# The mathematics of artificial intelligence.

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

1. ### DaveC426913Valued Senior Member

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No, it isn't.

You could grow a dozen ferns in a controlled greenhouse environment, and every leaf of every plant will be unique.

No, it isn't.

No. It's because real object follow real physics, not abstract math.

As you point out, growth instruction comes from DNA, not math formulae. DNA does not contain the Fibonacci sequence. The similarity to a pattern that can be described by the Fibonacci sequence is an emergent** property of physical processes, changing over time.

Emergent specifically means that the information for the end result is not contained within the initial configuration.

No. That is not how living things are built.

They are built by enzymes, coming and going, and the resultant growth rates. The resultant shape is an emergent property; it is not contained within the blueprints.

If the growth of a living thing is analogous to building a brick wall, then this is what happens:

- there is no architect looking at the big picture,
- there are no large scale blueprints of what the wall "should" look like.
- there is no formula that shapes the wall.

all there is, is
- each brick contains its own set of instructions about how to place it in its position. Any given brick knows absolutely nothing about the larger structure, only its neighbors. Its instructions simply tell it how to position itself next to its neighbors.

(In life, the instruction is not a formula; it is simply trail and error of what worked and produced more offspring. Leaves that don't overlap will get more sun, produce more offspring - that bit of enzyme-protein sequence gets passed on. There is no logic to the instruction; only the consequence of survival and offspring.)

When enough bricks lay themselves down - each with very similar, yet very slightly different values - you will see a gently curving wall of a certain height and length. And here's the kicker:

Nowhere, in the instructions of any given brick - in fact, nowhere in existence - are there instructions for building a curved wall - let alone a formula to follow. It is entirely emergent.

We humans have found that, when structures get built this way, with one or more factors changing slightly with each iteration, that we can describe it with a general formula that takes into account both the constant values and the changing variables - a formula that does not exist in nature.

Last edited: Jun 1, 2017

3. ### Write4UValued Senior Member

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True, but what you are describing are mathematical functions. That's the name we gave it.

But regardless of what you call it or describe it, it always comes down to the "mathematics" of the event.
It starts with Potential, a mathematical term.

What you seem to forget is that all knowledge is based on the description of inherent mathematical functions of values and behaviors of physical things.

Physics is a word, Mathematics is a word; sentences are a mathematical function of putting words together. Does the book know this? Of course not. But the author does,. That's why there is an entire branch of mathematics that's dedicated to the mathematics of words and sentences. It's utilized by the NSA.

You are looking to narrowly at the term Mathematical. It goes much deeper than just +, -, x, :

Last edited: Jun 1, 2017

5. ### DaveC426913Valued Senior Member

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Yes. We invented it; we named it.

I don't "forget" this; you've made it up as your personal idea. It's simply a baseless assertion, made by you.

Correct. The book knows only the mechanics of physics.

You are looking too broadly at the term. We already have a word for the mechanics of real things: Physics.

7. ### Write4UValued Senior Member

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I wonder how we came to invent it. Out of thin air?
. Oh really?
Quantity? Sounds like a mathematical term to me.
(and you may want to look up the full definition of the meaning and range of applications we gave the word Potential)
It definitely is not "word salad"
If it were so, I'd be in the company of some great scientific minds.
No, the book doesn't know anything, it is just a mathematical/physical construct.
Yes, those are the mechanics (physical expression). I wonder how these mechanics work. Must be a random function or something mystical maybe?

Last edited: Jun 1, 2017
8. ### DaveC426913Valued Senior Member

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Nope. By abstracting the mechanics and creating a language to describe it we call mathematics.

It should. It's one of the terms we use to describe the physics.

I know its meaning. It's your use of it here that is non sequitur.
You're using circular logic. Just becuase you insert a math term doesn't make it math.

such as Einstein, Hawking, Feynman, Newton or Galileo? That's 55 points right there.

They work by forces. Forces that we describe using an human-invented abstract language we call mathematics.

9. ### Write4UValued Senior Member

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It would have been if I had said that. But I did'nt. You falsely quoted my post. How many points is that on the scale? And I know what scale you are referring to, OK?
And these forces work randomly, willy nilly, without rules that govern their behavior? There are no patterns or logic to their behavior? There is no consistency to be found? The universe is just a chaotic collection of physical things and forces which engage in physicaling and forcing. I call that circular reasoning.

Or is there an underlying universal condition, which allows or restricts these physical values and forces to become expressed in a consistent predictable way? The intrinsic consistency of the rules which govern the universal natural permittive or restrictive conditions in which these events can be expressed.

What you are saying is akin to saying that Economics are not intrinsically mathematical, but economic forces.
Or saying that Soccer is not intrinsically a mathematical game, but just kicking (forcing) balls from one to another.
Or saying that Music is not intrinsically a mathematical combination of wave functions, but Musicking.

The lines dividing a highway into 4 lanes are not the road, but the mathematical guide-lines which allows traffic to flow efficiently and consistently, through curves and intersections. We don't call that "trafficking" or "roading" or "lining". We call them "traffic rules", or "rules of the road".
.
The rules of physics are consistent and predictable, permittive or restrictive, by certain natural conditional imperatives (traffic rules), some which we have been able to quantify and symbolize in a language we call mathematics.

One major oversight (lack of focus) by you, is that I have numerous times qualified my use of the term "mathematical functions" as an abstraction of "how physics (and everything else) must perform to work" .

Dave, humans also made up the word Physics to identify physical attributes, but it is a meaningless term in and of itself. We don't do the physics, we qualify and quantify physical values and functions from observation of physical behaviors.

In order to understand physics, you must understand their physical values and how these values interact. That's the mathematical part and we have created an abstract symbolic language that describes these natural values and functions. Can we agree on that?

What are the academic entry requirements of a physics curriculum? I bet you need to have advanced knowledge (if not a degree) in Mathematics. To my knowledge this is true. Is the reverse also true?

My point is that if humans can describe these values and functions in mathematical terms, we can say that in human terms the study of physics employ functions which in human terms consist of mathematical values and equations. And, if physics is the observed behavior of physical things, then by extension these behaviors are following certain inherent universal mathematically consistent natural imperatives..

10. ### Write4UValued Senior Member

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From my perspective "mechanics" are natural "applied" mathematical functions.,

11. ### DaveC426913Valued Senior Member

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I didn't quote you at all, let alone falsely. I simply asked a leading question that followed logically from what you wrote.

Well, I said none of that, so no.

Good thing I didn't accuse you of quoting me, eh?

A hypothetical volume of space has a field with a certain potential. A hypothetical particle has a mass and charge. There are physical things that physical object have. (i.e. physics).
That's all that is needed to create the emergent order we see in the universe.

I'm not saying any of that.

But I do find it telling that everyone of the examples you raised were invented by humans, not naturally occurring.

So you're kinda makin' my point for me here. Thanks for that.

Theng kewp. The court rests.

12. ### Write4UValued Senior Member

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Dave's court rests. Well the defense is not quote done yet.

It wishes to introduce some additional evidence of the mathematical nature of spactime and everything within it.

Exhibit 1; Philosophiae Naturalis Principia Mathematica (1687), commonly known as the Principia (Newton)

Exhibit 2; Mathematical Foundations of Quantum Mechanics, (John von Neumann)

Ehibit 3; In statistics, a power law is a functional relationship between two quantities, where a
relative change in one quantity results in a proportional relative change in the other quantity,
independent of the initial size of those quantities:
one quantity varies as a power of another.

Exhibit 4; The Principia Mathematica (often abbreviated PM) ( Alfred North Whitehead and Bertrand
Russell)

Exhibit 5; The Principles (Russell) inaugurated contemporary philosophy. Other works have won and lost
the title. Such is not the case with this one. It is serious, and its wealth perseveres. Furthermore,
in relation to it, in a deliberate fashion or not, it locates itself again today in the eyes of all those
that believe that contemporary science has modified our representation of the universe and
through this representation, our relation to ourselves and to other
s (Jules Vuillemin)

Exhibit 6; the application of mathematics to problems in physics and the development of mathematical
methods suitable for such applications and for the formulation of physical theories ( Journal of
Mathematical Physics

Exhibit 7; http://space.mit.edu/home/tegmark/mathematical.html

Last edited: Jun 3, 2017
13. ### DaveC426913Valued Senior Member

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Yup. all descriptions of the physics.

14. ### Write4UValued Senior Member

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19,783
Yup, all descriptions of natural mathematical values and functions expressed in our physical world.

15. ### Write4UValued Senior Member

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19,783
How about "conservation of energy" by cold blooded reptiles as a natural utilization of economy?
How about "triangulation" to isolate prey, by predatory pack hunters as a natural utilization of a natural mathematical function?
How about "singing" by song-birds, or the "subsonic" story telling by whales, as natural utilization of wave functions?

16. ### DaveC426913Valued Senior Member

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So you keep saying. but it continues to hold no water.

The mathematics is the description; the physics is the actuality.

17. ### DaveC426913Valued Senior Member

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Yup. All human-invented descriptions of emergent physical processes.

I think what you're failing to see is that the physical world does have a natural order. This is what keeps things regular. Ultimately, all physical processes in the universe are layer upon layer of behavior due to the simplest of forces: strong, weak, em and gravity.

eg. Gravity will gather lots of atoms together, and their jostling and settling will result in a structure where all atoms are as near to the centre-of-grvity as they can get before other repulsive forces come into effect. Each individual atom is subject to gravity to the same extent. The emergent result of this is that they happen end up in a spherish shape. But there is no math whatever involved in defining that spherish shape; it is simply atoms competing to fall to the CoG. All due to the 4 forces.

You keep thinking that somehow there's math in there, but the math (which is abstract) simply describes the physics.

A mathematical sphere does not describe a physical sphere as more than an approximation. There is no such thing as a (truly) physical sphere. There is a such thing as a mathematical sphere.

Last edited: Jun 3, 2017
18. ### Write4UValued Senior Member

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You just described a mathematical function of the universe, a hierarchy of behaviors which follow existing natural mathematical rules. David Bohm describes this hierarchy in detail in his book Wholeness and the Implicate order. The keyword here is "order", which is another human term for a mathematical abstract.

I am not arguing against physics and physical expressions. I am saying that physical expressions follow an existing or emergent hierarchy of universal constants or variable behavior patterns. These behavior patterns can be modeled with human mathematical symbols.

I repeat, I agree that human mathematics is the symbolic language which describes naturally emergent patterns (layers) of physical behaviors and interactions.

The behaviors are physical, the patterns are mathematical in essence. The natural rules of the game, so to speak. Just as soccer or basketball games which employ layers of defense, mid-field, and offense are mathematical games of triangulation and other more complex patterns, in order that the ball can physically be advanced toward the opponents goal or basket.

Chess and checkers are mathematical games, where the pieces have specific values and can only be moved in accordance to their value status, not by their physical values which can be wood, marble, plastic or a piece of paper with a letter. We never speak of chess as a physical game. It does require a lot of calculation...

Patterns are also not physical, but are the natural mathematical processes emerging in accordance with the extant potentials inherent in the physical geometrics, values, and functions at the prevailing spacetime coordinates.

Physical objects are in themselves a hierarchy (layers) of mathematically ordered physical values.

Last edited: Jun 4, 2017
19. ### DaveC426913Valued Senior Member

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OK, so you agree that physics is the real world and mathematics is the abstract description of it.
And you agree that the fundamental forces are all that is needed to result in all the physics we see.
I guess we're done here?

Last edited: Jun 4, 2017
20. ### Write4UValued Senior Member

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No, you are leaving out the abstract rules by which physical game must be played, which we have and are still discovering (and given them symbolic names and numbers). The mathematical essence of spacetime.

I will agree that physics and mathematics are inextricably entwined, much as space (physical) and time (abstract) itself, which have given the name *spacetime*.

An example is Maxwell's 4 equations of the rules which govern all the EM functions.

Last edited: Jun 4, 2017
21. ### DaveC426913Valued Senior Member

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And where, pray tell, does this abstraction live?

Since there was only a physical universe for 13.699 billion years, and abstract is distinct from physical, concrete things...

22. ### Write4UValued Senior Member

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It doesn't live at all. It's an inherent potential of the fabric of spacetime itself.
Someone mentioned there is no ideal circle in nature, yet Poincare shows that all thing tend to circle each other. In the case of a sphere, the first cell was circular. when you place a drop oil in water it forms circular droplets. True none of these are perfect because of their physical environment which interferes with the "attempt" to make a circle. Therefore a perfect circle exists in the abstract, regardless of how it is expressed, oval, parabola, etc. Fractality is based on
on the hypothesis that spacetime itself unfolds in a fractal manner, an abstract fundamentally triangulation. See Causal Dynamical Triangulation.
wiki

btw. did you know that we can construct a parabola from only straight lines.?

Yes, but we can agree that order emerged from chaos.
This requires an abstract fundamental tendency (implicate) to regulate the way physical things work. It is an idealized functional condition ( dimension?) which is permittive of some physical expressions and restrictive of other physical expressions in reality.

Permissions and Restrictions are a fundamental concept in mathematical philosophy.
Symmetry is a fundamental abstract concept in mathematical philosophy

The universe exists not as a random physical construct, there is an underlying hierarchy of mathematical forms of a transcending Order. I'll name It the Discipline of the Mathematical function..

Chaos = physical disorder (probabilistic)
Order = functional permissions and restrictions. (deterministic)
Patterns = permitted functional expressions (deterministic)
Symmetry = self similar opposite duality (efficiency, order)
Implicate = the abstract projection of that which has mathematical permission to become expressed in reality. (probability)
Potential = the inherent (latent) ability to perform work when in a dynamic state.(permitted or restricted)
Reality = the gross expression of mathematical functions from the very "subtle" to "gross" physical expression which is the end-product of the prior hierarchy of mathematical functions.

Last edited: Jun 5, 2017
23. ### TheFroggerBannedValued Senior Member

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In-tell-igence. To not tell someone.