.

Nature doesn't, for instance, know how many protons make a helium nucleus, even though in our macro view it takes a specific, whole number (no fractions... but what about quarks?). The fact that we can ascribe a precise quantity to the phenomenon in no way suggests that a helium nucleus even exists in any objective sense as a discrete entity, to which a specific value may be ascribed.

If I have an apple and you have an apple, how many apples is that? Two, you say? Well, what if mine has some bites out of it? Is it still a whole apple?

What if the bites were taken by a worm that still lives in the apple?

An apple isn't even "an" apple, necessarily. The seemingly simple, safe and reliable number is, in fact, indefinite, to be determined on a case-by-case basis by the individuals scrutinizing it.

Like seeing faces in the fog or omens in eclipses, seeing numbers in the universe is just another way we try to make sense out of it all.