Thursday, 19 June 2008

Core Theory- Part One



The philosophy of Crushed ultimately rest in core scientific beliefs.

The philosophy of Crushed rests in the fact that I studied Quantum Mechanics, evolutionary biology and Marx' theories simultaneously. I dissected them all together, re-evaluated all the concepts and out of that came what I believe to be a concrete, all encompassing general theory which actually backs up every position expounded on this blog.

On other words, its based in a belief system. A belief in HOW the universe works.

And the ultimate premise it rests on- is crucial.
If bewildering.

And I apologise for that. I'm about to challenge something you don't even think of.

2+2=4

It's true. But is it necessary for it to be so?

And here is the scary point.

NO. The statement rests on nothing other than empirical fact. It's true, because it happens to be something that empirical observation and the logic proceeding from that, tells us, that in this universe, it will always be true.

No evidence to suggest it would be true in ALL possible universes.
And THIS, actually turns out to be crucial in understanding HOW everything actually links up.

One of the great philosophical arguments since the time of Pythagoras was this. What DOES mathematics actually tell us?
As in, is it an insight in to the mind of God? A sign of the true perfect logic of the mind of God?
Or is it just the empirical study of the relationship of quantities?

In other words, is it necessarily so that quantities relate to eachother the way they do?

In other words, it is not possible for our minds to comprehend 2+2=5. Because 2+2=4, is a fundamental principle of our universe.

Mathematics is a system for understanding how quantities relate to eachother and developing a theory behind how they relate.
So basically, it's a theory to explain the fundamental properties of the universe we observe.

Things are what they are, because the way quantities relate to eachother in THIS universe, dictate it.

The fundamental constant, is quite simply the shape of spacetime- it dictates how the quanta IN the universe relate to eachother, and achieve heat death by the shortest route.

Read Kant's Critique of Pure Reason AFTER reading Steven Hawking's Brief History of Space and Time, and you'll get my point.

And actually, mathematics tells us this.
Because mathematics is full of little oddities.
Little things that tell us, it's not quite what we think. It doesn't always fulfill our expectations of logic.
And one very daunting way, it has a surprise up it sleeve. It doesn't follow the path we hope it does.

Something that deep down, is implicit in mathematical theory.

The numbers come to an end.

They must. Think about it. And think what that means.



That sounds a mad thing to say. Numbers go on infinitely, you say.
Well, it's implicit in our assumptions, and at the levels we operate, it makes no difference, but ultimately, there is a final numbers, but don't even bother trying to comprehend it, because even the string of zeros would LOOK infinite to you and me.

But let me explain WHY this MUST be so.
And what the implications are.

Normal numbers are real numbers, 2, 25, a million, they exist. They represent actual quantities that can exist.
-2,000 is not such a quantity. It only exists in financial accounting. The population of no place is ever going to be a minus number. It's a number we've made up. It only exists, because positive numbers exist elsewhere. It can never ACTUALLY represent a total.

But there are other numbers that don't exist. No fraction anywhere can ever be pi. It's not possible. There is no calculation of ANY kind you can possibly do that will give you pi as an answer.
Except one.
How many times can you get the diameter of a perfect circle in to it's circumference.

No other way you'll ever get that answer.
It's an irrational number.

Just as, if you see an answer 1.4151, chances are the question was 'what is the square root of 2?'

These are irrational numbers. We made them up, because we wanted numbers to do, what they don't do. Give us sensible answers to things WE think they should give sensible answers to. Pi is a bit inconvenient for us. But it's the answer the universe keeps giving us. Empirically, we know that answer will ALWAYS be correct. But it's not QUITE the rational answer we wanted. The universe isn't quite like that.

(As an aside an old legend says that Pythagoras had a student murdered for daring to challenge his misguided conclusion that Pi was 3, just so he could kid himself mathematics was perfect and the ultimate truth.)

And of course, we go further. Sometimes, we have to imagine numbers.

Most of these are pretty pointless. They actually just exist so we can do thought experiments about what quantities tell us.

They tell us, for example that you can't find the square root of a minus number.

Now when, in real life, are you likely to need to find the square root of a minus number?

Minus numbers only exist in acccounts books. When do accountants need to find the square root on a balance sheet?

So the question might seem stupid. But perhaps doing the thought experiment might be useful and having an imaginary number to represent this.
Or you could be tempted to say, as to be honest I am, people who do this for fun, need to get out more.

Thing is, one of the imaginary numbers IS quite important.

Infinity.

This is actually the scary thing mathematical theorists find so disconcerting.

The series of real numbers, that we know, that we know from EMPIRICAL fact----

ends in an imaginary number.

Now that's a problem.

What IS at the end? Is there an end?
And what do we find there.
What are the rules governing the end of the sequence? Are we not only looking at a microcosm of the TRUE scale of the numerical sequence?

Because it DOESN'T end with an imaginary number.
It ends in a real quantity.

And- I hesitate to state it- but we CAN represent it with an ACTUAL term.

It is the total number of energy quanta present in the big bang, to the power of itself.

No calculation of any genuine reality, can take place in this universe, and yield a result higher than that.
In other words, if you take the number immediately before, that number can't be doubled.
But our numerical theory rests on the assumption it can.

But it can't.



At some point on the numerical scale, way higher up the scale than we can even conceive of, the laws of mathematics, turn back on themselves and head towards the omega number, a kind of reverse zero.
And we can't really understand what that means. We just don't understand how quantities relate that far up.
There's no point just holding a mirror to zero- it's way more complicated than that. We haven't even begun to understand what the empirical evidence of how we are learning to relate quantities together works, tells us.
Because we seem to have pretty much sussed everything else.

And we've done that by understanding, that if the maths don't pan out, it,s wrong.

What we still don't quite understand, is what mathematics tells us about WHAT it is and WHY it works, what does work, and what doesn't.

So far all conceptual mathematics has taught us is that the idea of finding the square root of a minus number is just silly, and that our minds haven't yet the remotest idea what lies at the end of the rainbow.

So we just call it infinity.

Understanding this, will be the next great human breakthrough, it will be the next stage in the sequence- inventing fire, harnessing electricity, splitting the atom, understanding the structure of space so we can utilise the other dimensions of spacetime.

Mathematics is the final frontier of human understanding.

7 comments:

sparsely kate said...

Wow. Great post, really thought provoking.
My kids and I often talk about what is infinity..they try and get their little heads around it and I can tell my 10 year old really wishes she could figure it out.

You really think there is not infinity? What would that mean for us?

Welshcakes Limoncello said...

Interesting post though I never could follow mathematics. What a relief to know it doesn't exit!!

CherryPie said...

Like welshcakes I find the post interesting, but I too struggle with mathematics!

jmb said...

Another making my head hurt post Crushed, I think I'll retreat to the music for now and read it again later.

Fusion said...

Yep, Another challenge to thoughts, thanks Crushed.

No infinity, ay?

But where does it end then...

Crushed said...

Kate- Well, WE haven't. The fact is, we are dealing with uncomfortable concepts.
Kantor went made (literally) trying to wrestle with the concept of infinity.

It depends on what you mean. In one sense, yes. PRIMARY reality- that exising outside the universe- I have described as being infinite zero. By that I mean, it is infinite time, but utterly dimensionless in space.

A quantity (which, in effect, is what a universe is, a sum of quanta, is by definition, finite.

This means that the relationship betwween the components OF that quantity are dictated by WHAT that quantity is. If the quantity was different, the relationships would be different.

What it means for us? Not a great deal, really. Not in any calculation we are likely to do at present. Most scientists ARE agree on a rough estimate as to when the universe 'dies'- the wikipedia article on heat death is quite a good summary- and my view is that nothing in this post changes that. It's in the implications of how the universe works.

So all laws of this universe, all constants, everything else, stem from the fact that the structure of THIS universe, gives us the numerical relationships it does.

Welshcakes- Believe it or not, I'm actually a hopeless mathematician. This post is more to do with attempting to conceptualise WHAT is actually happening.

The next post in the series is partly reliant on the assumptions made in this one.

I'm saying it exists- in that it a system that we have devised- but the purpose of that system is essential to deal with empirical realities.

Ultimately, it's that- a system. Perhaps we need to realise thatv we're using it for two differing pirposes- which at that tiny scale we use it DO recomcile, but won'y on a macro level- those being understanding the relationship of quantities- and the second being as the truest form of universal logic we can find.

CherryPie- I think often it's poorly explained. Maths teachers don't tend to actuallt tell you what it is they are talking about.

Thw difference between the four types of numbers used in our mathematices ; Real, negative, irrational and imaginary, is so crucial- the concepts behind them are radically different.

jmb- Yes, I figured this one would make very little sense. The next one on this vein is more tangible, though perhaps no less disconcerting.

Fusion- it ends when every quanta runs flat. When there is no energy left.
Hence my selection of that value of the omega number; the total amount of quanta present in the begining, to the power of itself.

There are a finite number of planck ticks in the universe, and my guess is, that is their number. That is how long it will take to unravel the universe- which essentially, is what is always hasppening.

But don't worry- Imagine the universe is a year- we're still on New Year's day!

Anonymous said...

Interesting notions, Crushed, but infinity isn't a quantity, is it? It's a placeholder for the unknowable, and it doesn't follow the rules. In fact, it misbehaves so much, it's not even alone... there are an infinity of infinities.

I think you would be a real pain in the ass if you were ever to take a graduate topology course :)

p.s. I have to take square roots of imaginary numbers almost every day! Gotta know what the phase shifts of my linear filters are, doncha know.