The supreme irony of our planetary age is that the nightmare of the first phase - the nuclear winter - is the exact opposite of the nightmare of the second phase - runaway heating.
Very interesting post, dear Rajesh. Especially the connection between insights such as the Gaia Hypothesis and the current (and past) issues, and their reduced versions (global heating, nuclear winter).
The only part I seriously take issue with is your description of advances in the past half-century. While it is true that biology and information sciences saw enormous revolutions, and it is also true that physics saw its own revolution in the first half of the century, I disagree (deeply) with your glueing together mathematics and physics in that sentence. Mathematics had some revolutions in the first half of the century, true... but mathematics does not quite work by the revolution cycle. And I would daresay that the past half century has seen much deeper advance in mathematics than even those revolutions of the first half of the twentieth century. Those advances are incredibly mysterious (here, I would say the advances in biology and information science, while enormous, pale in comparison with the real deep changes we are still witnessing in mathematics). In many ways, the «blurring», the brutal «trans» aspect of current mathematics (trans-ferring ideas in very strange ways from one domain to the other) are of a nature similar (and perhaps deeply related to) the blurrings you mention in biology. But mathematics is unfolding in very surprising ways, and has not stopped doing so for the past decades!
Thanks for your comments, Andres! Let me first state one point of agreement: that mathematics isn’t captured well by the revolutionary/stable distinction. Apart from subjective assessments of what’s important and what’s not, I am also looking for the cultural influences - especially in intellectual culture - of developments in mathematics (or of physics/biology etc) and here, I believe that there’s been a sharp drop off in our lifetimes. That doesn’t mean mathematics isn’t evolving internally or that those internal developments aren’t momentous, but I was specifically looking for mathematical modes of thought that have become widespread in intellectual culture as a whole, just as computational modes of thought have become.
This is the beginning of a long conversation, but my gut instinct is that the real transformation that’s waiting to happen is in the amalgamation of mathematics with other formal disciplines and their practices: programming in particular. This will bring new cognitive styles into mathematics. For example, a great deal of (good) programming is about building systems (let’s say, a newsletter platform like Substack) and that means creating software structures that are modularizable, easy to repair etc. These qualities are complementary to rigor (exemplified in proof) and offer ooportunities for entirely new forms of mathematical system building.
Very interesting post, dear Rajesh. Especially the connection between insights such as the Gaia Hypothesis and the current (and past) issues, and their reduced versions (global heating, nuclear winter).
The only part I seriously take issue with is your description of advances in the past half-century. While it is true that biology and information sciences saw enormous revolutions, and it is also true that physics saw its own revolution in the first half of the century, I disagree (deeply) with your glueing together mathematics and physics in that sentence. Mathematics had some revolutions in the first half of the century, true... but mathematics does not quite work by the revolution cycle. And I would daresay that the past half century has seen much deeper advance in mathematics than even those revolutions of the first half of the twentieth century. Those advances are incredibly mysterious (here, I would say the advances in biology and information science, while enormous, pale in comparison with the real deep changes we are still witnessing in mathematics). In many ways, the «blurring», the brutal «trans» aspect of current mathematics (trans-ferring ideas in very strange ways from one domain to the other) are of a nature similar (and perhaps deeply related to) the blurrings you mention in biology. But mathematics is unfolding in very surprising ways, and has not stopped doing so for the past decades!
Thanks for your comments, Andres! Let me first state one point of agreement: that mathematics isn’t captured well by the revolutionary/stable distinction. Apart from subjective assessments of what’s important and what’s not, I am also looking for the cultural influences - especially in intellectual culture - of developments in mathematics (or of physics/biology etc) and here, I believe that there’s been a sharp drop off in our lifetimes. That doesn’t mean mathematics isn’t evolving internally or that those internal developments aren’t momentous, but I was specifically looking for mathematical modes of thought that have become widespread in intellectual culture as a whole, just as computational modes of thought have become.
This is the beginning of a long conversation, but my gut instinct is that the real transformation that’s waiting to happen is in the amalgamation of mathematics with other formal disciplines and their practices: programming in particular. This will bring new cognitive styles into mathematics. For example, a great deal of (good) programming is about building systems (let’s say, a newsletter platform like Substack) and that means creating software structures that are modularizable, easy to repair etc. These qualities are complementary to rigor (exemplified in proof) and offer ooportunities for entirely new forms of mathematical system building.