In mathematics, you sometimes find gems hidden within mounds of data and the rules describing it – analogies of life so obvious you’ll face-palm yourself. Every Evrika! moment of that magnitude deserves a drink, I always say. For now, let’s delve into the unknown and gaze into the abyss. Or, like I call it, let’s get philosophical.
There are things you see around you, this and that and the other, where you find yourself confused. Why are people doing such obviously idiotic things? How come people do them? What makes an individual go the Darwin Award candidate way? Well, not everybody is dumb. So how can we explain such behavior? Occam’s Razor might be a way to go if you’re ignoring part of the demographic, because many, many educated, smart individuals make illogical choices that’d bring shame even to famous Mr. Custer and his last stand. So why then?
In a sort-of-related joke, Sherlock Holmes and Watson went camping in the woods. Around 3am, Holmes started shaking Watson until he woke up.
– Quickly now, tell me Watson, what do you see and what do you deduce?
– Well, Mr. Holmes, after such a rude awakening, not much. I see stars, I see the moon – I’d say tomorrow will be a very nice day. Not a chance of rain, I’d say. Furthermore…
– Watson, you fool, Holmes interrupted him, don’t be an idiot – they’ve stolen our bloody tent!
What do we deduce from that? We can’t ignore obvious answers just because we assume we know what the person asking the questions wants. In mathematics, we use the word “trivial” for that. Let’s say an equation is a mystery the sort Agatha Christie used to make – there are variables, like events, there are constants, like the people (the innocent ones, me thinks) and there is that big X – the identity of the villain. Solving the mystery, finding the hidden X – sometimes can make even experienced detectives go overboard. Sometimes the solution is so simple, so obvious, that if you were to try that in a mystery book you’d never make it on the best seller list. Unless you’re Agatha bloody Christie – that bloody book messed with my head in ways only my wife is allowed (as in allowed now, because I’ve read that book around 1993 give or take a year or two, before getting married – which could explain the many, many things wrong with me). Never read that book when you’re having an existential crisis. Consider yourself warned.
Let’s get back to our flock of sheep – the simple solution, the simple structure, is what we call the trivial solution. Example – the divisors of any integer A have the obvious solutions: 1, -1, A, -A. There may be more divisors, depending on A being a prime number or not, but the obvious solutions to the find the divisor hide and seek are the ones I’ve listed. They’re also universally valid for any number, including prime numbers. Also – sometimes the vectors need it badly, like when we have something like A times X equals 0. A being a fixed square matrix and X a vector. You know a vector can be written down as a matrix. Sort of like multiplying two vectors, you can multiply two matrices. However, the trivial solution to the A*X=0 is the … drums rolling …. 0 (zero) vector. Nice, innit? In a similar note, if a solution to that equation is non-trivial, meaning X is not the zero vector, X can be called an eigenvector of A if there is a number (a scalar, actually, if we’re going to be boring), let’s call it “c”, and that number c is the eigenvalue of A – as in A*X=c*X. Think stretching an image over a specific direction – like an inscribed piece of rubber. Yep, that. No, not a condom, get your mind out of the gutter. Of course, it’s over-simplified – but for the sake of my sanity, let’s just say a trivial thing is what Holmes would see as a reason for his trademark “It’s elementary, dear Watson!”. Something obvious, but something that eludes us most of the time.
We’re trained to stop looking for the obvious. Ever hear the “Can’t see the forest because of all those trees..” thing? Sometimes the simplest explanation is correct – that’s what Occam’s Razor is all about: if you have several ways of explaining a behavior, pick the one with the fewer assumptions. The way to go, for most people, would be to use exactly this way of looking at the world. It’s an excellent way of detecting crap, innit? Well, like I do say most of the time, bullshit mon ami. It’s not.
Everybody and their mother uses lex parsimoniae (Occam’s Razor, for those not fluent in Latin) without knowing how to use it. I warned you about knowledge without understanding, didn’t I? Occam’s Razor, in lame terms, is to be used only to evaluate probabilities – not truth. It can help speed up the deduction process, but it won’t give you anything else. It also makes much use of assumptions. If what you assume is wrong, your final set of probabilities will also be wrong. Sort of like what happens when we find out a Darwin Award fellow is an educated, smart individual. The “he’s dumb” solution – the trivial one – is apparently wrong. Or is it?
If a brick falls down in front of you, you’d assume it fell from somewhere – like the wall you’re leaning on. It could be ghosts, like your now-dead-mother-in-law making sure you know she’s reached heaven. It could be a brick falling from passing plane (come on, I mean it could happen, you’d have to be really unlucky though). You’ll find many many other possible explanations – but the trivial one is it fell from the wall and something or someone nudged it a bit. It’s the most likely explanation – but that reasoning won’t give you more than that. You can’t use it to determine which particular scenario is true, only to assign an arbitrary value of our own choice to act as probability to the likelihood of the scenario being true. You can fool scientists with this one, too. Hell, you can fool almost anybody. Think IQ – you’ve all heard of it, you know what it does and when it’s used. Now give it to an Australian aboriginal. He’d laugh at you because the ability to find water in the desert isn’t listed anywhere, while you’d laugh at him for not knowing what to make of anagrams. If you knew only his results, what would you label that individual? Dumb? Right, step down son, take a seat and shut up. Sort of when they modified the BMI results in 1998 labeling 28 million Americans overweight (previously healthy) without them gaining a pound. The label changed, not the weight. Same thing with IQ results. Same thing with selecting questions in the IQ test. Chaos theory.
If you want to mess with the average individual, change what the results mean. If you want to mess with scientists, change how you pick the questions. It’s bias, pure and simple. And it’s making us think we’re dumb. You’re not convinced? Think science – it’s the process of finding the truth. Think quantum physics – it’s complex, it’s annoying, it’s hard to understand, but it looks for the correct answers. It’s easier to believe in god or in what others say because it looks right – but truth is truth regardless of what we believe. If things are proven wrong, then they’re not true. It’s not my job to prove the validity (or lack of validity) of someone’s statement – it’s their statement, let them prove it. This is what bias is all about – think Susan Boyle. The impossible can’t be done until somebody does it. That’s the whole point of triviality. It makes us stop trying to achieve the impossible.
We are trained, from our birth up until the moment we’re unceremoniously whisked away from this existence, to mistake probability with certainty. People tell us to learn from their mistakes and we do – this, I think, is a big mistake. Learning from the mistakes of others won’t make us successful, it will only make us avoid failure. The trivial solution to avoiding failure is not trying – like what I’ve been taught at one management seminar – if you promote people who won’t make mistakes, you’ll end up making managers out of the very people who avoid working. Only those who don’t work make no mistakes, and since you’re kicking up the rank ladder people based on the mistakes per work done ratio, those who aren’t working deserve to be promoted. Like Wally, only less obvious or recognizable.
They teach us cognitive shortcuts. Who’s they? Parents, teachers, friends, media, you name it. Cognitive shortcuts are useful, if they’re used correctly – as in the correct scenario, with the correct assumptions, and the correct time. Go out, to the park for instance, and look around. What do you see? What’s the first label you’d assign to people? Now look closer, does it still stand? Sometimes it does, sometimes it doesn’t. Would you judge yourself as dumb if what you initially thought of somebody is proven wrong? What would you label yourself? Here’s the thing – everybody does the labeling. Nobody (well, statistically below 0.1%, which is quite insignificant) thinks of that when they’re doing the labeling. It’s part of the road to success, you know. We all assume – sometimes we’re proven right, other times we’re proven wrong. This work, of mentally taking shortcuts that balance what we see or feel and what our behavior towards what we’re seeing, is what makes us take illogical choices. If all you got is a hammer, everything sort of resembles a nail. There is no spoon. We’re the ones doing the mind bending. We never think reality is more than just light hitting our eyes. The world is more than what’s in front of our nose.
If you see only the title of my blog and the nom de plume I’ve picked for myself, what would you think of me or the blog’s content? All about wine, beer, whiskey or whatever your poison is, perhaps. A defensive nickname to hide my raging alcohol problem? Does the title really define the content? Does my nickname define who I am? If I call myself musclefreak53, would you then assume I’m all about fitness and muscles even though I might be as full of muscles as a door?
The problem with simple, trivial answers is the potential for abuse. Reducing a complex problem to simple components makes more people think they understand it. If I define those components in a way that’s misleading but not very obvious, I might make people believe me – and in doing so I’m transforming different individual reactions into group-uniform reactions. It’s a way of brainwashing, actually. I’m making individuals think the same way, therefore the reaction to any event involving what is now a socially accepted assumption is easily predicted. You can’t say for certain how individuals behave – but you can change their cognitive shortcuts to match others and voila!… you’ve got yourself a manageable entity.
A person is smart. People are dumb, panicky dangerous animals and you know it. Fifteen hundred years ago everybody knew the Earth was the center of the universe. Five hundred years ago, everybody knew the Earth was flat, and fifteen minutes ago, you knew that humans were alone on this planet. Imagine what you’ll know tomorrow.
Men in Black. Sooo true.
If you ever find yourself looking at somebody doing dumb things, instead of readily assuming that person is either gone the way of the dodo or is dumb as a doorknob, you’d perhaps what to think a bit of why he’s doing them dumb things. Of course, you might want to try to stop him from hurting himself and do the thinking after that, I’d say.