I actually first heard that song in the home of friends in Beit Jala nearly 40 years ago, back in the days when it was common for Palestinians to attend universities in the Soviet Union. That was my introduction to the Russian "bards" and I still have the cassette tape somewhere, and I'm still in touch with the friends. It's a pretty song and the chorus is memorable; I understand the rest of the words but I don't claim to understand the point of the song even after 40 years, nor do I understand what it has to do with computers and mathematics.
Synonyms for вымысел include фантазия, сочинение, небыль, небылица, выдумка, none of which means "realization" as far as I can tell.
I’m puzzled by the anchoring on understanding. I learned Stirling’s approximation for n! as a sophomore with no proof. I’m pretty sure I understood it. Then I learned lots of probability theory without understanding very analytical proofs which still strike me as uninteresting and ‘technical’ - like proofs created by a machine. Yet I could apply the results happily, showing I understood, I think. In set theory, we learned Cohen’s forcing methods and understood ‘how’ the proofs work to establish independence results like the continuum hypothesis. But nobody understood quite ‘why’ the method worked, it was opaque. Kind of like Feynman on quantum mechanics. Understanding proofs is just one kind of mathematical understanding. As Wittgenstein would say it’s a family resemblance term. Most literate people understand positional value without understanding just how it works. We are often machine like in our understanding of lots of math. Indian mathematics eschewed proofs for centuries. Then there is Ramanujan. What of his mysterious understanding? Part of the difficulty is the shared social status of mathematical knowledge, making it possible to take advantage of others’ understanding for our own purposes. Machine learning is like that too. I’m also puzzled why there’s no controversy over computer ‘learning’. Polya showed learning is the royal road to mathematical understanding. Understanding as a corollary to learning so to speak. Here the machine seems less human. But then there’s Stirling’s formula….
I'm puzzled by your puzzlement. Over the past few years I have displayed numerous quotations indicating that "understanding" is a matter of importance for mathematicians as well as philosophers, and others that identifies "understanding" as a central stake in the development of AI. Yet there are few attempts to clarify what this means. Are you puzzled that I noticed this?
It is indeed important in the ongoing AI discussions. The section titles alone of your Paris notes show you unlike others take a non-essentialist perspective difficult in grant applications, the popular press and social media. And then a search for some single compelling interpretation takes command - an 'anchor' in place of 'family resemblance'. For AI, the family includes : novel machine performance; human 'mechanics' as neural-net-like; our varied understandings (!) of mathematical understanding; and our conscious experience through mathematical practice (from grade school onward) of 'what's it like', but absent in the machine. On top of that is a mostly unacknowledged unsteady intellectual and social ground such as described in mathematics w/out apologies. I've no horse in this race. I'm likely responding more to the AI zeitgeist than your posts.
Вымысел — не есть обман.
Замысел — еще не точка.
Realization is neither a deception nor is it t a full stop.
I'm not sure I understand the point…
https://www.youtube.com/watch?v=3ESdQRC5ldQ
I actually first heard that song in the home of friends in Beit Jala nearly 40 years ago, back in the days when it was common for Palestinians to attend universities in the Soviet Union. That was my introduction to the Russian "bards" and I still have the cassette tape somewhere, and I'm still in touch with the friends. It's a pretty song and the chorus is memorable; I understand the rest of the words but I don't claim to understand the point of the song even after 40 years, nor do I understand what it has to do with computers and mathematics.
Synonyms for вымысел include фантазия, сочинение, небыль, небылица, выдумка, none of which means "realization" as far as I can tell.
Please do rest assured that my considered, pertinent and detailed reply is to appear in due course (and before too long).
I’m puzzled by the anchoring on understanding. I learned Stirling’s approximation for n! as a sophomore with no proof. I’m pretty sure I understood it. Then I learned lots of probability theory without understanding very analytical proofs which still strike me as uninteresting and ‘technical’ - like proofs created by a machine. Yet I could apply the results happily, showing I understood, I think. In set theory, we learned Cohen’s forcing methods and understood ‘how’ the proofs work to establish independence results like the continuum hypothesis. But nobody understood quite ‘why’ the method worked, it was opaque. Kind of like Feynman on quantum mechanics. Understanding proofs is just one kind of mathematical understanding. As Wittgenstein would say it’s a family resemblance term. Most literate people understand positional value without understanding just how it works. We are often machine like in our understanding of lots of math. Indian mathematics eschewed proofs for centuries. Then there is Ramanujan. What of his mysterious understanding? Part of the difficulty is the shared social status of mathematical knowledge, making it possible to take advantage of others’ understanding for our own purposes. Machine learning is like that too. I’m also puzzled why there’s no controversy over computer ‘learning’. Polya showed learning is the royal road to mathematical understanding. Understanding as a corollary to learning so to speak. Here the machine seems less human. But then there’s Stirling’s formula….
I'm puzzled by your puzzlement. Over the past few years I have displayed numerous quotations indicating that "understanding" is a matter of importance for mathematicians as well as philosophers, and others that identifies "understanding" as a central stake in the development of AI. Yet there are few attempts to clarify what this means. Are you puzzled that I noticed this?
It is indeed important in the ongoing AI discussions. The section titles alone of your Paris notes show you unlike others take a non-essentialist perspective difficult in grant applications, the popular press and social media. And then a search for some single compelling interpretation takes command - an 'anchor' in place of 'family resemblance'. For AI, the family includes : novel machine performance; human 'mechanics' as neural-net-like; our varied understandings (!) of mathematical understanding; and our conscious experience through mathematical practice (from grade school onward) of 'what's it like', but absent in the machine. On top of that is a mostly unacknowledged unsteady intellectual and social ground such as described in mathematics w/out apologies. I've no horse in this race. I'm likely responding more to the AI zeitgeist than your posts.