Saturday, March 14, 2015

Why some assumptions are better than others

All reasoning has to start from assumptions.  Assumptions by definition can't be proven or disproven. So how can we evaluate our core assumptions?  If we try to use reason, that reasoning must itself be based on some assumptions like, "Reason is the best way to evaluate assumptions."  But since that is an assumption, how can we evaluate it without getting into a infinite regression?

For that matter, how can I be sure that the concepts in my head, which I am here rendering into words, correspond to the concepts that form in your head when you read these words?  How do I know that what I mean when I write, say, "concept" is the same thing that you understand when you read the word "concept"?

Here's how.

I want you to clear your mind for a moment.  Close your eyes.  Take a deep breath.  Then look at the following pictures and their associated captions.

Paka moja

Paka wawili

Paka tatu

Paka nne

Paka wengi

Paka kubwa

mbwa moja

Now I am going to make some predictions:  If I were to ask you, "What does 'paka' mean?" you will reply, "cat."  And if I were to ask you, "What does 'moja' mean?" you will reply "one".  And if I were to ask you, "What does 'wawili' mean?" you will reply "two". And if I were to ask you, "What does 'tatu' mean?" you will reply "three".   And if I were to ask you, "What does 'nne' mean?" you will reply "four".  And if I were to ask you, "What does 'wengi' mean?" you will reply, "many".  And if I were to ask you, "What does 'kubwa' mean?" you will reply "big".

Was I right?  If so, how did I do it?  Here are some possibilities:

1.  I got lucky.
2.  I have a magical ability to predict or control your actions.
3.  God told me.

Now, I am going to tell you that none of those are the right answer.  Of course, just because I tell you that doesn't mean that I'm right.  I could be mistaken, or I could be lying.  But here is what I believe to be the right answer:  I have a model of you that allows me to predict some (but not all) of your behavior.  That model is (to a first order approximation): you are a human.  Because you are a human, your brain is hard-wired to pay attention to certain visual stimuli.  Among those visual stimuli that your brain is hard-wired to detect are the creatures known as "cats" in English, "gatos" in Spanish, "katzen" in German, "chatulim" in Hebrew, and "paka" in Swahili.  The reason your brain is hard-wired to detect cats is that this ability conferred a relative advantage in reproductive fitness to some of your distant ancestors, probably because their feline neighbors were more kubwa than your typical modern nyumba paka.  (And how you know how to say "house" in Swahili.)

Of course, none of this guarantees that you and I mean the same thing when we say or hear the word "cat".  It's possible that the features of cat-ness that my brain cues in on are different than yours, and that some time in the future we will discover that what you mean by "cat" corresponds more to what I mean by, say, "furry".  But that's not likely.  Why?  Because in the little experiment above I not only associated the word "paka" with images of (what I think of when I say the word) cats but also with numbers, and numbers are concepts that go with nouns like "cat" and not adjectives like "furry".  It just doesn't make sense (to me) to say, "one furry, two furries..."  Maybe "paka" means "furry thing".  But that doesn't make sense either because then the last image should have been labelled paka moja too and it's not, it's mbwa moja.  (And now you know how to say "dog" in Swahili.)

Why do I believe that my explanation of my (limited) ability to predict your actions is the correct one?  Because it explains more than the other possibilities.  Consider theory #1, for example.  The odds of my predicting your actions with as much precision as I can by pure luck are indistinguishable from zero.  It's not impossible, but it's extremely unlikely.  And every time I do it it -- every time I interact with (the things that I perceive to be) my fellow humans and get responses from them that make sense out of the myriad possible responses they could produce if they were simply choosing responses at random, it becomes more unlikely.

Theory #2 is not so easily ruled out.  In fact, I cannot prove to you that it's false [1].  So why do I reject it?  Because it lacks explanatory power.  My ability to predict your actions is limited.  I can predict that you will be able to figure out that "paka" means "cat" from examples, but I cannot predict what your favorite flavor of ice cream is.  Again, it's possible that I am lying about this, that I really can predict (or control!) your ice cream choice.  But that just begs the question: are there any limits to my prophetic abilities?  If so, what are they?  If not, why do I not use my omniscience to work my will on people more often?

The fundamental problem with theory #2 is that "magic" is nothing more than a synonym for "mysterious unknown process."  So theory #2 is not really a theory at all, it's an oblique way of punting on trying to come up with a theory.  The whole point of this exercise is to get a handle on my ability to predict the future, and invoking "magic" is essentially saying, "I don't know."  Magic is not a valid theory, not because it's necessarily incorrect (remember, I already conceded that I can't prove that my abilities are not magical), but because it cannot possibly represent progress.  Invoking magic is not an explanation, it's giving up on all hope of finding an explanation.

Theory 3 is even harder to dispense with.  God is not quite the same as magic because God is knowable, at least partially.  So how can I convince you that I am telling the truth when I say that my ability to predict the future is not a revelation from God?

One possibility is to make another prediction: I probably don't have to convince you that I'm telling the truth.  You almost certainly believe me.  In fact, you probably believed that I was not having revelations from God even before I told you.  Your belief was probably so strong that my positing divine revelation as an explanation for the results of the cat experiment seemed like pedantry.

Am I right?  If so, how did I manage that trick?

Why, the same way I managed the first one, of course: I have a model of you.  I have a model of you even though I have no idea who you are!  How did I come by that model?  Through a life-long and on-going process of generating hypotheses, testing them, and discarding the ones that don't fit the facts.  This goes all the way down to hypotheses about what words mean, and which words I can rely on to have the same meaning in your brain as it does in mine (like "cat") and which ones I can't (like "God").

Rationality grounds out in having everything hang together in a way that grants me the gift of prophecy that I demonstrated at the beginning of this post.  No other mental process has that property.  Prayer might grant you inner peace and harmony, but it does not help you build bridges or restore sight to the blind or increase crop yields.  This is not to say that prayer is without value.  Inner peace and harmony are much to be desired.  There is not much value in being able to build an iPhone if your life is a continuous nightmare of existential angst, though improving crop yields and inventing vaccines should not be lightly dismissed either.  It's a lot harder to achieve inner peace if you are sick or hungry than if you are not.

The point is: the apparent infinite regress of rationality bottoms out in its effectiveness, in its ability to confer the gift of prophecy and hence the power to change the world according to one's desires.  That still leaves open the very thorny problem of identifying or selecting those desires.  The hardest part of getting what you want is, very often, figuring out what it is, and in this rationality offers less help, though it does offer some.  I'll explore that in a subsequent post.

---
[1] In the middle ages thousands of people died painful deaths because of the impossibility of proving theory 2 to be false.

38 comments:

Luke said...

> Rationality grounds out in having everything hang together [...]

This is the most interesting part of your comment, to me. Does this mean that 'rationality' has a way of grasping the whole? It would appear that both Aristotle and Bertrand Russell had this sort of idea; compare their words in the first two pages of de Koninck's The Unity and Diversity of Natural Science.

Now, does this mean that 'rationality' has to operate in a 'non-local' fashion? Coherence is not a property of a part, it is a property of the whole. Even if you go all blind men and an elephant, the blind men talking to each other start constructing this holistic picture that then seems to be analyzed, as a whole. You can gather the data bit by bit, but does rationality work by then moving over it only bit by bit, or does it also employ a kind of holistic perspective? The way Aristotle and Russell describe it, there is this holistic perspective.

> Prayer might grant you inner peace and harmony, but it does not help you build bridges or restore sight to the blind or increase crop yields.

This seems suspiciously like failing to credit the lights & sound folks for making a theater production a success. Or to use a better analogy, it sounds like discounting the careful calibration of a scientific instrument, before use of that instrument. But surely, the process of calibration involves truth, just as much as the resultant meter values? Indeed, fail to properly calibrate the instrument—mechanical or human—and the resultant operations may not be sufficiently accurate!

For now I will ignore the idea that thinking has the kind of limited power that you intimate. What I know is that more careful thinking has more power over reality. What the limit of that is, I don't know. We believe an awful lot of falsehoods in modernity; every falsehood believed places limits on the power of thinking. I'm curious about what happens as we eviscerate falsehood after falsehood, being careful to replace them with truth (strictly speaking, we go from 'wrong' → 'less wrong' a lot of the time).

> The point is: the apparent infinite regress of rationality bottoms out in its effectiveness, in its ability to confer the gift of prophecy and hence the power to change the world according to one's desires.

Ahh, but if you have enough power, you can use 'rationality' to define reality such that it is nice and comfy for you. By 'define', I mean that you manipulate others into creating that which you want, such that you didn't so much prophesy as bring into existence. So, to what extent are economists, sociologists, psychologists, and politicians discovering the structure of reality, vs. actively shaping it to their preconceived notions? (In other words: this definition of 'rationality' works much better for the hard sciences than the human sciences.)

Ron said...

> The way Aristotle and Russell describe it, there is this holistic perspective.

You're misinterpreting Russell. Rationality works locally, not holistically. This was not known in Aristotle's time, but Russell was definitely aware of it. The locality of rationality is a consequence of Alan Turing's work on the theory of computation. All computational processes can be emulated by a Turing machine. A Turing machine is the epitome of locality, looking only at a single bit of information at a time. Rationality is a computational process, hence it can be emulated by a TM, hence it is local, not holistic. Russell fully subscribed to this point of view. That's was the whole point of Principia Mathematica.

> the process of calibration involves truth, just as much as the resultant meter values

Sure. Calibration is a big part of what has to all "hang together." This is why experimental science is a profession unto itself. There are people who make their careers figuring out to calibrate things. It is far from trivial.

> For now I will ignore the idea that thinking has the kind of limited power that you intimate.

Excuse me??? When did I intimate that thinking has limited power? To the contrary, thinking is extremely powerful. Thinking is, quite possibly, the ultimate power in the universe.

> Ahh, but if you have enough power, you can use 'rationality' to define reality such that it is nice and comfy for you. By 'define', I mean that you manipulate others into creating that which you want, such that you didn't so much prophesy as bring into existence.

You and I seem to have very different ideas of what it means to "define" something. Yes, of course, those with power can use that power to manipulate their environment, including the people in that environment, to better suit them. (I nominate the Koch brothers as the contemporary poster children for this phenomenon.)

So?

> this definition of 'rationality' works much better for the hard sciences than the human sciences.

It's not the *definition* that works better, it's *rationality itself* that is easier to apply to the physical sciences than the social sciences. But that's just because the social sciences study the behavior of human brains, which are the most complicated things in the known universe. It's hardly surprising that studying complicated things is harder, and progress is slower, than studying simple things. That is hardly an indictment of rationality.

Tau Comini said...

Assumptions by definition can't be proven or disproved.
I think this is not completely correct. It is true that some assumptions can be neither proved or disproved, in math one calls these axioms, like the axiom of choice. The remaining assumptions fall into three sets: ones that can be proven to be true as (a logical) consequence of one or more axioms, ones that can be proven to be false because of the violation of an axiom, and finally ones that cannot cannot neither be proved nor disproved (Gödel's incompleteness theorems assure, there are always can be such assumptions, but then again such assumptions mostly can be shown to be an equivalent of an axiom, i.e. the Zorn lemma).
I agree with how you finish the post, is is a matter of efficiency. Most of the time the information about some topic is limited prohibiting a direct assessment of whether the corresponding assumption is true of false. That is why instead of giving up completely we instead calculate the likelihood of an assumption being true. Occam's razor is then a natural consequence: Because we are not trying to build a complete model, but an approximation of reality to the extent of a distinct scale of understanding, everything that does not act on that same scale cannot likely contribute to the probability of an assumption being true or not. This is also the reason why, while the "god assumption" cannot be disproved, it can still can be shown to be likely false on any scale of understanding.

Luke said...

> You're misinterpreting Russell. Rationality works locally, not holistically.

Russell was speaking of breaking wholes into parts, was he not? Are you perhaps arguing that there are ultimate atoms† of the proper type for the ontological category of thought?

I wonder what you're even denying, by saying that rationality does not work 'holistically'. It strikes me as obvious that the individual letters in 'whole' don't mean what the entire word means. And so, human reason must be able to look at the whole of W-H-O-L-E in order to capture the idea.

> Rationality is a computational process, hence it can be emulated by a TM, hence it is local, not holistic.

When it comes to QM, the slightest nonlinearity in time-evolution of quantum state would majorly falsify it. Is there some analog of this, when it comes to falsifying this model of rationality? You've thrown out figuring out Chaitin's constant, but that seems like a kind of falsification which isn't in the spirit of Popper's The Logic of Scientific Discovery. Popper argues that we should look for ingenious examples of falsification; figuring out Chaitin's constant seems 'outrageous', in a way.

Does the uncomputability of Kolmogorov complexity every bother you? (more) You seem to predicate some of the operation of reason on the ability to either compute K, or some approximation of K. But perhaps you just haven't been precise enough about what you meant and how you are using K?

† I will note, from Russell's Logical Atomism, that Russell did not require there to be atoms. See, for example:

>> Russell concluded that even if there are no ultimate simples, no fundamental layer of reality that analysis can in principle reach, this does not invalidate analysis as a philosophical procedure.

Luke said...

> Excuse me??? When did I intimate that thinking has limited power? To the contrary, thinking is extremely powerful. Thinking is, quite possibly, the ultimate power in the universe.

You said that prayer does not do various things.

> You and I seem to have very different ideas of what it means to "define" something. Yes, of course, those with power can use that power to manipulate their environment, including the people in that environment, to better suit them. (I nominate the Koch brothers as the contemporary poster children for this phenomenon.)

Point of clarification: Do you use the term 'reality' to refer to only one ontological category?

> It's not the *definition* that works better, it's *rationality itself* that is easier to apply to the physical sciences than the social sciences.

Can you differentiate 'rationality' from 'intelligibility'? We've once again hit that point where I really don't know what you are denying by the term 'rationality'. Obviously you are denying certain flat-out incoherence, although you are almost certainly ok with the fact that GR and QFT meaningfully contradict each other near black holes. Surely you know that we cannot always be 100% sure of the premises of arguments in complex situations, such that the correctness of reasoned-to conclusions is not guaranteed.

So, I obviously have a vague idea of what you mean by 'rationality', but not a precise one. I don't know what it is you are truly ruling out of possibility. Perhaps it would be helpful to reference The Incommensurability of Scientific Theories, and point out that this involves the crucial fact that there is "no common measure" between two ways of thinking about reality. Advanced by Kuhn and Feyerabend, the very idea challenged "the rationality of natural science". So, for example, Paul Feyerabend was ostracized from his field upon publishing Against Method. He threatened the very idea of rationality. And yet, his criticism has been accepted; for example:

>>     A deeper difficulty springs from the lesson won through decades of study in the philosophy of science: there is no hard and fast specification of what 'science' must be, no determinate criterion of the form 'x is science iff …'. It follows that there can be no straightforward definition of Second Philosophy along the lines 'trust only the methods of science'. Thus Second Philosophy, as I understand it, isn't a set of beliefs, a set of propositions to be affirmed; it has not theory. Since its contours can't be drawn by outright definition, I resort to the device of introducing a character, a particular sort of idealized inquirer called the Second Philosopher, and proceed by describing her thoughts and practices in a range of contexts; Second Philosophy is then to be understood as the product of her inquiries. (Second Philosophy: A Naturalistic Method, 1)

Thoughts? Do you simply disagree with Maddy? You like this form of argument, so I will tell you that if you can show her to be wrong about her "no determinate criterion", you could become famous in the philosophy of science. And yet, your EE&R does seem to be a "determinate criterion". Comments?

Ron said...


> I wonder what you're even denying, by saying that rationality does not work 'holistically'.

I was addressing this question:

> does this mean that 'rationality' has to operate in a 'non-local' fashion?

The answer to that question is definitively: no. It doesn't have to. (Of course, it *can*. Many computations can be parallelized. But it doesn't *have* to.)

> Is there some analog of this, when it comes to falsifying this model of rationality?

Of course: the exhibition of some process that could reasonably be considered "rational" that could not be emulated by a Turing Machine.

> You've thrown out figuring out Chaitin's constant

No, I have simply pointed out that Chatin's constant is provably uncomputable. But read my words carefully: to falsify the claim that rationality is computational you have to exhibit a rational *process* that can't be emulated by a TM, not simply an uncomputable *result*. The existence of uncomputable numbers (which has been known since 1936) does not falsify the Church-Turing thesis.

> Does the uncomputability of Kolmogorov complexity every bother you?

No. Why should it? To the contrary, I think it's kind of cool. It means that we can never know if we've reached the end of the process of optimizing our models, and so we will never have an excuse for intellectual complacency. I think that's a good thing.

> You seem to predicate some of the operation of reason on the ability to either compute K, or some approximation of K. But perhaps you just haven't been precise enough about what you meant and how you are using K?

No, I don't assume that K is computable (it isn't), merely that it exists (it does).

>> Thinking is, quite possibly, the ultimate power in the universe.

> You said that prayer does not do various things.

"Prayer" and "thinking" are not synonyms. Prayer is (I suppose -- I'm not an expert here) a kind of thinking, but there are many kinds of thinking that are not prayer.

> Point of clarification: Do you use the term 'reality' to refer to only one ontological category?

No, of course not. There are lots of different kinds of reality. There's physical reality, economic reality, political reality... all of these are different ontological categories.

Ron said...


> I don't know what it is you are truly ruling out of possibility

I'm ruling out hand-waving. For example, if you want to *rationally* claim that Jesus turned water into wine then you can't simply say, "It was a miracle." You have to go on and explain what miracles are, why they happen at some times and not others, whether Jesus did it within the bounds of the known laws of physics or whether he was able to suspend the laws of physics, or take advantage of currently unknown laws of physics that, once discovered, will allow us to repeat his feat, or something else. If you want to claim that Jesus was able to suspend the laws of physics then you have to explain why he did it, and more to the point, why he only did it that one time. What was the point? If it was to convince people that He was God, wouldn't it be more effective to do it more than once? (If he wanted people to have faith, why do miracles at all?) Could we perhaps solve the global warming crisis by asking Jesus to suspend the laws of physics and make CO2 not be a greenhouse gas any more (Mat 21:22)?

> you are almost certainly ok with the fact that GR and QFT meaningfully contradict each other near black holes

No, I am absolutely not OK with it. See my comments above about never getting complacent.

> the correctness of reasoned-to conclusions is not guaranteed

Of course it's not. They are almost guaranteed to be wrong. But reasoned-to conclusions are very likely to be less wrong than conclusions generated any other way. That's the best we can do.

> Do you simply disagree with Maddy?

Absolutely. Feyerabend too.

> you could become famous in the philosophy of science

Not me. Popper. And maybe Deutsch. I am simply riding on their coattails.

Luke said...

> Of course: the exhibition of some process that could reasonably be considered "rational" that could not be emulated by a Turing Machine.

Well, there's a lot that humans and animals do that we don't yet know how to do with Turing machines, if they can be done by Turing machines. So it would appear that your claim here is somewhat unfalsifiable, not in principle, but right now. Furthermore, it strikes me that science thrives on theory choice, where there are multiple vying theories and you don't know which one will win. But you don't seem to have much of any theory to truly compete with the Turing machine one. Is this correct?

Perhaps one of the hardest problems is hypothesis formation, which I know you don't know very much about. But I assume that you merely use EE&R—or at least the 'R'—to extrapolate and suppose that one day, Turing machines will do hypothesis formation just fine. Is this the case?

> No, I have simply pointed out that Chatin's constant is provably uncomputable. But read my words carefully: to falsify the claim that rationality is computational you have to exhibit a rational *process* that can't be emulated by a TM, not simply an uncomputable *result*.

What does it mean for a non-algorithmic process to be "rational"?

> No. Why should it?

I was under the impression that you think humans utilize [something like?] Kolmogorov complexity in thinking.

> No, I don't assume that K is computable (it isn't), merely that it exists (it does).

Why is its existence helpful, if we, being Turing machines, can never compute it?

> To the contrary, I think it's kind of cool. It means that we can never know if we've reached the end of the process of optimizing our models, and so we will never have an excuse for intellectual complacency.

But we can't actually know if we're getting closer to K, right?

> > > You and I seem to have very different ideas of what it means to "define" something. Yes, of course, those with power can use that power to manipulate their environment, including the people in that environment, to better suit them.

My understanding is that when folks like Bent Flyvbjerg and James Davison Hunter say that "power defines reality", they mean that power can so heavily determine what happens in reality and how people view reality that the word 'define' is only the smallest exaggeration. I'm not sure what restrictions the Shrödinger equation puts on politicians doing what they do.

An example of the use of this power has been to convince you that we really can separate into 'religious' and 'secular', with those words being natural kinds instead of confused distortions of reality. You are really quite convinced that this dichotomy is legitimate. Just suppose that it wasn't. It would be power which made you think that it was. If you want we can dive into the specific matter of 'religious' vs. 'secular'; I could even write a guest post, largely drawing on Steven D. Smith's The Disenchantment of Secular Discourse and William T. Cavanaugh's The Myth of Religious Violence: Secular Ideology and the Roots of Modern Conflict.

Luke said...

> I'm ruling out hand-waving.

Honestly, much of your use of the term 'reason' appears to be hand-waving. It is hard to distinguish it from 'intelligibility'. To say that 'reason' can be carried out by Turing machines is definitely an example of 'faith'; TMs cannot come even close to humans in their ability to 'reason'.

> For example, if you want to *rationally* claim that Jesus turned water into wine then you can't simply say, "It was a miracle."

That's fine; I don't think you'll ever find that I have used the term 'miracle' as you are, here. Hume set us back centuries with his definition of 'miracle' as "a breach in the laws of nature". This, even if the concept "laws of nature" is coherent, and if it matches reality as-observed. (I could throw out some quotations from Robert B. Laughlin's A Different Universe: Reinventing Physics from the Bottom Down on this.)

> > you are almost certainly ok with the fact that GR and QFT meaningfully contradict each other near black holes

> No, I am absolutely not OK with it. See my comments above about never getting complacent.

What I meant by "almost certainly ok" is that the bare fact of contradiction doesn't mean that, per the dictates of Reason, you have to throw out GR and/or QFT. Reason can permit certain kinds of contradictions to exist, at least for a time (and that time can be over a century long). This pushes in the direction of asking what Reason truly denies. It allows lacunae in understanding, contradictions, what else?

> But reasoned-to conclusions are very likely to be less wrong than conclusions generated any other way.

Ok; recall that the top-level question in this section was:

> > Can you differentiate 'rationality' from 'intelligibility'?

I'm trying to figure out precisely what it is that you are denying with your 'Reason'.

> > Do you simply disagree with Maddy?

> Absolutely. Feyerabend too.

How do I go about challenging your disagreement? Ostensibly, you used EE&R to come to your conclusion, and nothing from Maddy or Feyerabend has challenged this conclusion. Until I know with enough precision what you mean by EE&R, I don't even know how to challenge it!

Furthermore, it is very odd that Maddy would admit that she doesn't have a rock-solid method for defining 'science' if in fact there was one. She would absolutely love to have a rock-solid method. What I suspect is that your EE&R simply isn't formalizable in the way required for both philosophy or implementation in Turing machines.

> > you could become famous in the philosophy of science

> Not me.

Oh contraire, if you really do have a meaningful method which can solidly define what is 'science' and what is not for all time, then you could indeed become famous. Why are you shying away from this? You love to say that if I could solve X I could win the Field's Medal or Nobel Prize. But when this strategy is turned around on you, you merely demur. That doesn't seem like fair play.

Ron said...

> Well, there's a lot that humans and animals do that we don't yet know how to do with Turing machines, if they can be done by Turing machines. So it would appear that your claim here is somewhat unfalsifiable, not in principle, but right now.

No. You need to read what I wrote more carefully. I didn't claim that everything that humans and animals do is computable. I claimed that *rationality* is computable.

> Perhaps one of the hardest problems is hypothesis formation, which I know you don't know very much about.

How do you know that? I think I know as much about it as the average bear.

> But I assume that you merely use EE&R—or at least the 'R'—to extrapolate and suppose that one day, Turing machines will do hypothesis formation just fine. Is this the case?

No. TMs can formulate hypotheses today. They can't formulate very *good* hypotheses, but that doesn't matter. Science is perfectly capable of dealing with bad hypotheses. In fact, that's kind of the whole point.

(You keep bringing up hypothesis formation and I honestly have no idea why you think it's salient.)

> What does it mean for a non-algorithmic process to be "rational"?

I have no idea. The burden of answering that question is on whoever wishes to argue that rationality is not computable.

> I was under the impression that you think humans utilize [something like?] Kolmogorov complexity in thinking.

They do. So?

> > No, I don't assume that K is computable (it isn't), merely that it exists (it does).

> Why is its existence helpful, if we, being Turing machines, can never compute it?

Because it allows you to formalize Occam's razor.

> But we can't actually know if we're getting closer to K, right?

Not in general, no, but we can in most cases that we care about. We can even get all the way to K. What we can't do is know whether or not we've gotten all the way to K.

Ron said...

> My understanding is that when folks like Bent Flyvbjerg and James Davison Hunter say that "power defines reality", they mean that power can so heavily determine what happens in reality and how people view reality that the word 'define' is only the smallest exaggeration. I'm not sure what restrictions the Shrödinger equation puts on politicians doing what they do.

Well, for example, it will not allow the Koch brothers to avoid the negative consequences of anthropomorphic climate change no matter how much money they spend on propaganda campaigns. Physics trumps everything.

> You are really quite convinced that this dichotomy is legitimate.

Yes. The evidence is overwhelming. Science produces iPhones and antibiotics and atom bombs, religion does not. I honestly don't see how any sane person could doubt that there is a legitimate distinction between religion and secularism.

> Just suppose that it wasn't.

Can't do that. That's like asking me to suppose the earth wasn't round.

> The Myth of Religious Violence: Secular Ideology and the Roots of Modern Conflict.

Even if secularism produced the same deleterious effects as religion (it doesn't, but that much suspension of disbelief I am able to muster) that would still be light years away from showing that there are no legitimate distinctions between the two. That would be like saying that because wars have been fought in the name of both Jesus and Allah that there is no legitimate distinction between them.

> Honestly, much of your use of the term 'reason' appears to be hand-waving. It is hard to distinguish it from 'intelligibility'.

The sentence, "If martians liked cheese then pigs could ride surfboards" is intelligible. But it isn't reasonable.

> To say that 'reason' can be carried out by Turing machines is definitely an example of 'faith';

Nope, it's an example of a falsifiable hypothesis.

> TMs cannot come even close to humans in their ability to 'reason'.

*Existing* TMs can't. That doesn't mean that TMs can't.

A lot is known about what TMs can and cannot do in theory, quite independent of our ability to actually construct them. We know, for example, that a TM can compute if white has a forced win in chess despite the fact that we can't actually build a machine that will compute this.

> That's fine; I don't think you'll ever find that I have used the term 'miracle' as you are, here.

That's true, but miracles are mainstream Christian theology, so I'm not exactly knocking down a straw man here either.

> What I meant by "almost certainly ok" is that the bare fact of contradiction doesn't mean that, per the dictates of Reason, you have to throw out GR and/or QFT.

No, we don't have to throw them out, just as we didn't have to throw out F=ma after Einstein. QM and GR are almost certainly very good approximations to the truth. We have to refine them, not throw them out. Those refinements may well (in fact probably will) involve major conceptual changes, but they will also (almost certainly) have QM and GR as limiting cases.

> How do I go about challenging your disagreement?

Show me evidence that I'm wrong. And I've read "Against Method" so that won't do it.

> Why are you shying away from this?

Because taking the credit for other people's work is wrong. Defining science is a solved problem. (To be more precise, identifying those features of the scientific process that set it apart from other methods humans have tried to use to accumulate knowledge and make it more effective than those other methods is a solved problem. But it wasn't solved by me.)

Luke said...

> No. You need to read what I wrote more carefully. I didn't claim that everything that humans and animals do is computable. I claimed that *rationality* is computable.

Two thoughts:

1. I'm operating under your premise that EE&R is sufficient—that nothing else is required—in order to do science successfully. (If you don't actually hold to this premise, why isn't there a fourth letter?) So, for example, what if hypothesis formation requires intuition that isn't describable as 'Reason'?

2. I'm operating under your belief that the human mind is a Turing machine, or a DFA. Didn't you say something like this? If so, perhaps you could differentiate between "human mind" and "everything that humans... do".

> > Perhaps one of the hardest problems is hypothesis formation, which I know you don't know very much about.

> How do you know that? I think I know as much about it as the average bear.

I've asked you about it several times and didn't get much of anywhere.

> No. TMs can formulate hypotheses today. They can't formulate very *good* hypotheses, but that doesn't matter.

Hypothesis formation is the gold standard of machine learning, and I have from a recent MIT PhD recipient that machine learning doesn't employ much of anything one would possibly call "hypothesis formation". Do you have a different story to tell?

> (You keep bringing up hypothesis formation and I honestly have no idea why you think it's salient.)

For someone who loves idea-ism, I should think fostering better and better hypothesis formation would be quite important.

> > What does it mean for a non-algorithmic process to be "rational"?

> I have no idea. The burden of answering that question is on whoever wishes to argue that rationality is not computable.

Actually, you haven't shown your own idea to be falsifiable unless you can answer that question. You cannot merely assert that your idea is falsifiable, you have to show it.

> > I was under the impression that you think humans utilize [something like?] Kolmogorov complexity in thinking.

> They do. So?

How do they do this? Is there a part of cognition which is stronger than Turing machines?

> Not in general, no, but we can in most cases that we care about. We can even get all the way to K. What we can't do is know whether or not we've gotten all the way to K.

Do please tell me how you can rationally measure how close or far away you are from K.

Luke said...

> Well, for example, it will not allow the Koch brothers to avoid the negative consequences of anthropomorphic climate change no matter how much money they spend on propaganda campaigns. Physics trumps everything.

Well, yeah. See "peace, peace when there is no peace" in Jer 6:14, Ezek 13:10, and 1 Thess 5:3. The lesson though, is that an entire nation, or even world, can be caught in a "strong delusion", to take a term from 2 Thess 2:1–12.

> Yes. The evidence is overwhelming. Science produces iPhones and antibiotics and atom bombs, religion does not. I honestly don't see how any sane person could doubt that there is a legitimate distinction between religion and secularism.

I think we need to dig into what that single value is that lies behind EE&R, that you have yet to get around articulating. It's not clear that you have a coherent concept of 'religion' that captures precisely what you want to capture. One can have a concept of 'the good', of what will foster human thriving, without an explicit deity. Do you think 'religion' requires an anthropomorphic deity?

I could also start articulating the employment of human passion in the pursuit of scientific progress, from Michael Polanyi's Personal Knowledge. Generally, passion is seen as a part of religion, and it is often lambasted. Indeed, the whole Enlightenment had an animus toward emotion, one which is still alive today, despite solid science that shows this animus to itself be irrational.

> > Honestly, much of your use of the term 'reason' appears to be hand-waving. It is hard to distinguish it from 'intelligibility'.

> The sentence, "If martians liked cheese then pigs could ride surfboards" is intelligible. But it isn't reasonable.

Some would say that lack of an intelligible causal link reduces the actual intelligibility of this sentence. So, suppose that we take the subset of 'intelligibility' whereby enough people can discern a causal link. How do you differentiate that 'intelligibility' from 'reason'?

> > To say that 'reason' can be carried out by Turing machines is definitely an example of 'faith';

> Nope, it's an example of a falsifiable hypothesis.

You've yet to convince me of this.

> That's true, but miracles are mainstream Christian theology, so I'm not exactly knocking down a straw man here either.

That's fine. There are also a lot of stupid ideas of how quantum mechanics works.

> No, we don't have to throw them out [...]

My point is that 'Reason' can tolerate certain kinds of contradiction. It strikes me as making it more troublesome to actually formally define 'Reason'.

> Show me evidence that I'm wrong. And I've read "Against Method" so that won't do it.

It seems unfair that you are under no obligation to show me how you arrived at your current belief. Furthermore, why must I show you only evidence, instead of examining some or all of the EE&R which led you to this belief?

> Defining science is a solved problem.

Where is the most compact, yet plenty formal, definition of 'science' of which you are aware? I want to email it to Penelope Maddy and ask her why she didn't use it.

Ron said...

> I'm operating under your premise that EE&R is sufficient—that nothing else is required—in order to do science successfully.

It makes the process more efficient if you generate good hypotheses to begin with, but it's not strictly necessary.

> So, for example, what if hypothesis formation requires intuition that isn't describable as 'Reason'?

If you could prove that, it would be a major breakthrough.

> I'm operating under your belief that the human mind is a Turing machine, or a DFA. Didn't you say something like this?

Some processes are more easily modeled as TMs than others. We have a very good account of how reason can be modeled as a TM, not so good an account of other things (like emotions, intuitions). There are still good reasons to believe that these things *can* be modeled as TMs even though we don't yet have any idea how to actually do it.

> Hypothesis formation is the gold standard of machine learning

That's news to me. Who sets these standards?

> machine learning doesn't employ much of anything one would possibly call "hypothesis formation"

That's news to me to, and it seems to contradict what you just said.

Why are you bringing up machine learning all of a sudden?

> For someone who loves idea-ism, I should think fostering better and better hypothesis formation would be quite important.

Why? Idea-ism is a theory of morality. What could that possibly have to do with hypothesis formation?

> Actually, you haven't shown your own idea to be falsifiable unless you can answer that question. You cannot merely assert that your idea is falsifiable, you have to show it.

See this talk by Scott Aaronson to get an idea of some of the challenges involved in falsifying the Church-Turing thesis:

http://www.scottaaronson.com/talks/ect.ppt

(My claim is a weaker version of the CT thesis.)

> How do they do this? Is there a part of cognition which is stronger than Turing machines?

Almost certainly not. (See Scott Aaronson's talk.)

> Do please tell me how you can rationally measure how close or far away you are from K.

I just told you, you can't do that. What you can do in nearly all practical cases is, if you have two theories that make the same predictions, is tell which one is simpler (e.g. ellipses vs epicycles), i.e. which one is closer to K, and so we can tell if we're making progress.

> It's not clear that you have a coherent concept of 'religion' that captures precisely what you want to capture.

My definition of religion is the acceptance of claims on faith, i.e. without evidence. And many religious people I've spoken with endorse that definition. But if you want to use a different definition I'm happy to oblige. I don't want to quibble too much over terminology.

> My point is that 'Reason' can tolerate certain kinds of contradiction.

There's more than one kind of contradiction? I'm learning all kinds of new things tonight.

> Where is the most compact, yet plenty formal, definition of 'science' of which you are aware?

The Feynman Lectures, Volume 1, Chapter 1:

"The principle of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of scientific truth."

Luke said...

> It makes the process more efficient if you generate good hypotheses to begin with, but it's not strictly necessary.

Ok; why is the "strictly necessary" basis interesting? If you're truly going to pursue idea-ism, surely you will do more than what is "strictly necessary"? Honestly, it sounds like you don't actually care all that much about idea-ism.

> If you could prove that, it would be a major breakthrough.

Well, for a long time scientists were apparently convinced that there wasn't much to discover with regard to hypothesis formation. Here's some Popper:

>> I said above that the work of the scientist consist is in putting forward and testing theories.
>>     The initial stage, the act of conceiving or inventing a theory, seems to me neither to call for logical analysis nor to be susceptible of it. The question how it happens that a new idea occurs to a man—whether it is a musical theme, a dramatic conflict, or a scientific theory—may be of great interest to empirical psychology; but it is irrelevant to the logical analysis of scientific knowledge. The latter is concerned not with questions of fact (Kant's quid facti?), but only with questions of justification or validity (Kant's quid juris?). (The Logic of Scientific Discovery, 7)

I recently emailed an old philosophy of neuroscience prof and he noted that for a long time, philosophers thought there was nothing interesting to say about it, except perhaps for some psychology and sociology. Things are much different now. Indeed, I just bought David Braine's Language and Human Understanding: The Roots of Creativity in Speech and Thought.

> We have a very good account of how reason can be modeled as a TM [...]

Given that TMs can do very little of what humans do in the realm of 'reason', I don't know how you can possibly say that "[w]e have a very good account". You're not using EE&R here, you're using a helluva lot more R than you were even with the Oort Cloud. The R left the EE quite a ways back.

> > Hypothesis formation is the gold standard of machine learning

> That's news to me. Who sets these standards?

> > machine learning doesn't employ much of anything one would possibly call "hypothesis formation"

> That's news to me to, and it seems to contradict what you just said.

> Why are you bringing up machine learning all of a sudden?

I can ask my brother-in-law for details if you'd like. Why am I bringing it up? Because science cannot survive without hypothesis formation. We don't have TMs doing any sort of actual hypothesis formation. And yet you claim that EE&R are sufficient for doing science. Are you including 'hypothesis formation' under one of the E's, and not R?

> Why? Idea-ism is a theory of morality. What could that possibly have to do with hypothesis formation?

You don't see a strong connection between "coming up with ideas" and "hypothesis formation"?

Luke said...

> See this talk by Scott Aaronson to get an idea of some of the challenges involved in falsifying the Church-Turing thesis

I'm glad people are focusing on what is efficiently computable instead of just what they think is possibly computable, given ridiculous resources that we will never have. Other than that, I'm not sure what this says. For example, if real computation is demonstrated, with the measurable result satisfying the Bekenstein bound, does this falsify the Church-Turing thesis?

> > How do they do this? Is there a part of cognition which is stronger than Turing machines?

> Almost certainly not. (See Scott Aaronson's talk.)

See, I just don't have any idea how you can be so confident. How is this confidence not remarkably similar to Lord Kelvin's, in his "Two Clouds" speech?

> > Do please tell me how you can rationally measure how close or far away you are from K.

> I just told you, you can't do that. What you can do in nearly all practical cases is, if you have two theories that make the same predictions, is tell which one is simpler (e.g. ellipses vs epicycles), i.e. which one is closer to K, and so we can tell if we're making progress.

Ahh, point taken. The trick here is that you don't necessarily know if you're approaching some degenerate form of K (say, a local minimum that is far from the global minimum), instead of the actual K. That's probably what I was getting at.

> My definition of religion is the acceptance of claims on faith, i.e. without evidence.

But I thought we just got done with you acknowledging that you do accept some dogma? You said something about "not all dogmas being equal". Perhaps you mean the acceptance of beliefs with no expectation of a connection to reality? This allows one to accept a claim on faith, but with the expectation that one will ultimately be able to test it against reality.

> There's more than one kind of contradiction? I'm learning all kinds of new things tonight.

Yes; the R of your EE&R is clearly ok with some kinds of contradiction (e.g. QFT and GR) and not others. And thus, I say there are at least two kinds of contradiction. Do you really disagree?

> > Where is the most compact, yet plenty formal, definition of 'science' of which you are aware?

> The Feynman Lectures, Volume 1, Chapter 1:

> "The principle of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of scientific truth."

Do you interpret Feynman as meaning "scientific knowledge" by "knowledge"? And are statements about what constitutes scientific knowledge, themselves "scientific knowledge"? It's not clear how I can test this particular knowledge-claim via science. I sense some ontological category discussion coming as a response to this.

Ron said...

> > It makes the process more efficient if you generate good hypotheses to begin with, but it's not strictly necessary.

> Ok; why is the "strictly necessary" basis interesting?

Because if it were strictly necessary it would matter more.

> If you're truly going to pursue idea-ism, surely you will do more than what is "strictly necessary"? Honestly, it sounds like you don't actually care all that much about idea-ism.

You keep conflating science and idea-ism. They are not the same thing. Science is a process for discovering truth. Idaa-ism is a system of morality. Not the same thing.

> Well, for a long time scientists were apparently convinced that there wasn't much to discover with regard to hypothesis formation.

No, it's not that there's not much to discover (there obviously is), it's that the business of conducting science does not depend on discovering these things. If (when) we discover how hypothesis formation works that will be great because then we can build machines to help us do it more efficiently, but in the meantime we can still make progress, it just happens more slowly.

> Given that TMs can do very little of what humans do in the realm of 'reason', I don't know how you can possibly say that "[w]e have a very good account".

Because it's simply not true that TMs can do "very little of what humans can do." They can do a lot, and the range of what they can do keeps expanding. They can do math. They can play chess. They can play Jeopardy. And we've only been building TMs for a few decades. And the pace of progress is accelerating.

In fact, it is getting harder and harder to find things that humans can do and machines can't, and that is becoming a serious problem because it's getting hard to tell humans from bots.

> science cannot survive without hypothesis formation

That's true, but so what? We have a system that can form hypotheses (human brains) and that's good enough for now. The fact that we don't yet understand exactly how it works is annoying, but not a show stopper. We'll figure it out eventually.

> You don't see a strong connection between "coming up with ideas" and "hypothesis formation"?

Of course there's a connection, but they're not *identical*. Hypothesis formation is a proper subset of coming up with ideas.

Ron said...

>>> How do they do this? Is there a part of cognition which is stronger than Turing machines?
>> Almost certainly not. (See Scott Aaronson's talk.)
>See, I just don't have any idea how you can be so confident. How is this confidence not remarkably similar to Lord Kelvin's, in his "Two Clouds" speech?

Because science *converges*. The more we understand, the more parts of the story we have that hang together, the smaller the range of possibilities for extending that story in ways that continue to hang together, and the more extraordinary the evidence that is required to support radical changes to the story.

The story we have so far is that everything we know, everything we have any reason to care about, consists of configurations of atoms. We have an extraordinarily detailed understanding of the kinds of behaviors that arrangements of atoms are capable of exhibiting. Because of that, I can state with equal confidence that someone claiming to have built a perpetual motion machine is a fraud, and that someone claiming that human cognition can't be modeled by a TM is wrong.

> The trick here is that you don't necessarily know if you're approaching some degenerate form of K (say, a local minimum that is far from the global minimum), instead of the actual K.

It's actually even worse than that. Even if you actually get to K you can't know it. This is one of the most profound mathematical results that no one knows about, and it's also due to Chaitin. See http://www.flownet.com/gat/chaitin.html

>> My definition of religion is the acceptance of claims on faith, i.e. without evidence.
>But I thought we just got done with you acknowledging that you do accept some dogma?

Yes. My dogma is: experiment is the ultimate arbiter of truth. My claim is that this dogma is better because it gives me the gift of prophecy. Go back and re-read the original post.

> Yes; the R of your EE&R is clearly ok with some kinds of contradiction (e.g. QFT and GR) and not others. And thus, I say there are at least two kinds of contradiction. Do you really disagree?

Yes. As I said above, science is emphatically NOT OK with the contradiction between QM and GR. That is the single most urgent problem in physics.

> Do you interpret Feynman as meaning "scientific knowledge" by "knowledge"?

Yes, but it's an open question whether Feynman would admit to the existence of any other kind of knowledge. Alas, we can't ask him any more.

Luke said...

> You keep conflating science and idea-ism. They are not the same thing. Science is a process for discovering truth. Idaa-ism is a system of morality. Not the same thing.

True or false?: the more idea-ism is followed, the more science happens.

> No, it's not that there's not much to discover (there obviously is), it's that the business of conducting science does not depend on discovering these things. If (when) we discover how hypothesis formation works that will be great because then we can build machines to help us do it more efficiently, but in the meantime we can still make progress, it just happens more slowly.

This is only true if that "more slowly" doesn't grind to a halt as the complexity of science increases.

> Because it's simply not true that TMs can do "very little of what humans can do." They can do a lot, and the range of what they can do keeps expanding. They can do math. They can play chess. They can play Jeopardy. And we've only been building TMs for a few decades. And the pace of progress is accelerating.

Oh c'mon, doing 'math' (that is, what is meant by "computers doing math"), chess, and Jeopardy is hardly representative of what is meant by "humans engaging in reason". Can you offer some better examples of this "accelerating"?

> In fact, it is getting harder and harder to find things that humans can do and machines can't, and that is becoming a serious problem because it's getting hard to tell humans from bots.

Seriously? Are we talking completely uneducated humans, here? Let's distinguish between computers getting smarter and humans getting dumber.

> That's true, but so what? We have a system that can form hypotheses (human brains) and that's good enough for now. The fact that we don't yet understand exactly how it works is annoying, but not a show stopper. We'll figure it out eventually.

Oh, I don't doubt that we'll figure it out better and better over time. The question is whether we are warranted in saying that current building blocks in our understanding of reality are likely to be sufficient. You place an awful lot of confidence in our current building blocks, it seems.

As to your "so what?", I find it hard to believe that you can simultaneously hold that (i) we understand very little about hypothesis formation, and (ii) "it's getting hard to tell humans from bots". There seems to be a fundamental contradiction here, unless you wish to assert that very few humans actually do "hypothesis formation". In that case, the problem is that we need to help more and more humans actually do "hypothesis formation".

> Of course there's a connection, but they're not *identical*. Hypothesis formation is a proper subset of coming up with ideas.

My argument was never predicated upon them being identical.

Luke said...

> Because science *converges*. The more we understand, the more parts of the story we have that hang together, the smaller the range of possibilities for extending that story in ways that continue to hang together, and the more extraordinary the evidence that is required to support radical changes to the story.

Do you believe that this is true of the human sciences, right now? For example, do you think that the number of paradigms used in psychology is shrinking? I suggest a look at the table of contents of Luciano L'Abate's Paradigms in Theory Construction (x); you should be able to access it via Amazon's "Look Inside!" feature.

> We have an extraordinarily detailed understanding of the kinds of behaviors that arrangements of atoms are capable of exhibiting.

Was this true before negative index metamaterials were discovered?

> It's actually even worse than that. Even if you actually get to K you can't know it. This is one of the most profound mathematical results that no one knows about, and it's also due to Chaitin. See http://www.flownet.com/gat/chaitin.html

I don't buy your definition of "elegant program", because one could simply design a language that includes a primitive which produces "a given output". It all depends on your "generative model". If you want to generate a richer reality, you'll have a bigger "generative model", and therefore it will probably be able to produce certain outputs with fewer 'symbols', as it were.

> Yes. My dogma is: experiment is the ultimate arbiter of truth. My claim is that this dogma is better because it gives me the gift of prophecy. Go back and re-read the original post.

What experiment, or experiments, show(s) you that "experiment is the ultimate arbiter of truth"? The claim seems circular. What you'd really have to say, it seems to me, is: "experiment is the arbiter of all truths other than this one". That sounds suspiciously like special-pleading, in a way that is ugly, not just in a way that is necessary for e.g. bootstrapping. But hey, maybe that's just how it seems to me.

What you do remind me of is the "meaningfulness criterion" of logical positivism. That also has this special-pleading aspect, and that philosophy is "dead, or as dead as a philosophical movement ever becomes", per John Passmore.

> Yes. As I said above, science is emphatically NOT OK with the contradiction between QM and GR. That is the single most urgent problem in physics.

But then I can say I'm "NOT OK" with the apparent contradiction of the Trinity, and thus expect to come up with better and better conceptions of it which are less contradictory. My point is that the mere existence of a contradiction doesn't mean you have to throw out the contradictory bits.

> Yes, but it's an open question whether Feynman would admit to the existence of any other kind of knowledge. Alas, we can't ask him any more.

Then I will simply point out that this definition of "scientific knowledge" could be shown to be less effective at further exploring reality than some other definition. Or is this incorrect?

Ron said...

> True or false?: the more idea-ism is followed, the more science happens.

True. But it's important to note that it's not a zero-sum game. The more idea-ism is followed the more art and (certain kinds of) religion happens too.

> This is only true if that "more slowly" doesn't grind to a halt as the complexity of science increases.

Yes, that's true. But the pace of progress isn't slowing down, it's accelerating. (The failure to make progress in unifying QM and GR is an outlier.)

> Can you offer some better examples of this "accelerating"?

Nope. If the fact that we've gotten this far in less than 100 years isn't enough to convince you that we are converging rapidly on real AI then we'll just have to agree to disagree until we get more data.

> Seriously?

Yes.

> Are we talking completely uneducated humans, here?

Nope. Ken Jennings and Gary Kasparov were pretty well educated.

> The question is whether we are warranted in saying that current building blocks in our understanding of reality are likely to be sufficient. You place an awful lot of confidence in our current building blocks, it seems.

No, I place a lot of confidence in one meta-building-block: EE&R. And I put my confidence in it because it gives me the power of prophecy.

> I find it hard to believe that you can simultaneously hold that (i) we understand very little about hypothesis formation, and (ii) "it's getting hard to tell humans from bots". There seems to be a fundamental contradiction here, unless you wish to assert that very few humans actually do "hypothesis formation"

Why? Our understanding of hypothesis formation is improving, and as it does it gets harder and harder to design captchas. Eventually we'll need to resort to blade-runner-style Turing tests to tell them apart, if we can tell them apart at all (or if we even care about telling them apart at that point).

I really don't see the problem.

Ron said...

> Do you believe that this is true of the human sciences, right now?

Yes.

> For example, do you think that the number of paradigms used in psychology is shrinking?

I have no idea. But it's important to note that it doesn't converge *monotonically*, it just converges *eventually*.

> Was this true before negative index metamaterials were discovered?

Yes. NIMs are not really new physics, they're just a previously unrealized consequence of previously known physics. Just like the blue LED.

> I don't buy your definition of "elegant program"

It's not my definition, it's Chaitin's. And "elegant program" is simply a synonym for a program whose size is equal to the Kolmogorov complexity of the function computed by that program.

> because one could simply design a language that includes a primitive which produces "a given output".

No, you can't. This is a really crucial point to understand, and it probably deserves its own blog post. Kolmogorov complexity is defined with respect to a particular computational model, but because computation is universal you can also define the Kolmogorov complexity of the computational model itself.

Remember back when Publius argued that pi was proof of the existence of God because you could find little snippets of messages buried inside it? In fact, if pi is normal (which has not been proven but it very likely true) then somewhere in the decimal expansion of pi is an encoding of the entire Bible. Does this prove that God exists? No. Because pi also contains the Quran and the Book of Mormon and Dianetics and Hamlet and every other book that has ever been written or could ever be written (that's what "normal" means). Moreover, to specify *where* in pi you would find the Bible you would need about the same number of bits as it would take to encode the Bible. So yes, you can create a computational model where any given function can be encoded in a single bit. But then the Kolmogorov complexity *of that model* would be the same as the Kolmogorov complexity of the one function you chose to encode as one bit.

>> Yes. My dogma is: experiment is the ultimate arbiter of truth.
> What experiment, or experiments, show(s) you that "experiment is the ultimate arbiter of truth"?

There are no such experiments. That's why it's a dogma.

> But then I can say I'm "NOT OK" with the apparent contradiction of the Trinity,

Splendid! Do you in fact say this? Because this sort of discontent is the first step towards progress.

> Then I will simply point out that this definition of "scientific knowledge" could be shown to be less effective at further exploring reality than some other definition.

Of course it *could* be. But it *hasn't*, at least not yet. Demonstrating a more effective definition would be the biggest breakthrough in human knowledge ever.

Luke said...

> Luke: But I thought we just got done with you acknowledging that you do accept some dogma?

> Ron: Yes. My dogma is: experiment is the ultimate arbiter of truth. My claim is that this dogma is better because it gives me the gift of prophecy. Go back and re-read the original post.

Hold on a second. If all observation is theory-laden, something to which I recall you agreeing, then that actually isn't your only dogma. True, or false?

Ron said...

I'm pretty sure it's false. What other dogmas do you think I have?

Luke said...

> I'm pretty sure it's false. What other dogmas do you think I have?

If all observation is theory-laden, then by definition you have dogmas other than the one you identified. How can this not be true?

I can't necessarily identify those other dogmas, but if the growth of knowledge requires a nucleus that is a pre-interpretation of reality (e.g. not formed by evidence), then that nucleus constitutes dogma you hold to, unless you've completely moved away from that nucleus. Apparently there's evidence that we are pre-programmed to believe in the mechanical philosophy, in the sense that we think all cause is cause-by-contact. Both Noam Chomsky and Evan Fales† have noted this, based on research done on infants. And yet, how could one come to believe that the mechanical philosophy is false, if one assumes (by dogma) that the mechanical philosophy is true? This isn't a trivial problem!

† author of Divine Intervention: Metaphysical and Epistemological Puzzles, with whom I have emailed

Ron said...

> If all observation is theory-laden, then by definition you have dogmas other than the one you identified.

Not by my definition of dogma: "a principle or set of principles laid down by an authority as incontrovertibly true."

> How can this not be true?

Because I don't claim that my observations are incontrovertibly true. To the contrary, I explicitly allow for the possibility that some of my observations may be wrong.

> I can't necessarily identify those other dogmas

Maybe that's because they don't exist :-)

Luke said...

> Not by my definition of dogma: "a principle or set of principles laid down by an authority as incontrovertibly true."

Ok, let's pick a weaker word, for simply those beliefs which never get questioned. We might need to dabble with "successfully questioned"; I'm not sure. See, if you are born assuming critical aspects of the mechanical philosophy, who says you can ever escape those aspects via reason? If you use the mechanical philosophy to judge something true or false, how would you come to believe that there is a better option? Only if you could suddenly use a different set of beliefs to judge things. But if the mechanical philosophy beliefs have influenced all the other beliefs, removing them may not be possible.

> Because I don't claim that my observations are incontrovertibly true. To the contrary, I explicitly allow for the possibility that some of my observations may be wrong.

You can throw out crazy options for falsification that are not in the spirit of what Karl Popper meant when he sketched out what scientific falsification is, in The Logic of Scientific Discovery. You do realize that there are unreasonable types of falsification, right?

> Maybe that's because they don't exist :-)

This is only true if the nucleus I mentioned can ever be fully rejected. If it cannot, because of how theory-laden observations are, then a fundamental theory could be presupposed form the get-go, and never be sufficiently questioned.

I'm reminded of Isaac Asimov's Three Laws. Could those exist anywhere else than the core of the decision process of a robot, and do what they were supposed to do? Probably not. Could they be violated? No, otherwise they would entirely fail, except for perhaps a rational expansion, which is law zero. Could they have been added after-the-fact? Probably not.

The nucleus seems to matter quite a lot. If it didn't, that itself could be extremely problematic. The idea that one could be convinced to completely reject the nucleus seems the same as completely rejecting the entire set of beliefs at a future state. You would literally become a different person. (This is probably why in Christianity, the drastic term "born again" is used.)

Ron said...

> those beliefs which never get questioned

Doesn't help. All of my beliefs are open to question.

> successfully questioned

I think what you really mean here is: which of my (current) beliefs can you successfully convince me are not true. That's a higher bar, because my current set of beliefs are the result of a very long filtering process that left nothing but those ideas most consistent with the evidence. As a result, it is indeed difficult to find evidence that challenges my current beliefs. But it does still happen from time to time.

>> To the contrary, I explicitly allow for the possibility that some of my observations may be wrong.
> You can throw out crazy options for falsification

What crazy options? Take a look at this image:

http://r2-store.distractify.netdna-cdn.com/postimage/201409/26/885a15afe0f62056cb581e1dbec3e045.gif

When I look at that image I see motion. It is as obvious to me that that image is moving as it is that the sky is blue. And yet the fact of the matter is that image is static, and my observations are wrong. Coming to this conclusion is no trivial matter. In fact, it is so non-trivial that I can't describe it here in a blog comment. It won't fit. Instead I am going to make two more predictions: 1) you also see motion in that image and 2) I don't have to convince you that the motion is an illusion. You already believe it.

> a fundamental theory could be presupposed form the get-go, and never be sufficiently questioned

You have completely missed the point of the original post. The reason I can confidently say that the first image in the post is a picture of a cat is not because the proposition that this is true is not open to question, it's because the tentative conclusion that it is a picture of a cat is part of a very extensive story that hangs together and gives me the gift of prophecy. It may well be the case that it is not a picture of a cat, and that there is some other reason that I can make accurate predictions about it. I am open to that possibility. But if you want to challenge the (tentative) claim that it is is a picture of a cat then the burden is on you to actually produce such a story, and that story has to account for the fact that I have this rather uncanny ability to make accurate predictions.

Luke said...

> Doesn't help. All of my beliefs are open to question.

I'm not sure you can know this to be true. Again, if all observations are theory-laden, then we can ask whether that theory is arbitrarily revisable. This is not a trivial question. Whenever you make a judgment, you are relying on part of your belief system. Part of your belief system goes entirely unquestioned during the process of issuing a judgment. I can easily see beliefs underpinning judgments never being open to actual questioning.

Do you not buy this model? Do you think that no matter what errors creep into your belief system, you'll always have the resources to correct them, from within that belief system? (You evaluate all new beliefs by your current belief system.)

> I think what you really mean here is: which of my (current) beliefs can you successfully convince me are not true.

No. Instead, I look for whether you think your beliefs get fuzzy anywhere—known to be valid in this domain because of empirical evidence, but iffier as one heads away from known territory—or whether they appear to be correct everywhere. Oftentimes, you speak as if they're probably correct everywhere, or at least that this is a good method. I, on the other hand, am constantly looking for how my extrapolations might be wrong, how the inner workings I am positing as a generative mechanism might be different, etc. This seems to be a very different way of looking at reality. Incidentally, it seems to be a good way to charitably interpret what others said, instead of e.g. get stuck because I am holding the definition of one word in too brittle a fashion.

> What crazy options?

An example of a crazy option would be more-than-TM-powerful thinking would be evidenced by demonstration of a process whereby an uncomputable number is found. What is crazy is that you couldn't find something less-extreme as the first indicator that perhaps your TM model of human cognition might not be right. But perhaps it is my fault for using 'falsification', instead of "that which would start you questioning current models". The idea I'm getting after is whether you're trying to figure out how you might be wrong, and what the earliest indicators of that would be.

> Take a look at this image

I honestly don't find the image thing all that impressive. All you're doing is assuming that I am like you in some reliable ways. Honestly, I've had enough of people assuming I am like them in unreliable ways, and there are many of those ways, because people are actually quite different from each other in important ways that are often ignored. People don't like to admit where their models of reality get fuzzy and uncertain. They don't remain bound by the evidence.

> You have completely missed the point of the original post. The reason I can confidently say that the first image in the post is a picture of a cat is not because the proposition that this is true is not open to question, [...]

But I never disagreed upon the phenomena; I was talking about "fundamental theory". It seems like you need to [re]read my phenomenological matching vs. ontological matching.

Ron said...

>> Doesn't help. All of my beliefs are open to question.
> I'm not sure you can know this to be true.

I don't know it to be true. It might not be true. Like all my beliefs, it is open to question.

> Part of your belief system goes entirely unquestioned during the process of issuing a judgment.

Of course. Being *open* to question doesn't mean that I am constantly questioning all of my beliefs. I'd be mentally paralyzed if I did that.

> I look for whether you think your beliefs get fuzzy anywhere

Of course they do. There are vastly more things that I don't know than things that I do.

> demonstration of a process whereby an uncomputable number is found.

What do you mean by "found"? We already know the *definitions* of several uncomputable numbers. Do you mean "finding" their *values*? How exactly would that happen?

> The idea I'm getting after is whether you're trying to figure out how you might be wrong, and what the earliest indicators of that would be.

I'm constantly trying to figure out if I'm wrong. And I often am. (But not nearly as often nowadays as I used to be.)

> But I never disagreed upon the phenomena; I was talking about "fundamental theory".

I don't know what you mean by "fundamental theory." I have the gift of prophecy, and a story to tell about how I acquired it. If you have a better story, let's hear it. Otherwise. ipso facto my story is the best one we have. That doesn't mean it's *right*, it just means that it's the best until something better comes along. That's the best we can do.

Publius said...

You have some other (unstated) assumptions:
1. Other people have minds. A part of the subject-object problem.
2. Minds can be used to model other minds. [1]
3. Materialism.
4. Progress and effectiveness are ... good?

The Feynman Lectures, Volume 1, Chapter 1:

"The principle of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of scientific truth."


Whoa - if that is your definition of science, then a lot of "science" gets thrown out, as there are no "experiments". Say, theories on the formation of the Earth (a one-time event) and archaeology. Large chunks also get subtracted from zoology and biology.

Luke> This is only true if that "more slowly" doesn't grind to a halt as the complexity of science increases.

Yes, that's true. But the pace of progress isn't slowing down, it's accelerating. (The failure to make progress in unifying QM and GR is an outlier.)

But it has to stop at some point, due to human limitations, doesn't it? Could a human understand a proof that spanned 1 million pages? 1 billion?

Shinichi Mochizuki published a 500 page proof in 2012 of the abc conjecture. So far, verification of the proof has been very slow and perhaps no mathematician will devote the time necessary for verifying it.

My definition of religion is the acceptance of claims on faith, i.e. without evidence. And many religious people I've spoken with endorse that definition. But if you want to use a different definition I'm happy to oblige. I don't want to quibble too much over terminology.

I would make that "without scientific evidence." There are other forms of evidence - testimonial, personal knowledge, etc.

Remember back when Publius argued that pi was proof of the existence of God because you could find little snippets of messages buried inside it?

Hey, it was your hypothesis. I simply provided the proof - not only for pi, but for e as well! And we all know that exp(pi*i) +1 = 0, so that's the alpha and the omega. ;-)

It's a lot harder to achieve inner peace if you are sick or hungry than if you are not.

Even in good health and hunger fully satiated, people have trouble finding inner peace. Increased wealth can actually bring on more angst, as one has the leisure time to think of things to be offended by.

[1] Autism can be described by the inability to "virtualize the brain" - that is, using one's the brain to simulate another person's brain. This leads to socialization problems - which can be overcome by learning social rules.

Ron said...

@Publius:

> You have some other (unstated) assumptions:
> 1. Other people have minds. A part of the subject-object problem.

No, that's not an assumption, it's a conclusion. And there is overwhelming evidence to support it.

> 2. Minds can be used to model other minds. [1]

Again, there's a lot of evidence that this is true. In fact, that was the WHOLE POINT of the original post. (Sorry to yell, but it does get a little frustrating some times when I go to a lot of effort to present evidence for X only to have someone say, "But you're assuming X.")

> 3. Materialism.

I don't know what you mean by that. At the very least, an assumption must be a complete sentence.

> 4. Progress and effectiveness are ... good?

No, I don't assume this, I conclude it. The argument goes: I believe that life is good, and so hunger and disease are bad (because they destroy life) and so progress and effectiveness are good because (among other things) they can reduce the incidence of hunger and disease. And even my working assumption that life is good isn't really a dogma, it's a consequence of the fact that I'm alive, and believing that life is good provides incremental reproductive fitness over existential despair. It's a prejudice hard-wired into my brain by evolution. I've said it before: I'm a life bigot. (BTW, I didn't invent that phrase. I heard it from a planetary scientist whose name I can no longer recall when he was asked about the ethics of teraforming Mars.)

> Whoa - if that is your definition of science, then a lot of "science" gets thrown out, as there are no "experiments". Say, theories on the formation of the Earth (a one-time event) and archaeology. Large chunks also get subtracted from zoology and biology.

That's not true. My own birth was a one-time event too, but I can still provide a lot of experimental evidence that demonstrates that it happened.

In fact, *every* event is a one-time event. You can never precisely reproduce the circumstances of even the most rigorously controlled experiment.

[cont'd...]

Ron said...

> But it has to stop at some point, due to human limitations, doesn't it? Could a human understand a proof that spanned 1 million pages? 1 billion?

Not by themselves, no. But one of the wonderful things about humans is that we are not constrained by biology. We build tools. Those tools let us transcend biology. We can fly. We can survive under water and in outer space. And we even build tools that extend the capabilities of our minds, like computers. We already *have* proofs that no human can fully take on board in their own mind, like the proof of the four-color-map theorem.

Not only that, but we use tools to build more tools. Computers used to be designed by hand, but now they are designed by computer. No human can possibly know the full layout of a modern microprocessor chip. So the leverage we get from our tools builds on itself like compound interest. The only fundamental limits to what we might achieve are the amount of matter in the universe and the speed of light. (Actually, entropy matters more than matter, but I don't want to get too technical here.)

>> My definition of religion is the acceptance of claims on faith, i.e. without evidence.
> I would make that "without scientific evidence." There are other forms of evidence - testimonial, personal knowledge, etc.

Hm, that is a very good point. (See, I'm revising my beliefs here.) This, of course, begs the question of what counts as "scientific evidence" because that's an oxymoron. There is no distinction between scientific and non-scientific evidence. Evidence is evidence. So I'm going to have to re-think this.

>> Remember back when Publius argued that pi was proof of the existence of God because you could find little snippets of messages buried inside it?
> Hey, it was your hypothesis

Not quite. I said that what would constitute evidence of God was finding information about Him in a *physical* constant, not a mathematical one.

> Even in good health and hunger fully satiated, people have trouble finding inner peace.

That's absolutely true. Meeting of basic physical needs is neither necessary nor sufficient for inner peace, and excessive wealth can definitely be a spiritual burden. But I do think having your *basic* physical needs met (and not being sick) helps more than it hurts.

Luke said...

@Ron:

> > Part of your belief system goes entirely unquestioned during the process of issuing a judgment.

> Of course. Being *open* to question doesn't mean that I am constantly questioning all of my beliefs. I'd be mentally paralyzed if I did that.

True, but if one part of your belief system is used to judge the others and accept/reject based on its standards, how would shifting the beliefs used to judge not immediately accept the part that used to be doing the judging? It seems like one would quickly establish a kind of coherence such that some 'nucleus' would stay very much in-tact. Then, from then on, as new observations flow in, they will always be tested by this 'nucleus'. And so, it's just not clear to me that this 'nucleus' can necessarily be changed appreciably, based on the kind of new observations one is likely to get. Furthermore, I will yet again cite Grossberg 1999 The Link between Brain Learning, Attention, and Consciousness, which argues that if the pattern in your percepts† do not match patterns pre-existing in your longer-term-then-perceptual-neurons memory, you won't even become conscious of those percepts. This means that if the 'nucleus' doesn't have the ability to detect certain kinds of phenomena, maybe you'll never detect them.

This is very much a "growth of knowledge" question—you see that, right?

† That is, sense data in your perceptual neurons.

> > I look for whether you think your beliefs get fuzzy anywhere

> Of course they do. There are vastly more things that I don't know than things that I do.

All I can say is that I rarely see this fuzziness attributed. I am not sure the last time I have seen you recognize that some model of reality you have is very likely to be accurate in these areas, but may not be so accurate in those areas because you have haven't tested it over there.

> > demonstration of a process whereby an uncomputable number is found.

> What do you mean by "found"? We already know the *definitions* of several uncomputable numbers. Do you mean "finding" their *values*? How exactly would that happen?

Ok this is getting frustrating. How about you repeat what the minimal requirements would be, to get you to start questioning whether the human brain is at most Turing-powerful? You keep not liking my formulations, so how about you try again, at your own, satisfactory-to-you formulation?

> > But I never disagreed upon the phenomena; I was talking about "fundamental theory".

> I don't know what you mean by "fundamental theory."

Read phenomenological matching vs. ontological matching, please. Then, agree or disagree on whether multiple of what I am calling 'ontologies' in that Philosophy.SE answer, can generate the same ontology. I mean "fundamental theory" to match up with that kind of 'ontology'; one might also use the term "generative mechanism".

Luke said...

@Ron, try #2:

> Then, agree or disagree on whether multiple of what I am calling 'ontologies' in that Philosophy.SE answer, can generate the same ontology.

Should be:

> Then, agree or disagree on whether multiple of what I am calling 'ontologies' in that Philosophy.SE answer, can generate the same phenomenology.

Publius said...

Checking Off One Item of Evidence of God

Not quite. I said that what would constitute evidence of God was finding information about Him in a *physical* constant, not a mathematical one.

Surely you recall from Maxwell's equations:

magnetic permeability of free space: µ0 = 4*pi×1E-7 V·s/(A·m)

dielectric permittivity of free space: e0 = 8.854 187 817... x 10-12 F/m (farads per meter).

and the speed of light in a vacuum

c0 = 1/sqrt(µ0e0)

Then from Quantum Mechanics we have:

the reduced Planck constant
h-bar = h/(2*pi)
... which is the quantum of angular momentum

and finally

Integral[-inf,+inf] exp(-x^2) dx = sqrt(pi)

[profound pause]

Now let's update your list

Ron's List of Evidence for God's existence:
1. Information found about Him in physical constants

Ron said...

@Publus:

I'm not quite sure what point you were trying to make. Can you be a little more explicit? Were you trying to show that pi can be derived from physical constants?

@Luke:

> All I can say is that I rarely see this fuzziness attributed. I am not sure the last time I have seen you recognize that some model of reality you have is very likely to be accurate in these areas, but may not be so accurate in those areas because you have haven't tested it over there.

What can I say? I mostly write about things I know about, not so much about things I don't.

> Ok this is getting frustrating. How about you repeat what the minimal requirements would be, to get you to start questioning whether the human brain is at most Turing-powerful? You keep not liking my formulations, so how about you try again, at your own, satisfactory-to-you formulation?

The demonstration of any classical (non-quantum) physical process that could not be modeled by a TM.

I don't think you quite appreciate how profound and far-reaching the Universal Turing Machine and the Church-Turing thesis are. Maybe I should write a blog post about it. In the meantime, you can read this:

http://www.scottaaronson.com/democritus/lec4.html

> Read phenomenological matching vs. ontological matching, please.

I did. Several times. I also read the linked-to essay by Pigliucci.

> > Then, agree or disagree on whether multiple of what I am calling 'ontologies' in that Philosophy.SE answer, can generate the same ontology.

> Should be:

> > Then, agree or disagree on whether multiple of what I am calling 'ontologies' in that Philosophy.SE answer, can generate the same phenomenology.

Ah. I was rather scratching my head over that.

So your revised question does make a little more sense than your original, but only a little. "Phenomenology" means (according to http://plato.stanford.edu/entries/phenomenology/) "the study of structures of consciousness as experienced from the first-person point of view." So this question means, "can different ontologies generate the same study of conscious experience." I have no idea.

Did you mean to ask: can different ontologies generate the same *phenomena*? i.e. can two different physical theories generate the same predictions and thus be experimentally indistinguishable? This begs the question of what it means for two theories to be "different". Yes, it is possible for two theories that look very different to produce the same results. The general problem of whether or not two theories are equivalent is undecidable. But I don't know of any actual case that is undecided. It was the case for matrix mechanics and wave mechanics in QM for a while, but it is now known that they are equivalent. (Exactly who proved this and when is a little controversial.)

But since you asked me to read you charitably, I'm going to go out on a limb and take a guess at what you are really trying to get at: the question I *think* you are trying to ask is: does the fact that statistical mechanics doesn't predict phase transitions disprove reductionism? I don't really understand statistical mechanics well enough to give you an authoritative answer, but my guess would be that the answer is no. First, I don't actually know if it's true that statistical mechanics doesn't predict phase transitions. But if it is true, I'd be very surprised if this turned out to be for any reason other than some simplifying assumption made to make the math tractable that turned out to not actually be true. But the honest answer is I don't really know.

I see that someone did write a book about it though:

http://www.amazon.com/Statistical-Mechanics-Transitions-Science-Publications/dp/0198517300

Publius said...

@Ron
I'm not quite sure what point you were trying to make. Can you be a little more explicit? Were you trying to show that pi can be derived from physical constants?

Derived? Pshaw. Pi is woven into the very fabric of the universe - especially if you believe the universe is just made up of bits.