Imagination and Failure of Same

Recently, it seems, over and over the same theme keeps repeating. What passes for argument or reasons for believing or thinking a thing depends crucially on a failure of imagination. In rhetoric there is a list of known fallacies, it seems to me that “failure of imagination” is not given as one of those, but looking around seems to be perhaps one of the more important ones especially for it not being noticed so much. The structure of these arguments (as such) go as follows. Something is either A or B. It is not A therefore it is B. This fails (obviously) if possibility set (A or B) does not exhaust the possibility or the two sets A,B are not distinct. 

At the turn of the last century, it was thought throughout in the Physics community that an entity was either a wave or a particle and that it could not be both. Electro-magnetic radiation was the primary example of waves and it was thought that electrons and such were examples of particles. As it turns out, as we are all taught, was that wave/not-wave and that (not-wave=particle) were exclusive sets. That is to say a thing could not exhibit both wavelike and particle like properties. Quantum mechanics and the notion that things were both wave and particle was not considered. The argument that A=wave B=particle exhausted the possibilities was made and was believed. The failure of this argument to be the case was a failure to imagine that wave/particle exhausted the possibilities.

In recent discussions we talked about determinism and free will. The suggestion was made that the human mind, based on physical brains, were either A or B … where in this case A=deterministic or B=random (in which it is akin to wave/particle) that random=not-deterministic. The problem here too is a failure of imagination. Those who feel that the choice deterministic vs random exhausts the possibilities exhibits this a failure of imagination problem.  Truly random systems can be deterministic. Quantum mechanics provides an example of this. Quantum behavior such as will the spin be measured up/down is intrinsically (see Bell’s Theorem/Inequality) random. Yet the time evolution and the description of quantum behavior is entirely deterministic. The time evolution, construction, and behavior of quantum systems are entirely deterministic. Specifically the behavior of wave functions are completely deterministic. Similarly so-called deterministic systems, that is ideal mathematical systems described by classical mechanics with no input randomness can be random. That is the behavior of the system of classical systems (described by Hamiltonian evolution) can be ergodic. The three body gravitational problem is a simple example of that behavior. Random/deterministic are not useful (independent) criteria for describing the mind/brain.

In the context of that same earlier discussion on free will and determinism I too offered that I suffer from failure of imagination as well. I’ve offered that I believe that while we live in a deterministic (quantum) universe, that I fail to imagine how creative genius can exist without free will. And furthermore I had a partial point which needs some blank-filling to be made wholesome. That is to say that traditionally a connection between moral responsibility and free will is typically made, i.e., if you don’t have free will you cannot be morally responsible. In that discussion I had suggested that nationality is a social construct. National identity could be identified and assigned without reference to the subjects (humans) having or not having free will. Nationality is a social construct not dependent on free will. It might be the case that moral responsibility is too a social construct. Given that some social constructs not depend on free/not-free will it may be the case that moral responsibility too can be construed from social order and structures without requiring reference to free/not-freedom of will.

Another example, Mr Horowitz a few weeks ago offered as his outsider’s perspective on Lent:

 Rather than abstaining from habits that are thought to be indulgent, these people “instead take on a Lenten discipline such as [bible study], volunteering for charity work, and so on.” (An aside: I wish we would stop lumping in bible study with charity work. Those two are not really the same.) Whereas the traditional Lenten practices are misanthropic inasmuch as they blame us humans for everything that goes wrong while tacitly denying our ability to improve our own lot, the more liberal ones offer a chance for people to be more actively involved in their own self-reformation.

This is a splendiferous cornucopia of examples of failures of imagination all rolled into one exuberant post. Some examples of this include his notion that the Lenten practice of lumping ascetic practices of Lent (Bible study, fasting, and prayer) with other parts such as charitable work are “really not the same.” Can there be a meta-narrative which groups them together in some way. Mr Horowitz apparently fails to imagine such a thing so they are therefore to be kept separate. A and B are separate categories … but just like wave/particle there exist explanations which tie them together. A second example is his claim that Lenten practice are “misanthropic” because they (apparently) blame humans for everything and deny our ability to improve our own lot (… or they don’t … exactly?). So are the liberal versions not misanthropic but the Calvinistic/Reformed view is? What then is this thing called Sanctification? Why do Reformed Christians attempt to improve their lot, why were those New England Puritan Calvinists so hard working after all? Hmmm. Perhaps there is another missing meta-narrative and Mr Horowitz is suffering from a failure of imagination and using it is a argument?


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  1. Funny, because failure of imagination is one of the keystones of many conservative/religious arguments in my experience.

    I can’t imagine how evolution could explain the diversity of life and the complexity of the human brain, therefore God did it.

    I can’t imagine that we humans can be messing with something as huge as climate, therefore it’s either not happening or it’s not our fault.


    (Hey, I miss the email me with new comments button!)

  2. Oh and the big one, I can’t understand how the universe could have just popped into being, therefore God exists.

  3. Mark says:

    I don’t recall making any of those arguments.

    And, please if you have the time, test the email subscribe. I just loaded a plugin for that and turned it on.

  4. Mark says:


    Oh and the big one, I can’t understand how the universe could have just popped into being, therefore God exists.

    That works both ways (existence). You can’t imagine God therefore He doesn’t exist.

  5. Boonton says:

    As it turns out, as we are all taught, was that wave/not-wave and that (not-wave=particle) were exclusive sets.

    I’m not quite convinced they aren’t exclusive sets. But then ‘acts like a wave’ is a different set than ‘waves’. Yes waves all ‘act like waves’ but there are also things that aren’t waves that ‘act like waves’. So my imagination might say that particles are ‘not-waves’ AND ‘not-particles’ but rather something else that exhibits, depending on the context, some of the properties of both.

    In the context of that same earlier discussion on free will and determinism I too offered that I suffer from failure of imagination as well. I’ve offered that I believe that while we live in a deterministic (quantum) universe, that I fail to imagine how creative genius can exist without free will. And furthermore I had a partial point which needs some blank-filling to be made wholesome. That is to say that traditionally a connection between moral responsibility and free will is typically made, i.e., if you don’t have free will you cannot be morally responsible.

    I think we have a problem with getting A and B right, let alone wondering if A and B exhaust all possibilities! If you were to decide whether or not to vote for Obama by flipping a coin, I would say your voting behavior is entirely random. But I know you’re not going to flip a coin, I know you’re not going to vote for Obama. I would put forth in the limited case of the Presidential election your behavior is deterministic. But is it free or not free?

    If you decided to vote by flipping coins, that would be a free will decision on your part, but we’d all agree the votes you’d case would be random. But does being deterministic mean you’re not free? I’m not so sure.

    As for ‘moral responsibility’, how does it really apply? Like I said before, if you’re killing people because your’re a malfunctioning robot with no free will, well there’s no moral problems with having you melted down. If you’re killing people because you’re a robot that’s decided to be evil, well you bear moral responsibility for that act and we as a society can punish you by melting you down. Either way you’re going to get turned into recycled toasters.

    Oh and the big one, I can’t understand how the universe could have just popped into being, therefore God exists.

    Given that one’s brain is a subset of ‘the universe’, it seems a rather large leap of faith to assume a subset can encompass the whole. Not necessarily impossible I suppose, I could imagine a house that has a perfectly exact scale model of itself in the basement, even down to a tiny scale model in the basement of the model house and so on! But it is a leap of faith to argue that one’s brains can make definitive statements about such large matters.

    I think this should whip theists in the face when they try to make arguments like “something doesn’t appear out of nothing”….err well no human has any real experience with true nothingness and can say nothing about it. But it would also apply to atheists who would like to make definitive statements about whether God exists or something that could be described as both larger than human intelligence and intelligent itself exists. IMO, though, most atheists are rather thoughtful on that point. If you watch Christopher Hitchens debates on YouTube, for example, you’ll note that he does very carefully avoid saying he is claiming to really *know* anything about God or even an afterlife, he is just talking about whether or not the hypothesis is necessary or reasonable.

  6. Mark says:


    Yes waves all ‘act like waves’ but there are also things that aren’t waves that ‘act like waves’. So my imagination might say that particles are ‘not-waves’ AND ‘not-particles’ but rather something else that exhibits, depending on the context, some of the properties of both.

    In the 19th century imagination(s) held that wave/not-wave=particle exhausted the set of possibilities. That there weren’t such things that had properties of both. Particles that “acted like waves” … how do you describe that mathematically?

  7. Boonton says:

    I think there’s a logical error here. Particles are not waves and waves are not particles. But to say something is ‘like a particle’ is a very far distance from saying something ‘is a particle’.

    It’s still logically correct to exclude the middle. If particles and waves are mutually exclusive categories (as dogs and cats are), then no something can’t be both particle and wave just like a 4 legged animal can’t be both dog and cat. But you could have an animal sometimes seems to have cat properties and sometimes dog properties. This would actually not be so mind bending if you accept that the world is made up of more types of animals than just dogs and cats.

    I think the other error being made is a failure to recognize the limits to our perception. Particles and waves are real 3-dimensional things we can see, touch, feel, make pictures of, mold models out of clay. We make an assumption that the microscoptic world is just a scaled down version of the world that our perception operates inside of. So in the world of atoms things are either grains of sand or ripples on the water etc. But that’s just a working hypothesis that may be right or may be wrong. Once you see that then it becomes less mind bending to understand that things on the particle scale do not operate the way they do in the macro-scale our brains swim inside.

  8. Mark says:

    I agree there was a logical error. The thought at the time was that things were either waves or particles and there was no excluded middle. Particles, as was thought, did not exhibit wavelike properties and vice versa. It took an original thinker like Einstein to suggest that electromagnetic radiation, which were thought to be merely waves, were transmitted by photons. Quantum mechanics might be considered the unfolding/unpacking how that might come to be understood.

    “Once you see that, then it becomes less mind bending” … exactly. Failure of imagination not an argument. JA’s thinking that random vs deterministic fills the possibilities is a failure of imagination apeing argument.

    Today, you’re remark that considering illegal immigration dealt with locally is civil injustice is also a failure of imagination, i.e., you don’t consider or imagine that any way that could be posed/framed that might work forward without injustice. Just as, likely, I cannot see how you can deal out amnesty without both being unfair to those who legally immigrated or that doesn’t proffer clear inducement to law breaking in the future.

  9. Mark says:

    I should be more clear.

    Particles are not waves and waves are not particles.

    An electron (or a photon). Is a particle. It is also a wave. The notion that a thing is either one or the other is what is wrong. There are alternatives. And yes, the notion that it is one or the other is kind like an number is either even or it is odd … it can’t be both (or can it? … how about the integer at infinity is it not even and odd?).

  10. Boonton says:

    In terms of immigration, I think you are wrong in asserting that immigration should be a local issue. But let’s try to keep on focus here:

    What is a particle and what is a wave? Probably the most intuitive way we think about the two might be grains of sand on the beach and waves of water. We see water as continuous with waves being nice smooth curves. It is also easy to see grains of sand atomically (yes I’m sure even the ancient Greeks kinew you could split grains of sand into finer and finer grains but that’s tricky to do if you’re just on the beach thinking about things).

    The atomic hypothesis was that water was not really continuous. At some point if you kept ‘zooming in’ you’d end up seeing things that were more like grains of sand rather than a smooth curve. This might have been surprising as science developed in the Enlightenment and beyond but not really shocking. After all we know grains of sand can look like waves because the wind blows sand into wavey patterns.

    But we have no direct experience with things on the atomic scale. We make an implicit assumption that it is ‘like’ things on our macro scale. So when we are told a particle behaves like a particle, we think of a little grain of sand-like thing. When we are told it behaves like a wave we think of a continuous curve thing. All of that, though, is just extending an analogy of macro-experience to the micro-scale. We see a thing that appears to have some properties in common with a little ball of a sand grain and assume that what it would be like if we could shrink ourselves down to the size of an atom. But that’s an assumption that could be wrong and probably is wrong.

    So IMO it’s not the notion that it is ‘either’ that is wrong as much as it is the notion that experience on the macro-scale translates into useful knowledge of the micro-scale. Being very good at riding a bike may give yourself some good ‘intuitive’ knowledge that may help you learn to ride a motorcycle, but does being good at riding a bike help much in learning to ride a horse? Probably not as much. Our notions of particles and waves are built from our intuitive marco-experience and that may or may not apply to other scales.

  11. Boonton says:

    Here’s a slightly different way of looking at it, let me toss out a Binary Universe hypothsis. Say at the smallest scale, say down to the string level or even smaller than it, the universe is in reality a binary system. At that tiny scale the universe is made up of discrete cells that are either ‘on’ or ‘off’. All macro behavior we observe is simply the result of whatever system of rules govern the binary operations of the universe at its most fundamental level.

    So if this hypothesis was true, how would it apply to the ‘problem’ if ‘particle or wave’? It would seem to me that there would be no problem at all. The grain of sand is very ‘particle-like’ because the sum total of all the ‘ons’ are such that it seems like that, but the subatomic particle inside the grain of sand acts sometimes like a wave, sometimes like a particle, again because this is the result of the ‘universes programming’ flipping on and off the fundamental binary units. Asking to resolve the ‘logical problem’ would be like asking a cartoon to address the logical problem of having a talking dog when dogs’ can’t talk. The cartoon dog isn’t a dog, it’s like a dog in that it shares some macro-traits with other dogs that makes us think its a dog (like size, shape, color etc.) but it’s not a mbember of the category ‘dog’.

    If this sounds a bit like the Matrix, it is because it is. While the universe doesn’t necessarily have to be a Matrix running on some larger computer, a sufficiently large and powerful enough computer could construct a ‘binary universe’ with rules that mimic any given non-binary universe (except, perhaps, an onion type universe that just has an infinite number of layers of smaller and smaller scales each with its own set of rules ‘summing up’ to the macro behavior).

  12. Mark says:

    The problem with cellular automata as a basis of reality has a different set of problems. We can’t imagine how to make cellular automata covariant, i.e., make that compatible with special relativity. Think of it this way, if reality has a cellular array/grid, it has a preferred frame of reference.

    It also doesn’t get past the wave/particle problem, in that waves exhibit non-local interference, i.e., they have extended fields of interaction while particles interact in a pointlike “collision” fashion. Your cellular automata rules, typically interact locally, i.e., more like particles.

  13. Boonton says:

    Re extended fields of interaction: Pac-Man.

    If you need more info, ok in Pac-Man you slip out the side door to your left and immediately appear in the side door to your right. the ‘particle’, the little dot that you get points for eating, is consumed by something that should be far away (the pac-man who an instant ago was on the other side of the board).

    The preferred frame of reference problem seems more serious to me…but perhaps it’s solved by the fact that the only ‘frame of reference’ possible would be outside the actual universe. An entity inside the universe would have to be made up of the digital elements and its frame of reference would have to be localized. It helps to think of it in terms of a simulation. Could you write a simulation game that incorporated special relativity? I think you could, imagine a massive multiplayer space game that stuck to the laws of physics. Players on opposite sides of the solar system trying to coordinate an attack on earth would be required to contend with time delays in their messages to each other per the speed of light and so on.

  14. Mark says:

    “slip out side/appear on other side” is just that the left and right (and top and bottom sides) are topologically sewn together. They are close. See this.

    Time delay of messaging is one feature of relativity. Others include mass and time dilation effects and notions of simultaneity. A simulation game isn’t a cellular automata. The view of the automata needs to be invariant on Lorentz boost, i.e., should look the same no matter your velocity.

    I’m not sure how you embed a Lorentz invariant manifold inside a non-invariant one.

  15. Boonton says:

    Again could you not build a small scale simulation game based on relativity? If you could that would by definition be a ‘digital universe’. You’re right it may not be cellular automata but I think cellular automata would be a subset of the category ‘digital universe(s)’.

  16. Mark says:

    A simulation game != cellular automata/lattice. You don’t need to have any notion of a preferred frame of reference in a simulation. You do for an automata/lattice. That’s the point. I don’t know if there are proofs that you cannot, that might be interesting. But our (collective human) imagination fails when it tries to invent a Lorentz invariant lattice as far as I understand it.

    Right now, in our thinking, “inertial frames of reference” are in a preferred class, in that the laws of physics look exactly the same. A lattice as substrate for the universe gives a new preferred frame. That preference is non-physical, i.e., two observers traveling almost light speed perpendicular to each other should see the lattice as yielding the same properties for them. How do you do that?

  17. Boonton says:

    Help me out here, two rocket ships blast off at 99.99999% speed of light traveling at a 90 degree angle to each other. What will their observations consist of that you think wouldn’t work in a digitally built universe.

  18. Mark says:

    The issue is the lattice, not “digitally built.” A lattice will be “shrunk” in the direction of motion. However, if you are travelling without acceleration, you should not be able to detect that you are moving.

  19. Boonton says:

    So let me try to sketch this out, granted my training here is limited…..

    Two spaceships take off at light speed at right angles to each other. A year later they create a right triangle at 90 degrees. Normally the distance between the two ships should be about 1.41 light years via the the Prythogram Theorm. But because relativity says nothing moves faster than light, you’re saying the space between the two ships would have to appear ‘shrunk’ otherwise they would be able to increase their distance from each other at a rate faster than light.

    I suspect the problem in visualizing how this stretching or shrinking might work with space in a ‘pixel’ universe that is made up of digital on-offs in 3-dimensions comes from visualizing it as a type of TV screen. But if the pixels extend into at least the 4th dimension (as they must) for time, I suspect you may be able to solve the relativity issue nicely. The two spaceships conducting all sorts of experiments like measuring each other’s clocks against earth’s clocks are not only looking at pixels in 3-dimensions but are extending into 4-dimensions.

    Of course there’s another way to do it….all observations in the digital universe simply show up as if relativity is the case. The ‘brain in a vat’ ala the Matrix may simply be living in a universe of relativity beause that’s, say, an easy way to make space travel difficult thereby saving the computer the trouble to have to render distant planets and galaxies in detail.

  20. Boonton says:

    May want to check out this video….not as much animations as one would like…