The mathematics of artificial intelligence.

Discussion in 'Intelligence & Machines' started by Counter, Feb 4, 2017.

  1. DaveC426913 Valued Senior Member

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    If they were mathematical constructs, they'd be abstract.
    Since they're physical structures, they're manifest.

    Since math wasn't invented to describe nature until man came along, all that there was was physical structures subject to forces. We invented math to be able to quantify those physics.

    You don't get to manipulate the meaning of words to suit your ideas.
     
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  3. Write4U Valued Senior Member

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    deleted
     
    Last edited: Apr 1, 2017
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  5. Write4U Valued Senior Member

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    It's the mathematical values and functions which are deterministic of physical manifestations.

    You can say that the physical collapse of a star is causal to it going nova, but it is the mathematical values (size, mass) of the collapsing star which determine if it will go nova or not

    The mathematical potentials (values) always determine the physical expression in reality.
     
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  7. DaveC426913 Valued Senior Member

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    Values are numbers. Numbers were invented by Man.


    It is the the forces that determine the physical expression.

    An atom is drawn with a physical force to another atom. That's nature.
    I can describe the magnitude of the force, based on the distance. Guess what language I would use to describe it?
     
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  8. Write4U Valued Senior Member

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    Yes, and the mathematics of the forces determine the result
    Mathematics of course. But regardless of the language used, the result will always be in accordance with the mathematics of the physical potentials jnvolved in the function.

    You don't choreograph a tap-dance by telling the dancer to just tap his toes and heels (which is the force making the tapping sound). Tap-dance patterns have their own mathematical language/
    From wiki,
    Define value in math
    In mathematics, value may refer to several, strongly related notions:

    The value of a variable or a constant is any number or other mathematical object assigned to it.

    The value of a mathematical expression is the result of the computation described by this expression when the variables and constants in it are replaced by some numbers.

    Patterns are the observed quantifiable mathematics of a function.

    The Fibonacci Sequence is an abstraction of a recurring mathematical pattern in nature.
     
    Last edited: Apr 3, 2017
  9. DaveC426913 Valued Senior Member

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    5,643
    There are no mathematics of forces. There are physics of forces. There are mathematics that describe the physics of forces.

    Good. Acknowledgement that mathematics is a language. Language is a human invention.

    Only if we have applied the correct mathematics to describe the physics.

    We thought we had applied the correct mathematics (Newtonian) to describe the physics of gravitational lensing. But our math was wrong. We needed to invent new mathematics (Einstein's relativistic equations) to properly describe the physics we were seeing.

    Yes, which we invented.

    Yup. And numbers are a human invention. Heck, not even every culture uses the same numbers.
    Zero was not invented until after Rome rose and fell.

    There is no math in nature. There is physics that governs construction. Math describes that physics.
    And, again, the math does not always describe the physics correctly.
    We're tinkering with it, as we get more sophisticated at writing the language.
     
  10. Write4U Valued Senior Member

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    3,861
    Of course they do, everything (including forces, geometrics, functions, values) in the universe can be described by mathematical abstractions., it is the essence of the fabric of spacetime .
    No, it's a human discovery that forces can only function in accordance to strict mathematical instructions. Mathematics = Determinism.
    One physicist explained that if we ask the universe "nicely" (with correct mathematics), it will give us all the answers we seek.
    Yes , Newton's question was not fully formed and the answer was not fully revealed until Einstein asked the mathematical question correctlly using available knowledge from observation.
    Actually, Leibnitz already had symbolically described the patterns of gravity, long before it was named gravity.
    Because we have not yet discovered all the right questions to ask.
    I agree, we are still learning the language of abstract universal mathematical values and functions.
     
    Last edited: Apr 3, 2017
  11. DaveC426913 Valued Senior Member

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    We finally agree.
     
  12. Write4U Valued Senior Member

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    The only point we disagree on is the scope of description. You are arguing the physical aspect of reality. I include the abstract non-physical universal potentials.

    Potential = That which may become physical reality.
     
  13. Write4U Valued Senior Member

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    3,861
    Consider the abstract command: *IF THIS (value), THEN THAT (value)*.
    Where would you place it, in the realm of Physics or Mathematics?

    I have wanted to revisit the argument that different cultures have different mathematical systems and languages. This is true, but whereas the human symbols may differ, the observed natural function would be identical if given the same physical conditions, regardless of human symbolic representation.

    To achieve consistency, we have developed international scientific standards or translations, (perspectives). Different perspectives are the foundation for Relativity which is observer dependent even in the abstract, but does not interfere with actual physical behaviors. That's the problem between QM and Relativity. One describes the physical, the other describes a variable abstract truism.
    But both have Mathematics as a common denominator.
     
    Last edited: Apr 4, 2017
  14. DaveC426913 Valued Senior Member

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    If they're non-physical, then the universe doesn't use them.

    Actually, that's logic.
    Mathematics is founded on logic, in the form of axioms - statements that are taken (or declared) to be true, but cannot be proven to be true, such as a+b = b+a.
     
  15. Write4U Valued Senior Member

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    3,861
    The universe does not need to express it's latent potentials all at once. E = Mc^2, but not everything explodes either.
    Because the a priori inverse is mathematically false.

    a + b = a + b, anything else introduces a chronological variable to the equation, which becomes apparent when trying: a - b = b - a. Obviously we are dealing with mathematically inverse values.
     
    Last edited: Apr 4, 2017
  16. DaveC426913 Valued Senior Member

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    Nonetheless, the universe does not use abstracts.

    You asked where I would put your statement. It's logic; a foundation of math.

    The a+b=b+a is an example of an axiom. No reason to analyze it.
     
  17. Write4U Valued Senior Member

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    3,861
    Are you familiar with Bohm's *Implicate Order*?
    ???
    Is a - b = b - a an example of an axiom? It is a mathematically false equation, no?
    I can imagine this axiom: 2 + 2 = 2 x 2, even though they represent different mathematical functions.

    We differ only in that you view mathematics as a descriptive language only, without considering the implications of our ability to mathematically symbolize (describe) the observed patterns of physical expressions and functions in the first place and which imply an underlying self-ordering system which is not physical itself but which precedes and determines the actual form of physical expression. This is how I understand the abstract mathematical aspect of Bohmian Mechanics and the concept of an Implicate Order.
     
    Last edited: Apr 5, 2017
  18. Write4U Valued Senior Member

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    Here is an excerpt of wiki article on Bohmian mechanics, which IMO suggests certain fundamental, abstract, non-physical guiding principles in the form of universal *common denominators*. This information such as functional imperatives that ultimately determine how the active physics must become manifest in specific observable *patterns* and *gradient values*.
    https://en.wikipedia.org/wiki/Quantum_potential#Relativistic_and_field-theoretic_extensions

    Potential = That which may (mathematically) become (physical) reality.
     
    Last edited: Apr 7, 2017
  19. Write4U Valued Senior Member

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    Dave, thanks for making me do some serious research on the implied meaning of the word "value". As English is my second language, I often refer to dictionaries for definitions of a word and try to find some "underlying fundamental principles.
    From this I believe that your single definition is not adequate to describe the entire range of definitions inherent in the word "VALUE".
    It occurs to me that the definitions of the word *potential* is synonimous to the expression of inherent but "latent" quantifiable values., which would be an abstraction.
    I recommend that you do some deep research on both the definitions of *value* and *potential*,
    I am sure you will see that they have related (if not interchangeable meanings.
    IOW, values can exist in the abstract as potentials (values which may become expressed as quantifiable properties during physical expressionsn.
    http://www.bing.com/search?q=potential definition physics&qs=AS&pq=potential definition&sk=AS2&sc=

    IMO, the word "potential" (latent values and abilities) has profound implications on the orderly expression of physical evolution in reality.
     
    Last edited: Apr 8, 2017
  20. Counter Registered Senior Member

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    Not everything in the universe follows mathematics.

    A program can be written to determine the pattern followed as relating to it's position in the sequence:

    Number:2468
    Position:1234

    =position*2

    However as I have postulated, not every pattern follows the Law. If it did it would be quite useful to predict when traffic lights were going to change to green, and give it to the police or ambulance service.

    red=1
    amber=2
    green=3

    Colour:13232
    Light-:12345

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    You could however COUNT. Each number has an inherent weight, or value. As soon as one value has been counted, the next is counted immediately:

    <------------
    123456789
     
  21. Write4U Valued Senior Member

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    I see that your example uses mathematical symbols and equations and if you qualify and quantify their values and functions them (correctly or not) you are doing mathematics.

    The only difference is that humans can do bad mathematics, whereas the universe does not allow for bad mathematics.

    If you look deep enough, you will find values, patterns and equations We are not alone in the ability to do mathematical calculations. There are many animals who unwittingly use mathematics, such as gauging distance, angle of attack, triangulation, and a host of other inherent cognition of mathematical functions. A tree is a mathematical (fractal) construct. Daisies grow petals in accordance with Fibonacci sequence. They don't know they do this, but apparently nature has selected this mathematical function as an efficient way to gather or conserve energy.

    A flower does not know it has the value of red by counting its human symbolic representation of color values. It doesn't even know it's red. Natural selection has determined that certain wave lengths provides an attractive color to pollinating insects.

    The problem is that we think of mathematics as a human invention, but that is incorrect. The universe uses a mathematical function for all events, some of which we have been able to identify and qualify by a method of study which we named Physics, and using a symbolic language which we named Mathematics..

    But we did not invent the mathematical functions. They existed as an inherent ability of the universe, long before man climbed out of his tree.

    Gravity existed before we called it gravity and recognized a mathematical pattern which could be translated by a mathematical equation of the gravitational effects
     
    Last edited: May 31, 2017
  22. DaveC426913 Valued Senior Member

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    How would you know?

    A fern exhibits self-similarity in its growth (because: physics), but it is not perfect. If you measure an actual fern, you will find it has quite a wide variance from self-similarity.

    The mathematical formula we invented to describe an ideal fern is accurate, but that is abstract. The physics of a material object, (like, say the universe) is quite sloppy by comparison.

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  23. Write4U Valued Senior Member

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    True, but that is usually due to damage from an external object which inhibits the formation of a perfect leaf.
    Why don't all trees growth straight up? That is because it is prevented from doing so, by an external object, or it sprouted in a shadowy area and attempts to grow towards the light. Sometimes a growing plant may be so restricted that it fails to thrive and will die.

    And it is possible that the DNA is damaged and thus cannot provide the mathematical instruction for a complete growth pattern. People look different from each other because there is a combination of 2 DNA, which creates a new growth instruction from the DNA combination..

    But offspring from the Silvery Salamander are all female and true clones of the mother's DNA only, because it cannot receive male sperm.

    Thus the mathematics work flawlessly but the functional instructions may not always be complete or the same, especially in living things.

    What I find remarkable is that nature selected a fractal pattern to begin with. Ferns are very old species and millions of years ago, the fractal function was an efficient mathematical instruction for duplication.

    Why do all leafs on a tree have a specific similar shape? The fractal function..
    But ask. what greater mathematical efficiency can be achieved than by a simple instruction of a fractal function which is able to create thousands of self-similar leafs?
     
    Last edited: Jun 1, 2017

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