What are you reading now? (STEM only)

[MidgetDwarf]

Rereading Hubbard and Hubbard: Vector Calculus, Linear Algebra, and Differential Forms. I have a copy of Bartle: Elements of Analysis, which I believe is a superior book (read it). But I find Hubbard a more enjoyable book to read.

Ie., even a simple thing like why open sets are important in analysis, Hubbard explicitly states why they are important, while with Bartle, you have to digest the formal definition of the derivative to see why.

Ie., if try to take the derivative at a boundary point of a closed set ( or a set that is neither open or closed), it may happen that the f(x+h) term in the definition of the derivative, may not exist. Since x+h may be outside the domain of f.

I am also reviewing Friedberg: Linear Algebra for preparation for an applied linear analysis course. I am still trying to figure out what applied linear analysis, but it says that upper division linear algebra is a prerequisite. Although, I find it a bit boring, having studied from Axler.

Maybe hoping to restart Geometries and Groups when time permits. Such a fun little book.

 

[ergospherical]

The Physics of Cancer by La Porta and Zapperi - just short enough for my attention span.

 

[WWGD]

Found an almost free copy of a book on Relational Algebra ( re Relational Databases), which I only understand at intro level. Kind of curious of any Mathematical properties it has.

 

[Borg]

I just finished a small neuroscience article about how the brain interacts with the outside world. I'm always thinking of parallels with my AI work when I read those. Now I find myself thinking about why a tree isn't a number.

 

[Falgun]

Just finished Wigner's "The Unreasonable Effectiveness of Mathematics in Natural Sciences" and the part on the uniqueness of physical theories was the first time I consciously thought about it. And it's refreshingly short.

 

[haushofer]

Next stop: Dijkgraafs "unreasonable effectiveness of physics in mathematics" :P

 

[Demystifier]

Next stop: Dijkgraafs "unreasonable effectiveness of physics in mathematics" :P

Did someone wrote "Unreasonable effectiveness of philosophy in physical and mathematical sciences?". If not, I think I could do it.

 

[haushofer]

Then I'll write " the unreasonable effectiveness of Dinosaurs in the Jurassic Park franchise" :P

 

[Falgun]

Then someone needs to write "The unreasonable effectiveness of humans at doing science"

 

[martinbn]

Did someone wrote "Unreasonable effectiveness of philosophy in physical and mathematical sciences?". If not, I think I could do it.

Are there any examples of such effectivness?!

 

[vanhees71]

Did someone wrote "Unreasonable effectiveness of philosophy in physical and mathematical sciences?". If not, I think I could do it.

I think someone more appropriately wrote something about the "unreasonable UNeffectiveness of philosophy in the natural sciences". I'd even skip the word "unreasonable" here...

 

[Demystifier]

Are there any examples of such effectivness?!

Einstein, Schrodinger, Bell, ... For example, Bell discovered his Bell inequalities by starting from quantum philosophy.

In mathematics, I would mention Frege, Russell, Godel, Quine, ...

 

[martinbn]

Einstein, Schrodinger, Bell, ... For example, Bell discovered his Bell inequalities by starting from quantum philosophy.

In mathematics, I would mention Frege, Russell, Godel, Quine, ...

This is very different. The effectiveness of mathematics in physics is not just three people who, a hundered years ago, did something that is arguably mathematical and was usfull in physics. While the "effectiveness" of philoosophy in maths seems to be confined to logic, set theory and the foundations of maths. Things most mathematicians are not even aware of.

Take Einstein and GR, philosophy was holding him back (mach's principle, the hole argument,...), it was mathematics (the work of Ricci and Levi-Civita) that made GR possible. So, your examples, especially the maths ones, seem very isolated to say that philosophy is effective in mathematics.

 

[vanhees71]

Einstein, Schrodinger, Bell, ... For example, Bell discovered his Bell inequalities by starting from quantum philosophy.

In mathematics, I would mention Frege, Russell, Godel, Quine, ...

For me Einstein is rather an example for the ineffectiveness (even danger) of philosophy in the natural sciences. There's no doubt that in his younger years Einstein was one of the most creative physicist with an amazing imagination about how nature works, and he was in this time always "close to experiment", i.e., he had the observed phenomena in mind when developing theories, which is an creative act rather than some machinery of rational derivation. In his later years, he fell however in the trap of a philosophical prejudice against the implications of quantum theory, particularly the "inseparability" which was his real trouble wrt. the infamous EPR paper, as he clarified some years later in 1948. That's why he was looking for almost 30 years for a unified classical field theory of gravitation and electromagnetism, ignoring the newer experimental facts, according to which there must be more "forces" (or rather "fundamental interactions") than just electromagnetic and gravitational interactions as well as the fact that the quantum-theoretical predictions all were confirmed.

Further for me Bell's is to the contrary an example for the successful exorcism of philosophical demons by finding a clearly defined scientific approach to the philosophical quibbles of EPR, i.e., he made the philosophical unclearly defined "problem" a scientifically decidable question, i.e., to a quantitative prediction for the outcome of experiments assuming "local realistic hidden-variable theories" (thereby clarifying EPR's vague philosophical formulations) contradicting the predictions of QT, and the result is well known in favor for QT and not EPR's philosophical prejudice of how a physical theory must look like. Though, of course, the motivation for Bell was some philosophical question, thus he ingeniously resolved it by bringing it to the realm of scientifically well-defined, quantitative and thus empirically testable/decidable questions.

Mathematics for me is neither a natural science nor a humanity. Nowadays it's put into the third category of the "structural sciences". The quoted mathematicians were of course also philosophers to some extend, but also mathematicians, and I'd put "mathematical logics" clearly in the realm of the structural sciences and not so much of philosophy.

For me the "effectiveness of mathematics" in the natural sciences is simply explained by the fact that math developed from applications to real-world problems by abstraction, and not the other way around. That's why math started with natural numbers, then inventing the 0 and negative numbers, the rational numbers, and finally the real numbers in some centuries, until it was formalized in the 19th-20th century with the demand for more rigorous formulations after some "foundational crisis of analysis". The same holds for geometry: Euclidean geometry was in a sense discovered from real-world practice. E.g., in Egypt it was important to get the areas of the land precisely measured after each flooding by the Nile every year, making use of Pythagoras's theorem.

 

[haushofer]

This is very different. The effectiveness of mathematics in physics is not just three people who, a hundered years ago, did something that is arguably mathematical and was usfull in physics. While the "effectiveness" of philoosophy in maths seems to be confined to logic, set theory and the foundations of maths. Things most mathematicians are not even aware of.

Take Einstein and GR, philosophy was holding him back (mach's principle, the hole argument,...), it was mathematics (the work of Ricci and Levi-Civita) that made GR possible. So, your examples, especially the maths ones, seem very isolated to say that philosophy is effective in mathematics.

I disagree. The hole argument was Einstein's disability to view the metric as a gauge field. That's at least partially mathematical. Mach's principle was an important inspiration for Einstein to regard gravity geometrically, although later on he realized GR is not fully Machian. Finally, his emphasis on the equivalence principle and that it was a mere curiosity in Newtonian gravity can be considered philosophical (although its demarcation with physics remains blurry from my point of view.)

 

[Demystifier]

While the "effectiveness" of philoosophy in maths seems to be confined to logic, set theory and the foundations of maths. Things most mathematicians are not even aware of.

I think the same can be said about physics, most physicists are not aware of Bell inequalities and stuff like that.

 

[martinbn]

I disagree. The hole argument was Einstein's disability to view the metric as a gauge field. That's at least partially mathematical. Mach's principle was an important inspiration for Einstein to regard gravity geometrically, although later on he realized GR is not fully Machian. Finally, his emphasis on the equivalence principle and that it was a mere curiosity in Newtonian gravity can be considered philosophical (although its demarcation with physics remains blurry from my point of view.)

This shows that it is at the very least not so clear cut whether it is philosophy, nor whether it is useful. But if the Mach principle and the hole argument are so useful and effective, why are they not in every GR book?

I am still convinced that there is nothing even close to the effectiveness of mathematics in physics along the lines of "effectiveness of philosophy in physics and maths".

 

[martinbn]

I think the same can be said about physics, most physicists are not aware of Bell inequalities and stuff like that.

Exactly, but all physicists are aware (more than aware) of a lot of mathematics.

 

[Demystifier]

This shows that it is at the very least not so clear cut whether it is philosophy, nor whether it is useful. But if the Mach principle and the hole argument are so useful and effective, why are they not in every GR book?

Because philosophy is useful in the process of construction of new theories, not in their final formulations.

 

[martinbn]

Because philosophy is useful in the process of construction of new theories, not in their final formulations.

Then shouldn't your book be titled "The unreasonable effectiveness of philosophy in construction of physical theories."?

 

[vanhees71]

I disagree. The hole argument was Einstein's disability to view the metric as a gauge field. That's at least partially mathematical. Mach's principle was an important inspiration for Einstein to regard gravity geometrically, although later on he realized GR is not fully Machian. Finally, his emphasis on the equivalence principle and that it was a mere curiosity in Newtonian gravity can be considered philosophical (although its demarcation with physics remains blurry from my point of view.)

Interestingly enough this "hole argument" seems to have survived the philosophical debate although it's solved since 1915. As with all philosophical debates, this apparent "problem" stays unsolved for so long, because it lacks clear mathematical and/or scientific definition. Just yesterday, there was another paper about it on the arXiv. It's amazing, how much thought can be used to solve solved problems ;-)):

https://arxiv.org/abs/2206.04943

 

[Demystifier]

Then shouldn't your book be titled "The unreasonable effectiveness of philosophy in construction of physical theories."?

Yes, it should. But not the book, just a short essay.

 

[haushofer]

Interestingly enough this "hole argument" seems to have survived the philosophical debate although it's solved since 1915. As with all philosophical debates, this apparent "problem" stays unsolved for so long, because it lacks clear mathematical and/or scientific definition. Just yesterday, there was another paper about it on the arXiv. It's amazing, how much thought can be used to solve solved problems ;-)):

https://arxiv.org/abs/2206.04943

Oh, yes. I see the hole argument as historically curious. I tried to read the papers by Norton, Stachel, Weatherall, Landsman and others about this thing called "spacetime substantivalism", but I don't see why people are so excited about it.

What I like about the hole argument is that you can confuse a good deal of high energy physicists with it, even people working on SUGRA or string theory. That's why I added it to my own PhD-thesis (which was, quite suitably, about gravity as a gauge theory).

 

[haushofer]

This shows that it is at the very least not so clear cut whether it is philosophy, nor whether it is useful. But if the Mach principle and the hole argument are so useful and effective, why are they not in every GR book?

I am still convinced that there is nothing even close to the effectiveness of mathematics in physics along the lines of "effectiveness of philosophy in physics and maths".

Because a lot of books tend to neglect such historical or conceptual stuff, because...a lot of other books do too? I don't know the precise sociological reason.

D'Inverno is a nice exception to this.

 

[Demystifier]

Today appeared a paper arguing that Einstein's philosophy was often wrong, but his equations, being smarter than himself, were always right. https://arxiv.org/abs/2206.06831

 

[martinbn]

Today appeared a paper arguing that Einstein's philosophy was often wrong, but his equations, being smarter than himself, were always right. https://arxiv.org/abs/2206.06831

Which parts do you disagree with?

 

[martinbn]

I feel I derailed the thread, so I will post something on topic. I wouldn't say that I am reading, I am just looking through it and reading those parts that I like, but I came across "Compact Riemann Surfaces" - R. Narasimhan. I knew about the book, because it is often in the bibliography of textbooks, but I have never actually looked at it. I have to say that it is very nice. It is realtively short about 120pages. And it covers a lot of good complex geometry (and algebraic). If someone is going to study Griffiths and Harris, this might be a good start.

 

[Demystifier]

Which parts do you disagree with?

I'm not saying that I disagree. For making a true progress in science, it's almost necessary to be often wrong.

 

[vanhees71]

The only exception is Pauli, according to himself. There's this story about Weisskopf, who made some mistake in calculating some one-loop result for scalar QED and then went to Pauli reporting the mistake. Pauli replied that all physicists make mistakes in their calculations all the time, with the only exception being himself ;-)).

 

[martinbn]

I'm not saying that I disagree. For making a true progress in science, it's almost necessary to be often wrong.

It goes against your view about the unreasanble effectiveness of philosophy. It says that philosophy lead him to those mistakes.

 

[Demystifier]

It goes against your view about the unreasanble effectiveness of philosophy. It says that philosophy lead him to those mistakes.

Philosophy has a double role, it causes both progress and mistakes. Think of philosophy as a source of intuitive insights. In addition, the mistakes themselves often teach us a lot.

 

[atyy]

I think the same can be said about physics, most physicists are not aware of Bell inequalities and stuff like that.

Undergrads learn them nowadays.

 

[vanhees71]

Yes, even 30 years ago we learned about them, and without all the confusion we spread in this forum about the meaning of the word "local", because even moderators insist on the unclear use of other than physics communities, but that's another topic...

 

[haushofer]

Zee wrote another QFT book, apparently:

https://www.amazon.nl/dp/0691174296/

Disclaimer: I'm not from the future, so I haven't read it yet.

 

[malawi_glenn]

I'm not from the future, so I haven't read it yet.

https://www.physicsforums.com/threa...ply-as-possible-upcoming-publication.1012544/

on topic:
I am reading - Axler: Measure, Integration & Real Analysis. It is an open source book by springer, but I decided to buy it hardcover. Pretty good, it is not easy material (for me at least) but the author is trying to be very pedagogical and structured. Colored boxes on basically every page.