Polytropy

1. What if we could upload books to our brains?
2. What if a machine could tell us what was true?

We may speculate, and it is interesting that we do speculate, because I think the questions do not ultimately make sense—not the sense that seems to be intended anyway, whereby something can be got for nothing.

View from Şavşat

The first question was the title of an essay by Cathy O’Neil dated April 13, 2017. Now the second question is raised by Artem Kaznatcheev:

Imagine that you had a machine where you put in a statement and it replied with perfect accuracy if that statement was true or false (or maybe ill-posed). Would mathematicians welcome such a machine?

This is from a blog article of August 10, 2019, called “Process over state.” As I understand Kaznatcheev’s argument, we would not welcome such a machine, because we do mathematics for the process of reaching the truth, not having it.

Not only would we not welcome the machine, I would say, but the question of what we would do is ill-posed to begin with. We cannot have such a machine. The truth is not a gift; we have to seize it. There may be short-cuts to doing this, but we have to find or make them.

Of course we may be taught them; but we cannot be taught without doing the learning. When I was at school, I was told with excitement by an older boy that he could rewrite a polynomial in x as a polynomial in x − a, for any a. One could plug and chug, replacing x with x + a, simplifying to a new polynomial in x, and finally replacing x with x − a; but this boy had learned instead how to compute the coefficients of the new polynomial from the derivatives of the original polynomial at a. The teacher called Mr Brown must have taught him to do this; but he had taken the lesson to heart, understanding why it was true, making it is own; and this is what excited him.

One may object that Pavlovian conditioning is entirely passive, although it is considered to be a form of learning. At any rate, it is one of the examples of learning that Julian Jaynes describes, in the section headed “Consciousness Not Necessary for Learning,” in the first chapter of The Origin of Consciousness in the Breakdown of the Bicameral Mind. I would only observe that nobody seeks to undergo this kind of conditioning, as far as I know. They sign up for Facebook, where they are conditioned; but this is not why they sign up.

In the learning of skills, Jaynes observes,

Consciousness takes you into the task, giving you the goal to be reached. But from then on, apart from fleeting neurotic concerns about your abilities at such tasks, it is as if the learning is done for you.

It is as if  the learning is done for you; but you must set it going and keep it going. I did not learn to ride a unicycle, just by deciding I wanted to do it. My body learned to keep balance; but I had to keep pushing it to do this.

Cathy O’Neil was responding to the assertion of Ray Kurzweil that uploading books to our brain might be possible. Not only is such uploading possible, I would say, but we do it now. It is called reading, or perhaps listening. But the process is time-consuming, and presumably Kurzweil has a short-cut in mind.

There is already a short-cut, called speed-reading. Would-be instructors in this practice visited my college. The dean said they might offer their lessons, if they could speed-read the book he handed them. It was Aristotle’s Physics. They couldn’t do it.

One may still fantasize. My last article here, “On Causation,” referred to an earlier article, “War and Talk,” which discussed (among other things) Aristotle’s four causes. Though I had known that the causes were discussed in the Physics, I had to look them up in a physical volume from my shelf. They are in the Metaphysics too. With more ease, perhaps, I might have searched an electronic text: this is a short-cut that technology has made possible. Can I not go further, having the knowledge I want, just by saying to myself that I want it? If I can fantasize this, why should it not be possible?

Why not indeed? No reason, perhaps; but I have some questions.

1. If I wanted to upload the Physics to my brain, what exactly would I be uploading? A Greek text, a translation, a lot of translations? Cross-references, an index, annotations? Who or what would put these into a form useful for me?
2. If one is going to have grandiose fantasies, why not fantasize of learning how to convince people not to be selfish avaricious jerks?

Italo Calvino has a story, “All at One Point,” a fantasy of having lived at the beginning of the universe:

Naturally, we were all there,—old Qfwfq said,—where else could we have been? Nobody knew then that there could be space. Or time either: what use did we have for time, packed in there like sardines?

I say “packed like sardines,” using a literary image: in reality there wasn’t even space to pack us into. Every point of each of us coincided with every point of each of the others in a single point, which was where we all were …

That single point was the initial singularity. Kurzweil dreams of a technological singularity, when there is “no distinction … between human and machine.” In the initial singularity, there was already no distinction; why should it not happen again?

One could write a story about this, like Calvino’s. I know his story because I did write a story, about a rock in space that had a rudimentary form of consciousness. It achieved self-consciousness by becoming a meteor, burning up over a wheat field: dust from the rock was taken up by the wheat, which was used to make flour for bread, which was eaten by somebody who had seen the falling star and remembered it. The rock then knew itself. I wrote this story in a creative writing class, whose instructor (Mary Kay Zuravleff) then directed me to Calvino.

I had imagined my rock as feeling the gravity it was subject to, and as knowing the sources. This was a misconception on (at least) two levels.

1. Although in theory we analyze gravitational force as a sum of vectors pointing towards all massive bodies in the universe, we cannot recover these vectors from the sum alone.
2. You don’t feel gravity anyway; you feel tensions and pressures within your body.

My rock had a body, or was a body, and thus it might have felt variations, over its extent, in the gravitational field that it sat in. However, I don’t think I had this in mind. Maybe this is why I don’t write such stories now: I do have more things in mind.

Ray Kurzweil still has stories in mind. Maybe this is the spirit in which to take his fantasy of a singularity: it is like a story by Italo Calvino.

And the fantasy of a machine that can tell us what is true? David Hilbert had such a fantasy for mathematics, as Kaznatcheev reminds us. Versions of the fantasy have been shown, as by Gödel and Turing, to be not just impractical, but impossible.

One can still dream the impossible dream. Upload books to the brain, or just get the truth from a machine: why not? A more urgent task is downloading from the brain, when the brain belongs to a person with locked-in syndrome. This downloading is possible in principle, and at least some times in practice, though the locked-in person cannot move a muscle. She can still move her brain. She can compose a text that might be downloaded, because composing is an act of thought. In practice, we may compose with pen in hand or keys under the fingers; but those tools are not strictly needed, or one may learn to do without them.

Here is a key point though. Nobody and nothing else can compose what we want to say. I am putting together this essay, as it were, from bits and pieces lying around my brain; but no automated program can gather them up for me.

Is that right? The artist can say—speak, sing, paint, play—what we turn out to have wanted, though we may not have known it. In a sense, this is the artist’s job. But then it is our job to see that the job has been done. We have to look, listen, or read. Nobody and nothing else can do this for us.

To read a composition properly is to compose it again for ourselves. If this gives the reader too much credit, consider how the composition is made. As I write, I come up with words, phrases, and clauses, and I think whether they fit. If they do not, I discard them; if they do, I keep them and move on, though still I may come back to them.

That is what you do in reading. You come up with words by looking at a page or a screen. You cannot normally delete them physically, but you decide whether to accept or reject them in thought. You may just let them pass before your eyes like a landscape through a train window; but that is not reading.

In writing, where do I get words in the first place? That is mysterious, but no more so than reading something you have never read before, or even reading an old book in a new way.

Kurzweil’s imagined technology might make a composition available to us, without the need to move the focus of our eyeballs along lines of printed text. But this moving of the eyes is only an accidental feature of reading. O’Neil concludes therefore that Kurzweil must have something more in mind. He may think he does. O’Neil suggests two possibilities:

1. A book may be made a part of our memory.
2. The very meaning of the book may be adjusted, according to who we are.

She admits that she “would find the lack of active participation creepy.” It is more than creepy. It is proof that there is no alternative to reading a book. The kind of moving called reading is done with our thoughts. The brain can be moved, as by drugs, or by implanted electrodes, or by the “implants” there naturally, connected to our sense organs; but reading is something one does, not something done to oneself.

Uploading books to the brain sounds like an attempt to learn with the ease of watching television. I say this as somebody who has not watched television to pass the time since adolescence. I may pass the time now by reading Twitter; but a tweet may then provoke me to write something, such as the present essay.

As a child I would turn on the television when I came home from school. Then a psychologist recommended to my parents that I write a report on every program I watched. I restricted my watching to special occasions. Eventually the reporting requirement was forgotten, and my television watching may have picked up again. But apparently I didn’t watch prime time television; for when a new program such as Laverne & Shirley was discussed at school, I did not know what was being talking about. Neither did I feel like finding out, except when it was the teacher doing the talking, and he was talking about the previous night’s Star Trek rerun. Then I started watching, and became a Trekkie, and started a Star Trek club.

I say this about my childhood, because I think the truth cannot just be given to us; and yet children would seem to allow it to be given. Some of us continue to be children in this way, as by believing in politicians who say they will restore a Golden Age, even though it never happened anyway.

David Hilbert didn’t just ask for a machine to give us answers; he asked for an algorithm, which we could verify as doing what we wanted. This is a crucial difference. It was shown:

• by Presburger, in 1930, that there was an algorithm to tell us what was true about sums of counting numbers;
• by Gödel, in 1931, that there was no corresponding algorithm for sums and products together;
• by Turing, in 1936, that there was no algorithm of a certain kind (a “Turing machine”) to decide whether an algorithm of that kind would work;
• by Tarski, in 1951, that there was an algorithm to tell us what was true about sums and products of real numbers;
• by Matiyasevich, in 1970 (building on work of Davis, Putnam, and J. Robinson), that there was no algorithm to decide whether an arbitrary Diophantine equation had a solution.

There are various other results, both positive (as in A. Robinson’s book Complete Theories of 1956, mentioned in the article on Gödel’s Theorem) and negative. In each case, there is a theorem about the existence or non-existence of an algorithm. One can study the theorem for oneself, to verify the truth.

“The best thing for being sad,” replied Merlyn, in Chapter 21 of The Sword in the Stone of T. H. White, “is to learn something … you may see the world around you devastated by evil lunatics, or know your honour trampled in the sewers of baser minds. There is only one thing for it then—to learn.” You do it for yourself.

The quotation from White is found on various websites; I confirm it in the copy of The Once and Future King that I read for school in seventh grade. Could I have wished to be spared the trouble of reading then, or of reading the Iliad in a course of ancient Greek history, two years later? Would it have been more efficient to have the books mechanically implanted in the brains of my classmates and me?

I have been hearing of “puberty blockers,” which may be used to keep a child from developing the body of a sex that they do not want to be. The logic of Kurzweil’s thought would seem to call for puberty accelerators, to pass quickly through the nasty process of learning how to get along in the world. Let me just finish with some more examples of how that process went for me: they seem to involve learning the foolishness of certain fantasies.

In the intervening year between reading White and Homer, I became friends with a new boy at school, who had grown up in Francophone Africa. He offered to do my French homework. I considered the possibility, but realized that it would be of no benefit. Homework was not an empty exercise, but it made me more knowledgeable or skilled. This would only happen if I did the work for myself.

Thus do I make confession, if confession it be, to having been a dutiful student. In some ways I was not, but let me not go into that here. (I went into an example or two in “Impressionism.”) In school I think I understood my real duty as being to myself.

In tenth grade, a French teacher would assign vocabulary words, without bothering to tell us their genders. A classmate and I commiserated on having to look up the genders in our dictionaries, if we actually wanted to use the words in our French compositions. Apparently we didn’t think to make up genders. We were somehow too obedient. However, our obedience was to the truth. Maybe the teacher himself was not sure of the genders of the words, or didn’t care about them. He was French, a pied-noir. He was also abusive to the weaker students, and the unpleasantness of his classroom manner was a reason why I dropped his course after fulfilling the three-and-a-half-year language requirement. He was not somebody I needed to please.

In those adolescent years, in my neighborhood at home, I enjoyed playing the game called Twixt from a friend’s collection. The friend ultimately gave the game to me, and I have it here in Istanbul now. Back then I was playing the game with another friend, and I was winning, and she wished she could thwart me with a certain illegal move. This made no sense. The whole point of playing the game was to learn how to work with the rules. Winning was desirable, only as a sign of having learned. A win would be meaningless if achieved through a last-minute rule change, granted by some external power. Winning this way would be like—like having a machine that spat out the truth, or having a book uploaded to your brain.