It’s impossible to provide an absolute answer here as the question calls for an opinion, or judgment statement, and not a statement of fact. Nevertheless, if anything is to be considered important, we need to begin somewhere, and a conscious mind capable of making the consideration we refer to seems as good a place as any to begin.
When we look for the origins of the conscious mind we soon find that the only type of consciousness we have any evidence for is the type which emerges from matter, namely physical brains or central nervous systems such as our own. Since the emergence of these physical forms and their evolution are predicated upon pre-existing and consistent, underlying, mathematical relationships, patterns and geometrical forms, then it seems fair to suggest that the existence of these relationships, described by numbers, is fundamental to everything a conscious entity can think or do.
“Behold the heaven, the earth, the sea; all that is bright in them or above them; all that creep or fly or swim; all have form because all have number. Take away number and they will be nothing”….. Saint Augustine
“All things that can be known have number; for it is not possible that without numbers anything can be either conceived or known”….. Philolaus
In fact, it’s the existence of mathematical laws which gives rise to sentient beings capable of appreciating those laws in the first place. “Atoms with curiosity….” as the quantum physicist, Richard Feynman, once put it, “….who wonder why they wonder.” We can use the anthropic principle and a form of reductio ad absurdum reasoning to explain the necessity for mathematical laws of physics: If these laws didn’t exist, no sentient beings could have emerged to appreciate their non-existence. Nothing even remotely like the coherent order and structure we see in biological systems that give rise to conscious observers would have been possible otherwise. Therefore, physical law and the law of number must of necessity exist. This leads me on to my own variation on Descartes’ definitive statement:
Cogito ergo numerus – I think, therefore there is number.
The French mathematician, Henri Poincare, once said, “The mathematician does not study mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.”
The joy of discovering and decoding abstract theorems of number, and patterns in nature otherwise kept concealed from us, may be enough for the true mathematician, but it’s undeniable that these discoveries often prove incomparably useful all the same. The whole enterprise of science relies on the language of mathematics to bridge the gap between ignorance and understanding of the mechanisms and rules which govern our universe. We can then put this understanding to use by harnessing the resources of the environment around us and by developing tools and technologies which enable us to adapt our environment to suit our perceived needs and conveniences. This is where maths appeals, not just to those who appreciate its aesthetic, but also to those who would look to implement its discoveries to optimise their own analysis in just about any academic field imaginable.
I discuss the practical utility of maths and its diverse applications on my website www.mathsmadeelementary.co.uk so I will not repeat those points here. Instead, I thought I’d take a look at the importance of maths in an everyday, socio-political context.
Maths is not just the language of science, but the prerequisite for well-reasoned, logical and critical thinking. The world today is abound with fallacy, poor analysis, superstition, pseudo-science, credulity, unfounded political & religious ideologies and ideology-based mass movements, all of which exhibit an excess of dogma and a serious absence of healthy scepticism and training in the sciences. In fact, it’s not really a new phenomenon. This problem is as old as mankind.
Maths and science is the best antidote we have to combat our more primitive and baser instincts, and our demonstrably misplaced intuitions – instincts and intuitions which evolved, in large part, over tens of thousands of years in an environment where most of our ancestors’ decision-making needed only stretch as far as hunting and gathering. Contrast this with the modern-day environment we move in today with its demands for a multitude of rigorous and well-founded decisions and judgements. The situation is analogous to attempting to use a long out-dated operating system on a modern-day computer. Even a 10-year old operating system will struggle to keep pace with modern-day requirements. It’s little wonder then that our own particular operating system, which is millennia-old and slowly-evolving relative to modern environmental changes, is far from fit-for-purpose in our rapidly changing world today.
The solution to our cognitive shortcomings is maths and science. The timeless and universal nature of these disciplines provides us with an eternal and reliable resource against superstition, poor reasoning and fallacy. Our misfiring intuitions may be inclined to deceive and to lead us astray, but the numbers do not lie regardless of the era you happen to find yourself living in. Enlisting the help of these two reliable guardians, and making lifelong friends of them, should therefore be a top priority to anyone modest enough to appreciate the error-susceptibility of their own brains and to anyone with a strong enough desire to protect themselves against the perils of cultural conditioning and the pitfalls of those unavoidable and in-built, subjective limitations.
Should maths and science have the final say on all matters? Not at all. Perhaps the truth, if such a thing can be really said to exist, must always remain beyond the realms of articulation. To quote the mathematician, Henri Poincare, once again, “The facts do not speak.”
We’re not always comfortable that we know a thing unless we’re able to articulate it. But facts get along just fine regardless of whether or not we can articulate them or formally quantify them. And they got along just fine long before there were conscious minds around to perceive them.
This epistemic hunger and need to articulate and formalise everything before we can draw a line under it as ‘known’ is a trait which appears to be uniquely human, at least on this planet. But there is an omniscience within nature, of which humans are an integral part of course, which lies beyond articulation. After all, you are able to coordinate movement, regulate your heartbeat, control your body temperature, respire, convert food to energy, replicate cells, reproduce and perform a whole host of other functions independent of your ability to consciously and explicitly describe these processes.
Those who would remind us of the epistemological limits of maths and science would no doubt be quick to reiterate David Hume’s statement that “you can’t get an ought from an is.” I would tend to agree here with Hume’s verdict that you cannot derive values from facts. For example, science can show us how to harness nuclear energy from matter – the ‘is’ – but it has nothing to say about whether we should use this newfound knowledge to create weapons of mass destruction – the ‘ought’. We’re on our own with regards what we ‘ought’ to do with nuclear energy. However, I would also add this caution: About those things such as values, oughts and faith-based claims, for which maths and science must forever remain mute – since these hypotheses are untestable, non-falsifiable ones – there’s no harm in remaining open-minded and willing to reserve final judgement.
I suppose an unwillingness to assert one way or the other is technically agnosticism, but this is not the weak position it is often purported to be. The admission of the vast limits of our knowledge must always precede the acquisition of new knowledge and further advancements. For if we assert positively that we already know even nearly enough, we preclude ourselves from further learning and must remain forever in the infancy of our ignorance. I once heard the ethnobotanist, philosopher and lecturer, Terence McKenna, compare the sum-total of our knowledge with that of a bonfire viewed against the night sky (if I remember rightly, I think the metaphor may have been inspired by his brother, Dennis, on one of their joint trips (please excuse the double-pun)). By building up that fire, you’re simply illuminating, more and more, the vast extent of the night sky which surrounds it. In other words, we become more and more knowledgeable about how little it is that we actually know. I like the metaphor but I still think it’s worth the effort to continue building up that fire.
“Education is a progressive discovery of our own ignorance”…. Will Durant
“….to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me”…. Isaac Newton
You only have to pick up a newspaper today to see that we live in a world plagued by sensationalised mass hysteria, grossly misplaced priorities (you never know on what page you’ll find the ‘front page news’), bad reasoning, and a plethora of cognitive biases. I will not discuss specific examples here but I will no doubt allude to some of the more prominent ones in future articles. The media feed this mentality and are fed by it in equal measure. It’s hard to know which came first: the public demand for bad logic or the media supply of the very same? The question is somewhat meaningless when framed this way. The fact is the two entities co-evolved. The public and the media have always had a symbiotic relationship, of sorts, enclosed in a reinforcing feedback loop governed by the whim of market economics. Media figures do not fall from the sky but are drawn from the population at large. Their afflictions and cognitive blind spots are therefore shared by all of us to varying degrees.
Bad reasoning born from little or no training in maths and science infects individuals and institutions alike; the individuals in the highest seats of power and with the most responsibility, and those with the least; the average man on the street and the president or prime minister who governs over him. Perhaps the world really is run by C students as Norman Mailer once remarked. His estimation seems a tad optimistic to me. Douglas Adams may have hit the nail on the head when he amusingly stated in The Hitchhiker’s Guide to the Galaxy, “Anyone capable of getting himself made President should on no account be allowed to do the job!”
Ask yourself who you would rather go to on matters requiring lucid and well-reasoned judgement and decision-making: a mathematical philosopher of the calibre of someone like Bertrand Russell, or maybe a politician – high on spin and low on substance – whose self-evident lack of training in the sciences betrays an absence of logical rigour? Although it’s the former you may be more inclined to put your trust in, it’s much more likely to be the latter who sets himself up as the ‘go-to’ guy in the first place – a typical case of ambition grossly exceeding aptitude.
Of course, the only remedy for this state of affairs is education. Perhaps a bit of curriculum reform wouldn’t go amiss. No student should ever leave secondary level education not armed with an adequate fallacy-detector kit. Introducing an enjoyable and educational read into the school curriculum such as Carl Sagan’s ‘The Demon Haunted World’ probably wouldn’t be a bad start. Then we may just halt the proliferation of dogma, ideology and bad ideas which accomplish nothing other than keeping the population at large disempowered, deceived, infantilised and easy pickings for those few individuals or institutions among us whose intentions may be less benign; those individuals or institutions who would otherwise exploit – conscious of it or not – our susceptibilities to fallacy or simply infect us with more of their own.
On that hopeful, remediable, end note, it may be an opportune moment for one final quote:
“Human history becomes more and more a race between education and catastrophe” ….. H.G. Wells.
