When an AI system solves a difficult mathematical problem, the usual explanation is that it has become more intelligent.... [but also] AI has access to a vastly larger working memory than the human brain.Or, more precisely, it has access to an enormous external symbolic workspace that performs many of the functions that working memory performs in humans.This difference may be especially important in mathematics.
Emphasis in the original.
One AI recently informed me that I have "used 50x as many tokens as The Hobbit" on that platform. That's a silly thing to say. Tolkien didn't use tokens to write anything, so it's incommensurable; but his experience of authoring the book also involved his decades of study, wide reading in several languages, and so forth before he even sat down to write. (The process for composing LotR was far more intricate.) If you asked one to 'compose The Hobbit' it would not use anything like the number of tokens it would take to replicate in training cycles what Tolkien did in study; it doesn't have to do so.
The AI experience is that there have been vast cycles of training that have gone into building this 'working memory' (or, as noted, its analog). It can practically draw on much more than even Professor Tolkien, or than Thomas Jefferson dining alone.
That in itself makes AI extremely useful partners to humans in thinking. We should take care to continue to train our own memories, even to recover the benefits of the discipline of wide reading and study. Yet neither ought we to disregard the clear advantages of such a practical increase in working memory.
The size of memory matters a whole lot.
ReplyDeleteIn the early days of computers, the size of the unit, measured in bits or 1s and 0s, that could be stored (as well as the number of them) affected the quality of encryption and of passwords: 16 bits, 32 bits, 64 bits, 128 bits, 256 bits all represented successively less weak password/encryption capability. That extends to statistics. Regardless of the number of bits available to the computer, the size of a number that can be stored is finite, and so randomness can never be achieved, and from that, computer calculated statistical procedures always will be problematic at some remove.
The limit extends to algorithms. There is, for instance, a simple and straightforward algorithm a human can use to calculate a serviceable square root, even a cube root, in just a very few iterations on a common handheld pocket calculator that doesn't have its own square/cube root capability in its onboard functions. The algorithm even begins with a straight-up guess at the answer, and the guess can be wildly inaccurate.
The complexity of algorithms used by today's AI (and by organic brains, in which algorithms often resemble "intuition") is vast, but they're still only approximations of reality, if to increasing degrees of closeness.
The convergence is greater. Computers use discreet 1s and 0s for their sensing and processing. Quantum computing begins to blur the lines between 1 and 0 but they're still centered on those two states: quantum computing starts with 1 and 0 and uses varying degrees of their simultaneous existence for storage and algorithm manipulation.
Humans and any other animal with a nervous system are strictly binary in their sensing and processing of that which is sensed. Either the rod in the retina fires or it does not. Either the touch neuron in the finger tip fires or it does not. If the sensor's signal exists, the neuron relaying it either fires or it does not. The next neuron in the path either fires or it does not. Once having arrived at the central ganglion or brain, however complex the latter, either the neurons comprising the ganglion or brain fire in the processing or they do not.
Likely, it's in this convergence of binary-ness that AI will begin to match humans. It's important against this backdrop, though, to not confuse speed of processing with intelligence or ability to create.
Dad29 makes the case that creativity is only extant to the degree God imbues the capability in humans. Others see more secular bases for creativity. Maybe it's still far too early to tell regarding AI.
Eric Hines
The complexity of algorithms used by today's AI... [are] still only approximations of reality, if to increasing degrees of closeness.
DeleteIndeed, as calculus approximates. However, the subject of the article is mathematics, which doesn't have to approximate reality on its own terms. Many think that reality arises out of mathematics, from the Protagoreans to many modern day physicists. Whether that's true or not, mathematics on its own terms can dispense with reality if it wishes. As long as it's following the rules of mathematics, it doesn't have to map to anything physical. (As well you know, of course.)
"We should take care to continue to train our own memories, even to recover the benefits of the discipline of wide reading and study"
ReplyDeleteHere's an exanple I like. Jakob Dylan has a song that includes the following lines:
Cupid, don't draw back your bow
Sam Cooke didn't know what I know
Think of how much you need to know in order to understand these two simple lines:
1)You need to know that, in mythology, Cupid symbolizes love
2)And that Cupid's chosen instrument is the bow and arrow
3)Also that there was a singer/songwriter named Sam Cooke
4)And that he had a song called which included the lines "Cupid, draw back your bow."
"Progressive" educators, have long been insisting that students should be taught "thinking skills" as opposed to memorization. But consider: If it's not possible to understand a couple of lines from a popular song without knowing by heart the references to which it alludes--without memorizing them--what chance is there for understanding medieval history, or modern physics, without having a ready grasp of the topics which these disciplines reference?
And also consider: in the Dylan case, it's not just what you need to know to appreciate the song. It's what Dylan needed to know to create it in the first place. Had he not already had the reference points--Cupid, the bow and arrow, the Sam Cooke song--in his head, there's no way he would have been able to create his own lines. The idea that he could have just "looked them up," which educators often suggest is the way to deal with factual knowledge, would be ludicrous in this context. And it would also be ludicrous in the context of creating new ideas about history or physics. To use a computer analogy, the things you know aren't just data--they're part of the program.