Computability and Algorithmic Compression

By: Bruce
December 9, 2010

In a previous post I showed how to calculate PI and made the point that purely mental concepts, like PI, actually do exist.

Also, don’t miss this post on M* where I considered how to use math to measure the earth and the moon – a power once associated with Divinity.

Now I want you to think about PI again for a moment. Back in school I was taught to use 3.14 to approximate PI. If I needed more precision I used 3.1416. But actually PI is what we call an irrational number.

Do you remember doing repeating decimals? You know, where you divide a number out and a pattern forms. For example, you take 1 and divide it by 3. The end result is 0.3333… where the 3 goes on forever repeating. The way they teach you in school to write it down is to write 0.3 and then put a bar over the 3 after the decimal to signify that it just keeps repeating forever.

One of the amazing things about PI is that it never repeats. It’s actually possible to prove this because we can prove that no fraction in the form of X / Y can ever equal PI. (fractions in the form X/Y always repeat at some point.)

So PI is actually an infinitely long sequence of numbers that never repeats.

But here is something interesting. In my previous post I showed you how to calculate PI to any number of digits.

You Can Represent the Infinite Finitely

Now imagine that you are a computer programmer. If you can’t imagine that, then imagine you are hiring one. You take my previous post and you decide to take the steps I explained and you are going to write a computer program that calculates out PI to any number of digits that you specify. Because you understand the steps required to calculate PI, you know that it’s possible to write a computer program that does this calculation for you.

Now let’s define a few terms. When you write that computer program, you have to come up with a finite set of steps of logic that the computer will follow that will calculate PI. Those finite steps are what is called an Algorithm. Algorithms are just the set of steps you follow to get some result – any result desired so long as it’s logically possible through a set of logical steps.

If you can (at least in principle) program a computer to take certain inputs and then give a desired answer using an algorithm, then we say that the problem to be solved is Computable. As mentioned in my previous post in the footnotes if it’s computable, but too slow to be useful, we call it Intractable.

Now notice something interesting here. PI is an infinite sequence of numbers, but we can (at least in principle) calculate it out using only a finite algorithm. Isn’t that interesting? Seems a little counter intuitive to me. Yet it’s now obvious that it’s true. The infinite can arise out of the finite.

I actually didn’t need something complex like PI to prove this point. Physicist and author John D. Barrow, in his book Theories of Everything: The Quest for Ultimate Explanation, uses a much simpler example. Barrow uses the string of numbers 2, 4, 6, 8, etc. It’s easy for us to see that this infinite list of numbers can be fully represented as “the list of positive even numbers.” Again, we see that the infinite can be finitely represented without losing any information. Barrow goes on to say, “It is clearly non-random. A short computer program could instruct the machine to generate the entire infinite sequence.”

This ability to compress things by representing them through a set of steps he calls “Algorithmic Compressibility.” (Theories of Everything: The Quest for Ultimate Explanation, p. 14-15)

Science (and Math) Is The Search for Algorithmic Compressibility

He goes on to make a startling conclusion about the nature of science that is probably different than what you were taught in school. When I was in high school, and even in college, I was always taught that science was primarily about observations in nature. While this is clearly an important part of science, Barrow challenges this interpretation of science:

The goal of science is to make sense of the diversity of Nature. It is not based upon observation alone. It employs observation to gather information about the world and to test predictions about how the world will react to new circumstances, but in between these two procedures lies the heart of the scientific process. This is nothing more than the transformation of lists of observational data into abbreviated form by the recognition of patterns. The recognition of such a pattern allows the information content of the observed sequence of events to be replaced by a shorthand formula which possesses the same, or almost the same, information content. … On this view, we recognize science to be the search for algorithmic compressions. … Without the development of algorithmic compressions of data all science would be replaced by mindless stamp collection – the indiscriminate accumulation of every available fact. (Theories of Everything: The Quest for Ultimate Explanation, p. 14-15)

The Non-Algorithmically Compressible

If some things can be algorithmically compressed, does that imply some things can not? If so, what would a non-algorithmically compressible thing look like?

The short answer is that if a thing can’t be algorithmically compressed (that is to say, it is not computable) then the reason is probably because it’s random. [1] Imagine a random string of numbers. The shortest possible representation of that string of numbers is the string of numbers itself. [2]

So we now have a theory about reality, one that we need to consider further. Here is our theory: reality is split up into two fundamental kinds of things: those that are algorithmically compressible and those that are random. Later on, we’ll look at other types of phenomenon that challenge this category scheme. But for now, try your best to think of an exception and see if you can without looking it up.

This process of how we discover the truth about reality using reason is what we call epistemology.

So we find that Barrow’s view of science is that it is the process of how we use reason to find patterns in reality and then to algorithmically compress them into finite steps and formula that allow us to represent reality via processes that are computable.

For the moment this is our working theory about reality. I’ll cover some challenges to this view later.

So what do you think of Barrow’s view of science?

What is science anyway?

Why does science progress? (Does it progress?)

How does it progress?

What do you think of the idea of the infinite arising out of the finite?

Other than randomness, can you think of things that can’t be computed? (i.e. put into an algorithm?)

What about things like beauty, poetry, or consciousness? Can those be put into algorithms?

Notes

[1] In a future post we’ll see that there are other things that are not computable not because they are random but because they are rational contradictions. This also means they do not exist in reality, so I am eliminating them for now. Of more interest is the existence of non-computable phenomenon that do seem to exist in reality. These will be considered in future posts.

[2] The shortest possible representation of that string of numbers is the string of numbers itself. One possible objection here is that it is possible to write a computer program to create a random string of numbers. The key point here is that you can’t write a computer program to come up with a specific string of numbers. Not even in principle. If you could then by definition it would not be random and so it would be algorithmically compressible. (If a random string is finite, at least you could store them by rote. But, for the moment, that is cheating.)

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41 Responses to Computability and Algorithmic Compression

  1. Mike S on December 9, 2010 at 10:22 PM

    I really like this post. The concept of science as a search for algorithmic compressions is very appealing to me.

    This makes sense as a working definition for science, as an important part is being able to make predictions that can ultimately be tested. Things outside this, that can’t be tested, aren’t really “science”.

    I think science progresses as our algorithms get more and more refined. Initial algorithms might work under a small subset of all problems. As our observations get further away from “normal” into realms that are smaller, larger, faster, slower, older, etc., we may find that our approximations break down and we have to reengineer them.

    Infinite from the finite: Nice. A countable infinity that can be mapped onto the natural numbers in a one-to-one fashion.

    Some “strange” things can be put into algorithms. An “average” face has been proven in many studies to be more “beautiful” than any individual face. Algorithms can generate “Bach-like” music, etc. Movie producers can influence emotions through very calculated manipulation of music, lighting, etc. But at the same time, there is something magical about it all. Perhaps it is computable at the lowest level, but I like the idea of Muses.

    I’m thinking about things that can’t be computed to see what I can think of. Perhaps a single quantum waveform collapsing into either A or B? With enough, it will follow a wave function, but as a single particle ??? More later.

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  2. Badger on December 10, 2010 at 1:00 AM

    For those interested in reading more on this, allow me to recommend

    http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer3.html

    This is an article Gregory Chaitin wrote for Scientific American about these topics. Chaitin is perhaps the pre-eminent source of ideas of this sort. There is a link from the article to his home page, and although his primary work is inherently technical, he also writes more accessible technical explanations and philosophical viewpoints.

    Mike S, about your question about examples of things that can’t be computed, thinking of random objects is helpful in one way but misleading in another, because noncomputable is not different from random.

    Chaitin’s article (and probably Barrow’s book, too) talks about a a number between zero and one known as Chaitin’s constant, or just capital-Omega (Ω, if Unicode comes through for me). It is sort of the opposite of Bruce’s example using pi. It is a specific, mathematically well defined number that is literally indescribable by any algorithm. Its mathematical definition is precise but not algorithmic. If you’re familiar with programming you may know of the halting problem, which is unsolvable by computer. Omega ingeniously encodes a solution to the halting problem into its decimal (well, binary) representation, and so guarantees that it is not algorithmically compressible.

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  3. Badger on December 10, 2010 at 1:01 AM

    I meant, noncomputable is different from random.

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  4. Bruce on December 10, 2010 at 7:32 AM

    Badger,

    It was my understanding from Barrow’s book (I will give you the quote if interested) that random was noncomputable, but that noncomputable was not necessarily random. Is that correct? (This is a question.)

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  5. Mike S on December 10, 2010 at 8:28 AM

    Badger: Thanks for the link. That was an interesting article.

    Another real world type of application, though I don’t know if it fits the definition of something that can’t be computed: Does bumping against the Uncertainty principle count?

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  6. Bruce on December 10, 2010 at 5:56 PM

    Mike S,

    Deutsch points out that uncertainty principle is actually technically intractable rather than non-computable. The “U” procedure is all computable (but would overwhelm any computer) and the “R” procedure is random, but we can easily compute (over large enough numbers of particles) what it works out approximately to be.

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  7. Mike S on December 10, 2010 at 6:19 PM

    Thanks. I figured there was a different terminology as the concept seemed different to me, but did’t know what the right word was.

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  8. FireTag on December 10, 2010 at 6:59 PM

    Bruce:

    An interesting read. I look forward to seeing where you’re going with this.

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  9. Bruce on December 10, 2010 at 8:23 PM

    Um, I was supposed to be going somewhere with this?

    :)

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  10. Bruce on December 10, 2010 at 8:24 PM

    Don’t any of you want to take a stab at trying to define science? That’s the fun part. It’s a lot more difficult to do then it seems.

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  11. FireTag on December 10, 2010 at 9:56 PM

    Bruce:

    Well, one of the immediate questions to ask, is: “Does God have the capacity to compute Himself?” LDS theology can approach this from a very different point than any other part of Christianity, but it raises serious metaphysical questions if I really want to be happy with theism of a form where God is usually law-like.

    It’s why I personally end up imagining exaltation as a process of nested infinities, where humans progress within larger entities like the Kingsom, the way the irrational numbers are nested within the larger category of the real numbers or the integers nest within the rationals.

    There may indeed be other templates for intelligence where the statement “justice as hard as steel” or “mercy flowing like a river” aren’t simply metaphor.

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  12. Cabinessence on December 10, 2010 at 11:59 PM

    Chuck Norris has recited PI all the way through. Twice.

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  13. Badger on December 11, 2010 at 12:42 AM

    It was my understanding from Barrow’s book (I will give you the quote if interested) that random was noncomputable, but that noncomputable was not necessarily random. Is that correct?

    Conceptually, this is correct if you have the right notion of “random” in mind. In this context, a noncomputable number is one that cannot be finitely described by an algorithm as in your pi example. Loosely speaking, you only need a finite amount of information to characterize pi completely, but a noncomputable number like Chaitin’s Omega is “infinitely complicated” and is “too big” for a finite algorithmic description.

    Three examples:

    1. I’m going to toss a coin and get either heads or tails, with equal probability. Is the outcome noncomputable? It’s unpredictable, which might satisfy some definitions of “noncomputable”, but it’s not too big to describe algorithmically. After the coin toss, there will be an algorithm that can describe the outcome. We just don’t know yet which one it is.

    2. Now I’m planning to toss the coin an infinite number of times to produce an infinite sequence like heads, heads, tails, heads, …. This infinitely long random outcome will be noncomputable. There is no underlying principle to turn into an algorithm. It’s a mass of infinitely many details.

    This example is a little unsatisfying because it seems it will take forever to accumulate the necessary complexity. Any finite sequence of heads and tails is is describable by an algorithm: the algorithm that says “write down ‘heads’, then ‘heads’, then ‘tails’, …”. It’s a completely un-clever algorithm, no shorter than the sequence itself, but it is an algorithm. If no shorter algorithm exists, then the sequence is not algorithmically compressible, but that’s not the same thing as noncomputable.

    3. We can get rid of the “forever” aspect of example 2 by picking a (real) number between 0 and 1 uniformly at random. Its infinitely long decimal representation can be read as a sequence of coin tosses by taking the even digits as heads and the odd ones as tails. For example, 0.8274… would correspond to heads, heads, tails, heads, …. The entire sequence would be noncomputable, as would the number itself.

    I’ve sacrificed a little precision and left some issues unaddressed for the sake of clarity. I hope it worked!

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  14. Bruce on December 11, 2010 at 10:17 AM

    Badger,

    Worked for me. That matches my understanding after having read Penrose’s The Emperor’s New Mind. (Penrose’s real interest is the non-computability of Godel’s theorem, which is essentially the same as Chaitin’s number.)

    The problem is that this is all very new to me. I have a computer science background, so I had to take 1 class in computational theory. I did it my freshman year at age 18 and snoozed through it, considering it to be irrelevant to everything.

    So I had just enough background to read some of these books, but little more.

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  15. Bruce on December 11, 2010 at 10:18 AM

    Cabinessence,

    I heard he did it while doing pushups to push the earth out of the way of an asteroid.

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  16. Bruce on December 11, 2010 at 10:20 AM

    FireTag,

    “Does God have the capacity to compute Himself?” is a fancinating question to me and is what led me to explore this area of knowledge.

    I find it interesting that you relate this to God being law-like. I do too. But I think I might see this opposite from you. I think the idea that God is ‘computable’ (albeit perhaps by a ‘super-turing machine’ that we can’t currently conceive) implies that God will be law-like.

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  17. [...] Tares continuing my exploration of using reason as a guide to reality. My latest post was called “Computability and Algorithmic Compression.” I find it fascinating just how important ‘computability’ is to comprehending reality. But [...]

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  18. Mark D. on December 13, 2010 at 11:28 PM

    I am opposed to the idea that anything real has an infinite density averaged over a finite space. That is where rationality stops and magic takes over.

    If God is both temporal and a magician, in the strict sense of the term, we should just all pack up and go home, because everything we say is either wrong or will be tomorrow.

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  19. Bruce on December 14, 2010 at 6:51 PM

    Mark D,

    Interesting comment. Expand upon what you mean.

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  20. Mark D. on December 15, 2010 at 10:11 AM

    Bruce, I mean that unless the universe is constrained in some way, theology is impossible. For example moral realism is the proposition that actions ultimately have an objective moral or consequential value.

    Torturing kittens for example. Classical theism says that torturing kittens is wrong because God set up the universe that way creatio ex nihilo, and God never changes his mind, i.e. his creation is timeless in fundamentals.

    Mormon divine command theory (DCT) advocates, on the other hand, maintain that torturing kittens is wrong only because God has decreed that to be the case, and as a consequence God has within his power to make torturing kittens be a universal moral duty and right in every sense of the word tommorrow. In other words “natural law” (in both senses of the term) is a matter of divine discretion from day to day.

    Mormon moral realism, on the other hand, maintains that the ultimate moral value of torturing kittens is a reflection of natural constraints which are not now nor ever have been a matter of divine discretion. Literally, that God does not have the power to make the torturing of kittens either a universal moral duty, or a practice that makes the world turn out better than it would be otherwise.

    If you adopt the DCT as the only metric of morality, there is no moral realism, and no moral theology short of what has God said lately. No possible change in commandments, or capriciousness, or infidelity has any basis for complaint, because there is no metric by which divine commands can be judged save the commands themselves.

    The situation is worse than that, because the DCT implies that God himself has no rational basis for evaluating the moral value of his own commands. The DCT coupled with the idea of a temporal God implies that every divine command is irrational, capricious, and arbitrary. I call that Stockholm Syndrome theology, but it is really more an anti-theology, the theology that there can be no theology except submission. Might makes right, in other words.

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  21. FireTag on December 15, 2010 at 12:12 PM

    Bruce:

    I believe both the LDS and CofChrist D&C’s contain, somewhere around Sections 80-90 a statement that says something like “truth is knowledge of things aa they are, were, and are to come, and whatsoever is MORE or less than this…”

    I always wondered if we were not being told that there are non-law-like aspects of reality (chaotic) where God may tread, but human minds can’t survive.

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  22. Mark D. on December 15, 2010 at 12:31 PM

    If reality is not ‘law-like’ in fundamentals:

    (1) Science is impossible
    (2) Rationality is useless
    (3) God cannot be trusted

    All three because there is no continuity between the present and the past.

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  23. FireTag on December 15, 2010 at 1:05 PM

    Mark D, I don’t know if 22 was directed at me, but I’ll respond.

    Life exists and thrives right at the boundary of order and chaos. Science and rationality are both possible, and useful — just not unlimited. There are even branches of science that study the transition to chaos.

    God can ONLY be trusted, never compelled.

    God made time if He made space, matter, or energy, so past, present, and future don’t mean much where He’s involved. For that matter, nothing in our current understanding of natural law forbids the universe from collapsing into a lower vacuum state “tomorrow” and turning all the particles in our bodies into something unsurvivable. Life is just plain dangerous.

    Me, I’m a pantheist. I believe all of the aspects of God are natural (ok, add that to my already long list of heresies; if I’m wrong, I already can’t be in much more trouble)

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  24. Mark D. on December 15, 2010 at 1:31 PM

    Firetag, Chaos theory exists (indeed is only possible) within a realm where physical laws operate like clockwork.

    God made time if He made space, matter, or energy, so past, present, and future don’t mean much where He’s involved

    Now you are coming from a completely different perspective than predominates in (LDS) Mormonism, so you are going to have to be more explicit about what your assumptions are. Classical Mormon theism rejects the proposition that God made any of those things (time,space,matter,energy,intelligence,etc.)

    Joseph Smith said that God himself could not cause himself to come into existence. He also said the spirit / intelligence of man was eternal and can neither be created nor destroyed. The D&C states that “the elements are eternal”, and so on.

    Even if one maintains that many laws of nature are not really laws at all but rather divine dictates, those assertions place a pretty hard limit on how arbitrary a reasonably faithful Mormon theology of nature can be. No creatio ex nihilo, no violation of fundamental conservation laws, etc.

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  25. FireTag on December 15, 2010 at 2:36 PM

    In this post and an earlier post linked therein, I try to explain a different view of how one might reconcile Joseph’s visions into a cosmology more in keeping with modern physics:

    http://thefirestillburning.wordpress.com/2009/06/22/duality-and-divinity/

    The basic idea is that the spiritual and physical are not separate realities, but are rather alternative descriptions of a single reality. The analogy is that a single electron has two mutually valid, if seemingly contradictory, DESCRIPTIONS. It can be described as a particle or as a wave, even though there is only one electron, depending only on what features you CHOOSE to look for.

    I am suggesting that the physical description of reality ONLY should be based on space and time. In the spiritual description I envision, “space” is replaced by similarity of information content.

    Many of the most viable modern cosmological models predict that there are “parallel” universes as well as places in our own big bang that are exact or near duplicates of our part of the cosmos.So, in the spiritual description, I envision all of these physical regions will map to a single “spiritual region”; and they can also be treated as a single entity, interacting with other spiritual entities of the same type according to law-like descriptions of their own. But these interactions are simply different descriptions of what is happening in physical space. All things are spiritual and all things are physical, but there is only one reality evolving.

    The time analogue in this spiritual picture has to involve non-communitative algebra, just like physical quantum mechanics does, so I won’t go into that here. Suffice it to say, since physical states duplicating us have existed (in many cosmological models) eternally into the past and will eternally into the future, Joseph (particularly in the Book of Moses and the D&C) would, without understanding mechanisms, understand that our spirits are eternal.

    God is not the creator because he created at some time in the past; He is the creator because it is His eternal nature to be creating continually.

    I think God is the boundary of His own imagination, and is all there is. I, therefore, do not exclude the possibility that there are aspects to God that are chaotic, even though we are in a law-like portion of His nature.

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  26. Bruce on December 15, 2010 at 3:51 PM

    Mark D,

    Your #22 is spot on. I completely agree with it. It’s my ‘personal creed’ so to speak.

    FireTag,

    You are using ‘chaotic’ to mean ‘not law like.’ But I’m not sure classical chaos is ‘not law like.’

    Also, didn’t Deutsch say (in Fabric of Reality) that a quantum multiverse means there is no classical chaos at all? It’s really just the ‘classical’ view of quantum state reduction? (Did I say that right?)

    By the way, Mark D, FireTag is a physicist. I am gathering you have some sort of background in something related too. It would be a little weird for you to know this much just because. ;)

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  27. FireTag on December 15, 2010 at 5:05 PM

    Bruce:

    If I remember that discussion, Deutsch was talking about quantum chaos, which doesn’t happen in the multiverse interpretation because QM is strictly linear. (One way to radically alter our picture of QM would be to show there were non-linear components of the theory.)

    Chaos can still happen at macro levels of a single universe because at macro levels involving complex systems, the governing equations are most frequently non-linear.

    And while it would be true that I’m trained as a physicist, I’m just plain weird nowadays. Working in government for a couple of decades will do that to you. :D

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  28. Mark D. on December 15, 2010 at 6:54 PM

    Your #22 is spot on. I completely agree with it. It’s my ‘personal creed’ so to speak.

    Thanks Bruce.

    FireTag is a physicist. I am gathering you have some sort of background in something related too

    Yes, I majored in physics in college. In real life I am a software developer though, and always have been. I have never had a real job doing anything else.

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  29. Mark D. on December 15, 2010 at 7:16 PM

    God is not the creator because he created at some time in the past; He is the creator because it is His eternal nature to be creating continually.

    That is the general Mormon perspective, which I agree with. On the other hand Mormons generally rule out creatio ex nihilo (or the logical dependence of the existence of the universe on divine action) completely. The debate is about the contingency of natural constraints within the universe.

    I claim that a constraint that has an ongoing temporal contingency on the will or action of someone else isn’t a natural one, by definition. So the Mormon school of thought that says natural laws are temporally dependent on the will of God properly speaking is the same as the position that there are no natural laws.

    I think God is the boundary of His own imagination, and is all there is. I, therefore, do not exclude the possibility that there are aspects to God that are chaotic, even though we are in a law-like portion of His nature.

    Here we have to make a distinction about what is considered part of God’s nature. Unlike classical theism, I don’t consider the laws of physics to be a reflection of the divine nature. I don’t consider the nature of God to be strictly fixed either, but rather eternally progressing.

    I believe that God is a temporal being with libertarian free will (LFW). That means that his actions (and his relationship with us) is not deterministically predictable. Not chaotic, but willing.

    I do, however, allow that the law of unintended consequences may result in freely willed actions resulting in collateral chaos or thermal noise. Not on a net net basis though. I believe that LFW is the only available means of escaping the second law of thermodynamics, our only hope of avoiding the so called heat death of the universe.

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  30. FireTag on December 15, 2010 at 9:55 PM

    I’ll defer the heat death issue until Mike S. gets farther into his science and religion series and covers string theory, but, I’d like to suggest a different way of looking at free will that strikes a similar “dual description” note as above. We just don’t SEE free will in physics, even though it’s expected in Mormon theology.

    Deutsch pointed out in “Fabric of Reality” that those aspects of freedom that allow me to choose actions that I do not wish to choose are useless – quite literally – because I will not use them. The ONLY meaningful definition of freedom then is the ability to realize courses of action that are fully consistent with my own nature and desires. But this is precisely the aspect (and the only aspect) of freedom that is preserved in the multiverse. None of the individual copies or variants of us are ever forced by the existence of other realities to choose anything they perceive as against their own nature or desires. The absence of freedom, and the futile nature of attempting to be anything but what we were “intended” to be, is solely a “God’s-eye” phenomenon. From that viewpoint, the kind of freedom you seek to see would arise only as we “approach” the limit of God. We become free as we become more of Him according to His will.

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  31. Mark D. on December 15, 2010 at 11:14 PM

    None of the individual copies or variants of us are ever forced by the existence of other realities to choose anything they perceive as against their own nature or desires

    That is no comfort if the will of an individual is completely traceable to factors that he has never had the power to affect one way or the other. It reduces repentance and moral responsibility to epiphenomena.

    Given initial world state A, no LFW, and allowing for real randomness, a fellow robs a bank the next day with some probability P. But nothing ultimately traceable to any of his actions has any bearing on what the value of P actually is. His will and desires are purely epiphenomenal.

    Suppose P is high. Over the next twenty four hours he may yet experience a “change of heart” and avoid robbing the bank. But he does not deserve any moral credit for doing so, because again his change of heart is epiphenomenal to factors he never has nor ever will be ultimately responsible for, no matter how much he feels to the contrary.

    I might as well hold a computer program morally responsible for bugs in its implementation. It is not like the program itself is ultimately responsible for any of them.

    Without LFW, no one is ultimately responsible for anything. Not in terms of differential ability to intentionally change who they are relative to a computer simulation of themselves in the same circumstances. If a person is no better than a simulation, there is not much to be said.

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  32. FireTag on December 16, 2010 at 12:10 AM

    Mark D.:

    In which neuron of your brain does moral responsibility lie? In which neuron of your brain does consciousness lie? Is your big toe good or evil? :D

    I’m suggesting that these concepts are EMERGENT because our spirits are collectively associated with ALL of our copies scattered throughout spacetime — not with any single copy in a one-to-one relationship. The pre-existence isn’t “pre”. The afterlife isn’t “after”. Single human brains, IMO, are complex enough for consciousness to “emerge”, but NOT complex enough to house a human spirit. The latter takes vast numbers of copies. (See my earlier post here on Wheat & Tares, “The Spirit of the Earth”.)

    I never suggested it was comfortable. Nor do I suggest that either of us has any free will about how we feel about it. I certainly understand your issue.

    Historically, most Christians have been motivated to do good either by external pressures (e.g., threats of punishment, shaming, or offers of reward) or by internal drives “freely chosen” (e.g., the response to love, a desire for security, or a passion for justice). What is the motivation to do good when our choices are inevitable? Won’t people stop striving to do good if this interpretation is accepted?

    However, upon reflection, the problem of motivation, like the property of freedom, exists only from the individual copy perspective. From the God’s-eye view, the very inevitability of our “choices” makes the need for motivation moot: the moral (or immoral) behaviors that we will individually practice, to use the poetic language of the Old Testament, are already written into our “hearts”. From the dual, copy viewpoint, we may assign motivation to whatever source we believe plausible in a given situation. The assignment may well be “correct” when considering things solely from that copy viewpoint. From that viewpoint, we may with perfect validity continue to say we are motivated by love, or fear, or longing – as long as we do not forget that our responses are always consistent with our own nature. Our choices and actions make us what we always were; because of what we always were, we could choose no other way. Particle or wave. Neither description is more real than the other.

    Thus, like the target of the old Carly Simon recording, “You’re So Vain You Probably Think This Song is About You”, there would be those who revel in taking these ideas as justification to experience their baser natures more fully. But the God’s-eye corollary of such a copy’s viewpoint interpretation is that the individual who adopts it chooses what was consistent with his/her essential nature from the foundations of spacetime. And the evidence of that corollary is the existence of all of the variants of that individual who are exposed to these ideas elsewhere in the multiverse and yet do not embrace that baser nature.

    Similarly, there are many who strongly recognize something deep within them calling them to love, justice, mercy, and self-sacrifice. The nature of these individuals (in the God’s-eye view) drives their responses. Yet, from the copy perspective, causes and effects are always visible that create a story of why these individuals choose virtue. Each perspective predicts the same behavior, and each perspective is equally valid.

    Particle and wave. Predestination (on steroids) AND free will. Spirits to the places prepared for them; bodies existing over and over again (every Planck time, in fact.) Dual descriptions.

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  33. Mark D. on December 16, 2010 at 6:32 AM

    In which neuron of your brain does moral responsibility lie? In which neuron of your brain does consciousness lie?

    If there is an eternal, singular spirit/intelligence, like Joseph Smith said, the answer is none of them.

    If “intelligence” is a primitive property of matter (or spirit matter), the answer is all of them collectively. LFW implies property dualism somewhere.

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  34. Mark D. on December 16, 2010 at 6:46 AM

    FireTag: As to the free will issue, I suggest that the objective “God’s eye” view is the only one that really matters. Your position is similar to compatibilism (the idea that free will and determinism are compatible).

    i.e. people believe they have free will, perceive that they have free will, but free will is epiphenomenal in a scientifically accurate representation of every decision they will ever make. Essentially, the position that individuals are automatons.

    And if that is the case what gives an individual greater moral value than a robot? Complexity? Should we feel greater remorse over levelling a manufacturing plant than executing a human being? Just about the same? Much less?

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  35. FireTag on December 16, 2010 at 10:44 AM

    Mark:

    I think you’re close to the mark; God is experiencing all of the possibilities of His own being. As the limit of all being, only He has freedom to be all things and still fit the definition of free will ALways meaning the freedom to be exactly what we are. (We are never free to be the contradictory “something we’re not”. He values complexity highly, it appears, and we look kind of silly telling Him He doesn;t know what He’s doing.

    But, I would disagree with your framework that God is external to the system at all, and the God’s-eye view defines one description as more real than the other.

    That’s simply insisting “I’d rather think of it as a wave.” The language is not the thing it describes. The map is not the country.

    And when and if robots of alloy become as complex as robots made of organics, I do expect they’ll wake up and become just as valuable as you or I. The Kingdom itself may be more valuable than any of us as individuals.

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  36. [...] In my last post I considered Physicist John Barrow’s view of what science is: So we find that Barrow’s view of science is that it is the process of how we use reason to find patterns in reality and then to algorithmically compress them into finite steps and formula that allow us to represent reality via processes that are computable. [...]

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  37. Bruce on December 16, 2010 at 8:58 PM

    Mark and FireTag,

    Might I just say that both of you are rare human beings in that you both actually struggle to explain things and then willingly put your explanations out into the world and allow them to be criticized.

    I’m convinced that this is the hidden definition of rationality. You are both the rare rational person. (I’ll let you decide for youself if that is a compliment or insult.)

    FireTag said: “Chaos can still happen at macro levels of a single universe because at macro levels involving complex systems, the governing equations are most frequently non-linear.”

    Penrose wrote of two procedures in QM, U and R. U being the linear part. R being the non-linear random state reduction. Is this what you are refering to? Remember, non-physicist here. You can’t just fling statements like the above around without giving me a name to look up.

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  38. FireTag on December 16, 2010 at 10:35 PM

    Bruce:

    Non-linear equations is a pretty general field of study, but you might want to look more at Stuart Kauffman’s work on complex adaptive systems. Wikipedia has a good intro into his bibliography (I can’t remember if you cited him earlier in one of your posts.) What I’m talking about at the macro level is unrelated to the issues of chaos in quantum mechanics.

    Penrose is specifically looking for an explanation of consciousness in quantum uncertainty by looking into a theory in which QM has a non-linear component. This is not present in other interpretations of QM, is treated skeptically by most researchers of consciousness, but would be a strong test for his interpretation if ever demonstrated.

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  39. Mark D. on December 17, 2010 at 12:00 AM

    FireTag: I am fine with the assertion “all complete objective descriptions are created equal”. But transforming one complete objective description to another one is just a matter of mathematics.

    As far as wave particle duality is concerned, I see the world in Bohmian terms, so it doesn’t bother me at all. Wave function collapses are a figment of the imagination, one of the silliest ideas (when taken seriously) any physicist has ever had anywhere. Likewise any other form of scientific anti-realism.

    BTW, I don’t place God on the outside looking in. Accounting of a “God’s eye view” is a complicated question – I mean the term metaphorically (corresponding to classical theism), but I think it ought to be abundantly clear that that God in actuality approximates an external all seeing perspective to a degree we can hardly comprehend. Inspiration would not work otherwise. I think quantum realism might have something to do with that, namely superluminal coupling of some sort. If spiritual influences are not radically superluminal, I can’t possibly imagine how they work.

    Bruce: Thanks for the compliment. As you might guess from the above, I don’t think there is such a thing as metaphysical randomness, or random state reduction in actual reality. Any appearance to the contrary I would classify as a methodological artifact, with similar weaknesses as the concepts of “temperature” and “entropy” have.

    The standard definitions of temperature and entropy are subjective, model dependent quantities. Entropy is an energy weighted measure of what you don’t know about the exact state of a system. So if you do know the exact state (hypothetically speaking), there is no entropy.

    So if you want entropy to be real, you have to make some sort of statistical dividing line and ignore any information you may have about the microstates of the system below that level of detail. Same goes with “temperature”.

    So whenever someone says entropy is always constant or increasing, I want to ask either “from whose perspective?” or “according to what level of statistical filtering?” Without statistical ignorance, the second law of thermodynamics doesn’t mean anything.

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  40. FireTag on December 17, 2010 at 4:52 PM

    “But transforming one complete objective description to another one is just a matter of mathematics.”

    But the “just” is actually the whole point that has made duality such an important idea. Formally dual descriptions always would give the same result, but we don’t understand reality in EITHER description well enough to use it exclusively. What is intuitively obvious in one description is brutally hard to understand in the other description — and the utility of the descriptions switches in other situations.

    What I’m looking into is the notion that when we use a “spiritual framework” to describe reality, we’re looking from a view that focuses on the collective behavior of entities made up of things close together in information content, but greatly separated in spacetime. When we use a “physical framework” we’re focusing on things close together in spacetime, but far more separate in information content. So, superluminal transmission in spacetime involves going small distances in the information framework, for example, even if there is some analogue of the speed of light in the laws governing the spiritual description. I expect to have experimental confirmation (yea or nay) from being on the other side long before the mathematics gets resolved.

    I am motivated in this direction by the increasing number of deep connections that are emerging between gravity and information theory from attempts to reconcile relativity and quantum mechanics (and are recasting thermodynamic concepts like temperature and entropy in the process).

    I got sloppy in using “God’s-eye view” though. Tegmark and/or Deutsch use the terms “frog-eye” and “bird’s-eye” to differentiate the universe and multiverse viewpoints. I wanted to shorten the explanation, and probably confused things more than clarified them.

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  41. » Our Epistemology So Far The Millennial Star on October 1, 2011 at 9:02 PM

    [...] the physical universe that can be understood are understood through being able to convert them to computation. (At least so [...]

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