One thing that I remember clearly is the phrase "We are done," meaning that once we physicists have found the fundamental equations the era of basic scientific inquiry is over.It's certainly true that our current understanding of neurology (for example) is not reducible to our current understanding of physics. But that does not mean that such a reduction is in principle impossible.
...But the reduction of other sciences to physics does not work. Chemistry has its own concepts, not reducible to physics. Biology and neurology have their own concepts not reducible to physics or to chemistry. The way to understand a living cell or a living brain is not to consider it as a collection of atoms. Chemistry and biology and neurology will continue to advance and to make new fundamental discoveries, no matter what happens to physics. The territory of new sciences, outside the narrow domain of theoretical physics, will continue to expand.
What would it mean for a science (biology, say) to be truly irreducible in this way? Wouldn't it mean that the science depended somehow upon the non-physical? If so, isn't that a problem?
But I should emphasise that what Dyson seems to be getting at here (if I'm interpreting him correctly) is an epistemological, not metaphysical, issue. He isn't saying that living cells are made up of anything non-physical. Rather, he's suggesting that we cannot (ever) understand them using only the concepts of physics.
I'm not sure about this. It seems to me that if we ever advanced to such a stage that we truly did know everything about physics, then we should, in principle, be able to work out the answer to any biological question also (that is not to say that such an approach would be practicable). That is, I wonder if epistemological reducibility would follow from metaphysical reducability. (I assume Dyson accepts the latter - aren't most scientists materialists? Please do correct me if I'm wrong here though!)
Here's my argument to that effect:
1) All objects of scientific study are (metaphysically) fully reducible to the fundamental building blocks of the universe and their interactions. (Materialist premise)
2) Any fully-reducible object is identical with the totality of that to which it is reduced. (Otherwise it wouldn't be fully reducible, would it?)
3) If you know K about X, and know that X is identical with Y, then you know K about Y. (Knowledge is closed over identity, right?)
4) If we know the fundamental equations of physics, then we can work out everything about the fundamental building blocks of the universe and their interactions. (Such is physics)
5) If we can work out X, then we can know X
6) All objects of scientific study are identical with 'the fundamental building blocks of the universe and their interactions' of which they are composed. (From 1 & 2)
7) Any knowledge we seek of 'an object of scientific study' will be obtained if we gain that knowledge about 'the fundamental building blocks & their interactions' of which said object is composed. (From 3 & 6)
8) Therefore, any knowledge we seek of 'an object of scientific study' can be obtained if we know the fundamental equations of physics. (From 4,5 & 7)
But being theoretically capable of obtaining knowledge in no way guarantees that this is practicable. And even if we did obtain such knowledge, we still might not be capable of properly understanding it (which I think was Dyson's main point there anyway).
Plus, there's the difficult (practically impossible?) matter of knowing exactly what any given object reduces to (i.e. what precise arrangement of particles, or whatever). So even once we know everything about physics, we still have to figure out how to 'build up' all our other knowledge out of that - a process Dyson calls "synthetic science":
Theoretical science may be divided roughly into two parts, analytic and synthetic. Analytic science reduces complicated phenomena to their simpler component parts. Synthetic science builds up complicated structures from their simpler parts. Analytic science works downward to find the fundamental equations. Synthetic science works upward to find new and unexpected solutions. To understand the spectrum of an atom, you needed analytic science to give you Schrödinger's equation. To understand a protein molecule or a brain, you need synthetic science to build a structure out of atoms or neurons. Greene was saying, only analytic science is worthy of the name of science. For him, synthetic science is nothing but practical problem solving. I said, on the contrary, good science requires a balance between analytic and synthetic tools, and synthetic science becomes more and more creative as our knowledge increases.So while I think I would like to say that everything is ultimately reducible to physics (in theory), I certainly agree with Dyson that other sciences will continue to progress even after it seems that "we are done" with physics (if we ever are, that is!).