# The mathematics of artificial intelligence.

#### TheFrogger

##### Banned
Banned
Hello.

How many different operators are there in mathematics? Are there only so many base operators?

How many different combinations are there with these operators? Will any of these produce artificial intelligence?

Counter,

That's a strange question.

What do you mean by "operators"? Are you referring to things like "+" and "$$\times$$"?

How could a mathematical operator possibly produce anything other than a mathematical result of an operation?

Hello.

Yes, by operators I mean "+" and "*"

For example,

%=(x/100)*y
Sqrroot=?*?=y

Do they all include fundamental mathematical operators?

Would ALL combinations of these operators produce artificial intelligence? One of them must?

Hello.

Yes, by operators I mean "+" and "*"

For example,

%=(x/100)*y
Sqrroot=?*?=y

Those examples are meaningless.

Do they all include fundamental mathematical operators?
The examples?

Would ALL combinations of these operators produce artificial intelligence?
No of course not.
One of them must?
Why?

...because that's all of them...

...because that's all of them...
All righty then, I guess we are done here.

This is kind of like saying
'I've got a petri dish and I put all known elements in it. Why don't I have life?'

The term "operator" in mathematics can refer to lots of different things. For a start, you need to ask what is being operated on. The examples given so far only consider operations on numbers. To give you a different example, consider this:

$$\frac{d}{dx}(x^2)=2x$$

There, the differentiation operator $$d/dx$$ operates on a function and the result is a different function.

Yet another example would be to consider the two sets A={1, 2, 3} and B={4, 5, 6}, and the operation C = A U B, where "U" is the union operator that operates on the two sets to produce a third set {1, 2, 3, 4, 5, 6}.

There's still no apparent connection to artificial intelligence in any of this.

Counter: explain why you think that operators "must" lead to artificial intelligence, and how you think they would do that.

Would ALL combinations of these operators produce artificial intelligence? One of them must?

Although a right "combination" of items is ultimately key, the symbols of a discipline (like mathematics and many others) have no causal power in themselves to bring about AI anymore than the equations scribbled on Los Alamos chalkboards could have exploded. But they do have a representative effect upon human consciousness and can simulate a thought-project outside the brain (a kind of abstract precursor to making concrete tools, devices, and machines in that respect).

To whatever extent one might consider an intricate "configuration" to be a complex sign, then functionalism perhaps gets nearest to granting Platonic-like potency to "form" itself, independent of any specific substrate of "stuff" that eventually realizes such a systematic arrangement. But those structural relationships which guide operation still depend upon the selected physical phenomena ("stuff") to have the necessary properties which the scheme is manipulating, so as to engender or output an _X_ goal.

CC said,
To whatever extent one might consider an intricate "configuration" to be a complex sign, then functionalism perhaps gets nearest to granting Platonic-like potency to "form" itself,
This is what intrigues me the most.
IMO, Universal mathematical functions work because they exist in the abstract not as a causal force, but as consistent permittive and restrictive *rules* of physical interactions.
I really like this clip by Roger Antonsen, where he explains these rules and even creates an example of the abstract geometric *shape" of a number

or a better version

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Computer were originally calculators. They still are. Digital involves assigning a number to a colour or sound etc., i.e.

a speaker:

y
|1000000
|0010000
|0100010
------------x

The same is true of a spectrum to produce colours: a number is assigned according to how much Red, Green or Blue (RGB) is to be selected, and applied to a location on the screen (x,y.)

The movement of computer games involves moving these colours at specific locations to another x or y, or rotating the screen a specific angle, which gives the mirage of movement. However it is simply digital.

My question is this: would using ALL COMBINATIONS of operators, and using one to ten as values (there are only ten distinct digits in decimal mathematics) would one of them produce artificial intelligence?

Thanks, Counter.

My question is this: would using ALL COMBINATIONS of operators, and using one to ten as values (there are only ten distinct digits in decimal mathematics) would one of them produce artificial intelligence?
Still no.

Any more than putting all atoms in a petri dish would produce a living organism.

Or putting all the parts of a computer onto a big tray would make a working computer:

My question is this: would using ALL COMBINATIONS of operators, and using one to ten as values (there are only ten distinct digits in decimal mathematics) would one of them produce artificial intelligence?

Intelligence is a sophisticated "interactive arrangement of parts" that responds to the input of information from outside itself and from memory, in ways that qualify it for an institution's standards for sapience. So obviously there would be systematic configurations which engender such (given that human bodies exhibit the characteristic). But when simulated by signs upon paper (etc), it would require tokens which represent rules and relationships and procedures (the coordinated organization), not just passive measurements or sets of quantity in isolation.

When abstractly divorced from corporeality as a particular substrate (biological tissue, clockwork mechanism, hydraulic technology, electronics product, etc)... Artificial Intelligence would be a complex, working relational structure whose collective specialized functions equate to that summary label ("intelligence") deserving to be attached to it by human experts. Whatever system of signs and symbols (across multiple disciplines, not just mathematics) that was used to represent / simulate it beforehand "on paper" (before its construction / corporeal realization) would be just that: Those tokens lack causal power to yield anything apart from their influence upon people (those who understand what they mean).

John Searle's Chinese Room thought experiment was an early predecessor to the eventual symbol grounding problem. It illustrated the lack of meaning in symbol handling, in which signs circularly referred to each other like words in a dictionary, never escaping to the experienced world of consciousness with respect to what the words of a dictionary ultimately represented. Tokens have to be either converted into or connected to the things and actions in the real or sensible world which they represent, including when/if they're the kind used in the "planning stage" or an aspect of the mere blueprint for an AI.

Abstract signs (quantitative and otherwise) are placeholders used to depict a similarly abstract construct or to carry out a creative process / thought outside the mind (on display for others). They don't have the potency to be, or to conjure, any concrete _X_ or result which they might represent subsumed under their generality. "2+2=4" is empty or stripped of empirical content, it doesn't single out specific phenomena like "apples", much less one set of apples combining with another, nor does the expression conjure apples.

Computer were originally calculators. They still are. Digital involves assigning a number to a colour or sound etc., i.e. [...] The same is true of a spectrum to produce colours: a number is assigned according to how much Red, Green or Blue (RGB) is to be selected, and applied to a location on the screen (x,y.)

The movement of computer games involves moving these colours at specific locations to another x or y, or rotating the screen a specific angle, which gives the mirage of movement. However it is simply digital.

If we take into account the actual physical substrate of a computer which makes its procedural routines possible, there are no quantitative symbols / signs brutely found inside it or that are performing in place of the physical properties. But only the dense circuitry of microscopic electronic components etched / chemically doped onto wafers which manipulate electricity and exercise sets of on/off states within the boundaries of that intricate configuration or design (its connective scheme for operation). The higher level programming languages invented / entertained by the thought and discourse of people in the industry and their communications with each other, likewise evaporate into functional, connective arrangements of on/off states in terms of the computer technology itself.

But the relevant engineers and assorted wonks could descriptively superimpose upon or correlate numerical values and algorithmic processes to the applicable electronic states of the parts and active circuitry. Again, our useful "signs" can be be attached as identifications for the "stuff" of the physical substrate (depicting the functional roles which the components are playing and the scheme / template they are conforming to).

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It seems to me that a built-in *associative* (mirror function) program which recognizes *patterns* would be an essential component of thinking in the abstract.

As Antonsen showed, we recognize the leter *R* regardless of how it is written, as long as it has the basic pattern. To a computer this is a daunting task, whereas most mobile organisms have a *mirror neural system* which allows for instant cognition of specific patterns.

A Lemur can recognize fundamental quantitative patterns as well as humans.

Question: is the AI field working on this most essential part of memory?

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Thinking this trough a little deeper;

Functionally, the *brain = processor*. Without data input neither would be functional.
Perhaps we should look at the problem of intelligence from a viewpoint of the *hive-mind*, the total sensory input provided by the organism
Each extant species are a product of millions of years of evolution.
One could argue that In their "niche", they are the most inteligent .

We have computer processors equal to the processing power of the human brain. The difference lies in the sensory abilities of the AI, and a fundamental desire to use all senses and data simultaneously but selectively. Once the AI becomes aware of realities for itself as compared to human level plus the possible extra-human sensory abilities in the human experience.

Who knows? I think if it is mathematically possible, so it shall be.

We have computer processors equal to the processing power of the human brain.
Not so sure that's true.
But it hinges on meanings of 'equal', 'processing' and 'power'.

My question is this: would using ALL COMBINATIONS of operators, and using one to ten as values (there are only ten distinct digits in decimal mathematics) would one of them produce artificial intelligence?
Operators have no capacity to do anything by themselves.

What you're asking is like asking whether all combinations of the words in a dictionary would produce a living, talking William Shakespeare.

Any artificial intelligence will use operators, in some abstract sense, as part of its operations, just as Shakespeare used words to write his plays. But a bunch of words doesn't add up to Shakespeare the man, and a bunch of mathematical operators doesn't add up to a thinking machine.

Not so sure that's true.
But it hinges on meanings of 'equal', 'processing' and 'power'.
I tried to use those terms in context of a neural network system with the same processig speed limits @ *c*.

Imagine a single graphine based processor the same volume as our brainattached to arrays f sesory receptors, translators, selectively partitioning, etc/. In any case it would need time to learn at least as long as humans do in our limited way, in order to acquire cognition of *patterns*.
At that point the AI can use its own understanding of those patterns from memory.
IOW a form of mirror neural system and anticipation of subsequent results of a given pattern. IMO that gets close to *sentient*

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This is kind of like saying
'I've got a petri dish and I put all known elements in it. Why don't I have life?'
The problem here is that it requires a specific probabilistic sequence of chemical reactions. There is a probabilistic bottle-neck, but the required elements are abundant throughout the universe. The Yury-Miller experiment proved that it was/is easy to create biochemicals. When Robert Hazen repeated a similar experiment they ened up with a black goo with no apparent potential for unusual behavior, such as forming cellular structures when this goo was placed in water, suggesting that making cells is not unusual. The trick was to combine the right 500 or so chemical reactions in the right environment. On a planet like earth is was just a matter of time before such a probabilisticly rare event happens. See the Hazen lecture at the Carnegie Center on YouTube

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