I just became aware of this blog (I do read NYT from time to time), so I am digesting the posts backwards; apologies for being late to the party. At the risk of suspicion that I do not read beyond the headlines, this particular one reminded me of one of the most spectacularly devastating openings that I ever came across:
"This is a shallow book on deep matters, about which the author knows next to nothing."
I am inspired by your readiness for "reverse debate". What is your vision of what is to be done about our imminent encounter with "metamatheticians" (aleph-4, say)?
At least two conditions are missing for there to be a reverse debate in this space. In the first place, I'm not here in the place of an authority, much less a decision-maker, so there is no role to reverse. In the second place, reverse debate is a public process; participants don't hide behind pseudonyms.
Having said that, I've set aside space in a future post, probably in September or October, to address your question. In the meantime, although my ideas may change before then, I'm thinking it's similar to my vision of what is to be done about heat death of the universe.
The heat death of the universe strikes me as (a) cataclysmic event,
(b) about which we can do next to nothing, and
(c) which might happen in a terribly remote future (if at all).
While the arrival on the scene of meta-maticians might share some of the features of (a) and (b), I am not at all sure that (c) is applicable: If it would take for aleph-0 a decade or two (and this strikes me as a conservative estimate) to "work through all of the exercises in the Springer-Verlag Graduate Texts in Mathematics series", I personally doubt it would take much longer subsequently for aleph-4 to be able to submit a competitive paper to, say, Invetiones Mathematicae. (Another difference with the heat death of the universe is that the consequences of the latter would be much more equitably distributed.)
Although I'm less interested in speculation in the style of science fiction than in analyzing the narratives colleagues generate about the new technology, sometimes the latter requires a detour through the former. Your scenario is missing a back story. I tried to provide a back story in a three-part series in 2021, culminating in an attempt to reverse engineer Poincaré. Henry Wilton pointed out some flaws in my reasoning, and I will revisit them in the future post.
On DL replacing intuition : this is what some recent articles claim ,in the sense that instead of claiming intuition- whatever that means - has been replaced by the use of DL to produce some conjectures :
-- On your analogy with music:are you claiming DL might replaced mathematicians by robots-mathematicians ?
The analogy is quite the opposite. It is an invitation to imagine robots being the public for mathematics, however the latter is produced. I find this very difficult to imagine.
Moreover, as I also explained, I would never claim that DL replaces mathematicians or anyone else. Writing it this way suggests that deep learning either has an agenda of its own or is the working out of an inevitable tendency without human intervention. I would say that human managers can make the decision to replace human employees with algorithms or robots whose design makes use of deep learning. This may appear to be a merely grammatical distinction but it points to a strong tendency, which your sentence shares, to regard technology as an autonomous determining factor in the organization of society.
I just became aware of this blog (I do read NYT from time to time), so I am digesting the posts backwards; apologies for being late to the party. At the risk of suspicion that I do not read beyond the headlines, this particular one reminded me of one of the most spectacularly devastating openings that I ever came across:
"This is a shallow book on deep matters, about which the author knows next to nothing."
And your point?
I am inspired by your readiness for "reverse debate". What is your vision of what is to be done about our imminent encounter with "metamatheticians" (aleph-4, say)?
At least two conditions are missing for there to be a reverse debate in this space. In the first place, I'm not here in the place of an authority, much less a decision-maker, so there is no role to reverse. In the second place, reverse debate is a public process; participants don't hide behind pseudonyms.
Having said that, I've set aside space in a future post, probably in September or October, to address your question. In the meantime, although my ideas may change before then, I'm thinking it's similar to my vision of what is to be done about heat death of the universe.
The heat death of the universe strikes me as (a) cataclysmic event,
(b) about which we can do next to nothing, and
(c) which might happen in a terribly remote future (if at all).
While the arrival on the scene of meta-maticians might share some of the features of (a) and (b), I am not at all sure that (c) is applicable: If it would take for aleph-0 a decade or two (and this strikes me as a conservative estimate) to "work through all of the exercises in the Springer-Verlag Graduate Texts in Mathematics series", I personally doubt it would take much longer subsequently for aleph-4 to be able to submit a competitive paper to, say, Invetiones Mathematicae. (Another difference with the heat death of the universe is that the consequences of the latter would be much more equitably distributed.)
I am looking forward to reading your post.
-Alex Gamburd
Oh, it's you Alex. Why didn't you say so?
Although I'm less interested in speculation in the style of science fiction than in analyzing the narratives colleagues generate about the new technology, sometimes the latter requires a detour through the former. Your scenario is missing a back story. I tried to provide a back story in a three-part series in 2021, culminating in an attempt to reverse engineer Poincaré. Henry Wilton pointed out some flaws in my reasoning, and I will revisit them in the future post.
Curiouser and curiouser!
Mildly surprised at your comment that you wouldn't reread a proof for pleasure, but only for "practical" reasons... :)
Some remarks :
On DL replacing intuition : this is what some recent articles claim ,in the sense that instead of claiming intuition- whatever that means - has been replaced by the use of DL to produce some conjectures :
-- On your analogy with music:are you claiming DL might replaced mathematicians by robots-mathematicians ?
The analogy is quite the opposite. It is an invitation to imagine robots being the public for mathematics, however the latter is produced. I find this very difficult to imagine.
Moreover, as I also explained, I would never claim that DL replaces mathematicians or anyone else. Writing it this way suggests that deep learning either has an agenda of its own or is the working out of an inevitable tendency without human intervention. I would say that human managers can make the decision to replace human employees with algorithms or robots whose design makes use of deep learning. This may appear to be a merely grammatical distinction but it points to a strong tendency, which your sentence shares, to regard technology as an autonomous determining factor in the organization of society.