on my senior essay
I think that there are different ways of trying to understand the world around us - just like I believe that there are different kinds of intelligence. You can be physically smart - a good athlete, strong, graceful, healthy - and you could be smart about the relationships between people, and of course, you can have an academic intelligence, which is typically the one people most readily recognize as intelligence. I think that a lack of one kind of intelligence doesn’t mean that you aren’t smart, just that you aren’t smart in that one particular way. This doesn’t mean that I think we’re all equal, either. I certainly feel like I’ve known people who seem to have more than their fair share of intelligence, sometimes in all the categories, or at least more than one. But I have a hard time saying that people are UNequal either. I guess, in the end, I think that worth in people may be a judgment call you can’t make about those around you - we’re all so close. Maybe we can make historical judgments…and we can certainly make judgments about actions. But not about a person as a whole, as an entity.
Back to the different ways of understanding. I was thinking about two things that I often keep separate - poetry and mathematics. Or, as I don’t mean either of those specifically as just that one genre, but as a mindset. I think that poetry is one way of understanding the world around us - maybe I should rather call it art. Art, I think, is about creating images of the world - the inside world or the outside world. And images either in words or paint or clay or sound. In general, a poem is about trying to understand something - and in the end, I think that all poetry comes down to trying to understand poetry…trying to understand this particular way of understanding. Sometimes it looks like a poem is about a person, or a vision, an experience or a feeling. But when I look at poetry in the broad context of all poetry - each poem is about that same thing. This same certain understanding of the world.
And I think that I am certainly capable of trying to understand the world that way. What I mean is that I use poetry to express or question my world - not necessarily my own created poetry, but this poetic outlook, I guess.
But the other way of understanding that I notice in myself - mathematics. All science, I guess I mean really. It’s a completely different way of understanding the world. A way that often involves trying to mathematize a physical event or reality. This could be anything from biology, a lot of strict observation, to physics, trying to come up with the equations that perfectly describe or predict those observations, to pure theoretical mathematics…numbers or equations that don’t necessarily have any physical component seen in the world. Nevertheless, mathematics is an attempt to understand the world - a world that can be seen sometimes only in our heads.
Descartes was interested in two things. First, he wanted to systematize pure mathematics. He wanted to find a method which would enable anybody to solve any problem. Just follow a certain number of predefined steps, in this manner, and there will be an answer. Sometimes that answer might be - we don’t know. But there will always be an answer, and if you used the method truly, you will know not first that you used it correctly and that the answer is right.
The second thing Descartes wanted was to be able to apply this same method, this mathematical achievement, to what I think of as two different kinds of understanding. He wanted to apply the method to the mathematical sciences…but also to poetry - more specifically, to theology.
I think Descartes achieved the method that will work with the first understanding, but not with the second…and I think that this is not only the only result possible, but also a good thing.
I think that the method was needed for math. I’ve seen this again and again in tutorial - an idea that not everybody is able to ‘do’ math. People say, like it’s the end of the conversation, ‘well, I’m just not a math person’. I think that before Descartes this could have been true. In Euclidean geometry, everyone should be able to follow the steps, once they’re broken down far enough, and explained patiently enough. (remembering, is, of course, something else entirely). But not everyone is capable of coming up with these mathematical proofs on their own. It does seems to require a certain kind of mind - a math person. I have only very rarely had the experience of ‘just getting’ a proof, the way I see some people ‘just get’ math all the time. There’s a flash, a jump, something sudden and often indivisible…and then you see the answer. There seems to be no way to induce this in someone else. You can lead them to see the answer, but they can’t always just ‘see’ it.
After Descartes, however. His method, what we call algebra now, shows both the way to explain the proof AND how to come up with it. There is method for the whole process - a method that leads you to that flash - the moment when you ‘see’ it. That strange kind of seeing, mathematical insight perhaps, is included in the steps of the method. Is reduced to plain sight. I don’t think the magic of the process is lost - some of the mystery, yes. Perhaps some of the awe-fullness is lost. However, the result is worth it - is still that understanding that we all want, and that Descartes set out to capture for everyone. (set out to capture for everyone only so that it can be had at all - he wasn’t so altruistic just to want it for some sense of justice)
Descartes wants to achieve this with all understanding. He wants ALL HUMAN KNOWLEDGE to be reachable. I don’t think his method could possible apply to art or poetry. There is no formula for the creation of a poem, just as there is no formula for the analysis of a poem. That’s the difference, perhaps, that the building block of the method was there already for math…geometrical analysis (the ability to read and understand a proposition in a definitive “correct” way) already existed, indeed is necessary for science. Math needs to have an answer….poetry can’t have an answer.
If Descartes had been able to find a method that not only proved to him that there was a god, but also proved it to the rest of us…he would have found a method that eventually could have mathematized things like love, art…god. Things that can’t, and shouldn’t be mathematized. He would have reduced these two different ways of knowing, of trying to understand the world around us to one way. This certainly would be simpler for everyone. But it also would be a loss. We would lose a dimension of understanding. With the method applied to math, we gain one of those dimensions…at the very least, we hold it more securely.
I think this is why the liberal arts include both math and the so-called language arts. An education without either is incomplete. No one should be forced to choose between math and poetry - and no one should ever feel that they have access to only one. Descartes made it clear that it is possible for everyone to use math.
(Perhaps I’m still waiting for someone to make it clear that everyone can use poetry, although generally that is not as much in question. Doesn’t everyone feel a connection to some kind of art or other, even if it is not a creative connection? And maybe a proof of the accessibility of poetry is still asking the impossible, because any proof would need to use the other understanding.)
So yeah. Descartes makes it clear that it is possible for everyone to use math. And, today, in my life and in the lives of my classmates, St. John’s makes it clear that we don’t need to make a choice between math and poetry. In fact, St. John’s forces us to use and develop both understandings of the world. In the end, that is what an education is, I think. That is why I came to St. John’s in the first place - and that is what I finally see that I’m ending with. When I decided to write my paper on the Geometry, I was worried that I wasn’t writing about anything exciting or important…or worse, that I wasn’t writing about something that meant anything to me…not in the way the senior essay is supposed to. But it was something important to me. I never got into the other way of understanding…but I have the rest of my life to continue developing this. It really is something I believe in…something I have faith in, even.