Kurzweil’s How to Create a Mind, and mathematics

I listened last week to Diane Rehm’s interview with Ray Kurzweil, author of the book “How to Create a Mind: The Secret of Human Thought Revealed”  A transcript of the interview can be found here.

Published in mid-November, it is already a New York Times bestseller, and some of the responses to it from prominent colleagues introduce the book’s website. While it is an exploration of the potential for technological advancement in the computer driven field of artificial intelligence, it does this in the light of new opportunities to understand how we might reverse-engineer the brain.   It was these insights into how the brain learns or how it builds our symbolic worlds, that caught by attention, looking to me again very much like mathematics.

During the interview, Kurzweil talks about the neocortex which, while present in mammals, is uniquely developed in humans.

We can take a whole bunch of ideas, call that a new idea, give that a symbol and then use that symbol with yet other ideas and create another symbol and build up this whole hierarchy we call knowledge. Only the neocortex is able to do that. And it enables us to solve problems and learn new skills that are flexible.

Our neocortex can create metaphors so Darwin noticed a metaphor from geology that tiny, little trickles of water can carve out a great cavern.

The efficacy of symbol in the development of thought is the very life of mathematics, and metaphors are how we move around within these structures.

Kurzweil argued in a paper that he wrote at the age of 14 (!) that the heart of human intelligence is recognizing patterns.  This is what the brain does well.

that is actually the message of this new book 50 years later. But I describe in real detail how the neocortex does that. We have basically 300 million little regions that recognize patterns and they’re organizing hierarchies. So I’ll have one little pattern recognizer that fires when it–when it sees a crossbar in a capital A. And that’s all it cares about. It gets very excited when it sees a crossbar in a capital A.

At a higher level there’ll be a recognizer that recognizes a capital A. At a yet higher level there’ll be a recognizer that goes ah, it’s the word apple. Go up another 20 levels there’ll be a recognizer that’s getting input from different senses. It sees a certain fabric, smells a certain perfume, hears a certain voice and goes ah-ha, my wife has entered the room. Go up another 20, 30 levels as a recognizer goes, that’s funny, she’s pretty. That was ironic.

You might think that those higher level more abstract recognizers are more complicated, more sophisticated. They’re actually basically the same except for their position in this grand hierarchy. And that’s the essence of the neocortex. It’s organized in this very elaborate hierarchy from very low level primitive — recognizes — it just recognizes the edges of objects and simple things up to these very abstract features.

I’m intrigued by the idea that these recognizers don’t differ in any way other than position.   They are essentially content-less, like mathematical symbols, and acquire meaning only in relation to each other.  He goes on to say that the key is that we’re not born with this hierarchy:

We create that from our own experience. Everybody’s hierarchy is different because you are not only what you eat, but you are what you think. With every thought we make we create that elaborate hierarchy…But literally from the moment you’re born or even earlier — because our eyes open at age 26 weeks — we are laying down one conceptual level at a time. That’s another key is that we can only sort of learn one level of abstraction at a time. So I’ve got a one-year-old grandson now and so he’s managed to lay down a few levels. But he’s, you know, still learning the primitive features and patterns and language and so on.

And why is it that we might encounter so much difficulty when we try to see the more elaborate hierarchies of advanced mathematical ideas?  Perhaps it’s because we’re not motivated to make room for them.

…we actually fill up these 300 million pattern recognizers by the time we’re 20. And in order to learn something new at that point we need to forget something old…Now some people are better at giving up old ideas than others. I mean, many people are rigid thinkers and just happy with the neocortex they have and don’t want to entertain new ideas…It’s comforting to have explanations for everything. We have to realize the limitations of our ideas to gain new ones.

I may be in the minority, but I really like discovering the limitations of our ideas.  In the interview, Kurzweil also made a good argument for why we may be built this way, why the neocortex grew this kind of functioning – because our thoughts are like everything around us.

The world is hierarchical and you really can’t understand the world unless you can understand its natural hierarchy. The fact that, you know, branches lead to other branches and the whole assembly of branches makes a tree and this assembly of trees make a forest. And this is a natural hierarchy to the world. You can’t really understand it otherwise. This was the first mental organ that enabled animals to do that.

I have often suggested that mathematics happens, that we don’t actually descide to make it.  Yet intentionality plays a powerful role.  Kurzweil addressed the enigma of consciousness as well.

Most of what goes on in the neo-cortex and that is where we do our thinking is not conscious. We’re only consciously aware of a small part of it and that actually gets at the issue of responsibility and free will…But I cite some interesting studies where people actually begin to carry out a decision before they’re even consciously aware that there was a decision to be made. And this was very, very interesting research. It’s well-designed and people became aware that there was a decision after they already carried out the decision. So this brings up the mystery of consciousness.

I have long thought that mathematics may be bringing the less conscious aspect of thought to our awareness.

There are numerous press responses to this latest from Kurzweil that can be found on the book’s website.

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