Let’s Face It, We Are Numskulls At Math!
Noted mathematician, Timothy Gowers, talks about the importance of math
I’ve often written about Mathematics before Footnotes. As much as math helps us better understand our world (Modern Medicine’s recent strides have a lot to do with applied math for example), it also tells us how severely limited man’s common thinking is.
Humans and yes some animals too, are born with or soon develop an innate ability for understanding numbers. Yet, just like animals, our proficiency with numbers seems to stop short of the stuff that goes beyond our immediate activities of daily living (ADL) and survival. Because we are a higher form of being (or allegedly so, depending on your point of view), our ADLs are a lot more sophisticated than say those of, canaries or hamsters. And consequently you can expect to see a little more refined arithmetic being used by us. But fundamentally, we share this important trait – of being able to work with numbers from an early stage. A man who has a family with kids knows almost by instinct that if he has two kids to look after, that would mean breakfast, lunch and dinner times 2 in terms of putting food on the table. He would have to buy two sets of clothes for his kids. A kid soon learns that he has two parents. And so on. It’s almost natural. And when someone can’t figure out their way doing simple counting or arithmetic, we know that something might be wrong. In Medicine, we have a term for this. It’s called acalculia and often indicates the presence of a neuropsychiatric disorder.
It’s easy for ‘normal’ people to do 2 + 2 in their heads. Two oranges AND two oranges make a TOTAL of four oranges. This basic stuff helps us get by day-to-day. But how many people can wrap their heads around 1 divided by 0? If you went to school, yea sure your teachers must have hammered the answer into you: infinity. But how do you visualize it? Yes, I know it’s possible. But it takes unusual work. I think you can see my point, even with this simple example. We haven’t even begun to speak about probability, wave functions, symmetries, infinite kinds of infinities, multiple-space-dimensions, time’s arrow, quantum mechanics, the Higgs field or any of that stuff yet!
As a species, it is so obvious that we aren’t at all good at math. It’s almost as if we construct our views of the universe through this tunneled vision that helps us in our day-to-day tasks, but fails otherwise.
We tend to think of using math as an ability when really it should be thought of as a sensory organ. Something that is as vital to understanding our surroundings as our eyes, ears, noses, tongues and skins. And despite lacking this sense, we tend to go about living as though we somehow understand everything. That we are aware of what it is to be aware of. This can often lead to trouble down the road. I’ve talked about numerous PhDs having failed at the Monty Hall Paradox before. But a recent talk I watched, touched upon something with serious consequences that meant people being wrongfully convicted because of a stunted interpretation of DNA, fingerprint evidence, etc. by none other than “expert” witnesses. In other words, serious life and death issues. So much for our expertise as a species, eh?!
How the human mind struggles with math!
We recently also learned that the hullabaloo over H1N1 pandemic influenza had a lot do with our naive understanding of math, the pitfalls of corporate-driven public-interest research notwithstanding.
Anyhow, one of my main feelings is that honing one’s math not only helps us survive better, but it can also teach us about our place in the universe. Because we can then begin to fully use it as a sensory organ in its own right. Which is why a lot of pure scientists have argued that doing math for math’s own sake can not only be great fun (if done the right way, of course :-P) but should also be considered necessary. Due to the fact that such research has the potential to reveal entirely new vistas that can enchant us and surprise us at the same time (take Cantor’s work on infinity for example). For in the end, discovery, really, is far more enthralling than invention.
UPDATE 1: Check out the Khan Academy for a virtually A-Z education on math — and all of it for free! This is especially a great resource for those of us who can’t even recall principles of addition, subtraction, etc. let alone calculus or any of the more advanced stuff.
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