So SOMEBODY spread the word that the TOK paper was due on Monday, not to point any fingers (Michelle) So I wrote mine. When I probably could have spent the time better working on my History paper, or maybe the Extended essay. No matter. What is done is done… and the TOK paper is done. And for that matter I did a kickass job, so good in fact that I am going to post it for your reading pleasure. Woot!
If Math did not Exist What Difference Would it Make?
In order to imagine a world without math we would have to determine whether or not math is something that is discovered or something that is invented. I personally believe that math is something that is discovered. The symbols are merely a language to explain what has been discovered. I can’t just go and “invent” a formula and suddenly the world changes to accommodate my new formula and me. The world doesn’t work that way. So if I say that math is something that is an intrinsic part of life itself, its absence would be cataclysmic. In summary, if math is something that we discover as in it exists without people putting numbers to it, and it suddenly ceased to be. The whole of the universe would cease to be. The very laws that keep the universe together would fail.
So in order to put this into perspective I will analyze one tiny facet of math, the mathematical structure of ice. The structure of ice allows it to float on water. Without math ice would loose its unique structure and sink. All the icebergs around the world would sink the bottom of the ocean where they would remain frozen. Gradually the amount of ice on the ocean floor would become thicker and thicker, until it became an entire ocean of solid ice. With the exception of undersea volcanic vents, Earth would become an ice planet. All the crops would die and it would be the end of life on earth, with the exception of those volcanic vents. But with such a cold planet, it stands to reason the core would gradually cool too, so those volcanic vents would freeze too.
Now on our cold lifeless, dead planet, the mathematics of gravity suddenly stops working. We are rocketed at high velocity into the universe, and into whatever lurks there, be it planet, asteroid or alien (never mind that all the aliens would have died too). Simultaneously all the other planets and moons and black holes also loose their gravity so large objects are moving at random velocities in every direction and soon the whole Milky Way is a death trap for our poor defenseless, and dead ice planet. Well, taking into account the massive space between interstellar bodies, death trap might be too strong a word. Actually without gravity collisions would be less likely because we could sail inches from other planets and they wouldn’t hit. But no matter, without the heat of the sun our planet is dead anyway.
Now without gravity, what is to prevent huge chunks of planet from simply breaking off? The answer is inertia. Without inertial things that were stopped could suddenly start moving and things that were moving could suddenly stop or change direction. So suddenly half the earth stops moving and the whole planet is ripped apart by its own momentum. This is a bit far fetched but then again the whole idea of a universe without math is also far fetched.
I could argue that math is only what we put numbers to, in that it is an invention of humans to explain the complexities of the world around us. The math itself is only the numbers we put to it. This is the theory of invention. Now we are going to assume that without math the universe would still exist. Because writing about a non-existent universe does not make for a very good essay. So for arguments sake I am saying that math is something that we impose upon the universe, and not something the universe imposes on us. Because everything we see has foundations in math, even to the molecular level, but the actual numbers are something that we have thought up. So we are, for argument’s sake assuming that math only exists in our understanding of it.
How we need math, let me count the ways. Without math we could not be able to build computers. In fact we wouldn’t be able to build houses either. Say goodbye to math class, money, TV, communication in general, and all modes of transport (with the exception of walking) even horse drawn carriages employ math. Our entire economy would be reduced to a barter system. “How many camels do you want for that daughter”? In summary we would be reduced to the stone ages, or even for that matter before the stone ages because we wouldn’t even be able to make notches into sticks marking the passage of time. I hope that paints a vivid enough picture for you.
So here we are, suddenly thrown into the early stages of human existence. Because there could be no transportation (cars and airplanes require math) we would not be able to transport food. All the grocery stores would close down; there would be mass starvation. People would start eating their pets, or going to animal shelters for dinner. But that wouldn’t last us long, humans are very hungry and cats and dogs are at the bottom of the food chain. The only way we could survive it to set up a system of subsidence farming. Only one problem there, without transportation there is no way to get seeds! Not to mention that with our overpopulation there is no way tiny suburban yards could feed the nation. So here we are sitting here, starving to death. When suddenly people start becoming sick, there is no way to treat them, and people are dropping like flies from SARS, and Smallpox, and Tuberculosis, and Scarlet Fever in the cities. These people run away from the cesspools that are the cities and only end up in spreading the pandemic. Meanwhile the poor people in the suburbs have no idea what’s going on because transportation and telephones do not exist. So that being said most of the people starve to death and the people who don’t die of terrible illness that they cannot treat. About this time there would be a widespread panic and a decided rise in violence. The only people who would survive this whole ordeal unscathed would be some nomadic Nordic tribes and the Aborigines of Australia. Who didn’t use math in the first place.
But keep in mind that if math is something that we invent it is also something that can be reinvented. So there will survive some small pockets of people, and many years into the future someone might discover “the wheel.” Needless to say our entire culture would be demolished. And many millions of people would die. But it isn’t all-bad news it would be very good for the environment, and there would no longer be the dreaded math class, and people would get out of their caves (houses involve math) lots more. They would say fit, having to chase down, kill, skin, and cook dinner before eating it.
The lack of math would completely alter our perceptions of the world, what we see as “truth” would only be what we could see with our own eyes. People would forget that the Earth actually is round and that chlorophyll is what makes plants green. Logic is completely thrown out the window because it is based on math. So people would return to the glorious days of oral tradition, because fortunately for us language does not require math. I would like to point out that if math is something that we create, without it the universe would hold up fine, but our culture, and the vast majority of our population would die out. Personally I find this much more appealing than the ice planet theory, but I believe that math is something that we discover, and not something we invent.
A loss of math would entail a loss of understanding about the deeper workings of life. With this loss of understanding comes a loss of knowledge. Because even as an abstract idea, math is significant in the fact that it just works. We have built up a culture entrenched in the ideas of math. All great advances, such as medicine, technology, and architecture would be impossible without math. It affects how you perceive the world, and to what degree you understand it. There is a difference between going “very fast” and going at 90 miles per hour. When it comes down to it we can twiddle our thumbs and wonder at what the world would be like without math, and then again we can also twiddle thumbs and think about how many stars there are, for all the good that does us. A world without math couldn’t happen so we need not worry about it, except for entertainment value.
I love it ^___^
*whip-pish* back to work
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