What is Math?

Why does a clock rotate the way it does (‘clockwise’)?

Why is North on top of (most) maps?

Why is the x-axis positive to the right, and negative to the left?

Why do we count so easily in 10s? (but not say: 9s or 11s?)

Why are there 360 degrees in a circle? (and not say: 100?)

Why are there 60 minutes in an hour? 24 hours in a day? 12 months in a year? 7 days in a week?

Why do we work for 40 hours a day, 5 days of the week?

The Terror of Infinity

So, proto-humans started off with basic counting, often based on the digits they had free to count with (fingers – where we get our Base-10 system today – if we’d normally had 6 fingers, we’d probably use a Base-12), but soon they needed to do basic arithmetic, adding and subtracing come pretty naturally, but the concept of removing more things than are present doesn’t make much sense unless you have abstract concepts like ‘owing’ someone. It even took a long time to get to using a Zero – since you would never say you have ‘Zero’ apples, you would just say you don’t have any (no need for a number for that). But once humans embraced Zero and Negative Numbers, it began dawning on them that this ‘Arithmetic’ had in inherent unsettling impossible: what is the highest number, and if you can always add one to it, then where does it end? This is unsettling because humans are linear and finite. We have a steady progression towards a known end. Zeno nad others really brought the terror of this home with wonderful paradoxes of time, length, and motion. If you can divide every second in half, and that in half, and that, and that….then there are an infinity of divisions from one second to the next, so it should take infinitie time for each second to pass, and thus no time should every actually pass (and yet it does…).

Humans really find the infinite – which seems very likely to be an inherent aspect of our universe, and it’s rules of operation – to be terrifying. It’s really the postmodern problem’s root: maybe nothing matters, because it is possible that nothing matters, because ‘mattering’ could just be a delusion of complexity from a bunch of cells organized through the rules held in some DNA, but these cells are each marvels of molecular complexity, and the rules of every molecular interaction are guided by quantum mechanics, which itself relies heavily on the infinite-ness of even the behavior of the particles of a single atom. Trying to understand the nature of a single atom could drive you insane with it’s apparent complexity, so saying we ‘know’ the efferent condition we might call a ‘personality’ seems ludicrous. So humility seems like the order of the day. But humans, like all animals, would rather feel better than worse, so our base programming says any means of rejecting this terror will be welcomed, and there you can slip in fixes. Religion or Spirituality offer a rejection of it based on something seemingly absurd: blind belief in something unknowable as the means to reject something else equally unknowable. The easier route for most is simply distraction: to be allowed to mostly forget that they ever heard that terrifying thing. This may come in the form of drugs, consumerism, social hierarchy games such as gaining status in the form of wealth, success, popularity, or virtuosity.

But the infinite is always waiting there. Staring back at you. Taunting you that it may not even be real, and yet it is grinding your easy enjoyment of this existence to a halt, and making you envy a now-lost part of you: that you could just go blissfully about your day. The best you can do is be distracted from the terror for a long enough time to decide to try doing something, in the hope that doing things might actually matter – but soon you will be back, and for another moment you will contemplate how vast and terrifying it all may be.

So, let’s all just move on from terror-induced paralysis, and elect to believe doing stuff matters. This is no different than religion in it’s clear choice of belief in the face of these unknowable options – but religion is a rejection, saying that the other is NOT true, while this is embracing that both are equally possible, and working from that state of humility.

Go get some.

Is this real?

This is a question you should have convincingly asked for real at least once in your life. The Matrix and Descartes have told us it is very possible it is not real – and like Cypher in the Matrix, maybe this world is better than the one you would wake-up to, so maybe it’s best not knowing. Luckily it doesn’t need an answer – for the very reason that it might not be something that is actually provable from inside it. So either this is real, it is unknowable that it is not real, or we do prove it’s not real and may not like what we reveal.

The important lesson from Descartes for science is not whether you are real, but the vital humility we must operate with in our thinking: we must start all knowledge by fully acknowledging that we know nothing – nothing – as being 100% ironclad ‘true’. *

Starting with that, we can only make ‘reasonable assumptions’ (and that’s using reasoning equipment and rules that we have just admitted might be flawed). This is where Math and probability help out. We can’t know if this is real, but we can assume it is real. Why? Well, because, up to this point, no human ever has convincingly shown it to be otherwise. This does not mean that if everyone thinks something, it must be correct (we know that’s not true). But it does seem to put the odds very heavily in favor of: it is real, it is unknowable by humans if it is not real or we are very far from the point we can finally prove it and stop the lie). And all of these scenarios end in the same mandate: operate as if this is real and matters – in case it does.

So, we get our first mission: go ahead and pretend the world is real, and that it matters somehow – but with the utter humility that maybe it’s not real, and that would be really interesting to find out if someone could prove it one day.

From there we just believe things more and more based on Reasoninng. Reasoning come in two basic flavors Inductive and Deductive. Basically you believe something because you studied/tested the idea and the results seem pretty strong, or you belive it because someone else said it, and that source seemed reliable enough to just accept it. Deductive might sound really lazy, but it’s indispensible – not one has the time to test everything for themselves to decide if it is correct or not – at some point you have to trust what others say.

The problem here has become highlighted with the advent of the internet: is your source reliable? This is where Science comes in. It is a system built around a foundation for coming up with ideas that you can trust – not because of the source, but because of the system. Yes, Aristotle began us down a path toward the Scientific, and most people have had to do a lab report: Hypothesis, test Hypothesis, analyze results, decide if Hypothesis was correct (and then re-test – however many times you to need to be confident it wasn’t a fluke). The part of the process that most people leave out is probably the most valuable: peer review. This is a competitive world of ‘coming up with awesome idea ___ first’ on the line. No one is going o let someone claim a discovery if they can prove that it’s wrong, or better can show a mistake they made, but how they ‘saved’ the idea. This, any well-circulated scientific idea that has gained the acknowledgment of most of Science, is probably pretty reliably accurate (for now).

(*Descartes fans may invoke Cogito Ergo Sum, saying, ‘we think, therefore we must exist, in some form, to be doing the thinking – so we do know one thing: that we do not not exist.’ I like it, but many philosophers and quantum physicists have happily spent their lives trying to make even that seem uncertain.)