Abscissa – Autism and Techno Blog

Greetings, time for another blog.

Not sure if I have readers that go that far back but when it first started many moons ago, shortly after being diagnosed, maths was going to be a focus to blog about.

Never really happened as it doesn’t seem to be easy to write about or communicate. Nor did it ever seem particularly pressing. More a case of trying to find something to do with my maths degree.

None the less here I am now with a rekindled passion. It’s more the physics side of it. The unquenchable thirst for understanding reality ans how it works.

That it works mathematically is a long topic of debate for many. It may not make much sense as to why. It’s always been about logic. Ensuring the reality is non-contradictory. Consistent. Predictable to some extent.

I’ve been redigging into the bizarre world if quantum mechanics. Oh what fun!

Oh and relativity too just to ensure the world is baffingly unintuitive.

A brief history of me and mathematics. What I had an intuitive skill for was undoubtedly arithmetic and algebra. I used to do my older bros homework. Rearranging equations is an easy puzzle. Solving for x a simple pleasure.

Stepping up to secondary “big” school, I was not marked well in maths and never really understood why. Probably a case of not showing my working enough. Plus as new concepts came my way, perhaps it was evident that arithmetic was only going to go so far.

But the second year, I jumped up from level 3-4 to 7-8 and won a school wide math contest. Also won a special award for being the most improved student across my whole year group.

But why? I wasn’t really working any harder. Things just began to click for some reason. But it’s logic and reasoning at the end of the day. How important it is know what the math you do actually represents.

I should say a quick word about exams. I never quite scored the highest grade for being under the pressure of exams and not putting the work in.

When I was getting tested for autism I was asked the question “what do you do when you don’t know something?” and “do you ask anyone for help?”

The answer to these was nothing and no, no one.

If I don’t know it, I don’t know it. Simple as that.

I’ve got the feeling that I’ve talked about this stuff before so I won’t go into it much. But physics. Oh my days. It’s not so much that the math is difficult or complex, though it can be so, the maths is doable. Just understanding what to do and why? What it does it mean? What does it represent?

You have to understand the notation and the definitions and the axioms. Inner Products, Divergence, Curl, etc.

Complex numbers, what fun they are. That’s what the mathematicians do, rip up the rule book and invent new maths.

You’ll perhaps know that you can’t take the square root of a negative number. No real number can be multiplied by itself to make a negative number. Until someone says please can we make new numbers.

I spend many sleepless nights at uni pondering what the hell they are and what they have to do with anything. Then it finally came. The imaginary number i turns multiplication into a rotation, by 90 degrees or pi/2 radians to be precise.

The fun fact about i is that it’s multiplacative inverse is equal to it’s additive inverse. Eg 1/i is equal to –i.

This property feels distinctly useful and interesting. Imagine if you want to model a rate of change of something that is equal and opposite to that same something?

The complex numbers are represented in a 2d coordinate system so it’s easy to think they are just 2D numbers but with an interesting twist.

It is just a tool for modelling and doesn’t represent any measurable quality in the real world but there seems something very beautiful in putting it at the heart of physics.

I’ve a lot of thoughts and questions that I aim to explore, won’t put them all here.

Of particular interest is the nature of forces. Did you know the force equation of gravity G*M1*M2/r^2 and the electromagnetic force equation K*Q1*Q2/r^2?

They look similar don’t they? M is mass, Q is charge. G and K are universal constants of nature. r is distance.

What’s the connection between mass and charge?

Charges can be + or – and opposites attract and likes repel. Mass has only ever been seen as positive, never negative, and all mass attracts. Well they’re both forces. If you believe the physicists, electromagnetic force is hugely stronger than gravity.

I’ll get to those universal constants another day but so far they are just currency conversions for different dimensions. Dimensional analysis is a lot of fun.

My favourite constant without a doubt is h, Planck’s constant which appears literally everywhere in quantum mechanics.

Having the property of Action, which in physics is energy * time, it famously sets the limit of certainty in Heisenberg’s Uncertainty Principle.

It most directly sets the proportion of energy and frequency of a wave. Oh and by the way everything is a wave or some sort.

Of note is the actual number it represents to the order of 10^-34. Approximately 0.0000000000000000000000000000000001.

It should be noted the origin of QM comes from Planck’s idea that Energy should only exist in discrete packets such that only integer multiples of some unit amount of energy could ever be measured.

So the deep burning questions arise. Are time and space quantised likewise? Imagine digging deep into the dimensions of space and time to find they come in fixed solid blocks. We wouldn’t move in a continuous straight line but jump one unit at a time.

Well mercifully h is so ridiculously small that no one would ever notice.

Relativity is the other mind-bender. But to start with Galilean relativity, the truth that movement only has any meaning when relative to something else. You wouldn’t be able to tell the difference between moving and standing still without seeing some fixed point of reference.

And yet anything else that moves with us are fixed into our frame of reference. They don’t move relative to us and we don’t move relative to them. To embrace the romantic notion that they are connected to us and we to them. A force of some sort that holds us together.

I’ve got some pretty crackpot notions about Einsteinian relativity, a point where my understanding diverges from the scientific orthodoxy. The focus is on how to interpret what is subjective and variant versus what is actually universal and invariant.

Mathematical physics can’t function without something fixed to tie everything together.

The speed of light c was determined to be a universal constant and thus time and space were both found to be relative and subjective.

Spacetime was the invariant. The master of both space and time. Euclidean or Pythagorean geometry was ditched because that allowed one to travel any direction in time. Hyperbolic Minkowskian geometry was the answer.

Mathematically, it makes no difference but I rearranged the equation to restore Pythagoras and restore time as the absolute arbiter.

It makes all the difference to keep time absolute rather than “spacetime”. But what of spacetime? Well really as far as absolute conserved values go, that seems to represent mass or energy. Like many physical concepts, they seem to be the same thing from different perceptions.

Force, Momentum, Energy, Action etc, all proportional to mass. All have units in combination of time, space and mass. What of mass incidentally? Is mass not the third dimension?

Consider the dimensions of mass and space. Consider time as the hypoteneuse of mass and space. The distance in time is always bigger than the distance in space because it is the hypoteneuse.  Time can’t go backwards because the hypoteneuse doesn’t have direction at all.

The universal constants arise only to scale out our hopelessly arbitrary units.

Just the humble beginnings of a crackpot theory. No notions of 3D space or any of the forces that shape our complex universe. But I want to stress what it means for time.

I don’t think it is a true dimension we travel though. In fact if you think about it, we exist over all points in time from birth to death. In doesn’t make sense to say we only exist at one point at a time in time.

We don’t travel through time, we accumulate time. We accumulate memories of the past and have not yet accumulated anything from the future.  And that would be true for both space and mass

So c is the space speed limit. You may be wondering what the mass “speed” limit is. Possibly comes out as c^2/h.  A huge number. Why?

Alas, this is where things get complicated. Worth considering that we have complete freedom in 2 dimensions of space but gravity rules the 3rd. c^2 appears in many places.

E=mc^2!! Well actually, everyone says, m=E/c^2.

I’m far too drunk to understand what this all means but it was fun none the less.

I’ll bid you farewell, kindest regards xx