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Featured Randomness

Discussion in 'Science and Religion' started by Polymath257, Sep 13, 2018.

  1. wellwisher

    wellwisher Active Member

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    Consider a magic trick, like a magician levitating his lovely assistant. The goal is to create an illusion that appears to defy the laws of gravity. If the magician is good and trick is done well, your eyes and other senses will seem to tell you that this is possible.

    If you were a physicist in the audience, your eyes may be fooled, like the rest of the audience, if the trick is done well, and no wires can be seen. However, since you know about gravity, you would make use of your secondary perception; frontal lobe, connected to your education and experience in the laws of physics. You will assume this is not physically possible, based on decades of experience. It has to be trick. Also, knowing how gravity works and does not work, you may try to reverse engineer how the illusion would need to be organized, to get the observational output, you appear to see from this experimental demonstration.

    With statistics, things are placed in a black box. We are expected to only monitor the inputs and outputs, and from that, make predictions. However, in the case of magic, the black box takes the secondary perception; frontal lobe, off the table, so all that is allowed is direct sensory observation, which the clever magician is able to fool. With the frontal lobe off the table, even if you know this is a trick, it remains out reach.

    According to the theory of randomness, there are finite odds for anything, including antigravity affects on theater stages. If you accept the basic premises of the random religion; anything is possible with the God of Random, magic is a type of science.

    Once you get rid of the black box, the logic hidden within the black box; secondary perception, loads the dice such that gambling now becomes illegal. One cannot assume the same odds with naturally loaded dice as with manufactured dice. The black box is a way to remove the logical loading of dice, so magic is easier to swallow and accept.
     
    #141 wellwisher, Sep 16, 2018
    Last edited: Sep 16, 2018
  2. wellwisher

    wellwisher Active Member

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    Here is one more take on randomness.

    In engineering, entropy is a state variable. What that means is for any given state of matter; fixed temperature and pressure, for example, the entropy is measured to be a constant value. Entropy is often defined as connected to randomness and complexity However, in engineering entropy was found to be fixed number for any given state of matter. The entropy of water at 25C and 1 atmosphere is 6.6177 J ˣ mol-1 ˣ K-1.

    This value of the entropy of water, is a standard, and will be measured the same by all labs. It is not a random variable, even if the mechanism of entropy is explained as being connected to randomness. At the atomic level, the complexity of a system with 10 to the 23rd atoms or molecules; mole, in motion, might be modeled using statistics. However, the overall sum of the assumed randomness is always a constant value. Entropy, as a state variable, shows that random is a subset of determinism.

    One way to conceptually explain random, as a subset of determinism, is via an analogy. Say you wear glasses. The glasses allow the world to come into clarity. If you take off your glasses, you can still see, but the sharp points of clarity, become inflated and fuzzy.

    In this case, reality did not change when you take off your glasses. What changes is your individual perception of reality. Reality now appears to become more statistical, like a fuzzy election cloud. In the example, above, where the mole of water has a constant value of entropy at the macro-level, but is modeled as random at the micro-level, the glasses come off at the micro-level; too difficult to see.

    Note: The concept of entropy was first defined during the early development of steam engines. When doing energy balances, there was always energy that was missing. The measured energy input versus output were always off. Entropy was a term used to describe the missing energy. The developers of the concept did not try to explain how entropy worked, but they could measure it, and found that that it was a state variable. For any give state of matter, the entropy was always the same.

    The second law states that the entropy of the universe has to increase. This means that he path of the universe, and life, is from state to state, based on the amount of missing energy absorbed by entropy. The evolution of life, via entropy means state to state as well as goals, since a future state will have a fixed amount of entropy and be the goal if enough energy is absorbed by entropy. The formation of the DNA in water was predictable based on it being a state variable. Determinism leading random perception, helps the mind eye gain the correct eye glasses prescription for clarity.
     
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  3. shunyadragon

    shunyadragon Veteran Member
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    The multiverse hypothesis is not an alternative to the idea of design, and fine-tuning is a separate hypothesis based on the what is the degree possible change, effects and how variability of the physical constants determines the outcome of a universe. The reality is the possible range is unknown, and may not be a significant difference between universes, Fred Hoyle was a strong advocate of Intelligent Design and fine-tuning in his book 'Intelligent Universe'.

    The alternatives in science for the multiverse hypothesis (some nick name this the 'bubble universe hypothesis where every universe independently forms and dies.) are the cyclic universes, and the Black Hole universes, but both of these hypothesis are compatible with the multiverse hypothesis.

    Intelligent Design and the Fine-Tuning argument are in reality not falsifiable, and remain philosophical/theological arguments based on non-science assumptions.
     
  4. Ponder This

    Ponder This Well-Known Member

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    An interesting theory. How is that theory connected to the results of actual experiments?
    In what experiment, were the initial conditions verified and the results seen to be not dependent on them?
    And what do you mean by this not violating causality?

    As to the topic of randomness... what do you think? Are there 'conscious decisions' being made as to the position and momentum of particles?
     
  5. Polymath257

    Polymath257 Think & Care
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    The essence of Bell's inequalities is that any hidden variables would require certain correlations between distant objects to be smaller than some amount (because information can't travel faster than light...see below). But, quantum mechanics predicts a higher correlation than such (which is possible because it isn't a deterministic theory--no hidden variables). Actual observations show the quantum prediction is what happens in the real world.

    Well, to allow faster than light transfer of information (which would be required in a hidden variable theory to explain the observations) would *also* require causality to go backwards in time. So, the future determines the past. That is because faster than light transfer in one inertial frame is always transfer into the past for some other frame.

    In other words, if you want causes to go from the past to the future and you want the observations to be determined by the 'real' properties of the objects, then you *cannot* explain the observations actually made that violate Bell's inequalities.

    Now, quantum mechanics only allows correlations to travel at the speed of light or less, but objects in quantum theory do NOT have definite properties--they have probabilities instead.

    No. Consciousness is a much higher level phenomenon-at the level of brain circuitry, not at the level of subatomic particles. The only reason consciousness is involved is that it is complex enough to 'collapse' the wave function (I put scare quotes here deliberately). But *any* environment that is sufficiently complex will do the same. This is one reason is it so difficult to get a working quantum computer: quantum states, especially entangled ones, are incredibly delicate. A few stray photons can destroy them.
     
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  6. Ponder This

    Ponder This Well-Known Member

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    You mean... no local hidden variables can reproduce all of the predictions of Quantum mechanics.
    You are talking about a correlation between quantum entangled particles. There is nothing about that that says it's not a deterministic theory, is there?

    You are talking about local relativistic causality. But the Heisenberg Uncertainty Principle applies to observation - not causation.
    And when you say that
    "objects in quantum theory do NOT have definite properties - they have probabilities instead", ​
    what do you do actually mean by that? You may want to think carefully about this because we often associate 'probability' with 'randomness' (like when we throw 2 six-sided dice to get a random result and say that the probability that we get a total of seven is 1 in 6). So it's very important that you really know what you mean when you use this word here. Probabilities of what? Of particles having a certain position and a certain momentum?

    'No conscious decision' is consistent with the notion of something being 'random'.
    I also said that, in general, we take the point of view in science that there is a method to the madness of the universe. Perhaps you disagree. Perhaps you don't think that there really is a method underlying the results that violate the Bell Inequalities.
    But... Super-determinism evades the problem posed by the Bell Inequalities completely. Is there some reason we should reject super-determinism?
     
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  7. Polymath257

    Polymath257 Think & Care
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    The only alternative that way is a form of superdeterminism where *everything* is pre-determined in detail from the beginning. Since there is no way to tell the difference observationally, the difference is pretty meaningless.

    Not exactly. The Uncertainty Principle specifically gives an inequality between the standard deviations of the values of two variables (usually momentum and position, but there are other pairs). This comes about because the quantum operators for those variables do not commute.

    The wave function allows us to compute the probabilities of the particle having certain values for certain variables when observed. The variables can be momentum and position, but can equally well be the energy or the spin or any number of other observables.

    Before the observation, the particle literally does not have a definite value for any specific variable (unless it is in an eigenstate). So, there is a probability that it will be in some position. There is a probability that it will have some spin. There is a probability that it will have some momentum.

    What the Bell inequalities bring out is that we cannot say that a particle before observation has a definite, but unknown spin. We cannot say that there are hidden variables with some specific, but unknown values that produce the observed effects. Instead, all we have is probabilities of the different possible values and correlations between the values for entangled particles.


    Well, it is observationally indistinguishable from the randomness viewpoint and doesn't allow any further information to be calculated. As such, it is far more difficult to actually use in practice.
     
  8. shunyadragon

    shunyadragon Veteran Member
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    I would disagree. In super determinism "everything" is not predetermined. The role of Chaos Theory in all cause and effect outcomes, depending on the number of variables, alone would preclude "*everything* is pre-determined in detail from the beginning," In fact there is most likely no beginning. The following definition does not agree with your description.

    I do have difficulty differentiating terms like: just plain old determinism, fully deterministic?,and hard determinism or super determinism. My view remains that by the evidence just plain old determinism lies at the foundation of our physical existence. Some describe super determinism in terms of the laws of physics, but this is not a good way to go.

    From: Superdeterminism - Wikipedia
    "In quantum mechanics, superdeterminism is a hypothetical class of theories that evade Bell's theorem by virtue of being completely deterministic. ... But in a fully deterministictheory, the measurements the experimenters choose at each detector are predetermined by the laws of physics."

    Our Laws of Physics are descriptive from the limited human perspective, and not actual inflexible or absolute.laws. I prefer to consider the nature of our physical existence to be deterministic based on the underlying Laws of Nature, which our laws of Physics evolve to approximate.
     
    #148 shunyadragon, Sep 16, 2018
    Last edited: Sep 16, 2018
  9. Ponder This

    Ponder This Well-Known Member

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    Fair enough: the problem with Quantum Mechanics is the difficulty in settling on a particular interpretation and showing it to be the best interpretation. This is a very tricky topic to discuss. You don't need to accept or reject super-determinism; you just need to be aware that it resolves the problem posed by the Bell Inequalities.

    This comes about because it is what we observed. The math was created to fit. If we had designed the equations and discovered that they commuted, then we would've rejected it as not fitting the Uncertainty Principle.

    I put emphasis on: "when observed".
    I compute the probability for an outcome when I roll 2 six-sided dice (in other words, for when I observe the result).

    Now you are using the word 'probability' again, except now you aren't referring to an observed result, or are you? To what are you referring? Are you referring to the nature of the particle? What do you mean "Before the observation"? Is this a reference to causality?

    I'll have to think about this... However...
    something for you to think about is that when you throw a pair of six-sided dice, there is no definite but unknown initial state that yields the result on the throw. There are so many ways to throw dice, that you can't say anything about their initial state by observing the result. In other words, if you didn't observe the initial state to begin with, then you can't know what the initial state was. So I get a bit confused when you start talking about the state of the particles before they are observed. What does that mean?
    Maybe you can tell me the difference between throwing dice and spinning particles.
     
  10. Polymath257

    Polymath257 Think & Care
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    But, in contrast, if you had full knowledge of the state of the dice just after the throw, you *could* calculate the end result. They are NOT in a superposition of states like in a quantum system.

    Yes, observed. Between observations, the particle has a wave function, but that wave function will NOT be an eigenstate for all observables. In fact, it is impossible be such because the observable operators don't commute. That is why it doesn't have specific values for those observables.

    Yes, of course. The particle is NOT in an eigenstate prior to observation, so the values of that operator are not determined. All that is determined is the probability of the different values being observed.

    And that isn't correct, classically. There is a difference between being in a definite state that is unknown and using statistics to talk about the possibilities and NOT being in a definite state and the probabilities being inherent in the physics. The two can be distinguished observationally because the first has commuting variables and the latter does not.

    In a quantum system, an observation 'collapses' the wave function to be an eigenvalue for the operator corresponding to that observable. But such eigenstates *cannot* be eigenstates for non-commuting observables: the value for such are inherently undetermined (not just unknown).
     
  11. 1robin

    1robin Christian/Baptist

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    I didn't trash him, I said I don't like him. If he is the person I am thinking off, one of the 4 horsemen then I just think he is a very bad philosopher. It's not bias, I enjoy Hitchens very much. However I think Dawkins should stay in the lab, he is probably even worse than Dennet IMO (again if the Dennet I have in mind is the one you do, isn't his name Daniel Dennet?).

    Then I don't get it. How can you have choice but not freewill?



    It was originally your assertion I just denied it. The one making the first claim to knowledge has the first burden to demonstrate it if requested. So I request that you show that the range of possible events following an average intentional mind state are relatively small. BTW how are you going to introduce objective values for what is small, medium, or large here? This seems to me to be perfectly subjective.



    Right, that is why I am saying determinism (alone) isn't true. Only choice (free will) adequately describes how the events (thousands to trillions of them) all oblige to fulfill my intention. Lets say I decide I want to respond to your latest post. Since there are a multitude (as it appears from our perspective) of events that could follow that desire why are atoms in motion so obliging to allow me to turn on my computer, log in, find your post, etc.... and the thousands of other events I did not mention. Why are things centered around human intentionality so obliging when determinism has no desire to grant any intention? This is not that hard to understand but we seem to be talking about everything but this simplistic notion.



    Blind forces has been a scientific conception that has existed long before the Christian scientific revolution. Blind forces in this context means unintentional events.

    Exactly.

    That is my argument to the letter and my explanation in every detail. I don't know what happened here, maybe you made a formatting error or something.

    Good because if freewill is true they aren't. Only if determinism is the next action set without any hope of alteration.



    Simplistic incorrect description of what determinism proposes

    Ok, you definitely made a formatting error here.
    Again your assertion of blind forces is ID anthropomorphic foolishness. The problem is obviously your religious agenda asserting 'Libertarian Free Will,' and not the facts of the nature of our existence.



    I disagree but it definitely has not moved past Hoyle's claim here, it has only confirmed it.

    Yes, the modern scientific movement is characterized by being abstract. In fact mathematics and too a large sense much of science its self is abstract. 2 + 2 = 4 is abstract. Heck numbers themselves are abstract.

    You keep formatting your posts so that it looks like your saying what I said. I am not sure what mistake your making that can explain this.

    Natural laws are descriptive not prescriptive. They don't cause anything. 2 + 2 never created 4 of anything.



    I can't think of a single verse to quote that claims freewill is true. I am making a simplistic secular argument for freewill that I can't even get you to address.

    Please, lets get back to where this started.

    Lets say I want to go get a chicken sandwich (Events A), and lets say 30 minutes later I am eating the chicken sandwich (Event Z)

    So you have EVENT A........EVENT B - Y (x 1000s).......EVENT Z. (Multiply this type of event by trillions)

    I claim freewill explains events B - Y is the best inference to a conclusion.
    Are you actually claiming that unintentional events B - Y are merely the obliging results of atoms in motion (or determinism by any name, etc...)?
     
  12. Polymath257

    Polymath257 Think & Care
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    Well, that is NOT what I am saying, in any case. What I am saying is that the *intentional* events in B-Y are *made up* of lower level events for which the term 'intention' has no meaning. For that matter, the phrase 'wanting a chicken sandwich' is a collection of such lower level events (not just a single event), as is 'eating a chicken sandwich'.

    This sort of confusion often happens when jumping levels of description. To have an 'intention', a 'want' or a 'desire' is a description that encompasses many, many lower level interactions between atoms, molecules, neurotransmitters, cells, etc. This isn't 'merely obliging' the results of atoms, but *consists of* the interactions with atoms.
     
  13. 1robin

    1robin Christian/Baptist

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    Well you say it is debatable but you didn't debate it. I don't get it.



    So far there is nothing here requiring a response of me.

    I am the one denying randomness all together. Your making arguments proving my point. I never claimed atoms do anything randomly, you said that.

    I am not denying the actions of atoms obeying laws, I am saying that only having atoms obeying laws does not describe all the fulfillment of intentions we see around us all day every day. You do realize I am not denying determinism don't you, I am just deny it's lone sufficiency to account for all the events we observe.

    You keep arguing against things that are not part of my argument. I have a degree in math, I am aware of how natural law works.

    Let me go back to a previous thought experiment I used with another poster. You can perform the same thing your trying to do is space here on it instead.

    Lets say I want to go get a chicken sandwich (Events A), and lets say 30 minutes later I am eating the chicken sandwich (Event Z)

    So you have EVENT A........EVENT B - Y (x 1000s).......EVENT Z. (Multiply this type of event by trillions)

    I claim freewill explains events B - Y is the best inference to a conclusion.
    Are you actually claiming that unintentional events B - Y are merely the obliging results of atoms in motion (or determinism by any name, etc...)?


    If you think of freewill as agent causation that is where the decision is made than then puts all your atoms in motion. Mathematics can explain everything concerning the motion of the atoms when I put a kettle on the stove. But it can't tell you how I decided to make a cup of tea.

    Aerodynamics plus a few other things can explain why the plane suddenly inverted but it can't explain why I decided to a roll.

    Again: Determinism alone can't fully explain reality. Freewill + determinism can. I am not even sure we disagree at this point. Do you deny the freewill portion of reality?



    Trying to discredit Hoyle one level and praise him on the other seems desperate to me. I could quote a hundred of histories greatest scientists to back up freewill or teleology.

    Imagine the factors required for a universe to have flourishing intelligent life is winning the lottery. The universe won the lottery over and over and over and over ad nauseam. If in any real world situation where the same person won the same lottery over and over and over, etc..... every sane human being on the planet would think intelligent manipulation was behind it. Why are you employing a double standards?
     
  14. 1robin

    1robin Christian/Baptist

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    I don't care if your talking on a molecular or even a quantum level the series of events I described simply don't make sense without freewill. No matter how small you want to shrink things down you won't find anything that wants to oblige steps B - Z and so they can't be (at least the full) explanation of what is going on there. And keep in mind the amount of steps between a desire and most fulfillments are not as long as the alphabet they are as numerous as the letters on a DNA strand. You just aren't going to show they all obligingly line up for the trillions of events in billions of our lives no matter how microscopic you make them. In fact shrinking things makes it worse because you wind up with "less stuff" potentially capable of accomplishing anything.

    This is only true if you assume a desire is a deterministic event. You just can't (and really shouldn't assume it is). My being hungry is an entire different animal than my decision to get a specific piece of food, from a particular place, cooked a specific way, at a specific time. There is no solely deterministic series of events that can be shown to result in all that.

    Can't you accept the possibility that freewill exist. If you include freewill with determinism you get a perfectly harmonious description of events. If you only allow determinism you get mountains of stuff that just doesn't make sense.

    Think about it this way. Is the existence of the jet engine only due to physics and mathematics, or is physics, mathematics, PLUS FRANK WHITTLE not a more comprehensive explanation. Seems simplistic to me but maybe Malcolm Muggeridge was right.

    “So the final conclusion would surely be that whereas other civilizations have been brought down by attacks of barbarians from without, ours had the unique distinction of training its own destroyers at its own educational institutions, and then providing them with facilities for propagating their destructive ideology far and wide, all at the public expense. Thus did Western Man decide to abolish himself, creating his own boredom out of his own affluence, his own vulnerability out of his own strength, his own impotence out of his own erotomania, himself blowing the trumpet that brought the walls of his own city tumbling down, and having convinced himself that he was too numerous, labored with pill and scalpel and syringe to make himself fewer. Until at last, having educated himself into imbecility, and polluted and drugged himself into stupefaction, he keeled over--a weary, battered old brontosaurus--and became extinct.”
    ― Malcolm Muggeridge, Vintage Muggeridge: Religion and Society

    Please take the time to scan this, he was one of the greatest wordsmiths in history.
     
  15. Etritonakin

    Etritonakin Well-Known Member

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    Apparently, there is not only one such hypothesis (mutihypotheses?) -and there is indeed one which is an alternative to the idea of design
     
  16. Ponder This

    Ponder This Well-Known Member

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    To have knowledge of the state of the dice just after the throw, you would have to observe it (which would interrupt their fall).
    I might argue that if you had 'full knowledge' of the state of the particles just after you 'throw' them, then you *could* calculate the result, but, of course, we know that we can't have 'full knowledge' of the particles (uncertainty principle). So you still haven't actually explained why throwing dice is different.

    Or are they? The throwing of dice can be modeled as a linear system. So what stops us from seeing the dice as a superposition of states? Superposition of states works in quantum mechanics because the Schrodinger equation is linear. Therefore, this fails to explain the difference between them.

    Observation is the key point.

    If you took a snap shot of the dice, you would see that the dice being thrown are not in a definite state. In fact, the dice will not be in a definite state until they are observed. You are trying to say they are different because you aren't taking snapshots of the particles. That is logically insufficient to explain their difference.

    We can also determine the probability of different values being observed for dice.

    Quantum Mechanics doesn't have commuting variables because of the Uncertainty Principle. You may be getting confused. Equations model the things that we observe. This is why the equations predict the things that we observe.

    Also, the dice are not in a definite state when they are being thrown.
    For example, suppose I want to know if the total of the dice is seven. I throw the dice... while the dice are in the air, they don't 'add up to' or 'not add up' to seven. I could calculate the probability that the dice in the air add up to seven, but until the dice are observed by landing on the table, the dice are not in a definite state of being or not being seven.

    The sum of the dice is inherently undetermined (not just unknown).

    You've emphasized the non-commutative nature of the eigenstates. Does that play any special role in Bell Theorem? I found the following:

    Bell's Theorem, Uncertainty, and Conditional Events

    The Ultimate Loophole in Bell's Theorem

    This suggests that Bell disregarded the non-commuting nature of the variables in Quantum Mechanics and
    "Upon correction of this error, it is no longer necessary to invoke non-locality or non-reality to explain violation of the Bell inequality."​
    I find this sufficient to rebut your argument.

    Do you have any further objections to the way I've characterized Quantum Mechanics as it relates to Randomness? I think that when we talk about randomness in science, we are referring to a limitations of prediction.

    'random' means 'made, done, happening, or chosen without method or conscious decision'

    It's not that we can't force mutations to occur in a laboratory. We can. But that would be a conscious decision on our part to do so. The mutations that occur outside of our control are characterized as being 'random', but not because we don't know how they occurred or because we lack a knowledge of how they occurred, but because we don't predict what those mutations will be.
    We know how the random number generators for computers work and we create these random number generators as a conscious decision. However, we don't predict the result of a random number generator. In other words, we don't predict what number we get as a result.

    In light of this, I think it's worth asking: what experiment could scientists possibly conduct to confirm or reject the hypothesis that an event (such as a mutation) happened by conscious decision (or 'intelligent' decision)? We might want to start by discussing what a conscious decision is.
     
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  17. shunyadragon

    shunyadragon Veteran Member
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    The problem remains Design (ID) is not a scientific hypothesis it is a theological hypothesis that cannot be tested nor falsified by science, therefore it is not an alternative hypothesis as far as science goes.
     
  18. shunyadragon

    shunyadragon Veteran Member
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    Excellent post! Good explanation of random.
     
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  19. Polymath257

    Polymath257 Think & Care
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    Once again, even to say you have a desire means that there are the underlying neural firings, the movement of atoms, etc. Even the time scales are wildly different. Desires happen on the order of tens to hundreds of milliseconds, while atomic events are in the range of nanoseconds.

    Your being hungry is a certain chemical state (say, low blood sugar and an empty stomach) that is encoded in neural fire in the brain. That affects other neural firing that increases the chance you will have the pattern of neural firing that encodes 'deciding to get a sandwich', which in turn increases the change of the neural firing that activates muscles to actually go find a sandwich, etc. They *are* causally connected.

    Ultimately, both your feeling hungry and your decision to eat are patterns of brain activity, extending over a duration, not single events.

    Can't you just accept that mental states have descriptions at the level of neurons and, ultimately at the level of atoms? When you do so, everything makes sense, but if you don't, you can't explain mental states at all.

    A jet engine is made from atoms in particular arrangements. Knowing those arrangements and the environment it is in will completely describe the workings of that engine. In the same way, our brains are made of atoms in a particular arrangement. Knowing that arrangement and the environment will completely describe the activities of the brain and thereby all of our mental states.

    How that applies to the current debate is questionable, at least.
    Please take the time to scan this, he was one of the greatest wordsmiths in history.[/QUOTE]
     
  20. Polymath257

    Polymath257 Think & Care
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    And one aspect of this is that the quantum uncertainty for dice is small enough that a classical calculation is sufficient.

    And in isolation, that would be a valid issue. But, it turns out that for anything approaching macroscopic, simple background photons are enough to decohere that sort of superposition very quickly. But, since Planck's constant is small, such is not the case for electrons.

    The big different is that the background flux of photons is enough to decohere that superposition and force it into positional ground states. For dice this happens very quickly because Planck's constant is so small. This doesn't happen for electrons.

    Actually, I'd say the uncertainty principle is derived from non-commutation. Yes, this is a mathematical model intended to predict the results of observation: that's what it means to be a scientific theory. Any two theories that are observationally equivalent are viewed as the *same theory*.

    In quantum mechanical terms, yes they are. Or, at least, the range of, say positional superpositions is quite limited. And, again, because of the size of Planck's constant, you have very small variance in the values of any observable.

    You can observe them in the air using ambient light, which is enough to collapse the positional observable, and use a few images from microseconds apart to compute the rest of the trajectory classically and determine the result. There is simply not enough quantum aspect here (read: Planck's constant is small) for quantum effects to dominate.

    Yes, the violation of Bell's inequalities requires non-commuting variables. More specifically, the collection of all observables has to form a non-commutative algebra since commutative ones lead to ordinary probability measures which obey Bell's theorem.

    But the *essential* difference between classical mechanics and quantum mechanics is *precisely* the non-commutation of the observables! Once you have that, you are automatically equivalent to operators on a Hilbert space.

    OK, I disagree with that definition. In my mind random means 'cannot be predicted from previous events, even in theory". Consciousness is a *completely* unrelated phenomenon.

    Well, that is a very interesting question, I admit. But it seems to be a very *different* question than that of randomness as I understand the term. The action of gravity, for example, is not random, but it is also not the result of a method or conscious decision.
     
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