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Thread: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

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    Question Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    • Math Has a Fatal Flaw?

    Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer.
    • References:
    Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. — Dunham2013

    Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — Conway1970

    Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — Churchill2019

    Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — Gaifman2006

    Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. — Lnrt2010

    Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — Poincare

    Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — Irvine1995

    Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — Godel1931

    Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. — Russel1910

    Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — Godel1986

    Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — Cubitt2015
    Last edited by ExomatrixTV; 5th June 2021 at 14:38.
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    Default Re: Math has a

    If mathematics is incomplete, since it is based on logic, logic is incomplete. It is incomplete in the sense that we cannot get all the truths by logic. It also means that human thinking using logic has very great limitations. Therefore searching for the (ultimate) truth by philosophizing is futile. We may get some, but ultimately because our brain is not created for comprehending everything, we must eventually give up doing so. I prefer picking some words of wisdom and accepting them as truths by experiencing myself. Examples are "All is one and everything is connected to one another" or "There is only you". They may seem very illogical, but you can appreciate their truth only by experiencing them.
    Last edited by syrwong; 8th June 2021 at 11:48.

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    A clip of Roger Penrose on Joe Rogan. I started out as a math major and never finished, but I love this stuff. One of the most interesting books I ever read was Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter.

    Roger Penrose explains Godel's incompleteness theorem in 3 minutes
    The only place a perfect right angle ever CAN be, is the mind.

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Quote Posted by gord (here)
    Roger Penrose explains Godel's incompleteness theorem in 3 minutes
    But not very clearly!

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Quote Posted by Bill Ryan (here)
    Quote Posted by gord (here)
    Roger Penrose explains Godel's incompleteness theorem in 3 minutes
    But not very clearly!
    yeah, not very clearly and he could have done that in 20 seconds as well.. more clearly...

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Quote Posted by gord (here)
    A clip of Roger Penrose on Joe Rogan. I started out as a math major and never finished, but I love this stuff. One of the most interesting books I ever read was Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter.
    Roger Penrose explains Godel's incompleteness theorem in 3 minutes
    I think the punch line is in the last few seconds " You prove it's true by virtue of your belief in the rules" ...All Gibberish .

    The dark side has infiltrated and corrupted EVERYTHING ....

    If you get cancer they'll offer two cures either radiation , or chemo (toxic chemicals) ... both Cause cancer! ....

    If you go to an art gallery , you'll see this on the wall , worth millions $ , And the 'experts ' will tell you it's genius ...
    It has been admitted the CIA created the whole modern art movement , the reason they give is a lie , the real reason they do it is make you doubt your own judgment ,get you in the habit of shutting up and deferring to experts .... https://www.independent.co.uk/news/w...n-1578808.html

    ....

    So believe none of it , real math does not have a "Fatal Flaw" ... Just corrupted math has a flaw .
    And real medicine is not flawed , just corrupted modern medicine is flawed

    Some genius cosmologist , using just mathematics will crunch his numbers and prove beyond doubt that nothing can escape from a black hole ... then a decade later another one will prove " there are exceptions ", so it's all meaningless ...

    You can't trust this sort of Math , no more than you can trust modern medicine . ...

    The cabal love and promote this insanity .. their people control the Universities and decide who gets professorships , they go to people promoting non sense...

    Mathematicians can even be used to support the lie we live in a matrix / hologram , and recently the media has been full of 'experts' telling us they've proved mathematically the world isn't real ...cabal are keen to promote this idea , it will disempower any rebellion to their NWO ( what's the point of getting stressed out if nothing is real?) .... https://plus.maths.org/content/do-we-live-hologram
    Last edited by oz93666; 6th June 2021 at 09:28.

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Quote Posted by meat suit (here)
    Quote Posted by Bill Ryan (here)
    Quote Posted by gord (here)
    Roger Penrose explains Godel's incompleteness theorem in 3 minutes
    But not very clearly!
    yeah, not very clearly and he could have done that in 20 seconds as well.. more clearly...
    For anyone touching on this thread who's bewildered, here's the simple version.

    In math, true statements are almost always provable, and are proved. For instance, we can prove that 2+3 = 3+2. It's not just someone's theory! That's going be true throughout the universe, on every planet, for all time.

    And for those of you who remember Pythagoras' theorem (that in a right angled triangle with sides of length a, b and c, a2+b2=c2), we can prove that as well. The equation is always true.

    And so is the equation that the area of a circle is πr2, where r is the circle's radius. That's true, too, and we can prove that — for any circle, anywhere in the universe.

    But in 1931 Kurt Gödel proved — paradoxically! — that some statements in math are 100% true but can actually never be proved. No matter how smart you are. They're just totally unprovable.

    So, math is actually "incomplete", and can never be "completed". Not even by ETs with IQs of 400 who are a million years more advanced than us.

    That upset a GREAT many people. At first, mathematicians could hardly believe it. It's still disputed in some circles, but is now almost completely accepted.

    Gödel, meanwhile, suffered serious bouts of mental instability later in his life... which, one might wryly observe, might not have been surprising.

    Last edited by Bill Ryan; 6th June 2021 at 09:20.

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Quote Posted by Bill Ryan (here)
    That upset a GREAT many people. At first, mathematicians could hardly believe it. It's still disputed in some circles, but is now almost completely accepted.

    Gödel, meanwhile, suffered serious bouts of mental instability later in his life... which, one might wryly observe, might not have been surprising.
    "In the beginning, Math was created. This has made a lot of people very angry and been widely regarded as a bad, but paradoxically, good move"

    Whenever i see the complexity of Math and how we constantly fail to truly understand it, i always feel like 'someone' made it just like that, just to have fun with our frustration..

    This coming from a regular Math loser, btw


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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Quote Posted by Mashika (here)
    "In the beginning, Math was created."
    A lovely speculation might be that eventually, when we'd developed a powerful enough computer, pi would be calculated to a quadrillion digits.

    Then a sequence of zeros and ones would appear, and when translated from binary would read: "Well done, mankind. I was waiting for you to reach this point. Now you know that I exist."


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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Ok, here's my shortest description (my words):

    Any formal system sufficiently complex that it can be used to form statements about itself, can be used to form statements which can be neither proved nor disproved within that system.

    Off topic: Are legal systems formal systems which are sufficiently complex that they can be used to form statements about themselves?
    The only place a perfect right angle ever CAN be, is the mind.

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    42

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Quote Posted by I am B (here)
    42
    That answer's probably true, but I bet you can't prove it.

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    How can I prove anything I want it to be? e.e

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    If mathematics was complete, there would be no miracles.
    Empty your mind, be formless, shapeless — like water...Now water can flow or it can crash. Be water, my friend. Bruce Lee

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Quote Posted by gord (here)
    Ok, here's my shortest description (my words):

    Any formal system sufficiently complex that it can be used to form statements about itself, can be used to form statements which can be neither proved nor disproved within that system.
    Gord, your description triggered the following thought... Of course not, otherwise it would not be sufficiently complex. In other words, for the formal system to be complete it has to include all possible cases i.e. there will be true statements that cannot be proved or disproved.

    With this line of reasoning, it makes mathematics that much more powerful and complete.
    Happiness comes from within, nowhere else.

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Any system that deals with infinity has the problem of completeness.

    It could be said that the irreconcilable relationship between the finite and infinity is the proof of incompleteness itself.
    Empty your mind, be formless, shapeless — like water...Now water can flow or it can crash. Be water, my friend. Bruce Lee

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Quote Posted by Ernie Nemeth (here)
    Any system that deals with infinity has the problem of completeness.

    It could be said that the irreconcilable relationship between the finite and infinity is the proof of incompleteness itself.
    Yes. There was another set of apparent paradoxes — published by another great mathematician who ALSO ended up with mental health problems.

    Georg Cantor proved that there were several different kinds of infinity, some of which were larger than others. (Even that has been seriously disputed as being kind of meaningless, but the mathematical proofs, which are actually quite simple, are compelling and logical.)

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    This line of argument is based in the largest context, without going metaphysical, on the ungraspable concept of the ether. Modern science has almost entirely done away with the need for it, yet a malleable fabric that responds to the material it supports in a space/time continuum is just as mysterious.

    Somehow, an Infinite substance supports all the finite material of the universe. Calling it a space/time continuum instead does not eradicate the conundrum and nuisance of the fact that there is an ether: a uniform lattice that connects every part of the finite world to the whole of the infinite universal construct.
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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    Quote In math, true statements are almost always provable, and are proved. For instance, we can prove that 2+3 = 3+2. It's not just someone's theory! That's going be true throughout the universe, on every planet, for all time.
    I can give an counter example that disproves 2+3 = 3+2.
    If the numbers represent purely imaginary objects, then above equation is always true.
    If the numbers represent real objects that orientation of shape changes the total volume, then above equation has limited truth.
    For example, let's put five magnets.
    Make the number two with two magnets arranging [N S] [N S]
    Making the number three with three magnets arranging [N S] [N S] [N S]
    Applying the left side state 2 + 3, creates the number five states:
    [N S] [N S] [N S] [N S] [N S]

    If we flip one of the number two or three to create the number five, below is the result.
    [S N] [S N] <------------> [N S] [N S] [N S]

    Quote And for those of you who remember Pythagoras' theorem (that in a right angled triangle with sides of length a, b and c, a2+b2=c2), we can prove that as well. The equation is always true.
    It only works on uniform Euclidean 3D space.

    3D space such as human face, Pythagora's theorem is failed.


    Science always has limitation.
    For free society!

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    Default Re: Math has a "Fatal Flaw" (Godel's Incompleteness Theorem)

    I doubt that math, qua math, that is, the being-ness of math, has a flaw or that any flaw, so-called, is fatal.

    What is flawed is the ability of the human brain (but perhaps not the mind consciousness) to know and understand the deeper secrets of creation. Those secrets are unknowable. This is what separates the created from the creator.

    Intuition often fills the gaps between what we think we know and what confounds us. It gives us a sense of knowing, but not always. Uncertainty, undecidability, probability and luck (good or bad) are out there.

    I believe this is true. But I can’t prove it.

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