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stevestory



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(Permalink) Posted: Dec. 20 2008,09:40   

A thread for Missing Shade of Blue's questions.

   
Zachriel



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(Permalink) Posted: Dec. 20 2008,10:18   

Quote (Missing Shade of Blue @ Dec. 20 2008,01:25)
Consider the predicate grue, which translated into our language, means "green if discovered before 2012, and blue afterwards", and the corresponding predicate bleen, "blue if discovered before 2012, and green afterwards."

Quote (Reciprocating Bill @ Dec. 20 2008,07:09)
[ETA: I see Keiths has touched on this above as well: "Simpler means less expensive. If both systems are functionally equivalent during the evolution of the system, then natural selection will favor the less expensive one."

Exactly. and CURSES, Keiths.]

And complex systems, such as multi-year timers don't typically evolve in the absence of selection, which is clearly not an option for a one-time event. (But if it switched back-and-forth over time, then we might expect adaptation. Like day and night vision, or seasonal variations in behavior.)

More complex systems have a higher likelihood of breakage, causing embarrassing, premature grue, something to be avoided.

The timing system has no reason to be set on 2012 rather than any other time. Each organism might make a different bet. Those with early dates have already gone extinct due to inopportune, awkward bleen.

The best bet based on past experience is no date. Historically, finding a mate and making babies is a better strategy.



But, Missing Shade of Blue, let's take it one step further. There could conceivably be such a timer in the genomes of organisms. The Theory of Evolution would *predict* that no such timer would exist. By finding such a timer, you could overturn the Theory of Evolution. Do you consider this a reasonable career choice for a budding biologist? Or do you think that further investigation, based on all we know of biology, would mean this search would in all likelihood be futile?

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Wesley R. Elsberry



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(Permalink) Posted: Dec. 20 2008,12:54   

Quote (Missing Shade of Blue @ Dec. 20 2008,05:14)
Wesley,

I'm not claiming our inductive biases are perfect, especially when it comes to highly theoretical predicates like "phlogiston" or "caloric".


What, heat transfer is more complex than the chemistry of color perception and cognition?

I don't think so.

But at least we have an agreement that the "none have come to pass" claim was false.

 
Quote

But our folk inductive assumptions about medium-sized dry goods (stuff like shape, sensory properties, causal properties, etc.) works well enough to allow us (and all kinds of other animals) to get by pretty well. And that in itself is surprising to me.


So far, you haven't managed to communicate that surprise in a way that would make it contagious. For those of us with some grounding in the history of science, cognition, and zoology, the claim that perceptual systems represent "inductive biases" requiring supernatural tuning for their effectiveness does not look at all attractive. And I had to choke back quite a bit to make that description more neutral.

 
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The radical Humean skeptic about induction: "Hey, why do you think nature will continue to be so stable and uniform? How do you know Planck's constant won't change tomorrow? Or that your cat won't turn into some kind of evil fire-breathing demon?" This is the kind of thing people make fun of philosophers for.


We know, by induction, that future conditions will change. Populations here are not preparing for Sol's eventual red giant stage of stellar evolution.

 
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Goodman's skepticism is subtly different, and to me far more troubling. It's not "Why do you think nature is, to a large extent, uniform across time?"


But it isn't uniform across time. Paleontology tells us that.

 
Quote

It's "Granted that nature is uniform, what does that mean?" And the answer is that it depends on your choice of vocabulary. What it would be for nature to be uniform is different for creatures with blue-green vs. grue-bleen predilections. Now we were endowed with certain predilections in the distant past, and it turns out that so far, nature has actually been pretty uniform on our preferred descriptions.
Our biases haven't been perfect, sure, but our inductive expectations are very rarely shattered by everyday macroscopic phenomena millions of years after they evolved. And that fact in itself, I suspect, puts them in a set of measure zero in the space of all possible biases.


And 99% or more of all species that have ever lived are extinct. There's plenty of "biases" that didn't pan out over the long term. Keeping this in mind may help prevent cases of Panglossianism.

 
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As yet unobserved conditions or stimuli (as in the "ue" of "grue") are also unavailable to natural selection; why would anybody imagine that natural selection could develop systems corresponding to "grue-bleenism" prospectively?


It seems like the lack of clarity in my initial post has claimed another victim. I hope the response I wrote to Keith makes things a little clearer. The point I was trying to make was that "grue" and "green" are really on the same footing evolutionarily. In particular, "grue" does not involve unobserved conditions or stimuli any more than "green" does.


Sure it does. It requires an observation that color is temporally unreliable. And then there was the other consideration about such "potential biases"...

 
Quote

To suppose otherwise is to assume an asymmetry between the predicates that can only be justified by our inductive bias. And it is the emergence of that very bias that we're trying to explain. Note that the temporally disjunctive aspect of grue and bleen is merely an artifact of their representation in our blue-green basis. If we try to represent blue or green in a grue-bleen basis, then they would appear temporally disjunctive.


"Keiths" already pointed out the issue of simpler representations, a consideration that grounds "an asymmetry between the predicates" and has nothing to do with "inductive biases", making that claim of yours a false one, too. Look up the "universal distribution". This is stuff from algorithmic information theory, if that will help your search.

Something you apparently overlooked from the prior exchange:

 
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Now what confuses me is that it seems that it is basically impossible to come up with an evolutionary explanation for this apparent design.


Since the "apparent design" claim seems to be based on a false premise, it doesn't look like there is a problem in the offing.


The demonstration that "inductive biases" are, in fact, imperfect leads directly to the diminution of the force of the claim that preternatural effectiveness obtains.

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"You can't teach an old dogma new tricks." - Dorothy Parker

    
Missing Shade of Blue



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Joined: Dec. 2008

(Permalink) Posted: Dec. 20 2008,13:38   

Sweet. My own thread.

Thanks for all the responses, guys. A lot to think about, so you'll forgive me if I don't address every point made just yet. But I do think there's still a hint of circularity in some of the arguments I'm seeing.

To boil it down a little, my initial point was that it's hard to come up with an objective notion of simplicity on which blue-green is a simpler set of predicates than grue-bleen. The obvious suggestion would be that grue-bleen is computationally more complex than grue-bleen. To put it crudely, a fully consistent grue-bleen program (one that also gruified other relevant scientific predicates, such as wavelength) would be a lot longer than a blue-green program.

But of course, the algorithmic complexity of a particular problem depends crucially on the structure of the computer. One could construct computers for which the string 1010101010101010.... is simple and predictable. In fact, we ourselves are such computers. But we could also construct weird computers for which this string is quite complex, and the string 110001001000110101011.... is simple. It all depends on what the "natural language" is for the computer, and that depends on how the computer is constructed. Similarly for blue-green and grue-bleen. We happen to be blue-green computers. For us, these are natural and projectible predicates. The world will be simple if blue things stay blue; it will be less simple if blue things change to green at some arbitrary time. But grue-bleen computers, for which the exact opposite is true, are not inconceivable. So a syntactic notion of simplicity doesn't settle the matter.

[I should note here that I tend to prefer an ecological/embodied approach to cognition, so when I refer to humans as computers, I'm not just referring to what goes on in the head, but to a whole host of bodily mechanisms.]

It seems that some of you (keith, Bill, Zachriel) want to move the discussion up a level and talk about the complexity of the computer itself. You argue that while a grue-bleen computer may be possible, it would be far more complex than a blue-green computer and therefore more expensive to construct. Here is where I smell the vicious circle (or its slightly less dreadful cousin, the infinite regress).

If we describe things using our own natural predicates, then it is only to be expected that blue-green computers will turn out to be simpler than grue-bleen computers. After all, we ourselves are blue-green computers. The question is whether there's an objective sense in which blue-green computers are simpler than grue-bleen ones. Here's one suggestion: It takes fewer resources for a Universal Turing Machine to emulate a blue-green computer than a grue-bleen computer. Unfortunately, this doesn't work for the same reasons as before: it depends on the construction of the UTM. We can construct UTMs for which grue-bleen is more natural (and more easily emulated) than blue-green. Again it depends on our choice of description language.

It seems to me that every problem that arises when trying to adjudicate the complexity of the predicates themselves also arises when we move up a level to consider the computers that use the predicates. I hear you saying that grue-bleen systems are complex and more expensive because they require multi-year timers. But of course that is only under the assumptions that our inductive biases are right, that blue/green really are the natural and simplest predicates, that the giant evolutionary UTM is set up to more easily emulate blue-green computers than grue-bleen ones. From a grue-bleen perspective, none of these statements are true. According to them, it is us, the blue-greeners, who require multi-year timers to detect when grue switches to bleen. We are the ones who are more complex.

What I think is needed is a way to break this symmetry without surreptitiously sneaking in our own inductive biases in describing the situation.

  
Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,13:58   

One small correction:

In describing the two binary strings, I shouldn't have put ellipses at the end suggesting they're infinitely long. If they were, then it might well be the case that there is no UTM for which the second string is algorithmically simpler than the first one. Imagine the ellipses merely indicate that the strings are a billion digits long.

  
Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,14:11   

Wesley,

Thanks for referring me to the Solomonoff stuff. This may be the kind I'm looking for. Excuse me for a little while I look through it.

  
Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,14:12   

And by "kind" I mean "kind of thing".

  
keiths



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(Permalink) Posted: Dec. 20 2008,14:40   

MSB,

You're making this way more difficult than it needs to be.

Forget predicates and Turing machines. Let's look again at a simple organism that distinguishes green light from blue, and its counterpart that distinguishes grue light from bleen.

The first organism contains a black box with an opening through which light enters and two signal outputs, G and B. When the organism points the opening at a green object, the G output fires and the B output does not. When it points the opening at a blue object, the B output fires and the G output does not. When it points the opening at a red object, neither output fires.

The second organism has a similar black box, but the outputs are labeled G' and B'. The G' output fires when the black box is pointed at a grue object. The B' output fires when the box is pointed at a bleen object. Neither output fires when the box is pointed at a red object.

Supposing that each of the boxes has the simplest and cheapest possible implementation, what do you find when you look inside the boxes?

The first box (the green/blue box) has a detector (in reality, a pigment) that is tuned to respond to wavelengths in the green range. Its output is connected to the G output of the box. Likewise, there is a second detector tuned to respond to wavelengths in the blue range. Its output is connected to the B output of the box. That's it. Pretty simple, no?

Now open up the grue/bleen box. The simplest implementation that I can come up with for this box employs the same two wavelength detectors, but it needs three additional components: a multi-year timer and two multiplexers.

The multiyear timer has an output T that is inactive before the year 2012 and active thereafter. The multiplexers are arranged so that when T is inactive, the green detector's output is routed to the G' output of the box and the blue detector's output is routed to the B' output. When T is active, the routing is reversed.

Unless you can come up with a simpler design for the grue/bleen box, you have to concede that the blue/green box has on objectively simpler design. Agreed?

One possible gambit would be to use grue and bleen wavelength detectors in place of the blue and green detectors. If you did that, then the high-level designs would be symmetrical: the grue detector would connect to the G' output, and the bleen detector would connect to the B' output.

But all that accomplishes is to push the complexity into the wavelength detectors themselves. Now each detector has its own multi-year timer and mux. The decrease in complexity at the top level is more than offset by the increase in complexity of the wavelength detectors.

So again, can you come up with a design for the grue/bleen box that matches the simplicity of the blue/green box? If not, do you concede that the blue/green box is objectively simpler?

If you do, can you see how the problem of sensing grue and bleen is analogous to the problem of maintaining concepts of grue and bleen?

To return to the computer model, the complexity has to reside somewhere -- either in the program or in the computer itself. Grue and bleen are conceptually more expensive than blue and green.  Predicates have a cost.

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Reciprocating Bill



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(Permalink) Posted: Dec. 20 2008,14:54   

As I see it, the logic of selection itself breaks this symmetry independent of inductive biases.

In your scenario, green-blue and grue-bleen sensory biases are equally adaptive prior to 2012. Both are adept at responding to the pre-2012 blue green world. Moreover, given how crucial vision is to survival, both mechanisms would be sustained over generations by brutal normalizing selection. Prior to 2012, however, only the components of the grue-bleen system that enable functioning in the pre 2012 blue-green world would be subject to that normalizing selection. Those components and/or computational resources - however simple - that would enable continued success after 2012 would not be subject to normalizing selection prior to 2012 and, absent that selection, would deteriorate and become non-functional. Ultimately, in a blue-green world, only creatures with blue-green sensory functioning are predicted by current evolutionary theory.

This solution does not require a potentially arbitrary "complexity" metric with the potential for contamination from our inductive biases. Selection doen't "care about" complexity.

A more fundamental problem with your scenario is your characterization of inductive bias as "forward looking." Evolution is ever and always backward looking: organisms possess the features they do because those features were selected in the past. They were not selected "for" future survival and reproduction; they were selected BY past survival and reproduction. Inductive biases are present because they worked in the past, not because they will work in the future. Once you really wrap your head around this notion, puzzles like this evaporate.

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Zachriel



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(Permalink) Posted: Dec. 20 2008,14:54   

Quote (Zachriel @ Dec. 20 2008,10:18)
But, Missing Shade of Blue, let's take it one step further. There could conceivably be such a timer in the genomes of organisms. The Theory of Evolution would *predict* that no such timer would exist. By finding such a timer, you could overturn the Theory of Evolution. Do you consider this a reasonable career choice for a budding biologist? Or do you think that further investigation, based on all we know of biology, would mean this search would in all likelihood be futile?

Quote (Missing Shade of Blue @ Dec. 20 2008,13:38)
What I think is needed is a way to break this symmetry without surreptitiously sneaking in our own inductive biases in describing the situation.

In science, the way we test for bias is by making empirical predictions that are entailed in our hypothesis. If the predictions for a blue universe and a bleen universe are identical, then your claim is scientifically vacuous. If they are not, then you can make empirical predictions to distinguish between the two views.

Otherwise, your argument has nothing to do with the Theory of Evolution except that it's an argument about scientific induction. If you want to make that argument, then you should first dispense with the distraction about biology.

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Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,15:02   

Wesley,

Based on a preliminary review, I dont think Solomonoff induction addresses my concern here. If I'm correct, Solomonoff induction begins by assuming a particular description language for sequences. It then applies Occam's razor based on this description language: programs with lower algorithmic complexity when written in the chosen language are assigned a higher prior probability. In general, I think approaches that are based on Kolmogorov complexity will have to start with an assumption about the description language. They don't provide a language-independent notion of simplicity.

The question I had is logically prior to this whole process. Which is the appropriate language according to which we conduct our judgments of simplicity? Presumably there is at least one such language that is "natural". This would be the language according to which Occam's razor actually works, i.e. the simplest hypothesis in this language will actually be projectible. [Incidentally, this is what I meant by the uniformity of nature: Not that every single one of predicates is projectible, which would be equivalent to saying that nothing changes, but that a large cluster of our most basic observational and theoretical predicates are projectible, at least in our immediate environment, thus allowing for a myriad of successful inductions.] Now it might turn out that our predicates aren't actually the most natural ones. Come 2012 we might discover that the universe actually prefers grue-bleen.

While I admit this as a theoretical possibility, I am confident this will not happen. What is bothering me (and I guess I'm not able to communicate this concern adequately, but I'll try again) is that I can't give a non-question-begging justification for why I am confident the grue-bleeners will be proved wrong. And by the same token, evolution has no non-question-begging justification (apologies for the excessive anthropomorphization) for its choice of blue-green over grue-bleen or 1912 grue-bleen or 1812 grue-bleen or an infinite number of other possible inductive biases.

I see two sorts of responses here:

1) There is such a non-question-begging justification that involves the greater simplicity of blue-green, or of blue-green computers (humans) or of blue-green computer computers (the evolutionary process itself). In a previous post I said why I don't think this is satisfactory.

2) Our inductive biases are not particularly successful, and in so far as they are, it's just a lucky accident. Think of all the other species that went extinct due to bad inductive biases (the dodo, for instance). I don't find this satisfactory either. While evolution has no doubt sampled a large number of different sorts of inductive biases, and many have proved unsuccessful, it is also true that the number of biases sampled is an infinitesimally small proportion of the total number of possible biases. And yet it managed to hit on ones that have allowed a number of species to survive for millions of years after the respective biases evolved. This seems too improbable to be explicable as a lucky accident. So we should expect that the sampling wasn't random. There was some kind of search mechanism that looked for biases that more or less match the natural structure of the world. What I have been arguing is that this search mechanism could not have been natural selection, because when you lack information beyond a certain point in time, it radically underdetermines your judgments about which predicates are natural.

  
Zachriel



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(Permalink) Posted: Dec. 20 2008,15:09   

Quote (Missing Shade of Blue @ Dec. 20 2008,15:02)
What I have been arguing is that this search mechanism could not have been natural selection, because when you lack information beyond a certain point in time, it radically underdetermines your judgments about which predicates are natural.

No. What you've been arguing is the lack of a solid foundation for induction. Evolution by Natural Selection is just a type of inductive learning.

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Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,15:25   

Zachriel,

Quote
In science, the way we test for bias is by making empirical predictions that are entailed in our hypothesis. If the predictions for a blue universe and a bleen universe are identical, then your claim is scientifically vacuous. If they are not, then you can make empirical predictions to distinguish between the two views.


I agree. Grue and green universes are not empirically equivalent. They are just empirically equivalent up to 2012. But gruers and greeners will make different predictions about what happens after that. Greeners will predict that emeralds discovered post-2012 will be green, which means they will not be grue. Gruers will predict that these emeralds will be grue, which means they will not be grue.

Quote
Otherwise, your argument has nothing to do with the Theory of Evolution except that it's an argument about scientific induction. If you want to make that argument, then you should first dispense with the distraction about biology.


Ultimately, my argument is about scientific induction, viz. that our inductive biases are to a certain degree arbitrary and unjustifiable. But I don't think biology is a distraction here. Our inductive biases serve a certain purpose. They allow us to make inductive inferences well enough to get by. There are many other biases which would, at some point or another, fail at this task. A vast number of them would have failed before now. So here we have a crucial functional aspect of our biology, and usually I look for adaptive explanations for such features of our biology. But for the same sorts of reasons that I think the biases are arbitrary and unjustifiable, I can't see that any adaptive explanation could account for the continued functionality of this bias. I think natural selection is a beautiful theory that accounts (or can potentially account) for every other apparently designed feature of our biology, so this one holdout bothers me.

  
Zachriel



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(Permalink) Posted: Dec. 20 2008,15:36   

Quote (Missing Shade of Blue @ Dec. 20 2008,15:25)

Quote
Zachriel: In science, the way we test for bias is by making empirical predictions that are entailed in our hypothesis. If the predictions for a blue universe and a bleen universe are identical, then your claim is scientifically vacuous. If they are not, then you can make empirical predictions to distinguish between the two views.


I agree. Grue and green universes are not empirically equivalent. They are just empirically equivalent up to 2012. But gruers and greeners will make different predictions about what happens after that. Greeners will predict that emeralds discovered post-2012 will be green, which means they will not be grue. Gruers will predict that these emeralds will be grue, which means they will not be grue.

Or the year 2525. Or 3535. Or 6565. There are an infinitude of equivalent claims. In other words, it is scientifically vacuous.

Quote (Missing Shade of Blue @ Dec. 20 2008,15:25)
Quote
Zachriel: Otherwise, your argument has nothing to do with the Theory of Evolution except that it's an argument about scientific induction. If you want to make that argument, then you should first dispense with the distraction about biology.

Ultimately, my argument is about scientific induction, viz. that our inductive biases are to a certain degree arbitrary and unjustifiable.

Your argument is entirely about induction.

Quote (Missing Shade of Blue @ Dec. 20 2008,15:25)
I think natural selection is a beautiful theory that accounts (or can potentially account) for every other apparently designed feature of our biology, so this one holdout bothers me.

If you accept scientific induction, then we can reasonably say that a bleen universe is a vacuous concept, and we can substantiate the Theory of Evolution. If you reject induction, then we have to start with that.

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Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,16:25   

Keith,

A few thoughts:

1. You'll forgive me if I occasionally continue to use "predicate" and "Turing Machine". It makes things clearer for me to follow. This might be one of the reasons I'm having trouble seeing the arguments here. I might be a bit too inured to thinking in terms of language and representation.

2. Your wavelength detector example is useful. The suggestion seems to be that a blue-green computer is simpler than a grue-bleen computer not on some syntactic notion of simplicity, but according to a simple physical notion of simplicity. A blue-green detector can be constructed with fewer physical parts than a grue-bleen one. Maybe not just fewer. Maybe it's the case that for any grue-bleen detector, one could construct a blue-green detector using a proper subset of the grue-bleen's physical parts.

Here's my response. I'll have to think about the issue some more to figure out what I really think, but here's what I'm thinking right now:

Let's say you describe the physically simplest color discrimination device, say a pigment in a box, and claim its a blue-green detector. The grue-bleener might agree that this device is the simplest, but disagree that it's a blue-green detector. They say it must be a grue-bleen detector. Recall that you and the grue-bleener have different theories of the world, and that's going to affect how you predict this detector will behave post-2012. The blue-greener claims the pigment distinguishes grue and bleen, not blue and green. Now you can use all sorts of physical arguments to try to convince the grue-bleener that the pigment detects blue and green. The grue-bleener will just claim that your arguments are tainted by your use of bizarrely gerrymandered concepts (such as wavelength in nm). He has exactly symmetrical arguments for why the pigment detects grue. Both of your scientific theories are empirically equivalent up to 2012, but they disagree after that. Before 2012 there is no way to decide who's right without reference to our inductive bias.

Now comes the crucial part. We have the detector but we can't establish in a non-question-begging way whether it detects blue-green or grue-bleen. Your choice in this matter will affect how you think the device ought to behave once it has made the detection. If you think blue and green are the natural predicates, you set up the device to say "blue" when it detects 450 nm light. But if you're a grue-bleener you set up the device to say "bleen" under the same circumstances. Importantly, the detection part of these devices are identical. The only thing that differs is the response. Now one of these devices will get things wrong after 2012, depending on which set of predicates is projectible. But until 2012, we cannot say (without consulting our biases) which device is going to get things wrong. If we had a choice between setting up the blue response or the bleen response, we would have no non-biased rational basis to make it.

This is roughly the situation evolution was a long long time ago. Let's say the simplest sort of wavelength (or possible grue-wavelength) detecting machine has been constructed. There is a further decision to be made about the machine's response to these detection events, and this is where the inductive bias of the machine is set. Evolution chose (seemingly arbitrarily) for the responses to be blue-type rather than bleen-type, and this has worked pretty well so far. This is the puzzle.

In the previous discussion physical simplicity is not even a factor, because there is no difference in the detection mechanism. Inductive bias becomes relevant when constructing the response mechanism, and it is not at all obvious to me that blue-type response systems are more easily constructed than bleen-type systems.

  
Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,16:32   

Zachriel,

While I agree that the worry is a general one about inductive learning, I focus on evolution because it is, in our world at least, the mother of all inductive learning systems.

When I construct a learning machine, I endow it with a certain inductive bias. When asked to justify this decision, I can refer back to my own inductive biases. When asked to justify those, I can refer back to evolution's inductive bias. When asked to justify that, I can...?

  
Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,16:44   

On further reflection on keith's argument, it might be the case that there are systems with blue-type responses that are physically simpler than any bleen-type response system. So maybe evolution's particular inductive bias is attributable to the fact that it is easier (given, say, how organic chemistry works) to construct blue-type response systems. But of course, this is not a search strategy, so prima facie it provides no explanation for why the inductive biases embedded in these responses actually match the world into the future.

BTW, it seems like some people still harbor the suspicion that I'm some sort of ID fifth columnist. Maybe I should make it clear that even if my concern is valid and unanswerable (a huge if), this would not mean evolutionary biology should be consigned to the scrapheap of history. It would not affect the fact that natural selection is the best explanation for the majority of our functional traits. It would, however, suggest that the evolutionary story is incomplete if one of our most functional traits, our ability to make more or less accurate inductive inferences, lacks explanation.

Perhaps this is just one of those places where explanation bottoms out, but to me it's a peculiarly unsatisfactory bottom...

  
Zachriel



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(Permalink) Posted: Dec. 20 2008,17:04   

Quote (Missing Shade of Blue @ Dec. 20 2008,16:32)
Zachriel,

While I agree that the worry is a general one about inductive learning, I focus on evolution because it is, in our world at least, the mother of all inductive learning systems.

Science assumes basic induction. You can't discuss the nature of biological evolution without agreeing to the axioms of induction.

There is no absolute foundation for induction. The world may simply end tomorrow. But if you accept the existence of memory (or that we can make and read records), then we can define inductive learning axiomatically. We can even provide a level of "confidence" based in statistics.

You don't have to really think induction is meaningful. Just that when we talk, we agree to the meanings of our words. So, if I say the Sun rises every day in the East, you understand this is a generalization with a high level of confidence (even if you think to yourself that we don't know with certainty that it will continue to do so in the future).

The rest is merely details.

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Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,17:04   

Zachriel,

Quote

Or the year 2525. Or 3535. Or 6565. There are an infinitude of equivalent claims. In other words, it is scientifically vacuous.


Hold on. I agree that the difference between two theories is scientifically vacuous if that difference has no observable consequences. But that doesn't seem to be the notion of vacuity you're using here. What you're doing here is saying that if there are an infinity of empirically distinguishable theories that are all produced using the same sort of schema, then the difference between them is scientifically vacuous. This I don't agree with at all.

The theories make radically different predictions. They are not "equivalent claims" and I don't see why their infinitude matters. What notion of scientific vacuity are you using here?

I will say this. I agree that it is perfectly acceptable for scientists to use their inductive biases to eliminate hypotheses. I'm not challenging the use of Occam's razor in science. Without it, we would constantly be confronted with an infinitude of equally successful hypotheses. I am definitely not attacking this aspect of the scientific method. I agree: "All emeralds are green" is a good theory and "All emeralds are grue" is a bad one.

But there is one area of inquiry in which scientists cannot take their inductive biases as granted. This is when they consider themselves as cognitive systems and attempt to explain their own inductive predilections. It is only in this peculiarly reflexive case that I'm questioning the straightforward use of Occam's razor.

  
Zachriel



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(Permalink) Posted: Dec. 20 2008,17:09   

Quote (Missing Shade of Blue @ Dec. 20 2008,16:44)
On further reflection on keith's argument, it might be the case that there are systems with blue-type responses that are physically simpler than any bleen-type response system. So maybe evolution's particular inductive bias is attributable to the fact that it is easier (given, say, how organic chemistry works) to construct blue-type response systems. But of course, this is not a search strategy, so prima facie it provides no explanation for why the inductive biases embedded in these responses actually match the world into the future.

Induction doesn't work for one time events. As I mentioned, if the world alternated between blue and bleen, then evolution might be able to adapt, just as it adapts to night and day.

Quote (Missing Shade of Blue @ Dec. 20 2008,16:44)
It would, however, suggest that the evolutionary story is incomplete if one of our most functional traits, our ability to make more or less accurate inductive inferences, lacks explanation.

Nothing you have said would indicate that the evolutionary story is incomplete. If we somehow knew that the world was going to bleen tomorrow, it wouldn't change the Theory of Evolution. Unless you could show that organisms had somehow anticipated this one time event. I mentioned this above too.

Do you accept induction?

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Zachriel



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(Permalink) Posted: Dec. 20 2008,17:19   

Quote (Missing Shade of Blue @ Dec. 20 2008,17:04)
Quote
Zachriel: Or the year 2525. Or 3535. Or 6565. There are an infinitude of equivalent claims. In other words, it is scientifically vacuous.


Hold on. I agree that the difference between two theories is scientifically vacuous if that difference has no observable consequences. But that doesn't seem to be the notion of vacuity you're using here. What you're doing here is saying that if there are an infinity of empirically distinguishable theories that are all produced using the same sort of schema, then the difference between them is scientifically vacuous. This I don't agree with at all.

Proposing an infinitude of extraneous possibilities without any empirical justification is scientifically vacuous. It's not a valid induction.

By the way, stop by Callisto on this date in 3535. That's when my invisible pink unicorn becomes visible. It's unicorn mating season, you know.

Quote (Missing Shade of Blue @ Dec. 20 2008,17:04)
But there is one area of inquiry in which scientists cannot take their inductive biases as granted. This is when they consider themselves as cognitive systems and attempt to explain their own inductive predilections. It is only in this peculiarly reflexive case that I'm questioning the straightforward use of Occam's razor.

Nave induction may sometimes have that problem. That's why we have developed the scientific method. But as far as I can tell, we're still stuck on simple induction.

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Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,17:26   

Quote

Science assumes basic induction. You can't discuss the nature of biological evolution without agreeing to the axioms of induction.

There is no absolute foundation for induction. The world may simply end tomorrow. But if you accept the existence of memory (or that we can make and read records), then we can define inductive learning axiomatically. We can even provide a level of "confidence" based in statistics.

You don't have to really think induction is meaningful. Just that when we talk, we agree to the meanings of our words. So, if I say the Sun rises every day in the East, you understand this is a generalization with a high level of confidence (even if you think to yourself that we don't know with certainty that it will continue to do so in the future).

The rest is merely details.


Fair enough. I was hoping my question was a bit more localized than the problem of induction, but on reflection maybe it isn't. Doesn't that leave you with a deep and unsatisfying worry, though? After all, we are just contingent products of a gradual evolutionary process. In so far as we display ostensibly purposive or functional behavior it should be traceable to non-teleological causes. And when I say "it" I mean not just the behavior itself but its apparent purposiveness (excepting exaptations for the moment). In the case of inductive inference the behavior itself may have a non-teleological causal explanation (basically just a record of the particular series of biological changes that led to this set of inductive biases), but the apparent purposivity of the behavior has (and can have) no such explanation. To think otherwise would be tantamount to solving the problem of induction.

This is a troubling state of affairs for me. I guess ultimately we must think our continued ability to make inductive inferences is an exaptation, not an adaptation. If that's the case, what a whopper of a spandrel it is...

  
stevestory



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(Permalink) Posted: Dec. 20 2008,17:29   

Quote (Missing Shade of Blue @ Dec. 20 2008,14:38)
Sweet. My own thread.

Thanks for all the responses, guys.

No problem, William Dembski Missing Shade of Blue.

   
Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,17:32   

Quote

Nave induction may sometimes have that problem. That's why we have developed the scientific method. But as far as I can tell, we're still stuck on simple induction.


Wait what? Are you suggesting that there is some scientific notion of induction that doesn't suffer from the same sorts of foundational problems as naive induction? Or are you just saying (a la Popper) that the scientific method isn't inductive at all?

In both cases, I disagree. I think the best formalization of scientific belief revision would be along Bayesian lines, rather than Popper's hypothetico-deductive approach. And Bayesian reasoning has foundational issues regarding the choice of priors that are basically just technical versions of the problem of induction.

  
Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,17:42   

Quote
Nothing you have said would indicate that the evolutionary story is incomplete. If we somehow knew that the world was going to bleen tomorrow, it wouldn't change the Theory of Evolution. Unless you could show that organisms had somehow anticipated this one time event. I mentioned this above too.

Do you accept induction?


What you regard as a relevant "event" that needs anticipation is conditioned by your inductive bias. Incidentally, the fact that you talk about the world "going to bleen" suggests a minor misunderstanding. The sky is either bleen or blue. If it is bleen it will go from blue to green. If it is blue it will go from bleen to grue. But in the particular example I used it makes no sense to talk of the world going from blue to bleen.

Anyway, here's a way to rephrase your point. I haven't showed that evolution anticipated a switch (or lack thereof) in 2012. True enough. It might not have. What I'm pointing out is that evolution has aparently anticipated an infinitude of events that occurred prior to the present. These events are the lack of switch in color properties at times before now. You may not think a lack of switch is an event, but of course this is only a lack of switch when considered in a particular basis. The fact remains that evolution prepared us not to expect a switch in 1912 or 1812 or 1712... And in each of these cases the evolutionary prediction has panned out.

  
Missing Shade of Blue



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(Permalink) Posted: Dec. 20 2008,17:52   

Quote

No problem, William Dembski Missing Shade of Blue.


Curses. Foiled again.

In all seriousness though, I am definitely not Dembski, and I hope my rhetorical style has not been Dembskiesque (trans: arrogant, dishonest, dismissive and liberally sprinkled with fart jokes). I get the sense that I'm getting on peoples' nerves here. If that is the case, please let me know and I'll stop it. I don't want to be a troll.

I have an honest problem wrapping my head around the origin of inductive bias. My experience talking to theists in the past has been that many of them have explanatory itches that atheists just do not feel compelled to scratch. For instance, "Why is there something rather than nothing?" I just don't see that as something that needs explanation.

Maybe the line of inquiry I'm pursuing here is a similar phenomenon. Maybe there's an explanatory itch here that I find annoying, but this is just an idiosyncratic feature of my psychology.

And in a further pathetic attempt to bolster my non-ID credentials, you should check out my comments at UD. I've been posting there (sparsely) under the pseudonym Sotto Voce. You will notice that all my comments there have been critical. If I am a Dembski sockpuppet, this is quite an elaborate ruse I've got going.

  
stevestory



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(Permalink) Posted: Dec. 20 2008,18:01   

Quote (Missing Shade of Blue @ Dec. 20 2008,18:52)
Quote

No problem, William Dembski Missing Shade of Blue.


Curses. Foiled again.

In all seriousness though, I am definitely not Dembski, and I hope my rhetorical style has not been Dembskiesque (trans: arrogant, dishonest, dismissive and liberally sprinkled with fart jokes). I get the sense that I'm getting on peoples' nerves here. If that is the case, please let me know and I'll stop it. I don't want to be a troll.

Feel free to talk here even if you are Dembski. We don't ban people here.

Actually, I only 50% think you are Dembski. I'd be sure you were Dembski if you acted like a bratty 13-year-old. But you haven't done that here, you've been rather pleasant, so it's up in the air.

Carry on.

   
Zachriel



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Joined: Sep. 2006

(Permalink) Posted: Dec. 20 2008,19:05   

Quote (Missing Shade of Blue @ Dec. 20 2008,17:26)
 
Quote

Science assumes basic induction. You can't discuss the nature of biological evolution without agreeing to the axioms of induction.

There is no absolute foundation for induction. The world may simply end tomorrow. But if you accept the existence of memory (or that we can make and read records), then we can define inductive learning axiomatically. We can even provide a level of "confidence" based in statistics.

You don't have to really think induction is meaningful. Just that when we talk, we agree to the meanings of our words. So, if I say the Sun rises every day in the East, you understand this is a generalization with a high level of confidence (even if you think to yourself that we don't know with certainty that it will continue to do so in the future).

The rest is merely details.


Fair enough. I was hoping my question was a bit more localized than the problem of induction, but on reflection maybe it isn't. Doesn't that leave you with a deep and unsatisfying worry, though?

No. Confidence doesn't require certainty.

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Zachriel



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(Permalink) Posted: Dec. 20 2008,19:11   

Quote (Missing Shade of Blue @ Dec. 20 2008,17:32)

Quote
Missing Shade of Blue: But there is one area of inquiry in which scientists cannot take their inductive biases as granted. This is when they consider themselves as cognitive systems and attempt to explain their own inductive predilections. It is only in this peculiarly reflexive case that I'm questioning the straightforward use of Occam's razor.

Zachriel: Nave induction may sometimes have that problem. That's why we have developed the scientific method. But as far as I can tell, we're still stuck on simple induction.

Wait what? Are you suggesting that there is some scientific notion of induction that doesn't suffer from the same sorts of foundational problems as naive induction?

No, I'm saying the scientific method was developed to minimize the role of bias, such as through the use of multiple observers and other objective measures.

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Zachriel



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(Permalink) Posted: Dec. 20 2008,19:19   

Quote (Missing Shade of Blue @ Dec. 20 2008,17:52)
I have an honest problem wrapping my head around the origin of inductive bias.

I think we have to distinguish between the problem of induction and the problem of inductive bias. Can we accept induction for the purposes of further discussion?

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