Do "older" books provide unique insights?

[bacte2013]

Dear Physics Forum personnel,

I am curious what are your opinions about the "older" books in mathematics and physics (i.e. Neumann, Schrodinger, Dirac for QM, Hawking/Ellis for relativity, Russell for mathematics, etc.). From my experience with mathematical books, I found that I have liking to older books since they rather provide readers a chance to come up with their own definitions and understanding. For example, I had been reading Weinberg's book on relativity, but I did not understand the concept of perfect fluid until I read relevant sections on Hawking/Ellis. Also, it was not until I read Engelking to acquire intuitive understanding of paracompactness and the theories that govern the hierarchy of separation axioms, which I could not learn from more modern books in topology.

Do you think "older" books are better for first learning than more modern books in physics and math? I know that it is not quite efficient for biology and certain branches of chemistry

 

[Simon Bridge]

There are no special insights in older books.
The best books for learning, in general, are usually the more up-to-date ones. These benefit from the concepts having been taught for a while so mistakes may be ironed out, with some presentation issues corrected - they also benefit from more recent education research. Newer books will also be written with an eye on more recent research in the field - so what they focus on teaching you is more likely to be relevant later.

However:
1. all this depends on the subject area and the level it is to be taught - some changes are just fashion;
2. individual students vary - individuals are advised to use the most relevant work that they find they understand best.
... consult a range of texts to inform your education.

 

[mathwonk]

This question is so general I suspect it admits no one correct answer, since for one thing it depends on a measure of "best" for books. Some people will think this means most readable by a beginner, while others like myself will tend to prefer to value the authoritative depth of insight of a book. For that reason I prefer books written by real experts, and I must admit that in my opinion it was a tendency in older days for experts to be more likely to write books. Nowadays everyone writes his own book; even I myself have written books at graduate level in subjects I have later learned were treated vastly better eons ago by real masters.

To offer just a couple of examples in mathematics, it is my firm opinion after a lifetime of study and research in the area of geometry, that the absolute finest Euclidean geometry book is that by Euclid; nothing else is remotely close. I recommend approaching it however with the benefit of a good guide such as the book of Hartshorn, Geometry, Euclid and beyond. As an introduction to algebra, from elementary to advanced, I prefer Euler's Elements of Algebra. I am not a physicist but also in that field my few attempts to learn something have been frustrated by several relatively modern texts, while I greatly enjoyed texts and expositions by Dirac, Pauli, Einstein, deBroglie and Feynman.

Note some of these authors are not from olden times, like Feynman. Also in mathematics when it happens that a modern master takes trouble to write a book, I have appreciated that one as well. An example in modern algebra is the fairly recent book of Mike Artin, Algebra, which I prefer to the original classic Modern Algebra by Van der Waerden. Other excellent modern authors include Milnor, Serre, Mumford, Hartshorne, Arnol'd. As an illustration of the complexity of choice, and to illustrate a point made by Simon Bridge above, my favorite commutative algebra book, at least in terms of clarity, is the classic by Zariski and Samuel. But the topic of homological algebra had scarcely been created then, hence developments of that sort within commutative algebra do not appear much there. (They discuss tensor products but not perhaps Tor.)

So I agree with the last statements by the previous poster, that it depends on several factors and that a student must choose for herself which books "speak" most clearly to her (or him). I agree also with Simon Bridge that topics go in and out of fashion and modern books hew more closely to currently fashionable ones. This has pluses and minuses for the learner. Bill Fulton e.g. made his start in exploring intersection theory and enumerative geometry, culminating in his great book on it, by reading and trying to make sense with modern tools, of the classic work on the subject by Schubert, from 1874, I believe. This may not be quite accurate as a history of his book, since he was also trying to generalize the Riemann Roch theorem to singular spaces, but likely has some truth in it.

Another reason "old" works may be useful is the advice many of us believe in that original works are most insightful, i.e. those by the original discoverer. As time goes by these become old, and can never be replaced by newer ones, although of course people can reinterpret and offer newer versions of prior discoveries. Another example like this that I experienced, in addition to those authors mentioned above, was reading the original Michelson Morley experiment which I found much more clear and helpful than any textbook explanation of its content. Archimedes and LaGrange were also quite helpful to read, at least in places.

 

[vanhees71]

There are no special insights in older books.
The best books for learning, in general, are usually the more up-to-date ones. These benefit from the concepts having been taught for a while so mistakes may be ironed out, with some presentation issues corrected - they also benefit from more recent education research. Newer books will also be written with an eye on more recent research in the field - so what they focus on teaching you is more likely to be relevant later.

However:
1. all this depends on the subject area and the level it is to be taught - some changes are just fashion;
2. individual students vary - individuals are advised to use the most relevant work that they find they understand best.
... consult a range of texts to inform your education.

Well, there are exceptions. For me the 6-volume lectures on theoretical physics series by Sommerfeld is still outstanding. It's far better than many more recent books on classical physics. Only very little is outdated. The worst thing is that he uses the "$\mathrm{i} c t$ convention" for relativity.

 

[Simon Bridge]

Such exception prove the rule ;)

 

[mpresic]

Many older books are good. For example I have started to examine Whittaker and Watson, A course in Modern Analysis, and other books from Whittaker on rigid bodies and potential theory. Also I find older versions of many classic physics text as better. I prefer Goldstein's third edition to his later one with Safko, and Poole. I like the old Resnick and Halliday to the new editions after 1988. I think I also like Jackson Red to Jackson Blue.

But I do think many contemporary textbooks are also good. I like Shankar's quantum mechanics. Sakurai is also good.

Now that I think of it, I now see the books by whittaker and Watson, and whittaker should not be the first texts encountered even in graduate courses. They are too specialized and (probably) too advanced.

 

[Fervent Freyja]

Yep, they can provide insight. New knowledge gets diluted and can become biased over time. I have found quite a few older books have explained many things in physics that seems to be lost and misinterpreted by newer books. I think a mixture of old is fine, almost necessary to understand things more deeply. Learning about the history of the body of knowledge in physics has been helpful to my understanding, there is always more to learn in that regard. Most courses teach knowledge that was fixed a decade or more ago, that is obviously important to learn. But, because course material doesn't mention old knowledge or reflect recent knowledge or work, and not even in newly published books, reading studies and trying to be relevant to whatever field you are interested in is also important. Very much of new knowledge or new understandings aren't available to the public. There are barriers in place to some very good material. There are textbooks I'd love to own, but can cost in the high 1000's!

 

[Demystifier]

Modern books want to teach you the modern stuff, but modern books tend not to be bigger than the old ones, so obviously the modern books can spend less space to teach you the old stuff. Hence it is very likely that old (which doesn't mean obsolete) stuff can be better learned from old books.

In mathematics, there is one additional reason to read old books. Modern books on pure math are often written in the Bourbaki (theorem-proof) style, which was not so often the case with old math books. For those who do not like that style (and applied mathematicians or physicists usually don't), the old math books may look much more readable.

 

[vanhees71]

The Bourbaki style is awful. In my opinion it's the style to write math papers but not textbooks. Textbooks should also provide the intuition behind the very abstract way of representing modern mathematics. Without intuition also in math there's little chance of getting new ideas to make progress, although at the end of course the mathematician has to bring his/her intuitions into the formal strict form a la Bourbaki. A good mathematician is made by combining both skills!

 

[Demystifier]

I would like to see what @micromass thinks of the Bourbaki style.

 

[micromass]

I would like to see what @micromass thinks of the Bourbaki style.

Depends on what you use it for. If you already know the material, then it's a nice exposition with some results that might be new to you. As an actual teaching tool, it's horrible. I prefer books with more motivation, with more exposition, more applications, etc.

 

[vanhees71]

Another great old two-volume book is Max von Laue's Relativitätstheorie. I don't know, whether there's an English translation. Except for using the ict convention in the special theory it's written in a very clear style.

 

[Aufbauwerk 2045]

I've found special insights from reading some of the great books of the past, including math and science books. Sometimes it's because I learn how it all developed and how the great minds have worked. Reading someone else explaining how Newton thought and what he said is just not the same as actually reading Newton. The same is true reading Einstein's papers. I like to understand how physics developed by getting as much as possible from the masters.

But aside from the greats, I enjoy reading standard high school and university math textbooks from the 19th or early 20th century. I like the writing style, I like the way they explain things, and the material is not out of date, excepting a few topics such as calculating with logarithms and how to use the slide rule. (Not to disrespect the slide rule in any way, it's a very green technology and it was used by flight engineers during the Apollo missions as seen in the movie Apollo 13! )

 

[vanhees71]

Well, sometimes it's a hard task to understand old books. One example is Newton's principia. It's so utterly different from how we formulate his theory today (which is I think more due to Euler than Newton himself) that at least I had a hard time to understand it. It's of course no question interesting, how Newton derived his results in a geometrical way.

 

[bolbteppa]

There are no special insights in older books.
The best books for learning, in general, are usually the more up-to-date ones.

That is an unbelievable statement.

Show me one modern book with the insight you'd find in Goursat, Cartan, Dieudonne, Landau, Bourbaki, Van der Waerden, Whittaker and Watson, Sommerfeld, etc... there's about 50 quite literally unparalleled books, most more than 50 years old, there are simply and unequivocally no books that compare to these.

 

[George Jones]

I don't like it when people are prejudiced against old books.

I don't like it when people are prejudiced against new books.

 

[robphy]

It may be argued that old books might not be the best place to first learn various topics in physics.

However, there are insightful gems to be found in old books... but one has to dig and be discerning.
Certainly, some ideas didn't pan out... maybe they were just wrong... or maybe some ran into technical difficulties... or maybe didn't seem that useful at the time.

I have found some gems in old relativity books that have not made it into the modern relativity books.
For example, the seeds of the Bondi k-calculus (1962) (which seems to only appear in some modern books) are found in books by Milne (1940) and even earlier in AA Robb (1911). In fact, it's surprising that some of the ideas we have today [like "rapidity"] were developed there... but Robb's name is not familiar in the typical history of relativity. In addition, Robb's (1921,1936) Geometry of Time and Space have insights which are used in modern attempts to develop spacetime geometry and possibly quantum gravity from the causal structure.
https://en.wikipedia.org/wiki/Alfred_Robb

Occasionally, one finds "new research by ______" based on a variations of "an old idea by ___________".
For instance,
https://scholar.google.com/scholar?q="old+idea+by"+relativity
https://www.google.com/#q="old+idea+by"+relativity
One could probably change "relativity" to something else to find other examples.

 

[vanhees71]

I don't like it when people are prejudiced against old books.

I don't like it when people are prejudiced against new books.

Well, when I look at a physics book, no matter when it was written, I first look at it critically, and then I can decide after a while whether I like it or not. That's it.

 

[fedor slam]

Bolbteppa I would be very interested in knowing what the 50 books that were unparalleled are so that I could read them. Could you please list them?

 

[fedor slam]

That is an unbelievable statement.

Show me one modern book with the insight you'd find in Goursat, Cartan, Dieudonne, Landau, Bourbaki, Van der Waerden, Whittaker and Watson, Sommerfeld, etc... there's about 50 quite literally unparalleled books, most more than 50 years old, there are simply and unequivocally no books that compare to these.

Bolbteppa I would be very interested in knowing what the 50 books that were unparalleled are so that I could read them. Could you please list them?

 

[Aufbauwerk 2045]

To offer just a couple of examples in mathematics, it is my firm opinion after a lifetime of study and research in the area of geometry, that the absolute finest Euclidean geometry book is that by Euclid; nothing else is remotely close. I recommend approaching it however with the benefit of a good guide such as the book of Hartshorn, Geometry, Euclid and beyond.

I have the Heath edition of Euclid, which contains lots of notes. I have the Dover edition in which Heath's notes are fine print. Maybe it's the same size as in the original, in which case I wonder if the schoolboys used to read the notes with a magnifying gadget as I do.

In any event, after working on a Euclid-related AI project recently, I learned that any attempt to fit Euclid's concept of logic into our modern so-called rigorous logic seems like a hopeless task. There are many holes in Euclid's logic, if you try to fit it into something like first order predicate logic. But if you adjust a bit to his approach, such as his use of diagrams to set up the proof, then it's amazing what he accomplished, and it is possible to use a computer to generate proofs for Euclid. It's beyond interesting. For lack of a better word, it's a kind of "spiritual" experience.

I think one value of Euclid is he shows you how to prove things using a pure geometrical approach, as opposed to using algebra and Cartesian coordinates. Some may say this is out of date or not practical, but apparently people did not think so until the 20th century.

I wonder though if there are many schools left anywhere in the world that do teach kids geometry using Euclid. I would love to hear from someone who has been through that experience.

On a side note, I think crop circles show how useful a bit of Euclid can be.

:)

 

[atyy]

The need for a classical-quantum cut in the standard interpretation of quantum mechanics is not a unique insight. However, the only major textbook I know of that states this insight clearly is Landau and Lifshitz (1958). After that, one has to wait until Weinberg (2012) to find this stated, but even then not as clearly as by Landau and Lifshitz. Most other good books (eg. Gasiorowicz 1974), Cohen-Tannoudji (1977), Shankar (1984), Sakurai (1985), Peebles (1992), etc) fail to state this, and one book that is terrible but popular (Ballentine) gets it completely wrong. Of the old classics, Dirac (1930) does not state it (it would defintely have spoilt his style), while von Neumann (1932) does, in his special way.

On the other hand, I think no quantum field theory text deals with the Wilsonian viewpoint clearly until the very recent text of Schwartz (2015). It's in Peskin and Shroeder (1995), Weinberg (2005), Srednicki (2007), Zee (2010), but I think in a way which is not necessarily easy to understand or to know its importance.

 

[vanhees71]

Well, we agree to disagree. I don't see, why I need a quantum-classical cut anywhere. Fortunately this question is completely irrelevant to physics, because you can use QT with or without this assumption to get the same results connected with observations, and that's all what counts. You may assume the existence of little green men on Mars as well ;-)).

Also Ballentine is a very good textbook (although there's too much interpretation in it, but at least it's the minimal statistical interpretation, which does the least harm to understanding QT). It's also the only general textbook which introduces rigged Hilbert spaces on a level suitable for the QT practitioner and which treats the Galilei group in a very elucidating way.

Weinberg's QT book is also great, although I disagree with his all too pessimistic view on interpretation. I don't think that there are unsolved problems within the physics part.

Landau-Lifshitz vol. III is quite nice, I'd say but has not enough of the general Dirac representation, i.e., it's too much leaned towards wave mechanics. It's clear advantage is that it treats many applications that cannot so easily found elsewhere.

Sakurai is my favorite as the introductory book, Dirac's classic is just Dirac at its best. No gibberish but clear math, as also holds for all of his original research papers I've read so far. Of von Neumann's book the only part that's worth reading is the math part. It's the historically first attempt at a rigorous treatment of all issues with unbound self-adjoint operators. Of course, we are lucky today to have a well-developed modern version of it, called "rigged Hilbert space", making Dirac's intuitive insight as rigorous as von Neumann's traditional treatment. The other QT books I don't know enough to make statements.

Concerning the QFT books we agree, except that I find Zee's "Nutshell" the worst of the mentioned. It's trying to pack too much in the too little nutshell and fails badly. My favorite is Schwartz.

 

[atyy]

Also Ballentine is a very good textbook (although there's too much interpretation in it, but at least it's the minimal statistical interpretation, which does the least harm to understanding QT). It's also the only general textbook which introduces rigged Hilbert spaces on a level suitable for the QT practitioner and which treats the Galilei group in a very elucidating way.

That's why Ballentine is such a terrible book - it has too much interpretation, and it is not the minimal statistical interpretation, and therefore does the most harm in understanding it. The true minimal statistical interpretation is found in Landau and Lifshitz.

 

[vanhees71]

Hm, but according to your own understanding of LL's interpretation it's with collapse and quantum-classical cut. LL is great in having not too much interpretation though. It's in the good tradition of the Sommerfeld school, who present theoretical physics in the no-nonsense approach. The only problem I have with LL is that it is too much focused on the wave-mechanics approach.

Also if Ballentine's book is not the minimal statistical interpretation, what do you call the minimal statistical interpretation? In my understanding Ballentine's long digressions into interpretation tries to rule out all other interpretations.

Somehow this shows, how mediocre all these interpretation discussions are: Everybody can pick whatever he or she likes to read in any text on interpretation. It's soft science at best, usually however confusing. It's against good practice in the natural sciences to formulate clear statements in a mathematically concise way to be confronted to observation and experiments in the real world!

 

[atyy]

Hm, but according to your own understanding of LL's interpretation it's with collapse and quantum-classical cut. LL is great in having not too much interpretation though. It's in the good tradition of the Sommerfeld school, who present theoretical physics in the no-nonsense approach. The only problem I have with LL is that it is too much focused on the wave-mechanics approach.

Also if Ballentine's book is not the minimal statistical interpretation, what do you call the minimal statistical interpretation? In my understanding Ballentine's long digressions into interpretation tries to rule out all other interpretations.

Somehow this shows, how mediocre all these interpretation discussions are: Everybody can pick whatever he or she likes to read in any text on interpretation. It's soft science at best, usually however confusing. It's against good practice in the natural sciences to formulate clear statements in a mathematically concise way to be confronted to observation and experiments in the real world!

The minimal statistical interpretation has a classical-quantum cut and collapse - but one must recall that neither the quantum state nor collapse are necessarily real, and they are just means of predicting experimental results. The experimental results are real or "classical", just like the measurement apparatus and spacetime.

 

[vanhees71]

I don't see, where the minimal interpretation needs collapse and cut. To the contrary, it's agnostic about what happens with the system when measured. It just takes the Born rule and that's it. There's no need to have classical dynamics in contradistinction to quantum dynamics (cut), and it's usually not possible to describe the state of the system after ineracting with a macroscopic object (including the measurement device) in all microscopic detail, but it's sufficient to know the relevant macroscopic observables ("pointers" of a measurement apparatus) to relate it to the properties of the measured system, and that's described with sufficient accuracy by the classical approximation of quantum dynamics.

Indeed, as any mathematical description, QT is a description (as is classical mechanics or classical field theory). That's a tautology: A description is a description.

 

[Demystifier]

The need for a classical-quantum cut in the standard interpretation of quantum mechanics is not a unique insight. However, the only major textbook I know of that states this insight clearly is Landau and Lifshitz (1958).

Can you quote the exact words by which L&L introduce the classical-quantum cut?

 

[martinbn]

How did a thread, not in the quantum physics subforum, about the value of older books in general, got into a discussion about QM interpretations!

 

[Demystifier]

How did a thread, not in the quantum physics subforum, about the value of older books in general, got into a discussion about QM interpretations!

All roads lead to quantum interpretations.
It's a version of the Godwin's law https://en.wikipedia.org/wiki/Godwin's_law .

 

[atyy]

Can you quote the exact words by which L&L introduce the classical-quantum cut?

Bell quotes it in his "Against 'measurement'".

http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf

 

[vanhees71]

Well, what Bell quotes as one of the reasons LL is a good book, namely that it's "the closest to Bohr what we have", I'd take rather as an insult recommending a textbook on QT. If you want to get utmost confused about QT, just read Bohr or Heisenberg. LL fortunately is not close enough to Bohr, making it a pretty comprehensible treatment of wave mechanics. Usually the LL books strip off all unnecessary gibberish and offer a clear physically well-motivated mathematical treatment. I think, Landau has also been with Born and Paul long enough not to be too much spoiled by Heisenberg and Bohr . SCNR.

 

[RogueOne]

My coworkers and I prefer the older textbooks. The thought processes were clear, the concepts were written concisely, and the connection between qualitative phenomena and quantitative representation is very clear.

There are some great new textbooks as well

 

[atyy]

Well, what Bell quotes as one of the reasons LL is a good book, namely that it's "the closest to Bohr what we have", I'd take rather as an insult recommending a textbook on QT. If you want to get utmost confused about QT, just read Bohr or Heisenberg. LL fortunately is not close enough to Bohr, making it a pretty comprehensible treatment of wave mechanics. Usually the LL books strip off all unnecessary gibberish and offer a clear physically well-motivated mathematical treatment. I think, Landau has also been with Born and Paul long enough not to be too much spoiled by Heisenberg and Bohr . SCNR.

Yes, as we know from machine learning, bagging is a good trick. Personally, I think between LL and Dirac one has almost everything. The only thing missing is a simple example using spin 1/2 from Feynman or Sakural.

 

[vanhees71]

Another great book is Schwinger, Quantum Mechanics - Symbolism for Atomic Measurement, Springer Verlag. It's not recommended as a textbook to learn QT, because it offers more alternative mathematics than any other book (but as usual for Schwinger brilliant mathematics), but already the "Epilogue" is worth reading (and that's although it's without formulae and math at all ;-)).