Who is it that cares?

Why is this important to me?

I have this suspicion that ever since the first glimmers of my consciousness started to flicker into life in my mother's womb, I have been trying to solve the puzzle of what it is to exist. Of course, this is the job of every newborn. And like the vast majority of newborns, before the age of two I'd performed that everyday miracle of making sense of what initially must have seemed random sensory inputs and turned myself into a being who could successfully communicate with the other beings who had summoned me into the world. 

I hesitate to write about the small minority of newborns who fail this task. Is it possible that, for some of them at least, they have made a different sense entirely of the information streams they received, one that bears no relation to the sense their parents made but nonetheless is a making of sense, alien to us beyond our imagining? I suspect this is a romantic notion that any expert would rapidly debunk and any parent of such a child would find offensive, but it remains an idea I cannot quite shake off.

Everyday miracles aside, at this other end of my life I can't help but think that in making broadly the same sense of the world that my parents had made I was unknowingly locking myself into a consensus that others, not I, had established. 

Over the course of my lifetime I have increasingly questioned this consensus. Why money? Football? Advertising? Ground to air heat seeking missiles? X Factor? Postmodernism? Facebook? The space-time continuum?

Why do these people take great pride in drinking alcohol and these ones take great pride in not? Why do these people think it is okay to enslave those people? For these living things to eat those living things but not those living things? 

Why does she say I am a member of the patriarchy? Why does he say there is no such thing? Why does this other she agree with him?

Why three dimensions, not four? Or five, or six, or more?

How much do I have to strip away, to unbuild, before I find myself on solid ground? Or is there no solid ground?

When I was at primary school, mathematics was taught using wooden blocks of different lengths. Two blocks of length one (red feels like the right colour) side by side were the same length as a block of length two (green?). I don't know how long it took to dawn on me, but here was my solid ground. You can take whatever side you want in any debate, everyone agrees that one plus one equals two. Even people who believe the earth is flat believe that one and one equals two. Though frankly, who knows? Any flat earthers reading this? If so, great, thank you for being so open minded. Where are you on the great 1 + 1 = 2 debate?

I soon saw that mathematics not only gave you solid ground, through proof it gave you a way of creating more solid ground. Yes, the scientific method is always working with our best approximation, waiting for a better one to come along, but 1 + 1 = 2, that is provable (though, infamously, one pair of logicians took 300 pages to do so).

A proof is an argument that cannot be wrong. That put mathematics above science, I thought. Once you've proved that the square on the hypotenuse is equal to the sum of the squares on the other two sides then that proof is true for all eternity. 

I started proving things for myself. I was merely proving things that others had proven long before me -- nothing I have ever proved has been mathematical news. But the act of stepping through each proof was a whole series of "if this is true, then that is true" steps. Each step I had to stop and check. Does that follow? Yes? Sure? OK, go on. Each step took me from solid ground to further ground, no less solid.

In everyday life we hardly ever read things this way. Usually we try to follow what the writer is trying to say and feel we have done well if we get the general gist of it. Part way through we might decide that we disagree with the writer, that they are wrong, but it will hardly ever be because we can point to where they went "if this is true, then that is true" and say "No! That does not follow". More likely we will decide that the author is one of those people who believes different things from what we believe and abandon reading.

In mathematics, all mathematicians believe the same things. They might argue whether or not it was Pythagoras who came up with the theorem, some arguing that it was proved centuries beforehand in non-western cultures, but these are not mathematical arguments, they are historical ones. All mathematicians believe the theorem itself to be true.

Indeed, most of them would say that "believe" is not the word to use. They would say simply that the theorem "is" true -- belief does not come into it, as to believe suggests that you might be wrong.

The problem with mathematical certainty is that it only works in the abstract realm of mathematics. It is always going "if this is true then that is true". When it proves that 1 + 1 = 2 it says nothing about whether 1 or 2 are true, or what they are. These are part of its initial assumptions. For at the outset of every proof is an initial set of assumptions, which the proof will say are considered axiomatic. What "axiomatic" means is "we don't have to prove this bit". Or, to make it seem like a slightly less pointless exercise, mathematicians are essentially saying "in a realm where the following things are true, then it follows that these other things are also true."

If that is solid ground, then this too is solid ground. A mathematical point has no height, width or breadth. Fine, but when did you last see one of those in your realm?

If you are unlucky when first learning maths it will be tied to practical, tangible things, like being able to check you get the right change when you go shopping. If you are lucky, as I was, you will be introduced to it in a way that keeps alive the sense that it has higher purposes than mere buying and selling, or knowing which of two trains will arrive at the station first, or when the bath will overflow. To my mind maths teaching should be the teaching of abstract thought, and for by good fortune that is how my mind was introduced to maths and quickly learned to love it.

Yet it was only when I went on to read maths at university that I properly began to realize that mathematical solid ground did not necessarily relate to solid ground in the spacetime world around me. In this world, the best I could ever hope for is the contingent certainty of the scientific method. Science would provide an initial set of assumptions, and maths would go off and deduce things from them. If everything it deduced was true then science would use those assumptions as a working hypothesis, but if just one thing maths proved was inconsistent with what science had already tucked away in its bag of working hypotheses then at least one of those hypotheses -- the new one being tested or one of the old ones previously assumed to be correct -- was incorrect.

For a long time I had the hunch that the whole universe was somehow no more or less than mathematics. In fact, I still haven't really shaken off this idea. From this perspective, maybe the Big Bang was just starting with a "this is true" from which the universe springs into being as proof derives "and therefore this is true, and this, and this..."? If so, science's task was to deduce that initial statement of "this is true" from the universe it finds itself a part of, discovering interesting things along the way.

But a couple of years back, I came across a book by a pair of neuroscientists who make a compelling (i.e. people who are better at this sort of thing than I am appear to be giving it the time of day) argument that the way we "do" mathematics is intricately entwined with the way our brains work, arguing that different sorts of brains would do a different type of mathematics. Does this mean that the certainty I found in mathematical proof is only certainty because my brain is wired to see it as such? Would other brains find certainty elsewhere? In positing my hunch I had thought that mathematics was free from the subjectivity I was so carefully trying to ring-fence so that my thinking could proceed in perfect objectivity. If that was wrong, then so too was my hunch. Though of course, my hunch might be wrong for other reasons.

Whether this book turns out to be right or wrong, it comes from the same good place of questioning the way we have collectively agreed to interpret the sensory inputs we receive from the universe. Just as we stand on the shoulders of giants, with each generation that nurtures the next we also reinforce past assumptions about the universe and our role in it. 

At no time in my life have past assumptions been so challenged as now: gender equality, Black Lives Matter, non-binary gender, the discrediting of economics based on an assumption of infinite resource, that unbounded individual wealth creation will make the world a better place...

It is as though humanity is waking up. Just as well, it needs to, its house is on fire. But how much waking up is to be done, and of what sort? How often will we wake only to find ourselves in another dream? How deep is our sleep? More pressingly, will we wake in time to put out that fire?

*

This was originally written October 2019. Since I wrote it "woke" has taken on a very tumultuous life of its own. I also have a copy of the book that challenges the objectivity of mathematics, but I have still not - dared to? - read it to conclusion.