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Do You Believe In Scientism?

Discussion in 'Physical & Life Sciences' started by AV1611VET, May 6, 2021.

Do you believe in scientism?

  1. Yes

    5.3%
  2. Mostly

    5.3%
  3. Somewhat

    31.6%
  4. No

    57.9%
  1. sjastro

    sjastro Newbie

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    Leaving aside Miles Mathis' crackpottery, pi is one of those mysterious values that crops up in the most unexpected places.
    The calculation of the energy levels of the hydrogen atom has been around for about a century but recently a mathematician and physicist looking deeper into the calculation found pi lurking in quantum mechanics.
    A Classic Formula For Pi Was Discovered Hidden in Hydrogen Atoms

    Paper here:
     
  2. SelfSim

    SelfSim A non "-ist"

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    I'm way out of my depth here, but the Wallis product seems to start out by integrating:
    sin (x^n) dx between its limits.
    So anything describable using trig functions, (sin, cos, etc), ends up being physically based on circular motions of some kind(?), so surely its not so big of a mystery that pi then shows up in Wallis' formula(?)

    How pi ends up in the QM context I wouldn't have a clue, however, why would hydrogen energy spectrum levels in QM be exclusive of descriptions of circular movement? I mean we're talking about orbital jumps there aren't we?
     
  3. AV1611VET

    AV1611VET BELIEVE IN MIRACLES Supporter

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    That's not this guy is it?
     
  4. Kylie

    Kylie Defeater of Illogic

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    I don't think it matters, since I doubt you will take any idea of reality as being objectively true.

    You can't say a rock is subjective just because there are different kinds of rocks. What you're describing may have different people saying different things, but that's not because it's subjective. It's objective descriptions of different rocks. That's what accounts for the differences. I'd like to see if you can make this same argument regarding pi.

    I think you're taking my joke a little far here...
     
  5. SelfSim

    SelfSim A non "-ist"

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    Chuckle chuckle .. Ok .. Deal! .. (as long as you confess that you're a human, that is(?))
    See, the only demonstrably testable notion there I can apply for distinguishing between 'subjective' or 'objective', is the scientific method .. which defines 'objective'.
    Those folk who aren't thinking in scientific ways, can still agree with me that the rock 'exists', however .. thank goodness! How come, though?
    The conclusion I can then form, is that they have assigned a rock as 'existing' in some way other than via the scientific method, (which humans must've been doing since time immemorial) .. which is demonstrable .. whereas there's nothing showing us that the rock exists independently from either of our very human perceptions (namely because that's an untestable claim).
    So, we've then accounted for their perception and a scientist's and for the obvious observation that we share a common type of mindset (aka: human).
    Ok .. 'twas an interesting movie though .. (recommended).
     
    Last edited: May 8, 2021
  6. sjastro

    sjastro Newbie

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    Yes there is a connection.
    The motion of a particle around the circumference of a circle (= 2πr) is described by a sinusoidal function.

    It doesn't involve orbital jumps.
    What they did was to apply a variational method based on the principle of least action as described in this thread on Bohr’s ‘semi classical’ model for the hydrogen atom where an electron occupies an orbit in a particular energy level defined by its quantum number.
    The higher the quantum number the higher the energy level.

    The variational method involves making an educated guess of hydrogen’s wavefunction and optimizing the guess.
    They found as the atom’s orbital angular momentum increased with increasing quantum number, the theoretical optimized values for energy gradually equaled the experimentally measured energies.
    They found they could derive Wallis’s formula for pi from the ratio of the theoretical values to the experimentally measured values.
     
  7. SelfSim

    SelfSim A non "-ist"

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    Thanks for that. This is really bugging me.

    I understand the importance of this issue .. whenever two apparently independent methods arrive at the same conclusion, there's clearly evidence of dependency somewhere.

    So, in this case, is that evidence pointing towards an 'independent' physical reality, or evidence of some sort of commonality in the fundamental physics model (ie: the spectrum of the hydrogen atom) and the pure math model (ie: variational computation applied to the hydrogen wavefunction)?

    I'm still having difficulty in distinguishing between the pure math components and the physical models here .. which is all important for understanding how to position this in my thinking(?)
     
  8. sjastro

    sjastro Newbie

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    We humans suffer from a condition known as Apophenia or the need of finding connections between unconnected things.
    The exercise shows that pi can be derived using physics instead of mathematics.
    Is there some cosmic connection or deep meaning for this?

    Pi also turns up in Buffon’s Needle Problem.
    Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor.
    What is the probability the needle will lie across a line between two strips?
    If p is the probability, t is the width of strips, and l the length of the needle.

    p = (2/π)(l/t)

    Since Buffon’s needle problem and quantum mechanics both involve probabilities where pi turns up does this mean there is a deep connection between the two?
    Most likely no and just as likely there is no deep connection for the Wallis formula for pi to turn up in both physics and mathematics.
     
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  9. The happy Objectivist

    The happy Objectivist Active Member

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    I believe reason is the only objective means of knowing anything for humans. Science is a specialized method of reasoning.
     
  10. FrumiousBandersnatch

    FrumiousBandersnatch Well-Known Member

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    I (intuitively) thought the pi in Buffon’s Needle reflected the effect of the possible orientations of the needle with respect to the parallel lines... was I wrong?
     
  11. Hans Blaster

    Hans Blaster On campaign in Georgia

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    You were not. It comes from the calculation of the average orientation.

    If you define an angle theta between the direction of the needle and the direction of the lines between the boards, then the projection of the needle into the direction *perpendicular* to the lines between the boards is l * sin(theta).

    To compute the average projection length for any set of needles we integrate over all possible angles the quantity "l * sin(theta)". Because of symmetry we only need integrate from 0 to 90-degrees (or pi/2 as it is normally known). To compute the average of a continuous function we need to include a normalization factor. We average the function from [0,pi/2] so the normalization is 1(pi/2 - 0) = 2/pi.

    needle-projection.png

    The average projection length of needles dropped randomly will be 2l/pi.

    If the lines have spacing t and the needles have average projection in that direction of L, what is the probability that a needle with average projection L will be crossing one line with a spacing t?

    p = L/t = 2 * l / ( pi * t ) or

    p = (2/pi) * l/t


    [If you'd like you can take the angle from 0 to pi, then the normalization factor becomes 1/pi, but the definite integral becomes (-(-1) ) - (-1) = 2. I leave it to the reader to figure out why you don't integrate all the way to 2pi = 360 degrees.]
     
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  12. FrumiousBandersnatch

    FrumiousBandersnatch Well-Known Member

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    Thank you - it's nice to have a hunch confirmed! ;)
     
  13. SelfSim

    SelfSim A non "-ist"

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    Its interesting to note that the model here, (more or less by necessity), is a two dimensional one, which focuses on the effect of the angle between the needle and the boards .. Once again trig functions are visualised as a convenient way for tracking dependent variables in that model. Trig functions are also transformable into expressions involving pi .. does this mean pi is a constant upon which the variables in the model depend(?)

    What I'm trying to get to here is: why should we be surprised about it when pi shows up in a model which basically invokes triangles and circles?
     
  14. jayem

    jayem Naturalist

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    Getting in a bit late here. I haven't read every post and I don't know if this point has been mentioned. But good science (by which I mean honest, unbiased, and objective science) has a major advantage over religious doctrine. Good science is dynamic and self-correcting. When evidence shows that its models or theories are wrong, it admits the mistake and adopts new ideas. Religion rarely admits when it's been wrong.
     
  15. AV1611VET

    AV1611VET BELIEVE IN MIRACLES Supporter

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    That's why there are thousands of different sects to choose from -- and growing.

    HOWEVER, that doesn't excuse people staying atheists and agnostics.

    I can understand someone becoming one for awhile, but staying one over a long period of time is inexcusable.
     
  16. VirOptimus

    VirOptimus A nihilist who cares.

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    And those that are atheist all their lives?
     
  17. AV1611VET

    AV1611VET BELIEVE IN MIRACLES Supporter

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    Well ... God will take care of that.

    There are no atheists in Hell.
     
  18. VirOptimus

    VirOptimus A nihilist who cares.

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    As there is no hell thats actually true.
     
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  19. jayem

    jayem Naturalist

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    In fairness, some religious denominations have admitted error. Though rarely, if ever, were essential doctrines revised. It took until Vatican II in the 60s, when the Catholics decided that Jews (or at least modern Jews) shouldn't be blamed for Jesus's crucifixion. Southern Baptists apologized for originally supporting slavery, and racial segregation later on. Though it took them over 100 years. And though they never admitted error, the Mormons eventually decided that the time had come when black men could be full-fledged LDS priests, and participate in all the temple ordinances. But it also took over 100 years to get there.
     
  20. Bertrand Russell White

    Bertrand Russell White Active Member

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    These are good points. Scientific American did a recent article on this. p values are arbitrarily chosen. However, obviously at some level they become important. Since this system was created quite awhile ago, I agree with Scientists who are in favor of an overhaul. Since Science is supposed to be about knowledge and better methods to obtain knowledge, it would make sense to improve the methods and means for interpretation of information as well.
     
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