David Berlinski interviews self, calls self "crank"

I started to read one Berlinski book one time. After about a page he was mocking the other kids in Gauss's elementary school who didn't have Gauss's insight. I realized I was reading a book by a creep, and stopped.

The idea that there is out there a physical world which just happens to lend itself to mathematical description has always seemed to me to be incoherent. There is only one world --- the universe, in fact, and it has the essential properties of a mathematical model. For reasons that we cannot even begin to understand, that model interacts with out senses, and so without measuring devices, allowing us to pretty much confirm conclusions antecedently reached by pure thought.

Not excited by Newark, NJ, eh? I guess Professor Berlinski didn't enjoy his time teaching philosophy there (where I had him in an Intro to Philosophy course in Fall of '72).

The problem with Berlinski is that he's really really smart but viscerally feels the need for the NY Times to carry a headline, above the fold, that states: "David Berlinski Is Really Really Smart". At least once a week. Forever.

Unfortunately, it's hard for a peripatetic mathematician/philosopher to make that kind of name for himself as a populizer of science for the hoi-polloi and unnoticed novelist. Hence his contrarian dabblings as the only ID-affiliated "Jewish agnostic" instead of the heir to Einstein that he seems to wish he was.

Sad in a Terry Malloy, "coulda been a contendah" kind of way.

I moved a comment about "worst human being" to the Bathroom Wall. Let's not get carried away here, there is plenty of territory to cover just in pretentiousness and crankiness...

But Mr. Berlinski, no one would deny these points? GR is an extension of Newtonian mechanics. It goes further and because it does, we see better ... DB: An extension, maybe, but a consistent extension? Never. Consistent? If so, then Newtonian mechanics and GR must be satisfied in the same model by the compactness theorem. But how can a single mathematical model satisfy the postulates of both theories? It just can't be done. No, no, I'm not appealing to anything like a paradigm shift. It's perfectly possible to compare Newtonian mechanics and GR. One theory is better than the other. It explains more. It reaches for deeper principles. It is more elegant. I'm talking about Newtonian mechanics, of course. But the intersection of the set of sentences in both theories is inconsistent and so satisfied in no model whatsoever.

The EFE (Einstein Field Equations) reduce to Newton's law of gravity in the limiting cases of a weak gravitational field and slow speed relative to the speed of light.

For gravitation, the relationship between Newton's theory of gravity and general relativity is governed by the correspondence principle: General relativity must produce the same results as gravity does for the cases where Newtonian physics has been shown to be accurate.

The geodesic and field equations simply are a restatement of Newton's Law of Gravitation as seen from a local frame of reference co-moving with the mass within the local frame.

But in a mathematical sense they are *not* equal.

Sure, in some frames the terms get very very small and get very close to each other, but they are *never* equal.

Ask him if it is OK that sin theta = theta for small theta. 8^)

... as with antievolutionists generally, parody is often impossible to distinguish from reality.

Ask him if it is OK that sin theta = theta for small theta. 8^)

You're telling me. I started to parody Uncommon Descent, but I couldn't come up with anything more outrageous than the real thing.

This might be an obscure in-joke or something, and Berlinski is actually being incredibly sophisticated and ironic (or just pretentious --- take your pick).

But with Berlinski, as with antievolutionists generally, parody is often impossible to distinguish from reality.

Hence his contrarian dabblings as the only ID-affiliated "Jewish agnostic" instead of the heir to Einstein that he seems to wish he was.

David Berlinski, a mathematician and senior fellow of the Discovery Institute's Center for Science and Culture and a sharp critic of neo-Darwinism, also signed the statement of dissent. But in an e-mail message, Berlinski declared, "I have never endorsed intelligent design."

Newtonian mechanics and GR must be satisfied in the same model by the compactness theorem

Sounds like Larry. (shrug)

But to tell you the truth, I'm not at all sure I understand my own views, remarkable as they are. ... I'm sure that in this you are not alone, Mr. Berlinski ...

Compactness theorem? What the blazes is a theorem about propositional logic doing in a discussion of metrics, for christ's sake?

Somebody please shoot me before part III comes out.

Maybe this is just another April fools essay like he wrote for the Daily Cal last year. It is just a little early. The fact that you can't tell makes you wonder why the Discovery Institute still lists Berlinski as a senior fellow. It has to be embarassing to have given this guy something like over a quarter of a million dollars in stipends and then to have him come out and claim that he never bought into the ID junk before the Dover trial.

The only thing that I've seen from Berlinski is regurgitation of old failed creationist scam arguments. This junk piece could be about as original as Berlinski has ever gotten. He should probably have kept to regurgitation.

The fact that you can't tell makes you wonder why the Discovery Institute still lists Berlinski as a senior fellow.

(Or, as someone else once said, "If you can't beat 'em with brains, baffle 'em with BS."

— Bill Gascoyne

While Berlinksi's ego is at least as large as Dembski's, he's a heck of a lot more fun. My guess is the DI keeps him around for kicks. They surely aren't using him in the research department.

He obviously has an identity crisis, he calls himself an "Agnostic Jew" a bit like a non-practicing heterosexual or an anti-evolutionist who doesn't support anti-evolution. Why not just an agnostc?. An enigma wrapped up in paradox or not ....or maybe he's not sure. A true credit to philosophy ^smirk.

Being "Jewish" can refer either to religious practices or ethnic background (or cultural type, but that's not relevant here).

It most certainly is possible to be an Agnostic Jew. Whether it's a good idea to conflate all those meanings is another matter, but as things stand, it's a valid and meaningful statement.

While Berlinksi's ego is at least as large as Dembski's, he's a heck of a lot more fun. My guess is the DI keeps him around for kicks. They surely aren't using him in the research department.

"But in an e-mail message, Berlinski declared, 'I have never endorsed intelligent design.'"

What does Berlinksi think his audience is? Mathematicians?

Conflation was my point Caledonian. Does being an "Agnostic Catholic" or an "Agnostic Chinese" make sense? How about an "Agnostic Atheist"? On the surface an Identity Crisis. And interviewing himself? ...how Dante-esque ...Dr Pangloss sees his shrink (who is himself) and pronounces himself sane. Neither fish nor foul.Pointless. However note the subtext, consider the context and the intent. He is a religious apologist and a literal objectivst who believes or at least accepts perhaps unknowingly that goddidit. That is what he projects. Tremendously brave.

It is not particularly mysterious that Newtonian mechanics is a limiting case of GR

— Zeno

> It most certainly is possible to be an Agnostic Jew. Whether it's a good idea to conflate all those meanings is another matter, but as things stand, it's a valid and meaningful statement.

Yes, it always irks me when ignoramuses whine about supposed contradiction of being Jewish and not belonging to Judaism proper.

Maybe this is just another April fools essay like he wrote for the Daily Cal last year. It is just a little early.

Conflation was my point Caledonian. Does being an "Agnostic Catholic" or an "Agnostic Chinese" make sense?

"Clouserian"

I didn't miss that. Brilliant.

Man it looks like I stepped on a mine

Poppers Ghost picked up the other howler I was going to comment on
"No one cathedral is really built on top of the other."
In fact the whole last sentence is a howler

... But Mr. Berlinski, no one would deny these points?
GR is an extension of Newtonian mechanics. It goes further and because it does, we see better ...
(He asks himself in the third person)

DB: An extension, maybe, but a consistent extension? Never. Consistent? If so, then Newtonian mechanics and GR must be satisfied in the same model by the compactness theorem. But how can a single mathematical model satisfy the postulates of both theories? It just can't be done. No, no, I'm not appealing to anything like a paradigm shift. It's perfectly possible to compare Newtonian mechanics and GR. One theory is better than the other. It explains more. It reaches for deeper principles. It is more elegant. I'm talking about Newtonian mechanics, of course. But the intersection of the set of sentences in both theories is inconsistent and so satisfied in no model whatsoever. If this is so, then the whole image of science as a cumulative structure breaks down. What one really has is a collection of cathedrals on a kind of fruited plane. Some are taller and grander than others, others are smaller and more elegant. No one cathedral is really built on top of the other.

I recognize that paradigm, its Dembski's

The last sentence ...pedestrian rather than poetic Allusion.
Classic Blastifarianism, the whole structure breaks down? What structures?.... imaginary fruited Cathedral's?
Reality check.... GPS satellites with atomic clocks that need to be corrected for the relativistic effects from flying fast and not by mathematicians who failed at The Glass Bead Game".

hehe and popper said
Yes, it always irks me when ignoramuses whine about supposed contradiction of being Jewish and not belonging to Judaism proper

I couldn't agree more. You guys are being a bit over sensitive.
The comments were not pejorative.
The point I was making was perhaps too subtle, its about identity rather than semantics.
Lets look at the context.

Man presents credentials (his religious beliefs, science qualifications , ethnic goup? etc ...HIS identity) and rationalization** for supporting an organization that contradicts another statement he made ("But in an e-mail message, Berlinski declared, 'I have never endorsed intelligent design.'")

I'll get to a possible Why in a moment but first something you should understand about Jewish Identity, its not like being Irish, they come from a single geographic region or even an American Fundamentalist who thinks the US is a Christian Nation founded on Judaic Law (note NOT Roman Law this is important) they still consider themselves American.

Being Jewish does not fit one ethnic group or group from one geographic region. The one binding identity factor, that is to say, HOW they identify themselves is through Judaism. If Judaism did not exist there would be no Jews simple. A Jewish person doesn't have to believe in Judaism, it just IS the "binding agent". Most people outside that "identity group" are simply unable to conceive their own Identity tied into a strongly theistic culture that stands apart from their own country or ethic/regional group. For someone to reject Judaism is almost the same as rejecting being a Jew and that is why I said he had an identity problem, its my observation and an opinion and thus can be treated as such, thank you.
Note; Berlinski still, I presume, accepts the existence of god...the Jewish god which by coincidence is the Christian god.
If that is still too obscure them I can't be more help sorry.
A possible why...
Note; Howard Ahmanson the god father of the DI is a Christian Reconstructionist and it would be worth noting some Israelis find the Fundamentalist support from the US, which some would consider crazy, useful.
It all seems to fit the "Identity Politics" basket or he is just naive.

**To devise self-satisfying but incorrect reasons for (ones behavior): "Many shoppers still rationalize luxury purchases as investments" (Janice Castro).

Being Jewish does not fit one ethnic group or group from one geographic region. The one binding identity factor, that is to say, HOW they identify themselves is through Judaism. If Judaism did not exist there would be no Jews simple.

Fair enough ...I haven't communicated my point adequately.
But ask yourself this would Berlinski be supporting the DI if it were Buddhist or Hindu ?

Fair enough ...I haven't communicated my point adequately. But ask yourself this would Berlinski be supporting the DI if it were Buddhist or Hindu ?

Crank: Colloq, a crotchety person.

Crotchet: 2a. A perverse fancy; a whimsey b. A fanciful contrivance

Berlinski's arguments certainly are a fanciful contrivance, so at least he's honest in his self-assessment.

Comment #85947 Posted by wamba on March 11, 2006 03:48 PM (e) Fair enough ...I haven't communicated my point adequately. But ask yourself this would Berlinski be supporting the DI if it were Buddhist or Hindu ?

NAMBLA

To be a Jew is not to be a member of an ethnic group (there are many diverse such groups within the Jewish family), it is not to be a member of a particular race (there are members of different races within the Jewish family), and it is not to subscribe to any particular religion (atheists born to Jewish mothers are considered to be Jewish by all branches of Judaism).

To be a Jew is to belong to that extended family (or "clan") identified as such. You can join that family by conversion just as you join a family by adoption.

And you claim not to be atheist dogmatists. Just look at your posts. It's shameful.

To be a Jew is to belong to that extended family (or "clan") identified as such. You can join that family by conversion just as you join a family by adoption.

— Carol the Mistaken

Fair enough ...I haven't communicated my point adequately.

But ask yourself this would Berlinski be supporting the DI if it were Buddhist or Hindu ?

Absolutely false. One is Jewish by birth only. Only heretical Jews would argue otherwise.

Thank you for clearing that up Poppers Ghost
I WAS actually trying to get inside Berlinksi's own identity and not so much a whole tribal thing.
And the biz about religion and mathematics being the same (in his mind) I believed I addressed (obliquely) by the reference to the "Glass Bead Game"
Carol of course made a similar point about identity... er except the "conversion" part but hey that's how conversion happens, love trumps religion.
I'm still thinking a non Abrahamic DI would not suit Berlinksi.

(atheists born to Jewish mothers are considered to be Jewish by all branches of Judaism).

— carol clouser

To be a Jew is to belong to that extended family (or "clan") identified as such. You can join that family by conversion just as you join a family by adoption.

— Rilke's Granddaughter

Absolutely false. One is Jewish by birth only. Only heretical Jews would argue otherwise.

I assume you're just yanking Carol's chain, but it's best to do so on something a little more obvious.

Ruth being the most famous in the Bible
From where the word "ruthless" (might) come from.

http://bloghd.blogspot.com/2005/06/etymology-corner-shavuot-special.html

And you claim not to be atheist dogmatists. Just look at your posts. It's shameful.

Absolutely false. One is Jewish by birth only. Only heretical Jews would argue otherwise.

Hey, where did my last comment go?

I know that Berlinski doesn't claim to promote ID, but of course that's exactly what he does for the DI. The only difference between DB and the others is that he doesn't affirm ID.

That's as positive a status as ID can achieve, a sort of faith-statement that ID is responsible for life. And it is as meaningless as my praise for Odin. Everything aside from the assertion that ID is responsible for life amounts to an attack on evolution and the methods of science that have given us the evolutionary theory. Berlinski does engage in that, so effectively, though not in name, he is an IDist.

Of course his latest bit of tripe is nothing other than a flagrant attack on science in general, which suggests that it is ID in effect. The DI has to be happy with any and all attacks on "materialism", which is just the word they use for science.

The beauty of it for us is that their token "Jewish agnostic" sounds less and less plausible to just about everyone, probably even to DaveScot. He seems to have hooked up with the DI so that he wouldn't be talking only to himself, but it appears as if he's headed down that lonely road even with the pseudoscientists backing him.

Will they continue to send the checks no matter what? I am not sure that the DI is such a fun-loving bunch that they'll keep him around just for laughs even as his contributions become increasingly less convincing. The people who stupidly keep hoping that ID will become science, like Sal, can hardly gain great courage from pieces like these.

Glen D
http://tinyurl.com/b8ykm

Adin Steinsaltz, widely recognized as the formost Jewish scholar of today by all Jews, referred to by Time Magazine as "the scholar of the mellennium" and considered by many as the prime candidate for re-instituting the Sanhedrin after two thousand years, thoroughly analyzes the issue of "who is a Jew" in his book titled "We Jews", and concludes after careful analysis that Jews constitute neither an ethnic group, not a race, nor a nationality, nor a religion, but a family or clan.

To be "raised Jewish" by Reform Jewish standards means almost nothing, since they neither practice nor observe nor believe much of anything that is distinctly Jewish. And the vast majority of Jews, rabbis and the government of Israel recognize as Jews those born of Jewish mothers.

ah so...carol crouser...you mean...rike a tribe

That should be millennium. Please excuse.

I assume you're just yanking Carol's chain, but it's best to do so on something a little more obvious.

— William

RG if you think THAT is odd check this out

COMPARE SCIENTISTS (USING LIONS, ELEPHANTS ETC.).

or this one which alludes to usefulness vs dogma

A psychologist makes an experiment with a mathematician and a physicist. He puts a good-looking, naked woman in a bed in one corner of the room and the mathematician on a chair in another one, and tells him: "I'll half the distance between you and the woman every five minutes, and you're not allowed to stand up." the mathematician runs away, yelling: "in that case, I'll never get to this woman!". After that, the psychologist takes the physicist and tells him the plan. The physicist starts grinning. the psychologist asks him: "but you'll never get to this woman?", the physicists tells him: "sure, but for all practical things this is a good approximation."

To be a Jew is to belong to that extended family (or "clan") identified as such. You can join that family by conversion just as you join a family by adoption.

— carol

And the vast majority of Jews, rabbis and the government of Israel recognize as Jews those born of Jewish mothers.

k.e.: you missed the bit about "six inches".

A physicist, an engineer and a mathematician are taken prisoner by evil terrorists and locked in separate cells, with nothing but a can of food and - critically - no way to open it. After realising that their captors appear to have forgotten about them, they each come to the conclusion that their only hope of survival is to get the damn can open.

A month later, the police finally discover the terrorist lair. Sadly, it's too late for our heroes. In the first cell, the physicist's corpse is lying with a frustrated snarl on its face, and numerous dents in the walls attest to his failed can-busting efforts - he'd been throwing it around in the hope that it'd crack open.

In the second cell, the engineer's corpse is lying with an infuriated grimace on its face, and numerous dents in the floor attest to the method he'd attempted - he'd been jumping up and down on the can in the hope that it'd burst.

In the third cell, the mathematician's corpse is sitting propped up against the wall. The can is still sealed tight, and yet the mathematician has a calm, happy smile on his face. On the wall is written "First, assume a can opener..."

Of course Corkscrew ...er I was thinking it could be fun up to the last millimeter :)
Ok ok ok ...I know don't say it.

To be a Jew is to belong to that extended family (or "clan") identified as such. You can join that family by conversion just as you join a family by adoption.

And the vast majority of Jews, rabbis and the government of Israel recognize as Jews those born of Jewish mothers.

But so what, who cares? You are what you are.

A psychologist makes an experiment with a mathematician and a physicist. He puts a good-looking, naked woman in a bed in one corner of the room and the mathematician on a chair in another one, and tells him: "I'll half the distance between you and the woman every five minutes, and you're not allowed to stand up." the mathematician runs away, yelling: "in that case, I'll never get to this woman!".

I've got several orthodox friends who claim conversion is not possible.

— Rilke's Granddaughter

Anyway, a quick Google for "orthodox judaism conversion" will reveal who is correct.

A psychologist makes an experiment with a mathematician and a physicist. He puts a good-looking, naked woman in a bed in one corner of the room and the mathematician on a chair in another one, and tells him: "I'll half the distance between you and the woman every five minutes, and you're not allowed to stand up." the mathematician runs away, yelling: "in that case, I'll never get to this woman!".

— Popper's Ghost

Um, a mathematician is the least likely sort of person to yell that, since mathematicians can prove that Zeno's paradox is fallacious.

I think I know where Berlinski is coming from now.
He's had a gutful of all this religion free science and wants a revolution.
A good jihad needs a weapon.
Weapons of Math Instruction.

Since Zeno's paradoxes are claims about the real world, mathematicians qua mathematicians can neither prove nor disprove them.

Popper just interested.... are you a mathematician?

In this example, the usual Zeno paradox resolution models are useless, since the temporal interval between distance halvings remains constant.

Popper just interested.... are you a mathematician?

No, I'm a ghost.

I'm a ghost
Oh that's good ...so you don't have issues with professional/academic sex drive :)

Since Zeno's paradoxes are claims about the real world, mathematicians qua mathematicians can neither prove nor disprove them.

— Popper's Ghost

Hardly, since there wasn't really a race between Achilles and a tortoise. Zeno offered an argument that motion is impossible in principle, but his argument is fallacious, seen by showing that the sum of the infinite series of distances that Achilles must overcome is finite.

But the mathematician only has a problem if he considers himself absolutely bound by the conditions imposed by the psychologist --- but he obviously doesn't, since he stands up and runs. He could, of course, have run the other way.

"ID is all about preaching, and there is simply no way for them to preach without letting the whole world KNOW they are preaching.

It's why ID will never win in court."

And that's only the first obstacle. Then they have to show that it's science to teach in science class.

First, they have to actually do science. That seems almost as possible, since they want to forget that and do the preaching instead.

Second, they must base their theory on something else than nonfalsifiable hypotheses. Since they don't seem able to base it on anything else than preaching, they will probably never succeed.

Third, we know that if they come up with a new and falsifiable hypotheses that we all can actually do science with, it wont involve a creator, and if it's verified it will be compatible with, and support, evolution. Why they would like to do that instead of concentrating on preaching is paradoxical.

That's the other reasons ID will never win, in court, in science, or in informed religion.

Of course, in politics and uninformed religion they can win easily on their own terms, and all these other areas can be damned.

His argument is obviously fallacious, and everyone from Zeno onwards knew it, because motion is observed.

The point is the situation is a joke.

The humor comes from accepting the artificial condition that he treats a non-mathematical problem as if it were mathematical, and thereby misses out on the obvious.

to prove a fallacy, one shows that the conclusion doesn't follow from the premises; it isn't necessary to disprove the premises

I take it you mean to exclude biology altogether. Is that your view? ... DB: To a certain extent. My real view is that there is only one science, and that is mathematics, and that the physical sciences are really forms of experimental mathematics.

— The Master

No doubt. But it is odd, isn't it, that we really have no good views about science itself. Its existence is as much of a mystery as the phenomena that it explains. I know of nothing like an imagined overall theory that even begins to explain the role of science in the universe. No theory explains itself, after all, even if it could explain everything else.

He means something quite specific by the term crank science, and that is a willingness to deny the cumulative structure of modern physics, the fact that each great physical theory represents an enlargement of its predecessors. This is terrifically important as a rhetorical strategy because it means that the burden of skepticism becomes impossibly high with each new theory. This is just another way of protecting the sciences from criticism.

Now take Newtonian mechanics and compare it to general relativity. Is it true that GR is a consistent extension of Newtonian mechanics? ... Surely many physicists would say so ... DB: Yes, and they would be wrong. Newtonian mechanics is committed to the view that the spatial structure of the universe is classically Euclidean. Not so GR. Newtonian mechanics holds that if you accelerate a rigid rod, neither its length nor certain temporal intervals will change. GR holds the opposite. But why am I telling you all this. It's obvious. ... But Mr. Berlinski, no one would deny these points? GR is an extension of Newtonian mechanics. It goes further and because it does, we see better ... DB: An extension, maybe, but a consistent extension? Never.

But the intersection of the set of sentences in both theories is inconsistent and so satisfied in no model whatsoever. If this is so, then the whole image of science as a cumulative structure breaks down. What one really has is a collection of cathedrals on a kind of fruited plane. Some are taller and grander than others, others are smaller and more elegant. No one cathedral is really built on top of the other.

"Bereft of mathematics (which both codifies and grounds logical statements), macroevolution must rely on heuristic methods to settle disputes, which lead in turn to hunches"

Let's make a quick diagnosis:
1. Formal statements without empirical connection good.
2. Empirical statements bad.
3. Macroevolution bad.

Ie, the scientific method backwards and a distaste for evolution. Ghost must be an IDiot.

So it's no surprise he sits at Berlinski's feet and laps the dreg up from where it hit the floor. Pity he didn't look at the objections first.

Speaking of math, why is it that folks who bash evolutionary biology never seem to deal with the math in Fisher, Wright, Kimura, Crow, Brooks and Wiley, or even any issue of the journal, Evolution?

It's led to some howlers, like William Demsbki's casual statement, "Here I examine evolutionary algorithms, which constitute the mathematical underpinnings of Darwinism." This one is especially ironic, since Dembski goes on at length in TDI about Fisherian hypothesis testing, but seems to be completely oblivious to such sources as Fisher's The Genetical Theory of Natural Selection.

You mean the tortoise lied to me when it said I could never beat it?

His argument is obviously fallacious, and everyone from Zeno onwards knew it, because motion is observed.

— Popper's Ghost

I didn't say that it wasn't obvious. But the argument is fallacious even if no motion were ever observed --- something that isn't so obvious. And it's provably fallacious, even though it's "about the real world".

Whether it's about the real world is irrelevant since, to prove a fallacy, one shows that the conclusion doesn't follow from the premises; it isn't necessary to disprove the premises.

I'm sorry that you failed to appreciate the subtle humor of my treating a joke as if it were a serious comment. Although I think that your indignation is disingenuous, as it comes several posts too late.

But I think you're wrong about the source of the humor --- the physicist takes the conditions seriously as well, but doesn't consider them an impediment. The point of the joke --- obvious given the context in which it was offered --- is a stereotype of mathematicians as detached from the real world, and thus misapplying mathematical reasoning to it.

The idea that there is out there a physical world which just happens to lend itself to mathematical description has always seemed to me to be incoherent.There is only one world --- the universe, in fact, and it has the essential properties of a mathematical model. For reasons that we cannot even begin to understand, that model interacts with out senses, and so without measuring devices, allowing us to pretty much confirm conclusions antecedently reached by pure thought.

— improvius

This is pure solipsism.

Berlinksi is addressing the question of why our world is so amenable to mathematical reasoning. This question has been raised numerous times by respectable physicists and mathematicians, and no generally acceptable answer is known.

One popular line of argument is a kind of anthropological principle. Only in universes where there is sufficient mathematical structure can stable objects interact and change over time, thereby leading to the very possibility of intelligences existing, and having something to reason over in the first place. A modern day Descartes would say "I think, therefore I am in a mathematically modelable universe."

A variant of the above is that we are overstating our modeling capabilities, and in fact, have missed important aspects of reality simply because we are stuck in a mathematical rut.

Another point of view is inspired by statistical mechanics, ergodic theory, and Ramsey theory. These subjects involve the discernment of order and pattern out of generic formlessness, and philosophical reasoning along these lines suggests that on any grand enough scale, any universe will have no choice but to exhibit mathematical regularities.

"Berlinksi is addressing the question of why our world is so amenable to mathematical reasoning. This question has been raised numerous times by respectable physicists and mathematicians, and no generally acceptable answer is known."

I believe the more general question, when you involve physicists as well, is put as why we can model the world at all.

I must confess I have never really understood this part of the awe that one feels when a model checks out correctly. Perhaps I have been taking it as granted, and when I have thought of it I have been satisfied with the anthropic observation.

Your two explanations makes sense (and now I have to check what Ramsey theory is :-). But I would like to complement them with two ideas I have had, for all it's worth.

The awe, or the question raised, follows probably partly from an anthropic observer bias, which I guess is a tautological form of the anthropic principle.

And I think, but may be wrong, that mathematics isn't totally disconnected from science and observations.

The axioms of the formal parts, and perhaps some of the methods, are informed at their conception, in logic, quantum logic, mathematics, probability theory (and parts of philosophy), by abstractions from models of reality.

And now and then these models are applied and indirectly checked. There is also an influx of math from applied sciences, there these processes are again used at the construction.

Ie string theory was concieved around Lagrangians for gravity and whatnot, and produces some pure math results. I believe there has been periods when for example analysis and quantisation formalisms have been more or less corrected, since the initial formulations weren't good enough. Perhaps these corrections or rather deeper formalisations (I think) were driven by pure math, but I still believe it illustrates the idea that part of math originates from applications closer to reality than the foundations.

Then I'm writing this it occurs to me that this last idea doesn't work well unless the world is partly organised, which would rely on any of your two explanations.

Yes. Bereft of mathematics (which both codifies and grounds logical statements), macroevolution must rely on heuristic methods to settle disputes, which lead in turn to hunches, circular reasoning, and incoherent formulation (what constitutes a homologous structure? A selective landscape? etc.). The evolutionist cannot couple image to word, logic to meaning, and drifts ever further from Truth. Behold the power of babble.

— Ghost of Paley

Heh, heh (as GoP turns a whiter shade of pale).

GoP ...a night in white satin ^smirk....projects the vacuousness of his (Arthurian) vacuum said:

Yes. Bereft of mathematics (which both codifies and grounds logical statements), macroevolution Creationism must rely on heuristic methods to settle disputes, which lead in turn to hunches, circular reasoning, and incoherent formulation (what constitutes a homologous structure? A selective landscape? etc.). The evolutionist (whatever that is)Creationist Biblical Idolaters cannot couple image to word, logic to meaning, and drifts ever further from truth/reality _{The one true word of **insert favorite deity**}TM. Behold the power of babble.

...The devoid void...
ghostly hows your love life? You should de-materialize once in a while and ...er do some dancing...that's not aghast (`0') your religion is it?.

Are you going to give us the definitive biblical mathematical Truth pi=3

Really why don't you THINK for 5 seconds before posting.

Are you the guy behind "The Men who stare at goats"? The military project run by a new age pseudoscience guru to develop super soldiers who could walk through walls.

I agree with Popper's Ghost: It's important not to attack Berlinsky on where he is right. Berlinsky is right about Relativity Theory and right about Compactness theorem (which is not a theorem of propositional logic but of model theory for first order predicate calculus). He is simply wrong in the conclusions that he reachs from there.

No present philosopher would still use the very old positivist conception of intertheoretic reduction; it is well known that this conception (proposed by Nagel) is full of problems (it does do justice to the Newton-GR case, for instance, but neither to the reduction of Mendelianism to molecular genetics). Alternative to Nagel's conception have been proposed (e.g., Bickle's) which preserve the idea that science grew from a kind of reduction of old theories to new, more precises ones.

No need to appeal to the opposition of "practical" common sense vs "too abstract" pure logic or philosophy. Berlinsky seems just to be doing bad philosophy with good logic, as far as I know.

"Philosophy and the study of the actual world have the same relationship to one another as masturbation and sexual intercourse". -- K Marx

Tancrède,

"Berlinsky is right about Relativity Theory and right about Compactness theorem (which is not a theorem of propositional logic but of model theory for first order predicate calculus)."

I don't see how the compactness theorem applies here. (But I have never heard of it before, and haven't seen the context or a proof, so I might misunderstand my speedreading of it.)

But newton mechanics, special relativity and general relativity are consistent in the sense that you can find areas where the simpler theories approximate each other. For example, newton mechanics and his gravity models masses under low speeds in a gravity field, otherwise it would never have been accepted. So they are consistent in the physical way, and that is what matters here, however much Berlinski tries to muddy the waters.

Perhaps the last part of your comments says that isn't how a philosopher thinks about science ("intertheoretic reduction" ?), but I find it hard to believe we can find complete and allencapsulating descriptions of what science do and how scientists thinks. Already the method of science is hard to describe generally, and since it's a method and not a recipe, it will do things we don't expect, on stuff we haven't figured out yet.

Since you seem to like philosophy, it seems to me what I saying is like the consequences of Goedels first incompletness theorem, that we will forever add to our formal theories. Maybe you can show that trying to describe how science works is as science itself, ie it will never be complete. It wouldn't surprise me.

"Philosophy and the study of the actual world have the same relationship to one another as masturbation and sexual intercourse". --- K Marx

But Mr. Berlinski, no one would deny these points? GR is an extension of Newtonian mechanics. It goes further and because it does, we see better ...

An extension, maybe, but a consistent extension? Never. Consistent? If so, then Newtonian mechanics and GR must be satisfied in the same model by the compactness theorem. But how can a single mathematical model satisfy the postulates of both theories? It just can't be done. No, no, I'm not appealing to anything like a paradigm shift. It's perfectly possible to compare Newtonian mechanics and GR.

One theory is better than the other. It explains more. It reaches for deeper principles. It is more elegant. I'm talking about Newtonian mechanics, of course.

But the intersection of the set of sentences in both theories is inconsistent and so satisfied in no model whatsoever.

— Tancrède Plasma

I agree with Popper's Ghost: It's important not to attack Berlinsky on where he is right. Berlinsky is right about Relativity Theory and right about Compactness theorem (which is not a theorem of propositional logic but of model theory for first order predicate calculus). He is simply wrong in the conclusions that he reachs from there.

For starters, neither CM (Classical Mechanics) or GR (General Relativity) is a first order theory in the sense of mathematical logic. In fact, neither is a second order theory. Both are game plans, so to speak, except in both cases the rules are only partly defined. For an excellent description of the near impossibility of treating GR, even in theory, as merely a branch of mathematics, see Sachs and Wu General Relativity for Mathematicians.

The authors do a fantastic job of translating large parts of GR into Definition/Theorem/Proof style, and also of explaining why this fails as physics. As they point out, even something as presumably simple as rigorously defining a "particle" leads to unphysical decisions and contortions.

Berlinski is ignorantly treating CM and GR as amenable to first order logic, and then bluffing his way from there. In fact, it's very easy to give a "model" that satisfies CM and GR, properly defined. One doesn't treat CM as merely a certain set of differential equations, but as a certain set of differential equations with accuracy limitations. This is actually more realistic, and easily "consistent" with a GR model, as known since Einstein.

And none of this has anything to do with the compactness theorem. Berlinksi, in essense, is cheating. Physicists use "consistency" in one sense, logicians in another, and Berlinksi is just conflating the two in an incoherent and incompetent manner. Whether this is defective intelligence on his part, or defective morality, is hard to tell. But it's the same style nonsense that typifies his Commentary articles, only this time he's selecting a smaller audience of people who know what he's talking about.

The compactness theorem is a basic fact in symbolic logic and model theory and asserts that a set (possibly infinite) of first-order sentences is satisfiable, i.e., has a model, if and only if every finite subset of it is satisfiable.

"Philosophy and the study of the actual world have the same relationship to one another as masturbation and sexual intercourse". --- K Marx

As I've noted before, this quip from the world's most influential political philosopher doesn't carry much weight.

William, thank you for your explanation. It seems you, I and Tancrède have come to compatible (but not necessarily consistent :-) views.

"So if GR is a satisfiable set of first-order sentences, and CM is another, then their union is satisfiable too."

I think this is incorrect, and can be the source of some trouble. Since CM and GR overlap, are nearly the same in some regimes of overlap, but have different predictions in some other regimes of overlap, their union can't be satisfiable.

If you insist to see them as two sets of sentences, you will have to get rid of some CM sentences when you merge it into GR, assuming GR is the correct theory. It seems to be belief revision you are discussing.

"So if GR is a satisfiable set of first-order sentences, and CM is another, then their union is satisfiable too." I think this is incorrect, and can be the source of some trouble. Since CM and GR overlap, are nearly the same in some regimes of overlap, but have different predictions in some other regimes of overlap, their union can't be satisfiable.

The compactness theorem is a basic fact in symbolic logic and model theory and asserts that a set (possibly infinite) of first-order sentences is satisfiable, i.e., has a model, if and only if every finite subset of it is satisfiable.

— Tancrède Plasma

So if GR is a satisfiable set of first-order sentences, and CM is another, then their union is satisfiable too.

I'm not sure if this is your misreading of the compactness theorem or Berlinksi's, but nothing in the statement refers to the union of two theories. It refers to the union of all possible finite subtheories of a given theory.

I'm not a physicist, but it's certain that you can find a consequence of GR that is in contradiction to a consequence in CM (even if the two sentences are very similar). So the conjunction of the two theories doesn't have a model if they are first order theories. (A model is an interpretation of a theory in a mathematical or physical structure under which the theory is true.)

So Berlinsky use an old positivist doctrine that not many philosophers would still endorse together with (if W E Emba is right) false premises.

So if GR is a satisfiable set of first-order sentences, and CM is another, then their union is satisfiable too.

A union of satisfiable sets needs need be satisfiable. For example, Euclidean geometry, with an axiom that says space is two-dimensional, is satisfiable. So is Euclidean geometry, with an axiom that says space is three-dimensional. Their union is not satisfiable.

— W E Emba

There is no a priori expectation that CM and GR as theories... would use the same first-order language.

about the only thing I'll put my foot down and insist is correct is that the philosopher's job is to explain how science works and that it cannot dictate to scientists how to do their job.

William and Tancrède,

I would like to thank you both about teaching me more about theory basics, and how to think about them. It seems one must have a deeper view on theories and their different formal languages. This was especially helpful for me which has very little knowledge in this field. (Disclaimer: I'm not a philosopher.)

I'm not a physician