I am sorry, this is not going to be a funny post.
If you like dark comedy, well, maybe yes. I have been suffering from a severe
form of apeirophobia since the age of 5. Concentrating on the problem of
infinity, on the idea that I am a finite human being with a capacity for a
potentially infinite thinking, scares me to death: I feel entrapped, in a cage,
choking. I am serious! I go insane, until I find distraction. Being raised a
Catholic does not help, for the concept of eternity works as a materialized
version of the pure panic I experience when I try to grasp the heavy concept of
infinity. When I encountered Maths, I felt attracted and disgusted at the same
time: it looked like a brave, possibly self-delusional, attempt to symbolize
and systematize what cannot really be symbolized and systematized. I
preferred to take refuge in language(s): I identified with its openly
acknowledged confusion, imprecision, arbitrariness. What I failed to
understand is that Maths could have actually helped me to contain and give
shape to my logical and existential uneasiness. Leibniz's idea that "human
thought can be reduced to calculation" (Davis 121) never crossed my mind:
using thinking to control thinking, embody thinking and make it more efficient,
but most of all, using thinking to understand the same mechanisms of thinking and
to free it from its own paradoxical limits, is something I never really took
into serious consideration.
After an intimidated and "foggy" reading of Davis, a question of limits emerges as a crucial point in my reflections. Let's try to think in these terms: computers are limited machines that respond to algorithms imposed by limited human beings. We give them inputs, and they do it. We delimit what we think is computable and we create these machines that each time redefine our logical limits. In fact, we cannot keep everything under control, Leibniz's optimistic "calcolemus!" is not enough. Among other things, the undecidability of the so-called halting problem is a negative answer to the Entscheidung problem, and again, it poses a question of limits. There is something that inevitably escapes our logical thinking, we are still dwelling between the finite and the infinite, we try to delimit our thinking and, yet, we can't.
After an intimidated and "foggy" reading of Davis, a question of limits emerges as a crucial point in my reflections. Let's try to think in these terms: computers are limited machines that respond to algorithms imposed by limited human beings. We give them inputs, and they do it. We delimit what we think is computable and we create these machines that each time redefine our logical limits. In fact, we cannot keep everything under control, Leibniz's optimistic "calcolemus!" is not enough. Among other things, the undecidability of the so-called halting problem is a negative answer to the Entscheidung problem, and again, it poses a question of limits. There is something that inevitably escapes our logical thinking, we are still dwelling between the finite and the infinite, we try to delimit our thinking and, yet, we can't.
Reading Davis not only made me feel extremely fascinated by - and full of intellectual respect for- logic, but it also made me smile ironically at my long-time
rejection of Maths as "the enemy." Obviously enough, things are not so simple, and
abstract maths and logic are in fact naturally interconnected with what we
call "the humanities." In this sense, Davis' book can be used to prove
"traditional humanists" wrong in regarding computers as "the
enemies," because, in the end, they are not only products, but also
representations and co-actors of our own human thinking. And what do they do
for our thinking? They empower it, and they help it to move further: they
embody its limits and push them forward. In this sense, they are subjected to
our thinking, but they also change it, they are our slaves and our masters. They depend on us and we depend on them. DH, then, can be regarded as a rather
pragmatic acceptance of the new ways in which we try to make sense of the
world, an acceptance that will presumably, gradually bring to a renovated
understanding of how we form knowledge and of what we consider knowledge to be.
I really like the way you’ve phrased the relationship between language and logic here. I had never considered the question of calculation as being a way to ‘delimit our thinking,’ but I find that it is an absolutely apt way of explaining it, at least to someone who is coming to the realm of math an logic from that of the humanities. I think, too, that having to enforce limits or structures on our language can allow us to discover some of that which has previously escaped us. In a way, the limits of logic can be what lift some of the limits of our previous capacity for understanding.
ReplyDeleteThe thought of our finite being is a topic that many find intimidating. Embracing the concept is something that makes us all human. The idea of computers as "beings" of infinite knowledge is irrational. I agree with the thought of logic and mathematics being "the enemy." Many feel the same way. By embracing that concept, computers have become commonplace for many. Computers are only as good as the person who programmed them. So where does that leave us?
ReplyDeleteCaterina,
ReplyDeleteI share your idea that “math” or in other terminologies “engineering” and “humanities” have certain commonalities and both develop what we call “knowledge”. How essential it is that both are interconnected and work in coordination with each other. The “math” is the “how” and “humanities” is the “why” and none can make sense or exist without the other. In other words, “humanities” probe what it means to be human and who we are and “math” or “science” articulates that meaning in a very sophisticated way. Imagine a life where you are a graduate from an “engineering” Dept. and can’t even locate a place on the map. So, they are both inseparable and belong to human knowledge.