Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mathematical models

  1. Jan 20, 2007 #1
    "In these and similar ways, the progress of science has itself shown that there can be no pictorial representation of the workings of nature of a kind which would be intelligible to our limited minds. The study of physics has driven us to the positivist conception of physics. We can never understand what events are, but must limit ourselves to describing the pattern of events in mathematical terms; no other aim is possible - at least until man becomes endowed with more senses than he at present possesses. Physicists who are trying to understand nature may work in many different fields and by many different methods; one may dig, one may sow, one may reap. But the final harvest will always be a sheaf of mathematical formulae. These will never describe nature itself, but only our observations on nature. Our studies can never put us into contact with reality; we can never penetrate beyond the impressions that reality implants in our minds.

    Although we can never devise a pictorial representation which shall be both true to nature and intelligible to our minds, we may still be able to make partial aspects of the truth comprehensible through pictorial representations or parables. As the whole truth does not admit of intelligible representation, every such pictorial representation or parable must fail somewhere. The physicist of the last generation was continually making pictorial representations and parables, and also making the mistake of treating the half-truths of pictorial representations and parables as literal truths. He did not see that all the concrete details of his picture - his luminiferous ether, his electric and magnetic forces, and possibly his atoms and electrons as well - were mere articles of clothing that he had himself draped over the mathematical symbols; they did not belong to the world of reality, but to the parables by which he had tried to make reality comprehensible. For instance, when observation was. found to suggest that light was of the nature of waves, it became customary to describe it as undulations in a rigid homogeneous ether which filled the whole of space. The only ascertained fact in this description is contained in the one word 'undulations', and even this must be understood in the narrowest mathematical sense; all the rest is pictorial detail, introduced to help out the limitations of our minds. Kronecker is quoted as saying that in arithmetic God made the integers and man made the rest; in the same spirit we may perhaps say that in physics God made the mathematics and man made the rest.

    To sum up, physics tries to discover the pattern of events which controls the phenomena we observe. But we can never know what this pattern means or how it originates; and even if some superior intelligence were to tell us, we should find the explanation unintelligible. Our studies can never put us into contact with reality, and its true meaning and nature must be for ever hidden from us. "


    The above is a quote from physics and philosophy by sir fames jeans

    I want to know if the position he stated in this passage hold for most philosophiers and scienctist? ( note: i am not asking for your opinion. I am asking if the position that is stated is widely accepted or not.)
     
  2. jcsd
  3. Jan 20, 2007 #2

    verty

    User Avatar
    Homework Helper

    Is it held by you?
     
  4. Jan 20, 2007 #3
    If is curious that you even ask.
     
  5. Jan 20, 2007 #4

    verty

    User Avatar
    Homework Helper

    You were the one who posed the question. It just seemed like you should start by giving us your interpretation.
     
  6. Jan 20, 2007 #5
    No, modern philosophers or respectable scientists would not identify themselves with these (rather elementary) views:

    This is no more true of science then it is of everyday human experience i.e. when I look at a table my passive brain devises a pictorial representation that is not true to reality. Obviously we are satisfied with these "partial aspects of truth" rendered comprehensible through "pictorial representations and parables" i.e. the parable of the table.

    Perhaps this philosophy would find solice in contemporary nihilism, because those philosophers argue using many of the same techniques which are used by logical positivist. The bottom line is that humans have not evolved to the point where positivism is appropriate, there is still too much out there too learn i.e. in ptolemy's day only the kinematics of planetary motion were discussed and not the dynamics because positivism was in vogue.
     
  7. Jan 20, 2007 #6

    than may i ask what is the modern conception?


    my take on it is rather if this "partial truth" is ever "enough" to understand the deepest level of reality. You example is rather "simple". My question is: Can we really understand the deepest level of reality using using human pictorial representation. I think we can pretty much know how billiard ball works, but can we really using it to understand the behavior of subatomic particles? It is like saying A is like B, and B is like A. We are going nowhere. Let using take another example. I always feel that there is something mysteries about the laws of nature. Let us take newtons inverse square law. Why is it exactly 2 and not 2.34.... or Why is it that the magnatic field always in the direction obey by the right hand rule when the current is going in a certain direction? We have have many interpretations/"theories" of how nature works( feynman gave three different models of how the inverse square laws, ), but nature seems to only speck in one single language, that if of mathematical "models". The question of "why" nature is the way it is? I don t see how science can every answer that. So in that sense, the think the passage is correct.
     
    Last edited: Jan 20, 2007
  8. Jan 20, 2007 #7

    ok. My answer is some where bettween yes and no.
     
  9. Jan 20, 2007 #8

    verty

    User Avatar
    Homework Helper

    If mathematical models didn't fit nature, wouldn't that be more odd?
     
  10. Jan 20, 2007 #9
    That are two way of look at it. You can reckon that nature might be like a giant chess board, and that a sort of pictorial representation is possible, and that the underlying rules are really very simple, and sciencetist using math to quantifies rules, pattern, regularity in this giant chess board. The problem with that is that it is no the case in the real world.
     
  11. Jan 20, 2007 #10

    verty

    User Avatar
    Homework Helper

    It isn't? .
     
  12. Jan 21, 2007 #11

    Yes. read feymann ` s character of physical laws
     
  13. Jan 21, 2007 #12

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I disagree entirely with the philosophy espoused in the opening post.

    Mistake #1: equating "human pictorial representation" with "understanding".

    (just what the heck is "human pictorial represntation" anyways?)

    Mistake #2: assuming that we cannot picture things faithfully.

    Mistake #3: assuming that observation is insufficient for studying reality.
     
  14. Jan 21, 2007 #13

    If "pictorial representation" is not the way to ture understanding, and i am curious as to what "is" true understanding? People can reduce physical phenonmen to fundemental laws, and even reduce those those laws from a more fundenmental set of physical laws, but we will never be able to explain the origin of those laws, why they exist, or why they have the form that they do. Therefore, I assert that true understanding can never be attained. We can only content with what we can do, which is to extract patterns and regularities in nature.
     
  15. Jan 21, 2007 #14

    verty

    User Avatar
    Homework Helper

    Paraphrasing: "We must be content with what we can do, which is to extract patterns and regularities in nature."

    Okay then.
     
  16. Jan 21, 2007 #15

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Then why did you post all that other stuff irrelevant to this assertion?

    (And how can you assert that when you don't even know what true understanding is?)
     
  17. Jan 21, 2007 #16

    the reason i ask is not because i " don t know". I was merely trying to understand your point of view.

    Don t tell me it is irrelevent if you can t see the connection. If all we can understand are patterns, but without deep understanding of why they are what they are, then how can there be complete understanding?
     
    Last edited: Jan 21, 2007
  18. Jan 21, 2007 #17

    verty

    User Avatar
    Homework Helper

    Let's suppose that you did know by some miracle why those patterns were there. That would mean that you knew about some other existents in another universe or whatever. But then you wouldn't know why that other universe was there. You would still not have complete understanding, right?

    So perhaps complete understanding would be understanding those why's to infinity, an infinity of why's. But then why is it that there is an infinity of why's? So what is it exactly that you could know to complete your understanding, if you could know it?
     
  19. Jan 21, 2007 #18


    I don t know what you trying to say here. It is too vague for me.
     
  20. Jan 21, 2007 #19

    verty

    User Avatar
    Homework Helper

    You say our understanding is not complete, but that must mean that you can delimit that which is missing from our understanding. But if what is missing from our understanding is the why of the commonalities and principles of nature, then the why of the why is also missing, and the why of the why of the why.

    Suppose by some miracle you know the why of these patterns, that God configured the big bang and caused it to bang. Now, why did God do that? Why was God in such a mental state as to do that? See, there is another why to be answered. So what is it that would complete your understanding?
     
  21. Jan 21, 2007 #20
    I don t see how that might be the case. We might see more clearly what can t be done, say it is unknowable. To imagine you can extract more information from it is absurd.
     
    Last edited: Jan 21, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Mathematical models
  1. Mathematical Modeling (Replies: 4)

  2. Mathematical Modelling (Replies: 12)

  3. Mathematical Modelling (Replies: 5)

Loading...