Wednesday, August 17, 2016

God is a Meta-Mathematician

This article on What It's Like to Understand Higher Mathematics (HT Happy Acres) touches on a lot of the ideas discussed in our previous post on Guided Ignorance and Faithless Stupidity.

So, what is it like to be a genius at math? Ironically, it cannot be quantified, and mathematicians usually lack the qualitative/literary skill to express themselves mythsemantically. But this one is quite clear, and many of the skills he describes are generalizable to other fields, say, medical diagnosis. A skilled diagnostician can filter out all sorts of noise that may distract and deceive the novice, and hone in on subtle clues missed by the uninitiated.

Thus, "You are often confident that something is true long before you have an airtight proof for it." We call this "intuition," but that doesn't mean it isn't rooted in a kind of real perception (or perception of reality).

Rather, "you have a large catalogue of connections between concepts, and you can quickly intuit that if X were to be false, that would create tensions with other things you know to be true, so you are inclined to believe X is probably true to maintain the harmony of the conceptual space."

This is one reason why it can be frustrating to try to explain a higher or deeper truth to someone who isn't as intelligent or perceptive as you are. You may not be a particularly systematic thinker, so you may not even be able to articulate the implicit steps that led you to your conclusion. You could say that it's a "feeling," but it is much deeper than that.

For example, I always have a particular "feeling" when I read Schuon, but it's not merely an emotion. It's very hard to describe, because it is what it is and not something else. But it includes a kind of deep and expansive pneuma-cognitive satisfaction, almost comparable to how we are somehow satisfied by a musical piece. Why should music satisfy us at all, and what is being satisfied? There's something about the logic of the piece, as if everything about it is inevitable and complete.

When I read Schuon, there is a strong feeling that he goes as far as thought can take us. In that regard, it is very "satisfying." Again, what is being satisfied? Well, being that man is made to know, it must be a kind of comprehensive satisfaction of that need.

I suppose scientists and mathematicians experience something similar, but it's hard for me to imagine anything approaching total satisfaction from those fields. So much is left out of even their most sophisticated models, that they would leave me hungry for more.

I have read any number of biologists who talk about the deep intellectual satisfaction that accompanies their appreciation of natural selection. Well, yes. I am well aware of that feeling myself. Maybe I just have a bigger appetite, but I consider it only a first course. Metaphysics is the dessert. And theology is the after dinner cigar.

Polanyi was a "meta-scientist," as it were. He basically examined the logic of scientific discovery, and built a more general theory of knowledge based upon it. Thus, "imagination sets actively before us the focal point to be aimed at, but it is intuition that supplies our imagination with the organization of subsidiary clues to accomplish its focal goal, as well as the initial assessments of the feasibility of this goal. Intuition thus guides our imagination" (Prosch).

And all of this action takes place beneath the surface of consciousness. We are always guided by we-know-not-what. But it doesn't mean we aren't being pulled by this invisible gradient of meaning, AKA a nonlocal attractor.

Indeed, many if not most of the things we believe are due to prior non-conscious "commitments" to ideas, principles, concepts, and conclusions of various kinds. For Polanyi, these can never be rendered fully explicit, but we can in a sense know them by that to which they point. So, if, say, an atheist tells you that you cannot specify all the reasons why you believe in God, it is no different for the atheist: nor can he specify all of the implicit and subsidiary clues that led him to his conclusion.

A key thoughtlet occurs to me: if you believe all of your evidence can be rendered explicit, you have to be a pretty shallow individual. This was the philosophy of positivism, and although it has been discarded by philosophy as such, there are still a lot of crude scientistic positivists running around.

I recently evaluated an intelligent young woman who said she had discarded her Catholicism for Science. The problem is, you can superimpose Science on yourself from above, but it won't do anything to speak to all of those implicit clues demanding an answer. Therefore, you have to dismiss them as irrelevant, which can lead to a kind of existential pain that doesn't seem to have any "cure."

Here is another example of what it's like to be a math wiz: "You develop a strong aesthetic preference for powerful and general ideas that connect hundreds of difficult questions, as opposed to resolutions of particular puzzles."

Now, such ideas can obviously mislead, and we have to be cautious about indulging this ability. For example, Marxism is a quintessential case of a "powerful and general idea that connects hundreds of difficult questions." It is also utterly false, but that doesn't diminish its appeal to the susceptible.

To be perfectly accurate, we all have this susceptibility to total explanation by virtue of being human. It comes with the standard package. But is a total explanation even possible without God at the top? No, it is not. For starters, if there is no God, then there is no top or bottom at all, just as Darwin says. And there is no reason in the world we should pay attention to the pompous declamations of a randomly evolved talking monkey.

The piece concludes with a good one: "You are humble about your knowledge because you are aware of how weak math is, and you are comfortable with the fact that you can say nothing intelligent about most problems."

However, this particular mathematician just said a number of intelligent things about human problems. But it wasn't via math per se, rather, a meta-mathematical analysis of the mathematician's cognitive abilities. Quality trumps quantity every time, for the same reason that semantics can never be reduced to syntax. Math has no meaning that isn't ultimately self-referential. It requires a deeper insight in order to extricate oneself from that closed loop and make contact with the transcendent real, AKA God.

God is like a good accountant: he's surely adept at math, but can also tell you what to do to avoid an audit.


mushroom said...

The problem is, you can superimpose Science on yourself from above, but it won't do anything to speak to all of those implicit clues demanding an answer.

John 15:16 -- "You did not choose Me, but I chose you ..."

John 6:44 -- "No one comes to Me unless the Father who sent Me draws him. ..."

I heard that when they asked Morgan Freeman if he believed in God, he replied that he was god. It was probably tongue-in-cheek, but that is essentially what the I-fucking-love-science crowd thinks.

I did have a choice, but it wasn't a positive choice. I could have rejected the truth I was offered, but I can't choose or create my own version.

Gagdad Bob said...

Celestial clues are everywhere. One can arrive at a theory that ignores them, but it won't make the clues go away. A good theory answers questions without un-answering many more in turn. Science un-answers the whole dimension of transcendence, while God in no way un-answers science.

julie said...


Again, what is being satisfied?

There is a whole internet meme these days of "oddly satisfying" video clips. Taking a step back, it seems that satisfaction has to do with something being completed, made whole, or brought to a conclusion. Placing the rug that ties the room together, as it were. Like scratching an itch in a place you can't touch.

Abdulmonem Othman said...

God in not a human sitting somewhere in this ever-expanding cosmos nor an idol to be worshiped. God is the operating system of our cosmos and what it contains, in both its dimensions that of creation and command. The physical and the non-physical and the call is to the consciousness in the physical to know the consciousness of the non-physical and that is why truth matters and it is the first that matters that must be pursued in the light of the non-physical command. Misplaced attention and intention is waste of energy that must be avoided. Studying physicality must not veiled us from what is operating this physicality or attribute to this physicality something which we are not sure of. The story of the devil comes to mind when he refused to bow to Adam saying he is better that adam because he is made of fire and fire according to his thinking is better than clay and how he was reminded that the issue is not the make up but the command. I was wondering about the value of the study of the fractal manifestations in Joyce fannagan wake, or for that matter of those who want to know what our cosmos is made of and forgetting to study the purpose of all these astonishing phenomena and highlighting the awakening calls of all these signs.I find in your writings some valuable nourishment to my soul that pushes me to communicate because I never know when the catcher will catch.

Joan of Argghh! said...

That's like someone is using a kind of an AI bot convo generator making a big play for attention. It's of a foreign extraction but has scraped your blog enough to mirror back in an almost human fashion! Fascinating!

Magnus Itland said...

In one word, what connects mathematics and Schuon is *beauty*.

A genius within mathematics or physics is drawn to the beauty of certain equations and sense in this the proof of their truth. Likewise with Schuon. Although Schuon definitely has his own "human margin", we also see an undeniable beauty in his works.

Joan of Argghh! said...

The satisfaction we feel when we gaze upon beauty is because the Golden Ratio shines through so much that is "perfect." As Magnus said, beauty is the proof of their truth. Not all of us are born to be that expression of the outward and limited proofs of beauty, but all of us are born to be that expression of unlimited proofs of the most Beautiful, in all its forms.

Ephrem Antony Gray said...

Definitely a case for Schuon's old adage: "Beauty is the splendor of the True".

Philosophers were/are definitely drawn to the beauty of certain forms of thought - I seem to recall in programming we call code which is at least superficially beautiful "elegant".

Like above, mere elegance is not proof of truth... though the true is pretty much always elegant. Sometimes the elegance of the truth is harder to see, I think, in that false elegance is simply invented to satisfy the superficial cues we have associated with elegance, like soda pop entices the taste buds. Kind of like when a woman hyper-dolls herself up, simply pulling obvious triggers. To one with a bit more sensitivity and sensibility, the mask is obvious and rather insulting!

I seem to recall that for a time the left was on to certain truths, but they were always presented as 'ugly' truths, as if the most important thing to do was shock people into belief. The consequence of this idea as a formula of course applied itself to beauty in the exact same way - making things ugly to make them seem true.

julie said...

Along those lines, there's been some interesting news trickling out of the Large Hadron Collider experiments (via Vanderleun's sidebar). Apparently, nature is (to a physicist's mind) disappointingly ugly. I suspect the real problem is that nature is what it is.

katzxy said...

"Math has no meaning that isn't ultimately self-referential. It requires a deeper insight in order to extricate oneself from that closed loop and make contact with the transcendent real, AKA God."

Yes, math is self contained. Yet it is awfully effective in practical matters. The disconnect, that self contained feeling, may be an artifact of how practitioners want to see themselves and their field of study. The effectiveness points to a deep connection. Or I could be giving in to wishful thinking and be staggeringly wrong.

doug saxum said...

Quite the post! Time to reread it to lick up the left over crumbs on my coon plate.

doug saxum said...

Love it when you put musical comparisons in.

It's very satisfying....