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Next Book Suggestions?

  1. Jul 22, 2005 #1
    I just stumbled across this forum a days ago. It is quickly becoming my new favorite place to spend those slow times at work. :tongue2:

    Anyway, I was wondering on some books suggestions. I am not really too far along in my classes so really technical books might be a tad hard to get through.

    Since the first of the year I have read:

    Hyperspace
    The Universe in a Nutshell
    A Brief History of the Universe
    Principia (only the first 400 or so pages then the math got a bit too much so I am waiting until I can finish it)
    The Elegant Univese (both book and dvd)
    The Fabric of the Cosmos
    Some Random papers here and there

    I think that is about it.

    I would like to stay on that level of reading since I am not too far along with school yet. All those books I listed were pretty easy to follow, except Principia of course. :wink:

    Thanks for the help. :smile:
     
  2. jcsd
  3. Jul 22, 2005 #2
    Road to Reality and that one for stephen hawkign bday like 2-3 years ago...
     
  4. Jul 22, 2005 #3
    well I suggest "The theory of everything" by Stephen Hawking and
    a book that I'm currently reading "the code book" by Simon Singh i found them very interesting books and I think you'll like them too. ;)
     
  5. Jul 23, 2005 #4

    honestrosewater

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    I'm not really into physics, but I've loved everything that I've read by Feynman. You might be interested in QED: The Strange Theory of Light and Matter. I suggest checking out whatever Feynman books your library has so you can get a feel for how he writes and teaches and see if you like him. Even his autobiographies are informative.

    I assume you're talking about Newton's Principia, not Russell and Whitehead's Principia Mathematica. But just in case you're talking about Principia Mathematica, I really wouldn't try to learn math or logic from it; It's not that kind of book.
     
  6. Jul 23, 2005 #5

    selfAdjoint

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    It's also badly out of date. A century of tremendous progress in mathematical logic has come and gone since it came out.

    In general I want to raise the issue of whether we should go back to original sources in learning physics and mathematics. The original discoverers often had only a murky understanding of the fields they discovered. Sort of like learning geography from Columbus.
     
  7. Jul 24, 2005 #6

    honestrosewater

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    Other than some inspiring moments, like
    "This preservation of favourable variation and the rejections of injurious variations, I call Natural Selection."​
    trying to learn from the 'originals' has always left me discouraged. Either they were writing for an audience of their peers (which I wasn't) or it was just old- the bad kind of old. It may depend upon the book, but the ones I've read were better for inspiration - there are some great moments - or adding to your appreciation and perspective.
     
  8. Jul 25, 2005 #7

    It is the one by Newton, translated by Cohen and Whitman. It was a bit much and gave up a little over half way through.

    I have downloaded a couple Feynman lectures, they were pretty good. I'll go check out some of his books as well. Thanks. :smile:

    I have the code book as well. My mom got it for me a while ago. Pretty good, I don't think I finished it though. :rofl:

    And I hate to say it, but I like reading the newer books a lot more. For some reason they just hold my interest a lot better.
     
  9. Aug 2, 2005 #8
    You should most definately look into reading more by Michio Kaku.

    - Parallel Worlds
    - Visions
    - Einstein's Cosmos
    - Beyond Einstein

    Black Holes & Time Warps by Kip Thorne is also very good.
     
  10. Aug 2, 2005 #9
    I agree. Trying to learn from the classics is difficult. I suppose its like trying to learn to speak english by reading shakespeare. But once you understand the subject matter, even if only in principle, I think it is a great idea. Like you said, to read 'evolution of species' or 'principia' and think to yourself "This is what started it all," is really inspiring.
     
  11. Aug 2, 2005 #10
    Here's some books from my tiny library:

    - Surely You're Joking Mr. Feynmen (Feynmen)
    - The Character of Physical Law (Feynmen)
    - The Scientists (Gribbin)
    - Euclid's Window (Mlodinow)
    - Feynmen's Rainbow (Mlodinow)
    - The Men Who Measured the Universe (Gribbin)
    - In Search of Schrodinger's Cat (Gribbin)
    - E=mc^2, A Biography of the World's Most Famous Equation (Bodanis)

    - Feynmen Lectures on Physics (Feynmen) [these are nice, but I'd say they're above the rest mentioned.]

    I'd say generally anything by John Gribbin is nice.
     
    Last edited: Aug 2, 2005
  12. Aug 4, 2005 #11
    I just finished Demon Haunted World: Science as a Candle in the Dark by Carl Sagan... I highly reccommend it.

    Next on my list:
    The Selfish Gene by Richard Dawkins
    Cosmos by Carl Sagan
    Pale Blue Dot by Carl Sagan
    The Fabric of the Cosmos by Brian Greene


    I'm open to other suggestions as well.
     
  13. Aug 8, 2005 #12
    I just finsihed that one not too long ago. One of my favorites so far.


    I ended up with Six Easy Pieces and Six Not So Easy Pieces, both by Feynman. They were pretty good. The local bookstore didn't have much at the time. I think I'll try some of those others by Michio Kaku.
     
  14. Aug 11, 2005 #13
    Did it repeat a lot of the same stuff from The Elegant Universe?
     
  15. Aug 11, 2005 #14
    I've been told that no one has ever read the book through. Russell didn't read all the parts that Whitehead wrote, and Whitehead didn't read all the parts that Russell wrote.
     
  16. Aug 11, 2005 #15
    No, not really. I can't remember a ton from the Elegant Universe book, but I watch the Nova stream at work a lot when I am bored. The Fabric of the Cosmos goes into a lot more detail. I remember I liked it a lot more than The Elegant Universe book.
     
  17. Aug 12, 2005 #16

    honestrosewater

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    That wouldn't surprise me. :zzz: :wink:
     
  18. Aug 12, 2005 #17

    mathwonk

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    in reference to posts 5,6, i disagree in the strongest possible terms. as Abel is reported to have answered to the question as to how he obtained such an in depth understanding of mathematics, he replied: "because I read the masters and not the pupils". anyone who has not read euclid, einstein, newton, galois, or riemann or gauss, cantor or mumford or serre, or hirzebruch, does not know what he is missing.
     
    Last edited: Aug 12, 2005
  19. Aug 12, 2005 #18

    honestrosewater

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    Funny, it was that very quote that encouraged me to attempt to 'read the masters'. :smile:
    Sorry, let me clarify and correct myself. I don't think people should skip the masters; I remember finding some very helpful spins on familiar ideas from some masters. Euler's Foundations of Differential Calculus comes immediately to mind. And I was referring to new, poineering material, discoveries, inventions, etc., not to just any writing by a 'master'. I meant that the ones I've seen weren't good introductions to a subject. I think they weren't good introductions because they seemed to be written for the author's peers, professionals who already had the knowledge and experience necessary to analyze these new concepts, and/or the author was making a full blown defense of their ideas - and none of this is what I want in an introduction. And for some older works, you have to deal with an antiquated style too. It's also just a generalization, as I was careful to note. Do you disagree with this point?

    Edit: I also wasn't tailoring my advice to stand up to being taken out of context. The OP clearly set a level of difficulty, which I had in mind and don't think the 'originals' are at. I think they would leave the OP discouraged, as they did me.
    And I thought of an exception. It may not be familiar to people here, but Adam Smith's Wealth of Nations was my introduction to the subject, and I loved it. I don't quite understand why, but while, for example, I found Darwin's numerous examples tedious, Smith's equally numerous examples were fascinating and made the book that much better.
     
    Last edited: Aug 12, 2005
  20. Aug 12, 2005 #19

    mathwonk

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    my apologies. of course you are right some old works are more useful than others.

    i recommend reading the old masters perhaps after learning something about what they were trying to say from modern sources.

    i myself greatly enjoyed reading riemann after a long career studying modern interpreters of his ideas. even then it was clear he understood the material he created far better than our own contemporaries do.
     
  21. Aug 12, 2005 #20

    honestrosewater

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    I'm glad you brought it up; I obviously didn't give the right impression. :smile:
    I don't know how old his work is, but that's amazing that people haven't made more progress.
     
  22. Aug 13, 2005 #21

    shmoe

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    His "On The Number of Primes Less Than a Given Magnitude" dates back to 1859. It was some ~30-40 years later that some of the statements he made were actually proven, though of course the Riemann hypothesis is still kicking. It's hard to judge the amount of progress that's been made on the Riemann Hypothesis without really knowing what reaching the end goal will entail. There have certainly been many advances on RH since his time and a whole boatload of related material has been inspired by his paper.

    It's definitely a must read for anyone interested in the subject though it's probably also a very difficult read if you aren't already familiar with a more modern treatment.


    I may as well recommend some related books, I think "Prime Obsession", by Derbyshire is a nice go at explaining Riemann's paper to the laymen and it gives a good historical look of his life as well. The math in Derbyshire is mostly drawn from "Riemann Zeta Function" by H.M.Edwards which itself is a textbook treatment of Riemann's paper, and contains a translation of it. So one can read Derbyshire and if they hunger for more details, consult Edwards (and Riemanns paper).
     
    Last edited: Aug 13, 2005
  23. Aug 13, 2005 #22

    mathwonk

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    Interestingly after a lifetime of hearing other people discuss Riemann's hypothesis and not quite understanding myself what the heck zeroes of the zeta function could have to do with primes, I read Riemann's own paper, and found it much cklearer and more elementary than any of the later explanations.


    As I tried to explain above, Riemann made it clear throughout his own work that to understand a complex function, one should consider it as intimately associated with its maximum domain of definition (via analytic continuation) but that it is completely determined in any open set. Moreover it is also best characterized by its full set of zeroes and poles in that maximum domain.


    Hence consider the following reasoning: by euler's product formula, which contains only the primes, the zeta function is completely determiend by the set of primes, i.e. their distribution. Hence knowing the location of all the primes is equivalent to knowing the zeta function.

    On the other hand the zeta function has as its natural domain of definition the full complex plane, in which it has exactly one pole at 1, and an infinite number of zeroes (apparently). Hence the zeta function is also essentially determined by knowing exactly where all these zeroes are.

    So we have a function, the zeta function, and it is essentially determined in two different ways: 1) by knowing where all the primes are.
    2) by knowing where all its zeroes are (the one pole is at z=1).

    Hence the two pieces of data: zeroes of zeta, and distribution of primes, are merely two sides of the same coin, and that coin is the zeta function.

    hence these two data must contain almost the same information.


    More precisely, Riemann shows that Gauss's approximation Li(x) to the number of primes less than or equal to x, overestimates the actual number. I.e. he shows it estimates instead the number of primes plus the numbers of squares of primes plus the number of cubes of primes, ..... He states this very clearly.


    Then he writes out this statement as an equation and "solves it" for a better formula estimating the actual number of primes, by "mobius inversion".


    Throughout the process he makes various statements about how many terms can be ignored in his estimates, and these claims are still unproved to some extent. That is the famous hypothesis.

    I did not know any of what I have just explained until I read Riemann's own version of it.

    The later versions attempt to prove his claims and fill in the gaps in his sketchy arguemnts. That makes them longer to read and more technical. Riemann himself is very clear in many ways, and very intuitive, much more so than his followers.


    So although at one time I spent up to a week per page reading his abelian functions paper, (on which I thought I was an "expert"! hah!!), on the other hand the number theory paper was relatively easy to at least peruse for its main points.

    I repeat: shake off your reluctance to read riemann: his short paper is much clearer even than edwards' excellent book about it. Edwards himself says this! that is why edwards provides a translation of riemann in his appendix.




    An example from my own field was the "Brill Noether" estimate of just how large the genus of a curve needs to be before we can expect all curves of that genus to admit a "d to 1" branched cover of the projective line.

    I almost never understood clearly why this number was what it was until I read Riemann. He deduced it very quickly just from his proof of the riemann roch theorem, and until i spent that week thinking about it i had never relaized it could be deduced from just that data.

    indeed although it is called the "Brill Noether" number, Riemann deduced it several years earlier than they did. current books on the topic, do not credit riemann with this discovery and do not give his own argument, but rather credit brill and noether.

    Thus I say riemann understood these matters better than do our contemporaries who have apparently never read him.

    the original discoverer of a topic is in my mind always the best source for the deepest understanding of it. This is of course based mainly on my reading of gauss, riemann, euclid, mumford, serre, kempf, artin, grothendieck, galois, wirtinger, weil, andreotti - mayer, weyl, kodaira, newton, cantor, milnor, eilenberg - maclane, einstein, galileo, van der waerden, and others.

    I did not get this impression from my reading of principia mathematica by russell-whitehead, and in my opinion there is a reason for that.
     
    Last edited: Aug 13, 2005
  24. Aug 13, 2005 #23

    mathwonk

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    the point is that riemann is not the place to go for details, but is the place for an overview, and a clear statement of the main ideas.
     
  25. Aug 13, 2005 #24

    mathwonk

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    heres another one that took me 40 years to understand:

    if you have two integers n,m then the smallest linear combination of them is also their gcd.

    an algebraic proof goes like this: if q = an+bm, then any number that divides n and m also divides the right side, hence also the left side i.e. q. so every common divisor of n,m is a divisor of q hence less than or equal to q.

    on the other hand if we divide n say by q, we get n = xq + y where y is less than q. then substituting into q = an+bm, we get an expression for y as a linear combination of q,n,m, and hence also just of n,m. but y is smaller than q a contradiction unless y is zero, i.e. unless q divides n. whew!


    but how do you think of that?

    now when i read euclid i found out that he thought of all these numbers as lying on a line, and the word for "divides" was actually "measures"! i.e. he was laying off copies of q to try to measure n exactly, instead of dividing it. that makes it clear that the remainder is less than q. i.e. suddenly the "division algorithm" is obvious.

    anyway, if you think about it, it is fairly obvious that the smallest length you can measure using both n and m is also the largest length that measures both of them.

    i.e. the full set of lengths you can measure using both of them has a smallest one (we may assume), and then we have a family of points on the line all equidistant, as is fairly intuitive. then..... well think about it.

    so in this case just knowing the one word "measures" made it all clear.

    in riemann's case it was just that he deduced the "brill noether" number immediately after giving his argument for riemann roch, that made it clear it must be posssible to do so.

    the modern books mention "riemanns inequality", but do not give his matrix argument for it. it turned out it was merely that fact that he used a matrix that allowed him to deduce the b-n number. omitting his matrix makes it impossible to understand where his insight came from.
     
    Last edited: Aug 13, 2005
  26. Aug 13, 2005 #25

    shmoe

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    If this was aimed at me, then I must have given the wrong impression. I think Riemann's paper is fantastic, it's concise and contains only the essentials. It was not only enlightening to my understanding to see Riemann's views as first hand as I can get without reading German, but had the "wow, this is where it began" quality. However I think it could be an extremely confusing and possibly discouraging place to start for someone not familiar with the theory, doubly so if they aren't comfortable with the fundamentals of complex analysis and fourier series. I could be mistaken here- I'd welcome any input from a non-mathematicians point of view on what they were able to glean from the original (not to say your take isn't very interesting! just a different perspective is to be had from a non-mathematician).

    My recomendation for Derbyshire is aimed at the layperson (though I did learn some interesting history from it), Edwards for the more advanced. One of the strengths of edwards is that he's trying to present the work very close to it's original form, essentially filling in the details of Riemann's leaps that most mortals can't keep up with. Reading Edwards, it is mandatory to read Riemann as well and I'd be willing to call it tragic not to do so, especially since it's sitting in the appendix.
     
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