This blog is not mathematical. It’s about exploring the “real” fear we have of mathematics. The fear isn’t about numbers and factorials and stuff. Some people can change a punctured tire on my car, and I’m not intimidated by that fellow. Some fellow discovered penecillin and I don’t find that threatening to me. I think most of you figured out I don’t know how to spell “penecillin”, and that doesn’t bother me either. However, some fellow is a professor of logic and somehow all of us become defensive (come on, accept it) in front of him/her. In order to overcome this fear, we must verbalise it. This blog attempts to do just that.
The fear is about definitions. Mathematicians live by definitions and they can hold you accountable for them. We don’t even fear definitions so much as we fear the way mathematics applies definitions – absolutely, impartially, impersonally, objectively.
I recently had a discussion with a junior of mine who wanted to do “something creative”. Readers familiar with my “Project Guidance” blog will understand just how much that must have frustrated me.
I tried to give him an idea of what “problem” means, and the fellow went on about some grand world-saving philosophical schemes. A typical “Impressive Project” (Definition here) enthusiast. I realised perhaps my explanation on problems wasn’t clear, so I took the trouble of writing a followup to that entry.
I know it’s very difficult and frightening and scary to define use-case scenarios. And I know it’s very difficult to live with “definitions”. And I know no authority figures in any of your colleges live by definitions. But that’s just how I’m built. Without definitions there is no accountability. I am always eager to upgrade definitions. I never said they don’t need to be fixed from time to time. As a discussion progresses, a definition can and must change. However, to not have a definition itself, is something I am not willing to live with. You have to take me as I come – else don’t deal with me – it keeps you happy in your subjective world, and it keeps my frustration levels low.
Let me explain by what I mean. I’m sure 99% of readers are going to dismiss this entry as some kind of “mathematical” crap, or “everything isn’t hard and fast”. But if you’ll bear with me a minute, you’ll realise that I don’t claim everything is hard and fast either. I don’t claim everything can be absolutely understood and mapped out. However, I do claim that everything can be absolutely defined. Let me illustrate.
When you pass out from high school, there is a certain criteria that determines what college you get admitted in for higher studies. The criteria is almost always based on some marks. Within this, the criteria is somehow connected to marks you obtained in your high school courses. Now, this is a “definition” of admittance to the college. We live with it. Not because it’s what everyone is happy with, or because it defines intelligence. Simply because we need to admit _someone_ and that needs to be done in a finite period of time. It so happens that generally those who do get admitted are the ones who go on to have good careers and help in breaking down the need for definitions themselves (while still applying many definitions around them for their benefit).
The topper of your high school board exam won’t admit that the definition of a “top scorer” is simply “answering the set of questions amounting to a larger total of marks than anyone else, while maintaining the answers as close as possible to the model answers available with the examiner”. (Doesn’t that make them seem a lot more human and vulnerable than what they would like you to believe?) It so happens that this person most probably goes on to become a major celebrity and thereby perpetrates the notion that high school scores define “intelligence” itself. However, if a lower-scorer claims that’s not necessarily true, the topper will answer by, “Yes, but everything isn’t absolute. You can’t define a top scorer as simply someone who answered all questions as close as possible to the model answers.” (You’ll notice I don’t use the word “correctly”)
All around us, society is afraid of definitions because those in power would find themselves brought down to the level of us mortal human beings. Ironically, those of us already mortal humans don’t want definitions either, because by hook or crook, we hope, someday, that we shall be in power, and God-forbid we be haunted by the very definitions we helped create. More and more I realise why the Greeks thought the last of the evils to come out of Pandora’s box was “hope”. They didn’t mean hope as in, “I hope someday crime will stop”, but rather, hope as in, “I hope someday I become that crime lord I’m so jealous of. I’d better not demand laws against crime, lest my hopes should be realised.”
The more commonly encountered version of this is the ‘not-all-questions-have-a-yes-no-answer’ argument. We all know whether or not to send a soldier to certain death has no clear answer, but we either do it or don’t do it. It is this scenario of mathematics that frightens us. Maths makes us responsible. Maths makes us accountable. When India is attacked, regardless of the propriety of our soldiers being sent to death, the mathematical fact that they died does not change. And that’s what frightens the shit out of people. And that’s one reason why regardless of what you may think, I respect our elected leaders. Either they don’t send our soldiers to die, and I possibly die out of it, and they are accountable for my death. Or they do send our soldiers to die, in which case I may be saved, or even so the enemy may overpower them and kill me. Regardless of what happens, good or bad, the elected leader made a choice.
The reason we’re afraid of the yes-no answer not because we’re unsure of ourselves, but rather because we’re sure of ourselves. We’re sure we’re going to be dishonest in the future. We’re sure we’re lying our ass off! We’re sure any “answer” will haunt because we use dual standards everywhere.
To illustrate my point of how “impressive projects” are cowardly, I found an interesting joke:
A guy is celebrating his 25th anniversary of happy marriage without arguments with his wife. A fellow sitting next to him asks, “How come you went through 25 years without a single argument?”
The first guy says, “That’s because we have an understanding. I don’t bother her about all the minor and insignificant issues, and I only think about the things that matter. She looks after the groceries, cleaning, cooking, etc. I only speak about Bush’s war on terror, and Saddam Hussein’s capture.”
I never found a more fitting parable to the “impressive project” syndrome. Those people only talk at the meta level on how to design a grand all-unifying OS, or how to define a grand UI framework to end all UI frameworks. The minor problems like shipping, delivering, etc. are not their concern.
However, enter mathematics (or any real science for that matter) and all of a sudden you have definition. You have words like, “discriminants”, “quantifiable”, “measurable”, “repeatable”, etc. which scare the shit out of anyone.
Mathematics says, “Don’t tell me what opinions you have. Show me the quantifiable difference made by your opinions in this world.”
And suddenly, regardless of how insignificant her contribution may be, your wife seems to have an epsilon-above-zero contribution to say the least. Your contribution (unless you’re Bush himself – even this many people will debate) is nil! And that’s when crap like, “Hey everything cannot be measured” comes up.
You’re sitting in a board meeting pretending to be a bigshot who knows his stuff and while you’ve pretend to be paying attention all along, what’s really going on in your head is, “Hey there was a hot blonde on my way to work today. Need to strike up a conversation with her. Wonder what happens if my wife finds out?”
Then suddenly you’re asked, “Hey so do we sell this product or not?” Your rival is sitting across the table and had laid out an impressive argument against selling it. But he doesn’t matter anything to anyone (yet). Now if you say “yes”, and if it works out, you win bigtime. If you say no, and it turns out it became a big hit anyway, your opponent wins. That’s when you use the old, “Well, you know… there’s no real answer. It’s a product. It depends on whether the customer will accept it or reject it.”
Well done! Bravo! All of us fools in the meeting thought the product would make money off trees. We had no idea customers need to accept it! You got some real genius there, sport!
Of course the freakin’ customer needs to buy it! That’s what we’re asking. Do you think the customer will buy it or not? That’s what you’re being paid for you retard! And suddently you realise that if everyone understood mathematics or science even remotely your position would go to a chimp scratching his butt with sticks and being paid bananas.
With enough people like you in the world, and it’s not surprising why:
a) People think of mathematics as purely numbers and figures.
b) People think mathematics is all about absolutes and unchangeble definitions while the world is “fluid” in nature.
c) People think mathematics doesn’t apply to “real world” problems.
I am myself personally the paradox of having definitions, but I do not break them. I may oppose a definition and will fight my whole life to have it changed. But under no circumstances will I allow anyone to say, “There is no definition. It cannot be hard and fast.” Not for some grand long-term philosophical benefit of mankind either – but for my own benefit, and possibly the benefit of my kids (I meant that as a figure-of-speech).
I am by definition stupid and dumb. I scored horribly low in my high-school and college exams. By definition, I went to a bad college. By definition I am supposed to be in a “bad profile” (I prefer the word job, but I live with current definitions). Ironically, I have a job that toppers would die for. This paradox clearly indicates that either of two contemporary definitions needs to be upgraded. Either high school standard scores are not indicative of intelligence, or the job which most people seem to want is in reality a very horrible one.
There’s a very specific reason why I won’t say “remove the criteria for college admissions.” Because that puts me in a situation of unwieldable power myself. It makes the system subjective. Subjectivity is more dangerous than stupid objectivity. I am ready to face torture due to a definition, so long as there exists one, because it is uniformly applicable.
You can visit a certain department in the Pune Univ to find out for yourself. Over time, they acquired so much power, that now that can literally (yes, I kid you not!) “grant marks” based on overall student’s “intelligence”. The positive side now is that there is no way to beat the system. You can’t just score high if you fit in their “definition of intelligence” (the way it happens with high school). It seems great on day one. All alumni from even colleges (who understood nothing of this system) supported this move. Afterall, it was the perfect system! “True Intelligence” was rewarded, because there was no definition!
And suddenly, one day, one guy woke up and found himself being failed in a subject where he feels sure of being able to defend his answers even in front of Alan Turing if need be. What the heck happened? Now what does he do? How does he beat the system? He asks for the professor to evaluate him – and they do evaluate him, and he answers everything correctly. However, the scores come out again, and he’s still failing. He goes and asks the prof what happened, and the prof says that he thinks the student has no intelligence to speak of. So the student asks if there is anything he can do to convince the prof of his intelligence. The prof replies that all the alumni have certified him as being able to measure intelligence and by that authority he is failing the student. The student has beaten such systems before – in High School by mugging up answers to “come as close as possible to the model answer”, in College by using various rules and regulations to gain marks by default. And wait – he forgets – his seniors have created an unbeatable system! A system where there are no definitions except one – the prof defines every student’s intelligence.
That student was me!
