Can artificial intelligences suffer from mental illness?

Discussion in 'Intelligence & Machines' started by Plazma Inferno!, Aug 2, 2016.

  1. someguy1 Registered Senior Member

    That's not what Tegmark says. Tegmark says the universe is embedded in mathematics. That I believe is another thing entirely, and one that's as false as it is provocative.

    Tegmark says the universe literally is a mathematical structure. But that cannot be the case, and for the exact reasons you give.

    Yes. Physical. But mathematical structures are not physical. They are abstract. Things like sets, groups, rings, fields, topological spaces, measure spaces and so forth, are highly abstract ideas that you have to learn from specialized teachers and textooks. There's nothing obvious about them and nothing physical. They do have applications to physical science, but their nature is that of abstract entities.

    Mathematical structures are not physical. And therefore the universe, being physical, can not possibly be a mathematical structure.

    Tegmark is thus refuted.

    Yet millions of serious-minded and educated people believe him.

    It's one thing to read his MUH because he's "interesting even if he's wrong." That's how I'm planning to approach the project. I know I'm going to hate every word. But reading his paper will make me smarter.

    But to actually believe that the world literally is a mathematical structure. I don't see how anyone can take that position.

    Math is part of the world. But the world itself is NOT a part of math. For being such a smart guy, Tegmark is mixing up the abstract with the physical. Perhaps that's his intention.

    Right. We're in complete agreement that Tegmark's MUH is wrong. Interesting, but wrong.
    Last edited: Feb 11, 2018
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  3. someguy1 Registered Senior Member

    Einstein said that God does not play dice with the universe. Niels Bohr famously responded, "Albert, stop telling God what to do!"
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  5. someguy1 Registered Senior Member

    What was weird about all this is that I never buy lottery tickets. I just got momentarily swept up in noticing these guys playing, and the clerk noticing me noticing, and saying, "Two hundred million dollars," and out came my wallet. I figured that with such random circumstances leading me to buy a ticket I'd had no intention of buying, I had to be the winner! For some reason that didn't happen. Probabilities. Very mysterious things, really.
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  7. Write4U Valued Senior Member

    IMO, you are looking at this from an incorrect perspective.

    As I understand Tegmark, he proposes that all physical objects have a single or combinatory physical "value", these physical values combine to form specific physical structures, which then attain an inherent structural value.

    Mathematics is a human invention and therefore abstract, but "values" are the combined properties of physical objects. The measurement of these comparable or relative values gave rise to the creation of mathematics, the tool by which we can measure and identify these values.

    I don't think anyone would object to the notion that all physical things have a value of some kind. Some are causal, some not.

    Thus instead of saying the universe is a collection of values which in the main we can symbolize through mathematics, Tegmark reduced it to "a mathematical universe", which implies that anything with a value and interacts in a consistent manner can be symbolically represented through our mathematics.

    How else could we identify "physical laws of nature" or create "equations", which are also abstract but symbolic mathematical representations or descriptions of natural values, behaviors, and interactions.
    Last edited: Feb 11, 2018
  8. iceaura Valued Senior Member

    There's chaos. There's also probability and evolution.
    I don't recall saying that. What I said was that failure to "solve" the halting problem was irrelevant for a computation postulated to produce time as an output.
    And some of your posted reasons for rejecting the possibility were themselves problematic - hence my posting.
    Countability establishes the capability of ordering - by definition, a one to one correspondence with the integers, which are ordered. A TM can then start at one, then 2, then 3, and keep going. In this way a TM not subject to constraints of time or space could execute a computation involving stepping through every rational number between 0 and 1. Or an infinite number of such computations.
    "Preserving" order is not at issue.
    "A set S is countable if there exists an injective functionf from S to the natural numbersN = {0, 1, 2, 3, ...}." (Wiki, but it's standard).
    No, I said that as far as we know (the evidence indicates) a TM can emulate some things - as closely as necessary - whose computability I don't care about. The three body problem, for example. Or the behavior of the human brain. Any given part of the universe.

    Have I mentioned that I'm usually arguing the "other side" of this issue? I don't actually think there is any realistic possibility of emulating the behavior of the human brain without essentially duplicating it physically, in real life. It's a bit like the Borges story of the map that was as large as the territory it mapped - in principle one could make such a map, but why?
    What I said was that for all you know - and in line with current theory in physics - any computation that was producing the universe was producing approximations in the first place. That the difficulties faced by anyone trying to establish an exact position, velocity, time, etc, were intrinsic. That the argument (against a TM producing the universe) based on the impossibility of a TM solving certain problems exactly was empty - it doesn't have to.
    And likewise, a TM emulating parts of the universe would not have to. In theory.
    Last edited: Feb 11, 2018
  9. Michael 345 New year. PRESENT is 69 years old Valued Senior Member

    Found this in

    The extract below seems weird to me. I have highlighted my weird bits


    My starting assumption, the external reality hypothesis, states that there exists an external physical reality completely independent of us humans. When we derive the consequences of a theory, we introduce new concepts and words for them, such as “protons”, “atoms”, “molecules”, “cells” and “stars”, because they're convenient. It's important to remember, however, that it's we humans who create these concepts; in principle, everything could be calculated without this baggage.

    But if we assume that reality exists independently of humans, then for a description to be complete, it must also be well-defined according to non-human entities – aliens or supercomputers, say – that lack any understanding of human concepts. That brings us to the Mathematical Universe Hypothesis, which states that our external physical reality is a mathematical structure

    I don't follow that one follows from the other. I do not know enough about Tegmark and his works / books. From my very limited understanding the views seem to be on the fence between "outstanding insight" to "Woo Woo"

    That brings us to the Mathematical Universe Hypothesis, which states that our external physical reality is a mathematical structure

    Could that also be stated as

    That brings us to the Physics Universe Hypothesis, which states that our external physical reality is a physics structure


    Not having seen much of his work what evidence has been put forward for the physicality of the Mathematical Universe Hypothesis?

    Is just looking at the physical world and calling it Mathematical enough?

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  10. Write4U Valued Senior Member

    Perhaps not, but it seems that everything we do know about how the physical world functions can be symbolized with mathematics.
  11. Michael 345 New year. PRESENT is 69 years old Valued Senior Member

    Agree. Stranger still are those who would not buy tickets for a 50 million lotto but when it gets to 100 million will start coming in

    Really??? You pass up a chance for 50 million for a chance for 100 million? You have something in mind where 50 million is not enough but 100 million ya that'll work?

    As I don't do Lotto would I be correct in thinking the more people who come in the bigger the jackpot becomes which then feeds back to more people coming in?

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  12. Michael 345 New year. PRESENT is 69 years old Valued Senior Member

    Fair enough

    But the Universe operates per physics. Why pick Mathematical over Physicality?

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  13. Write4U Valued Senior Member

    Because physics identifies a state of being, whereas mathematics assigns specific values to those physical states.

    A rock is a physical object, but it tells us nothing about the rock itself other than that it is a rock as a general physical identification. But a rock has a specific composition of ingredients which makes it a rock with specific values, such as a value of weight (gravitational pull), composition of elements, porosity, etc.
    From this mathematical information we can deduce that a rock of Pumice is able to float on water rather than sink, unlike most other rocks.

    A mundane exercise as moving a rock immediately invokes the interplay of relative values.
    If I am able to lift 150 lbs, but the rock weighs 300 lbs, I don't need to try and lift it. I know that I won't be able to lift such a value of weight and will find another way to move the rock. I used the weight value of the rock to calculate that it is too heavy for me to lift and that I need to augment my physical strength with an additional 150 lbs of additional "leverage" (force), which will allow me to move 300 lbs. An everyday exercise in mathematics.

    In Physics this practical approach already begins with the Table of Elements, which assigns an atomic weight (among other values) to the element which allows the physicist to identify and use the mathematical values of the element in various ways.

    Without mathematics (symbolic representations of values) we would not be able to do theoretical and/or applied science.

    Whereas the universe has no symbolic value representations per se, except as forming recurring physical patterns and behaviors, it can only function in accordance to mathematically permissible actions. If it did not, we could not represent purely physical actions at all. We would end up only with rudimentary general value judgements of "heavy or light", "more or less", which are already employed by a few other animals.

    Your question is similar to asking, why pick Literature over Storytelling. IMO, literature allows us to print the story, because we have been able to symbolize expressed words and meanings with letters (alphabetical values).

    Mathematics allows us to print the story of physical events in exquisite detail. Of course we don't know the whole story yet. This is what Tegmark is after. The single equation which explains how the abstract mathematics function and their expressions of the universe enfold and unfold.

    The orderly mathematical processes every instant in time, suggests an underlying , deeper ordering system.

    a hierarchy of Ordering Constants ,
    an Inherent Fundamental Imperative ,
    a Universal Law which permits or restricts physical events (including quantum) to occur at any given time at any given place in the Wholeness.
    a mathematical mirroring system which gives rise to duplication or enfolding and unfolding of the universe itself..

    I see this concept expressed in many other advanced models of cosmology .

    CDT (causal dynamical triangulation) by Renata Loll, et al, which speaks of an "unfolding spacetime fabric",
    and Bohm's "guiding principle' in his Pilot Wave model , and Tegmark's proposition that what we have named mathematics is in fact the fundamental nature of our reality or, represents an accurate understanding of the fundamental functional nature of spacetime itself, including ourselves...., eventually........

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    Last edited: Feb 11, 2018
  14. Michael 345 New year. PRESENT is 69 years old Valued Senior Member

    Got it - the concept


    This is what Tegmark is after. The single equation which explains how the abstract mathematics function and their expressions of the universe enfold and unfold


    Don't think he, or anyone else, will get - The single equation - as in my dumb ass way I don't think it exist

    Will certainly keep a eye out for papers on the matter and good luck if it is found. Somewhat like the god particle but much more cerebral


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  15. Write4U Valued Senior Member

    Question is; "would we know the difference"?

    Best guess by the human brain would be a mathematical function in itself.

    Computable? Copyable? Transferrable (to some extend)?
    Last edited: Feb 11, 2018
  16. someguy1 Registered Senior Member

    Yes of course the brain could be modeled by some mathematical function. They would not BE a function. They would just be something we can MODEL with a function. Map, meet territory.

    Mathematical functions are very general. A function is just an association of the elements of one set with those of another. Unlike in high school, where every function is given by some rule; generalized mathematical functions are NOT necessarily given by rules. They are random, in the same sense as I've been using it. Not necessarily the output of a Turing machine.

    So for example if your input set (or domain) is all possible brain patterns that can be generated by the atoms in your brain; and the output set (or range) is all the possible states of the what a human can be or experience or run through their brain; then the mapping of input states to output states is some mathematical function.

    But that doesn't really say much, because mathematical functions don't need to be defined by a rule or make any kind of sense. The only thing that matters is that they're functional, meaning that a given input always produces the same output. If you input 5 into the squaring function you always get 25. That's what makes it worthy of being called a function.

    But then that raises a question. Why should the brain mapping be functional? Maybe there's an element of randomness, so that it's not a mathematical function. Or it's a function at a deeper level. These are very murky waters.

    Well, that's the question. If there is any functional relationship at all between brain and mind; then the question is whether it's computable.

    Copyable, that's interesting. Because if it's not computable, I don't see how we would encode it physically. It would require an infinite amount of information to store, like a noncomputable bitstring.

    And if we couldn't physically encode it, how could we copy it? One bit at a time I guess ... so we could stream it, just like they stream videos. We could stream consciousness. Gives a new meaning to the stream of consciousness. Maybe there's something to that. Maybe the world is just some universal program streaming its way through all of us ...
  17. someguy1 Registered Senior Member

    If there's probability, then God plays dice. Take it up with Einstein. He says God does not play dice.
    Produce time as an output of a computation. I confess I do not understand what that means. Computations flip bits. That's what they do. You can dress them up any way you like, but every computation can be reduced to a TM flipping bits.

    How can that produce time? I wish you'd explain this more clearly.


    In the next paragraph you have given a very clear account of your idea about bijecting the rationals to the positive integers. You're still wrong, but you're no longer "not even wrong." It's a great improvement IMO. I appreciate that you've provided substantive points I can comment on.

    That's not true. Every set can be ordered in many ways. The real numbers are ordered, and so are the rationals.

    They're not well-ordered. The natural numbers are well-ordered, and so are all the transfinite ordinals.

    Ordered sets are studied in elementary set theory. There are partial orders, orders, well-orders, dense orders, and lots of other kinds of orders.

    Every set can be ordered. You may be thinking of the positive integers (or natural numbrs), 1, 2, 3, 4, ... That's a well-ordered set. Every nonempty subset has a smallest element. That's the def.

    But you don't need countability to order a set. In fact it's a theorem that every set can be well-ordered, even uncountable sets. It's very counterintuitive.

    Sure, the integers are ordered. So are the rationals and the reals. Even disordered sets can be ordered. There are sets that don't have a "natural" order in some way, but we can still order them one way or another.

    For example there's no order on the complex numbers that is compatible with addition and multiplication; but if we wanted to we could put the lexicographic order on the numbers a + bi and that would be an ordered set. In other words 2 + 5i < 3 -7i because 2 is less than 3; and if the real parts are the same, go by the usual order on the imaginary part. The reason nobody does this is because it doesn't respect the arithmetic operations. But it's still an order, just not a very satisfying one.

    Yes, a TM could go on forever. It could fail to halt. But in that case it has not computed anything. It's useless. It can't compute the universe, it can't even compute 2 + 2. If you had a calculator that when you input 2 + 2 it spins forever and never comes back, that wouldn't be very useful, would it?

    That's why the definition of a computable object is one that is the output of a TM that halts after finitely many steps.

    You are right a TM could spin forever, but then it wouldn't compute anything. It would be like a car alarm going off outside your window. You can't stop it and it's not doing anyone any good!!

    I see your point now. You are saying that if I have an infinitary computation with steps 1, 2, 3, 4, ..., then via a bijection to the rationals I could relabel them 2/3, 47/12, 118/5, 993/22222, and so forth.

    Yes that is true. I am happy to agree. If you think of the steps of a computation as a set of big wooden shipping boxes with their respective numbers painted on their side in big letters, 1, 2, 3, ... and so forth; then we could hire Cantor's paint company to change all those markings and replace each one with some rational number; and every rational would appear on some box.

    Yes we could definitely do that. You are absolutely correct.

    However ... as Hillary said at the Benghazi hearings ... "What difference could it possibly make?"
    I hope you can see that all we've done is come along and repainted the boxes. They're still discrete, because the bijection would induce the discrete topology on the rationals.

    You seem to be thinking that now ok, we have some dense order like the rationals, but each rational represents a step in the computation.

    Yes, but the bijection bounces all over the place (I'm sure you see that) and induces a discrete order 1, 2, 3, ... on the rationals.

    So nothing has changed. You have gotten my agreement that you can relabel the steps of a computation with rationals. But if the computation is infinite, then it can't compute anything! Your relabelling has not changed the subject or added any insight!

    Does that make sense?

    If the computation halted to start with, the relabeled (with rationals) computation also halts and reaches the same result. And if it doesn't halt, it just runs forever and never computes anything. Whether you label the steps with positive integers or rationals or any other countable set.

    An infinite number of infinitary computations, each of which does not compute anything, would still not compute anything.

    In order to compute something, by definition that something must be the output of a TM that halts after finitely many steps. In fact that's redundant: "Halt" means halts after finitely many steps.

    Ok. But you understand that a bijection is a relabeling. The Cantor paint company comes over and paints a different name on each object. But the objects themselves are unchanged.

    A bijection is a relabeling. The rationals ARE ALREADY the positive integers, just with different names. And the order properties of either one can be imposed on the other, via the two respective directions of the bijection.

    This is an alternate way to think of bijections. Instead of imagining two different sets that happen to be in bijection, we imagine only one set of objects, but two different sets of names. Like going house to house on your street and changing the house numbers. You have changed the symbols written on the houses but you have not changed anything about the houses themselves.

    Yes, thank you. I'm aware of the definition.

    If you're interested, you might have a look at the basic math of order theory.

    And check out the picture here of a few of the transfinite ordinals, to see how strange a well-ordered countable set can be.

    (I'll reply to the rest of your post separately).
  18. someguy1 Registered Senior Member

    (continuation of my reply to your most recent post)

    Sure, but if it's only approximation then the world can't actually work that way. The approximation only gets "close enough" at each step. And with any physically realizable computation, subject to constraints on computational resources, chaos will make your approximation wildly inaccurate after a sufficient number of steps.

    Yes I think you did. I'm not sure what sides we're arguing. I'm just trying to introduce some precision into some technical terms being bandied about, like computation. If the world is a computation, that places some limitations on the nature of the world. And personally, I don't like to believe that my essential nature is no different than a copy of Microsoft Word on a floppy disk from 1983.

    Perhaps. And even then, at what level? Neuron by neuron? Molecule by molecule? Atom by atom? Quark by quark? Probability wave by probability wave?

    If we are not dualists we must agree that at some level of duplication, we'd duplicate a mind.

    But then again we have the bird argument. Why should human-made minds work on the same principles as biological minds? Human-made flight does not work the same way as biological flight, right?

    Good one.

    There's a theorem in math that if you place a map on the territory it maps, there must be some point on the map that's directly over the territorial point it corresponds to.

    I think I have great problems with this idea. If the universe is truly being instantiated at every moment by the output of a program, then how could it be an approximation? How does the universe know how to behave if the program only gives it a fuzzy probability or approximation of how it should behave? Something is missing -- namely, whatever tells the universe to do EXACTLY what it does.

    Intrinsic to what? To the universe? Or only to our knowledge? Is the measurement problem ontological? Or epistemological?

    I don't get it. I strike a billiard ball with my cue. It hits the cushion. The universal TM computes the APPROXIMATE angle of reflection. Then how does the ball know EXACTLY how to reflect off the cushion?

    I don't think your approximation idea works. It can model reality to a good order of approximation. But it can't calculate reality.

    Well, you haven't convinced me. In fact I think you have a hole in your argument. How does the billiard ball know exactly how to reflect off the cushion, if the TM only computes the answer approximately?
    Last edited: Feb 12, 2018
  19. someguy1 Registered Senior Member

    Yes, and that turns out to be the wrong strategy. When the jackpot is "only" a few million, fewer people play. When the jackpot gets huge, proportionately more people play. You're better off only playing the lotto when the jackpot is small.

    I don't even know anything about how it works. I was just in this store and the spirit of the moment came over me and extracted two bucks from me almost without my will being involved. That's exactly why I should have won. Fate teased me!

    Just in the past 24 hours I came across these two stories of chance.

    * A guy was going to fly to his home town with his girlfriend in Russia. While he was there, he was going to buy a new car from a dealer. The dealer called him and told him his car would not be ready for another week. So he cancelled his flight. The plane he would have been on crashed, killing everyone on board. It's straight out of the Twilight Zone.

    * A couple sold everything they owned to buy a sailboat to sail the world. On their second day out, they hit something under the water and sunk their boat.

    If the world is a computer program, it's one with a very weird sense of humor.
  20. Michael 345 New year. PRESENT is 69 years old Valued Senior Member

    Your lucky it doesn't tell the oneso who run Lotto to shoot the loosers

    Some years ago I saw a National Geographic magazine

    It was running a competition. Two questions. For some reason I knew I could win

    Bought magazine, wrote two poems, one based on Banjo Paterson Man from Snowy River and a 8 line why I should win

    I did. $3,000 trip with airfare and 2weeks hotel with bonus excursions plus some National Geographic merchandise

    I got the call to say I won. I asked how I chosen. Was not just picked out of a hat. Was voted the best entry from 900+ entries. Ya

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  21. Write4U Valued Senior Member

    The universe does not produce approximations, it does what it is mathematically (physically) allowed to do.

    It is humans who can only approximate all the forces and values "in play". Which is understandable as the volume of input far outstrips the human ability to receive and process ALL the incoming information.

    Our sentience is at a very gross (identifiable) level, which enables us only to make a best guess which directly applies to our relationship to the object we are observing. Our brains may receive billions of bits of additional information, but if not directly related to our point of mental focus, this extraneous information is ignored.

    Actually our focusing ability is extremely limited (relatively speaking). A perfect example is found in this little mind blower:
  22. someguy1 Registered Senior Member

    Please explain that to our colleague iceaura, who appears to be making this claim.
    Last edited: Feb 12, 2018
  23. iceaura Valued Senior Member

    If the probabilities are as current theory indicates, He loads them.
    It doesn't.
    How does a billiard ball know how to reflect off the cushion at all? In quantum theory it does not - its wave function reflects in all directions, and cancels itself out in all but a narrow band.
    You appear to be making a statement of faith, without evidence and in conflict with the clear implications of much theory.
    To the universe. According to the best theory we have at the moment.
    Hence my objection - why emulate when you end up essentially duplicating, at great effort? There are much better ways to make more human minds - at least, I prefer them - and what we want from our machines is a different kind of thinking anyway.
    Human made flight is not an emulation of bird flight. I don't see the issue.
    It is physically allowed to produce both ambiguities and approximations, according to the mathematics of the theory we have so far.
    But the universe does exhibit chaos, and of course "inaccuracy" is irrelevant to the universe - it's not an approximation of something else. As far as our emulation, it only has to be good enough to fool us for a little while - say a million years.

    And by "fool us" is meant, on this thread, exhibit mental illness we can recognize

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