# AI and the singularity

Discussion in 'Intelligence & Machines' started by arfa brane, Jun 9, 2017.

1. ### arfa branecall me arfValued Senior Member

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Think of it in terms of numbers, of a certain type, like real or integer for example, with operations defined on them.

Say, the integers with addition. Subtraction isn't defined except where you add a negative integer. The negative integers are all defined as additive inverses of their corresponding positive integers.

But with multiplication defined on integers you immediately have a problem with inverses. Hence the integers are said to not be closed under multiplication; the multiplicative inverses of integers in fact divide other integers.

However, the ring of integers does have addition and multiplication defined. A ring is generally an Abelian group under addition (and additive inverses exist), which also has an associative multiplication that is left and right distributive over addition (and multiplicative inverses need not exist).

A ring with multiplicative inverses for all non-zero elements is called a division ring. Note that multiplication by zero has no inverse. (another way of saying multiplication by $0^{-1}$ is not defined).

3. ### Michael 345New year. PRESENT is 69 years oldValued Senior Member

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@
I'm no mathematician either but this came up on a TV show called QI

Zero is a number and it is a even number because it lies between two odd numbers
-1 and 1

At the same time you cannot fit a zero between any two other numbers

Counting up you will reach the number of the most of what you are counting

Counting down you will reach zero of the things being counted

Since you cannot have negative physical items you stop

Scales like temperature it's fine to have negative numbers since zero is a arbitrary designated measurement value

Below zero the lowest you can go is Absolute zero and no more

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5. ### Write4UValued Senior Member

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Are you not neglecting "memory", the storage of previously calculations of input?

A learning AI can recognize (by means of sensory abilities) and store that information in memory, possibly in separate compartments dedicated to that type of information and later, after receiving more information, access that information in memory and append it, i.e. a house is 4 walls and a roof of a specific size.

Later the AI sees a larger house, still constructed of 4 walls and a roof. Now the memory has been appended to recognize a house of any size as long as it has 4 walls. Then it sees a house with additions, i.e. more than four walls or roofs. It would still be able to make a best guess that it is looking at a house. Of course this may not be always correct, it's a guess.

But now it also sees people moving in and out of the many forms of houses, and memory is appended with "people live in houses". Then it sees a barn where cows move in and out and memory is appended to cows and people live in certain houses, usually very large, and usually with 4 walls and a roof.

IMO, in learning AIs, pertinent information is stored in memory and when it receives new information it sorts this information by some basic attributes and directs the information to that specific memory area, where it becomes integrated and the AI keeps adding more and more information, sometimes testing various paths.

The internet is a perfect example; type in (or expose) the AI to a single word and it will find a host of sites where information about that information can be found.

The difference, IMO. is that the internet itself is not programmed to actively search for information by its own volition. But is that impossible to program? If this could be done does anybody know if the internet itself may not become sentient in some way?

Last edited: May 3, 2018

7. ### Write4UValued Senior Member

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As a follow up to the above, this lecture by Max Tegmark may be of interest.
"Consciousness is a mathematical pattern"
(I would modify that to "Consciousness is an emergent effect of certain mathematical patterns")

8. ### arfa branecall me arfValued Senior Member

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Here's my "big picture". It's about numbers, and about what a number is when the context is mathematical and when physics 'intervenes', as it does in a quantum computer.

If you're a mathematician, physics is an abstraction in which certain symmetry groups are "embedded"--nature is full of patterns. A physical system, mathematically speaking, is just a bounded system in which certain kinds of equations define a behaviour which follows "laws" of physics. The boundary can be for instance, a set of values for an overall total energy for some system (of particles, generally).

Physics 'abuses' mathematics, or rather physical theories do this. To a physicist, mathematics is a kind of algorithm library, these can be 'approximated', tuned and so on to fit our statistical measurements of whatever the system "is doing", the behaviour that is to say, of the particles (however abstractly we might choose to define these).

In a modern digital computer, a "particle" might be taken to be a unit of charge, or a small quantity of a fluid with this charged property (an electron gas or liquid, say). What about quantum particles, though, in a quantum computer? These are isolated as much as possible from what I'll call a thermodynamic boundary, which defines a kind of boundary between useful and not useful, type of thing.

A number in a digital computer is a 'string' of bits, composed physically as a row of transistors or capacitors, each independently in one of two binary states which depend entirely on the presence or absence of a 'unit' of charge. In a quantum computer a number is something else altogether (something a lot harder to envisage). But the mathematics here describes 'non-physical' things (perhaps existing in multiple separate realities), these numbers appear to span a much larger space somehow, as they 'compute' some measurement.

Last edited: May 5, 2018
9. ### arfa branecall me arfValued Senior Member

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So the idea of a number seems to be upended: from a distinct kind of thing like 1 or 0 (e.g. "full" or "empty"), we have to go to something that we don't seem to be able to define in "this" universe, because it seems to "live" in many possible universes (to our view, or one of them). The past and the future also seem to be able to switch places.

All our theories up to now have depended on a past that has to include certain discoveries, or realisations about the natural world (electricity and electronics, hydraulics etc). These theories mean we can predict a lot of things these days, we can predict the future to some extent. For example, we can predict with some confidence, that current and future observations of the CMB will answer some questions about cosmology. We were able to predict, with a lot of confidence, that the experiments at the LHC would confirm or exclude the possibility of the existence of the Higgs boson.
Und so wieter.

10. ### Write4UValued Senior Member

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I agree completely.

I believe this is what in effect Tegmark is saying. He does not treat mathematics as a collection of numbers, but as values or sets of values which can be symbolized, and their interactions (functions or work) which consistently result in specific behaviors or patterns, which again can be symbolically translated as values and equations and gives us the ability to predict at least some of these physical phenomena, for now.
Which, IMO, confirms the power of our mathematics as a reliable symbolic prediction engine, when done correctly.

What strikes me as the most convincing testimony is the fact that most practising cosmologists (theoretical physicists) assert they are discovering these values and the patterns formed by interactions between these values, i.e. the "laws of physics" (the mathematics) were there all along and guide the "way" (the how) things happen.

In physics we speak of "quantum mechanics", but what do we mean by that term?
And be translated into symbolic mathematical values and equations.
And be unexplainable, if it were not for our ability to measure their associated values and behaviors as mathematical entities and calculate their inherent mathematical/physical potentials to do work.
https://en.wikipedia.org/wiki/Subatomic_particle

And suggests that quantum mechanics are not strictly local?

If I take a gallon of water from a lake (a field), I create a hole in the water. But that hole is immediately filled with water from the lake and restores the broken field, but the result is that the waterline of the entire lake everywhere drops by a very small fraction. Thus a local phenomenon in a field can affect many different values of the entire field.

If we were to view an AI as a field of interconnected quantum patterns would this analogy be similar? If so, would the AI field experience a change?

Am I way off the mark with this simplified perspective? If so, what am I missing?

Last edited: May 5, 2018
11. ### TheFroggerValued Senior Member

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Numbers' symbols hold specific values. Three is larger than two, and two larger than one. The only symbol to NOT hold a value is zero. The Arabic number system is without such a value. This is because it is without value and density, and it is sacrilege to quantify such a thing. It cannot be done.

12. ### arfa branecall me arfValued Senior Member

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I'd say that depends on the context. Zero is an additive identity in any number system; under addition adding zero or subtracting zero is equivalent.
As mentioned above, multiplying by zero has no inverse (unlike addition, but the additive inverse of zero is identically . . . zero; this trivial fact is not true for any non-zero number).

There is no multiplicative inverse because multiplication by zero takes any number to zero (identically!), so since the "result" is zero, an inverse if such a thing existed would take zero to any number. However in a ring, zero is a trivial ideal, so you can quotient the ring by the zero ideal (not by the value zero), i.e. R/{0} is well-defined. Moreover, zero is always both a left and a right ideal, but it's no big deal, it's something that must be vacuously true (!).

Hence, "quantifying" zero can be done. No sacrilege here; move along please.

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14. ### river

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Hmmm...

Vacuous truth defined " In mathematics and logic , a Vacuous Truth is a statement that asserts that all members of an empty set have a certain property. Example , the statement " all cell phones in the room are turned off " will be True whenever there are no cell phones in in the room .

Zero is still zero . Vacuous truth , is irrelevant .

15. ### RainbowSingularityValued Senior Member

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OR ... !
the scientific mathamatical binary measurement of current human capability renders consciousness into a simplified formula which enables the ability to sell door tickets.
?

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16. ### arfa branecall me arfValued Senior Member

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But if I claim that a particular number divided by zero is equal to any number you like, that's vacuously true because there is no number you can divide by zero, including zero itself. (i.e. the set of particular numbers divisible by zero is empty).

Vacuous truth is like P => Q when P is false. But P => Q is logically equivalent to not P or Q. Hence if P is (always) false, not P is true and so P is equivalent to P or Q.
Logic really sucks sometimes.

17. ### Write4UValued Senior Member

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But why does it necessarily have to be complex to begin with? Seems to me that the deeper we look, the simpler things get. It is the incredible amounts of simple things, which create the apparent complexity, at least in our brains and admittedly in the universe.

But as Hellstrom said; "insects are not concerned with the meaning of life or how the universe works, because they never ask the question".

As to commercialization of a "product" which may have taken years to develop, why put it on a shelf and hope someone will come along to read it?

18. ### river

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But if I claim that any number divided by zero , is actually , zero , which it is . Then the set is not only empty , but could never exist in the first place .

19. ### arfa branecall me arfValued Senior Member

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Sure you can claim that. Can you prove it though?
Which set is empty and doesn't exist? Be more specific, please.

20. ### river

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Both sets don't exist . Never have , never will .

Zero is not about a mathematical set , never has been .

The original concept of zero , originated in accounting , money , assets .

21. ### arfa branecall me arfValued Senior Member

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Which sets are those? Please be more specific.
But realise when you do so, that "a set that doesn't exist" is contradictory. It's very much like saying there's a number with a value that doesn't exist.
Au contraire, it always has been. The set {0} is the set with a single element, 0, in it. So your statement above is clearly wrong. However 0, not the set containing 0, clearly isn't "about a set". It's "about a number", since 0 is a number (it is because you can add it and multiply it, etc).
. . . for humans, maybe.

22. ### RainbowSingularityValued Senior Member

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indeed.
the simplicity of higher consciousness is something i like the sound of.

my comment was maybe a little too obtuse.
i was referring to the concept of turning something into a profit vehicle simply to make profit as a trend marketing ploy detracting from the high end tech concept of seeking highly advanced computing.

simplistically a living processor that is like a tank of algae that is a computer.

23. ### Write4UValued Senior Member

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I would call it a metaphysical condition, which allows or forbids events to take place, depending on the function
required by the event.
IMO, there is overwhelming evidence that mathematical functions (patterns) which we can recognize, occur as far as we can see.
It seems to be a "common denominator" of the universe. And why not?
Oh, I agree.
IMO, unfortunately "greed" is also a natural extension of a mathematical survival technique.
Darwinian evolution is a mathematical process, with a build-in restraint of "natural selection".

OTOH, why are we building AIs, with say the intellectual ability of an ant?

The ant is a remarkably successful species, due to it's mathematical survival function, which emerged and evolved over billions of years and withstood every "extinction event", is just a small expression
of the implications of universal potential granted by its inherent consistency.
In effect, Yes,
IMO, anything that has a dynamic quality such as growth, must be orderly by some form of mathematical function from some nano scale values to atoms, or chemical elements, or molecules contained in the living algae
, e.g. life itself.