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Friday, December 07, 2012

Algorithms and Reductionism

Ken B. makes an interesting point in the comments, although not, perhaps the point he intended to make!

The question is, what do we make of an algorithm? Well, if we are true materialist reductionists, we would have to say that an algorithm really just is its physical manifestation, e.g, the microchip on which it is running and the electrons moving about in there: this is what it means to be a materialist reductionist, after all.

But now consider a particular algorithm, say, the Sieve of Eratosthenes. That algorithm can be implemented on an old-time mainframe built with vacuum tubes, on a iPad, with a large set of hot and cold water taps, or even in my brain. These physical structures are about as different as can be, and yet Ken admits that it is the same algorithm implemented on each of them. Therefore, what is the same in these wildly physically divergent cases (which I would call the idea) must, necessarily, be something not physical.

So there are parts of reality which are not physical. QED, reductionist materialism is false.

UPDATE: Ken asks me to add the following: "I am not arguing for what you call materialism. I am arguing that no soul is needed to explain or account for consciousness, and that consciousness will be explicable in terms of the physical substrate just as cancer is, or adaptation is. That's my position actually, mind is a darwinian adaptation of meat. I don't deny for example Bob Murphy's confusion over the debt exists, only that that existence is an aspect of the workings of the brain in his head. No brain no confusion."

12 comments:

  1. Photo-sensitivity can be implemented with old vacuum tube like structures, or with silicon or with organics, and most definitely in biological structures. These physical structures are about as different as can be, and therefore photo-sensitivity must be necessarily something non-physical.

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    1. This is the point where reductionists become willfully stupid. In the cases you cite, there are different physical structures that all happen to display a similar PHYSICSAL property. Can you say name the PHYSICAL property that makes all of these "same" algorithms the same?

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    2. No, Arun, as soon as I answer one silly objection, you throw up another silly objection. I'm sorry, I have no time for that.

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  2. I think you've skipped a few steps in this proof Gene.

    Why aren't these just regularities in material things which, in this case, we've manipulated purposely because we find operationalizing this particular regularity beneficial. How does this prove the sieve is a thing outside our brain's organization of material regularities we've purposefully manipulated?

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    1. "I think you've skipped a few steps in this proof Gene."

      No, it's done exactly right.

      "Why aren't these just regularities in material things..."

      It's fine: if you want to say it is NOT the same algorithm running, then my proof does not work: it is targeted at someone who admits that it is. If you want to say it is the same algorithm but that is only because the same physical process is occurring, then tell what that "same" process is that is common in all of these instances.

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    2. It is the same algorithm. Just like all furry brown things with long tails running around my yard are the "same animal", a squirrel. I don't think I have to assume there is some immaterial squirrel floating around. I just think that's the way my brain (thanks to the taxonomic work of many generations before me) organizes all the material I observe into a single idea so that I can function more efficiently.

      You are not really getting at why it's any different for an algorithm.

      But it this way - a caveman who does not know about computers or algorithms will look at these material things and if you asked him if they were doing the same thing, he would say "no" (assuming sufficiently diverse interfaces... he may say yes under some circumstances). It's a regularity that our brains identify and exploit.

      That seems to undergird what we mean when we say they are the "same algorithm". I don't see how there's anything more than a particular way that we tie certain behavior of the material world together.

      I'm not even a reductionist or a materialist (or put it this way - I'm an agnostic on materialism. I can see why people would go down that road but I'm not sure I have enough information to make that claim strongly), but I don't see your argument here.

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    3. "Just like all furry brown things with long tails running around my yard are the "same animal", a squirrel."

      I'm pretty sure squirrels are grey.

      But in any case, with squirrels I can point you to a wealth of PHYSICAL similarities that make all of these things "squirrels." Just for a start, think of the similarity of their DNA. Their similar physical structure. Their ability to breed.

      "You are not really getting at why it's any different for an algorithm."

      You are doing a fine job of this yourself, by utterly failing to come up with a single PHYSICAL similarity that unites all of the instances implementing the Sieve that I named.

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    4. I would have thought the physical similarity is that they all come up with what brains interpret as the set of primes.

      Just like one apple, one squirrel, and one copy of the General Theory all call to mind the concept of "one", which as far as I know does not have any independent reality except as an organizing concept used by brains.

      Another way of putting it is that if these variously operationalized algorithms didn't come up with something that we could understand as the set of primes we would not recognize it as the algorithm.

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    5. "I would have thought the physical similarity is that they all come up with what brains interpret as the set of primes."

      So you don't actually think it is the same algorithm they are running, except our "brains" happen to interpret it as such. So if my brain thinks my iPad is running a travelling salesman problem, it is! And if your brain thinks a penguin computes all primes, it does!

      And you wonder why I keep throwing up my hands and calling these replies silly.

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  3. I'm not trying to be willfully dense, but I'm not really sure that your analogy proves your point. The systems that you're talking about are really quite complex. Moreover many aspects of computation get tangled up with issues in symbolic representation.

    What about talking about a simpler system like a circle? How does the reductionist account fail? There are some tricky problems here. For example, if someone has never seen a circle, can I teach them what a circle is without showing them one? If the answer is "no", it seems to me that the anti-reductionists are going to have a problem. If you have to show me a circle to teach me what a circle is, then my conception of "circle" is mainly just an association between a pattern on my retina(the image of the circle) and a vibration in my ears(the sound of the word "circle")

    I would argue that my ability to recognize many things as circles that do not project the same shape on my retina comes from the tedious process of learning to see and talk. A parent teaching a child about circles may orient the circle at different angles or distances but still keep saying "circle", I eventually come to associate the term "circle" with a large collection of different retinal projections; a process that takes years, millions of retinal projections, and is fraught with much trial and error.

    That I may see a circle in many different instantiations(patterns on cloth, orbits of planets, ceramic dinner plates) doesn't really speak to universality; other than the fact that every one of those things eventually creates one of those projections on my retina that I associate with the word "circle"; projections derived from my process of childhood learning.

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    1. "If you have to show me a circle to teach me what a circle is, then my conception of "circle" is mainly just an association between a pattern on my retina(the image of the circle) and a vibration in my ears(the sound of the word "circle")"

      Right. And "an association" is not a physical thing!

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    2. And anyway, the whole comment is silly through and through: what anti-reductionist claims we learn all things without experience?

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