This is beautiful. Thank you. The entire universe participates in God. That is why it can be comprehensible to us through science and math. (It is also why we, creatures of physical carbon and hydrogen and oxygen) can reason at all. How on earth can matter become conscious if the nature of the universe isn't imbued with God because He created it? Doesn't seem to compute any other way.
As mother to high schoolers about to enter the post-secondary world, AND as a university instructor myself, I am at an impasse about where to send these kids. The only advice I have for them, as well as for my students is: 1) Don't train yourself to think like a machine. Be human. 2) Find a career that requires your body to do it, something that can't be replicated by a machine. Is there a place where we can send these kids of ours? (I have a few ideas in mind for B...)
More to the point, however, Matthew: given your competence at physics, shouldn't Girl Math be perfectly intelligible to you? If a pair of shoes costs $500 but you get them on sale for $250, that means you have literally CREATED $250 worth of savings! And if the average girl has, like, I don't know, 20 bathing suits and another female has only, let's say, I don't know, 14, she is literally investing in the futures market of bathing suit investments. It's investing! Not spending frivolously. And, finally, if a chandelier, let's say - hypothetically speaking - costs $3,000, but it makes the wife happy whenever she walks in the room, that's like money in the bank for a man because now he is unburdened of having the anxiety about spending anymore of his assets. It's already taken care of for him! Girl Math!! I know it *sounds* more complicated than physics. But it only sounds more complicated because it is less reasonable.
I detect a fallacy here. You have both reasoned from the goodness of swimsuit expenditures, but this is not generalizable. Swimsuits reveal the Forms, and it is for that reason alone that they are good.
Thank you. You’re one of the only writers that makes me want to go back to the philosophy I didn’t really get in college and try to understand it in a deeper and more useful way. That’s quite a gift, and I am deeply obliged to you.
(1) The mathematician does not really want to know that something is true. He wants to know why it is. And not only that: he wants to know for himself why it is, not just to be told why it is. In brief, he wants understanding. Constructing or re-constructing mathematical proof is how the mathematician comes to this understanding. This is why proof is the mathematician's stock-in-trade.
What I charitably glean from your discussion of Tawney, then, is that what he calls mathematical truth should be thought of as that which is seen when one experiences mathematical proof. Mathematical truth is not that which becomes known when one comes to know that a theorem is true. It is that which becomes known when one comes to appreciate for oneself why a theorem is true.
Brute-force, black-box computer derivations of mathematically interesting theorems, then, would seem, on Tawney's view, not to count as proofs. And rightly so. ("What computers can't do," and all that.)
(2) The sign-configurations mathematicians draw on paper or in the imagination are the necessary means of experiencing proof. In several respects, Plato seems to recognize this. To pick just one respect: he locates mathematical objects "between" the forms and sensible objects. In so locating them, Plato seems to recognize the "in-betweenness" of mathematical objects of understanding — their sensuous mode of intelligibility.
What is really interesting, though, is that this seems to entail that the mathematical sign-configurations read or drawn in the course of bringing off a proof, an experience of mathematical truth, are sites of the purest formal embodiment — sites where the material and ideal are in the most direct harmony a reasoning animal may experience.
Coming as this does from you, whose cast of mind, from what I can discern in your remarks here and elsewhere, is itself uniquely vibrant, I take this as high praise. So let me thank you, sir!
That'd be something! The Walkers I descend from were Oklahoma folk, with some Cherokee, whose descendants settled in Wyoming and California. Further back, we were Welsh, I believe.
Interesting. Mine were (as yours were?) Ulster Scots who came over around 1720, moved to, and crossed, the Pennsylvania frontier in the 1780's, and moved westward through Indiana, ending up in the Bay Area in the 1850's. Does any of the pre-Indiana background sound familiar to you?
I'm an idiot: Only just now did I notice your reference to Wales--after having fantasized a common Ulster Scots lineage for you. My apologies for some less than careful reading.
Great post, and thanks for pointing out the new book. And I believe you should develop the Heidegger point further. When I was at Deep Springs in high school I was introduced to Goedel, sort of, and majored in mathematics, though I didn't finish . . . and this sort of thing has bothered/lurked my whole life.
I was going to quip that all mathematicians are Platonists, and Plato is certainly erotic, so math is erotic. QED.
Thanks for your postscript. Nerd calls unto nerd, hence the following response.
The fact that we can represent material things mathematically can plausibly be interpreted as a sign that material things somehow afford us such representation.
In that sense, the material world as mathematically representable is not other than the material lifeworld that is our phenomenological ground zero. Rather, the former is an abstract model of the latter--an abstract model that, like abstract art, can reveal important truths about the original.
That said, mathematical physicists are subject to the temptation to collapse the distinction between mathematics and matter, and so to replace matter in their thinking with idealizations that come to seem more real than materiality. This replacement, in turn, both generates and expresses a failure to appreciate that matter is--as a friend of mine puts it--an "image of the Good."
I'm not saying that this temptation exhaustively defines what mathematical physics is or can be. I'm merely pointing out that the temptation is there, and that the tendency to succumb to it is a thread woven into the history of modern science, which is hard to disentangle from, though not identical with, various philosophical "isms" that would make the temptation plausible.
As for "the Good," I agree with Marilyn Simon. The affordance-structure of the world is itself a structure of self-diffusing intelligibility. Such a structure is a this-worldly trace of a Principle, one that is in itself the plenitude of self-diffusing intelligibility ("the Good") and, for the same reason, the plenitude of enjoyment of, and investment in, that self-diffusing intelligibility ("God").
It's this divine Principle, which is at once metaphysical and personal, which Christ claims to reveal as his Father--thus disclosing an intra-divine self-diffusion and reception, to an eternal begetting and being begotten.
Here's what Maximus the Confessor says about this (quoting and glossing Gregory of Nazianzus):
For we believe in a monarchy that is neither “begrudging of its bounty” (in the sense of being restricted to a single person), nor “disorderly” (in the sense of “being poured out ad infinitum”), but which is “constituted” by a Trinity that is equal in honor by nature: Father, Son, and Holy Spirit, “whose wealth is their identity of nature and the single manifestation of their splendor,” and “whose divinity is neither poured out beyond these three, lest we introduce a multitude of gods, nor bounded within them, lest we condemn the divinity of penury.”
Thanks for all the great stuff you're sharing with the world.
God is the Good. Now, "the Good" sounds impersonal. We need to retain that connotation in our statement that "God is the Good," because we want to make it clear that God is not a finite individual. But: Personality is not the same as finite individuality. Rather, it can and does have the dimensions of the (infinite) Good. Thus, we have to say that "the Good is God."
There are two ways of thinking anthropomorphically about God. One is to assume that he is a finite individual like us. The other, more subtle, is to think of him simply as the negation of our finite individuality.
Both of these ideas miss the way in which personhood, in the created realm, is a reflection of, and capacity for, divine personhood, understood as personality having the dimensions of the (infinite) Good.
Maximus the Confessor goes so far as to say that God and man are "models" for each other, in that man is called to be divinized, even as divinized man serves simultaneously as a kind of humanization of God.
“Only in the ethical is there immortality and an eternal life; otherwise understood, the world-historical is perhaps a spectacle, a spectacle which perhaps endures—but the spectator dies, and his contemplation of the spectacle was perhaps a highly significant way of killing time.”
― Søren Kierkegaard, Concluding Unscientific Postscript: to Philosophical Fragments
Your "nerdy" piece of work with the added question mark in title, helped me think better about things.
As I'm sure you already know, the Greek word μαθητής (mathétés) is the scriptural word for disciple: a student, a learner, a follower. I don't think it's an accidental connection that we, as mathetai of our Lord, are students of the one Logos in heaven and the logoi on earth.
This is beautiful. Thank you. The entire universe participates in God. That is why it can be comprehensible to us through science and math. (It is also why we, creatures of physical carbon and hydrogen and oxygen) can reason at all. How on earth can matter become conscious if the nature of the universe isn't imbued with God because He created it? Doesn't seem to compute any other way.
As mother to high schoolers about to enter the post-secondary world, AND as a university instructor myself, I am at an impasse about where to send these kids. The only advice I have for them, as well as for my students is: 1) Don't train yourself to think like a machine. Be human. 2) Find a career that requires your body to do it, something that can't be replicated by a machine. Is there a place where we can send these kids of ours? (I have a few ideas in mind for B...)
More to the point, however, Matthew: given your competence at physics, shouldn't Girl Math be perfectly intelligible to you? If a pair of shoes costs $500 but you get them on sale for $250, that means you have literally CREATED $250 worth of savings! And if the average girl has, like, I don't know, 20 bathing suits and another female has only, let's say, I don't know, 14, she is literally investing in the futures market of bathing suit investments. It's investing! Not spending frivolously. And, finally, if a chandelier, let's say - hypothetically speaking - costs $3,000, but it makes the wife happy whenever she walks in the room, that's like money in the bank for a man because now he is unburdened of having the anxiety about spending anymore of his assets. It's already taken care of for him! Girl Math!! I know it *sounds* more complicated than physics. But it only sounds more complicated because it is less reasonable.
If math is erotic, does that mean that multiplying bathing suits is closer to the heart of mathematics than reducing their number?
hahaha! I'm dying, Adrian. Yes. Yes it does. This is Girl Math metaphysics.
Let's go further: Money is a symbolic enactment, in the social world, of the affordance-character of the natural world.
Ergo, the more you spend, the more you reveal the good.
I detect a fallacy here. You have both reasoned from the goodness of swimsuit expenditures, but this is not generalizable. Swimsuits reveal the Forms, and it is for that reason alone that they are good.
(Still, wait for a 50% off sale.)
I guess I have to admit defeat.
Especially when I consider that some swimsuits, when worn, reveal forms that fall pretty far short of the Forms.
Sounds good to me!!
Are you paying attention to this, Matthew? I am doing the Lord's work.
Not that I'm trying to take sides or anything . . .
Thank you. You’re one of the only writers that makes me want to go back to the philosophy I didn’t really get in college and try to understand it in a deeper and more useful way. That’s quite a gift, and I am deeply obliged to you.
Another lovely essay, Matthew. Thank you.
(1) The mathematician does not really want to know that something is true. He wants to know why it is. And not only that: he wants to know for himself why it is, not just to be told why it is. In brief, he wants understanding. Constructing or re-constructing mathematical proof is how the mathematician comes to this understanding. This is why proof is the mathematician's stock-in-trade.
What I charitably glean from your discussion of Tawney, then, is that what he calls mathematical truth should be thought of as that which is seen when one experiences mathematical proof. Mathematical truth is not that which becomes known when one comes to know that a theorem is true. It is that which becomes known when one comes to appreciate for oneself why a theorem is true.
Brute-force, black-box computer derivations of mathematically interesting theorems, then, would seem, on Tawney's view, not to count as proofs. And rightly so. ("What computers can't do," and all that.)
(2) The sign-configurations mathematicians draw on paper or in the imagination are the necessary means of experiencing proof. In several respects, Plato seems to recognize this. To pick just one respect: he locates mathematical objects "between" the forms and sensible objects. In so locating them, Plato seems to recognize the "in-betweenness" of mathematical objects of understanding — their sensuous mode of intelligibility.
What is really interesting, though, is that this seems to entail that the mathematical sign-configurations read or drawn in the course of bringing off a proof, an experience of mathematical truth, are sites of the purest formal embodiment — sites where the material and ideal are in the most direct harmony a reasoning animal may experience.
This is brilliant, sir. Thanks.
Coming as this does from you, whose cast of mind, from what I can discern in your remarks here and elsewhere, is itself uniquely vibrant, I take this as high praise. So let me thank you, sir!
Thanks very much!
We have the same surname--very cool. Could we be distant cousins?
That'd be something! The Walkers I descend from were Oklahoma folk, with some Cherokee, whose descendants settled in Wyoming and California. Further back, we were Welsh, I believe.
Interesting. Mine were (as yours were?) Ulster Scots who came over around 1720, moved to, and crossed, the Pennsylvania frontier in the 1780's, and moved westward through Indiana, ending up in the Bay Area in the 1850's. Does any of the pre-Indiana background sound familiar to you?
I'm an idiot: Only just now did I notice your reference to Wales--after having fantasized a common Ulster Scots lineage for you. My apologies for some less than careful reading.
Great post, and thanks for pointing out the new book. And I believe you should develop the Heidegger point further. When I was at Deep Springs in high school I was introduced to Goedel, sort of, and majored in mathematics, though I didn't finish . . . and this sort of thing has bothered/lurked my whole life.
I was going to quip that all mathematicians are Platonists, and Plato is certainly erotic, so math is erotic. QED.
Keep up the great work.
Hi, Matt:
Thanks for your postscript. Nerd calls unto nerd, hence the following response.
The fact that we can represent material things mathematically can plausibly be interpreted as a sign that material things somehow afford us such representation.
In that sense, the material world as mathematically representable is not other than the material lifeworld that is our phenomenological ground zero. Rather, the former is an abstract model of the latter--an abstract model that, like abstract art, can reveal important truths about the original.
That said, mathematical physicists are subject to the temptation to collapse the distinction between mathematics and matter, and so to replace matter in their thinking with idealizations that come to seem more real than materiality. This replacement, in turn, both generates and expresses a failure to appreciate that matter is--as a friend of mine puts it--an "image of the Good."
I'm not saying that this temptation exhaustively defines what mathematical physics is or can be. I'm merely pointing out that the temptation is there, and that the tendency to succumb to it is a thread woven into the history of modern science, which is hard to disentangle from, though not identical with, various philosophical "isms" that would make the temptation plausible.
As for "the Good," I agree with Marilyn Simon. The affordance-structure of the world is itself a structure of self-diffusing intelligibility. Such a structure is a this-worldly trace of a Principle, one that is in itself the plenitude of self-diffusing intelligibility ("the Good") and, for the same reason, the plenitude of enjoyment of, and investment in, that self-diffusing intelligibility ("God").
It's this divine Principle, which is at once metaphysical and personal, which Christ claims to reveal as his Father--thus disclosing an intra-divine self-diffusion and reception, to an eternal begetting and being begotten.
Here's what Maximus the Confessor says about this (quoting and glossing Gregory of Nazianzus):
For we believe in a monarchy that is neither “begrudging of its bounty” (in the sense of being restricted to a single person), nor “disorderly” (in the sense of “being poured out ad infinitum”), but which is “constituted” by a Trinity that is equal in honor by nature: Father, Son, and Holy Spirit, “whose wealth is their identity of nature and the single manifestation of their splendor,” and “whose divinity is neither poured out beyond these three, lest we introduce a multitude of gods, nor bounded within them, lest we condemn the divinity of penury.”
Thanks for all the great stuff you're sharing with the world.
Warmly,
Adrian
God is the Good. Now, "the Good" sounds impersonal. We need to retain that connotation in our statement that "God is the Good," because we want to make it clear that God is not a finite individual. But: Personality is not the same as finite individuality. Rather, it can and does have the dimensions of the (infinite) Good. Thus, we have to say that "the Good is God."
There are two ways of thinking anthropomorphically about God. One is to assume that he is a finite individual like us. The other, more subtle, is to think of him simply as the negation of our finite individuality.
Both of these ideas miss the way in which personhood, in the created realm, is a reflection of, and capacity for, divine personhood, understood as personality having the dimensions of the (infinite) Good.
Maximus the Confessor goes so far as to say that God and man are "models" for each other, in that man is called to be divinized, even as divinized man serves simultaneously as a kind of humanization of God.
Your postscript reminded me of Kierkegaard's:
“Only in the ethical is there immortality and an eternal life; otherwise understood, the world-historical is perhaps a spectacle, a spectacle which perhaps endures—but the spectator dies, and his contemplation of the spectacle was perhaps a highly significant way of killing time.”
― Søren Kierkegaard, Concluding Unscientific Postscript: to Philosophical Fragments
Your "nerdy" piece of work with the added question mark in title, helped me think better about things.
As I'm sure you already know, the Greek word μαθητής (mathétés) is the scriptural word for disciple: a student, a learner, a follower. I don't think it's an accidental connection that we, as mathetai of our Lord, are students of the one Logos in heaven and the logoi on earth.