HUMAN REASON AND ITS DISCONTENTS: The number 1 lives in a fairyland!

WEDNESDAY, MARCH 18, 2020

And other high-end mumbo-jumbo:
We asked the question yesterday. What goes through the mind of a very smart person who writes something like this?
LIVIO (page 2): Millennia of impressive mathematical research and erudite philosophical speculation have done relatively little to shed light on the enigma of the power of mathematics. If anything, the mystery has in some sense even deepened. Renowned Oxford mathematical physicist Roger Penrose, for instance, now perceives not just a single, but a triple mystery. Penrose identifies three different "worlds": the world of our conscious perceptions, the physical world, and the Platonic world of mathematical forms....
Roger Penrose "identifies" three different "worlds," including "the Platonic world of mathematical forms?" So this author said.

That passage was written by Mario Livio, who is, by any normal metric, an extremely smart person. By any normal metric, Penrose is extremely smart too.

That said, what goes through the mind of a person who writes something like that? Also, what goes through the mind of a major publisher who puts such work into print?

What went through the mind of NPR when it decided to highlight Livio's 2009 book, Is God A Mathematician? What went through that upper-end news org's mind when it decided to post the very excerpt from Livio's book in which this passage occurs?

What goes through the minds of these high-end players? We ask because of what happened when Livio tried to explain what Penrose was said to believe.

Few people will be puzzled by the claim that a "physical world" exists. Is there also a "world of our conscious perceptions?" That's a slightly awkward construction, but most people would understand what such a claim probably means.

But how about that third alleged belief by Penrose—the belief that a third "world" exists, "the Platonic world of mathematical forms?" Will anyone reading Livio's book know what claim could possibly mean? We ask because of the mess which occurs when Livio tried to explain what Penrose means:
LIVIO (continuing directly): The first world is the home of all of our mental images—how we perceive the faces of our children, how we enjoy a breathtaking sunset, or how we react to the horrifying images of war. This is also the world that contains love, jealousy, and prejudices, as well as our perception of music, of the smells of food, and of fear. The second world is the one we normally refer to as physical reality. Real flowers, aspirin tablets, white clouds, and jet airplanes reside in this world, as do galaxies, planets, atoms, baboon hearts, and human brains. The Platonic world of mathematical forms, which to Penrose has an actual reality comparable to that of the physical and the mental worlds, is the motherland of mathematics. This is where you will find the natural numbers 1, 2, 3, 4,..., all the shapes and theorems of Euclidean geometry, Newton's laws of motion, string theory, catastrophe theory, and mathematical models of stock market behavior. And now, Penrose observes, come the three mysteries. First, the world of physical reality seems to obey laws that actually reside in the world of mathematical forms.
According to Livio, "the physical world" is "the one we normally refer to as physical reality!"

With that, we're off to a possibly unimpressive start. But then, we see the remarkable way Livio explains what Penrose means when he says that there is a "Platonic world of mathematical forms."

What does Penrose mean by that? According to Livio, Penrose means this:

According to Livio, Penrose thinks this Platonic world "has an actual reality!" What kind of reality wouldn't be actual? We're left to guess about that.

Let's set that aside as nitpicking. As he continues, Livio says that Penrose believes that the Platonic world of mathematical forms is "the motherland of mathematics."

He then says that Penrose believes that this motherland is "where you will find the natural numbers 1, 2, 3, 4,..." It's also where you will find "all the shapes and theorems of Euclidean geometry [and] Newton's laws of motion," among other assorted entities.

Question: Will any reader have any idea what this mumbo-jumbo means?

According to Livio, Penrose believes that the world of Platonic forms is a motherland which has an actual reality. It's where you'll find the number 1! Can this be distinguished from madness?

Will any reader have any idea what this presentation means? The reader is told that she will find the number 1 in the world of Platonic forms. What can that possibly mean?

Will the number 1 introduce itself when she finds it there? It's been claimed that one is the loneliest number. Will it ask her to stop for a chat?

Meanwhile. what does it means when we're told that we'll also find Newton's laws there? In what form will those laws exist when we find them in this motherland, which has an actual reality?

So far, no one reading this mumbo-jumbo could possibly have any hope of explaining what it might mean. At this point, we're on page 3 of an extremely smart person's book. But if we're sensible and experienced, we're probably already looking around, hoping to locate the exits.

If we're perhaps a bit more trusting, we may have a different reaction. We may assume that Livio—by any normal metric, he's one of the smartest people around—will start to untangle those problems.

Experienced people will be less sanguine. Indeed, by the time we hit page 9 of this well-regarded book, Livio will be saying this:
LIVIO (page 9): As I noted briefly at the beginning of this chapter, the unreasonable effectiveness of mathematics creates many intriguing puzzles: Does mathematics have an existence that is entirely independent of the human mind? In other words, are we merely discovering mathematical verities, just as astronomers discover previously unknown galaxies? Or, is mathematics nothing but a human invention? If mathematics indeed exists in some abstract fairyland, what is the relation between this mystical world and physical reality? How does the human brain, with its known limitations, gain access to such an immutable world, outside of space and time?
Ignore the useless semantic debate about discovery versus invention. This debate has long been loved by high-end mathematicians, people who aren't logicians—by very smart people who are, in effect, playing out of position.

Instead, look at where we find ourselves after nine pages of this discussion. It seems that we're now being told that the world of Platonic forms can be thought of as "some abstract fairyland"—as a "mystical world."

Apparently, that's the actual reality of the "world" where we "will find the number 1" (along with Newton's laws). We'll find it in a mystical world, whatever that will be like.

True believers may assume that we're being unfair to Livio. Such true belief will be wrong.

We will extend the basic fairness to which we've just alluded. Livio, an extremely smart person, is a high-ranking astrophysicist. More specifically, he's a high-ranking astrophysicist who is playing out of position when he heads down the road which takes us to the actual reality of this mystical fairyland.

Livio isn't a professor of philosophy. More specifically, he isn't a logician. Presumably, he's never been trained to avoid the shoals on which his discussion quickly foundered.

Livio is extremely smart, but he's playing out if position. That said, here's the saddest point of all:

When our logicians threw the later Wittgenstein under the bus, they sanctioned high-end mumbo-jumbo of this familiar type. This mumbo-jumbo exists today because our logicians have walked off their posts—because our logicians permit it.

The later Wittgenstein's seminal text, Philosophical Investigations, was published in 1953. Almost seventy years later, the kinds of conceptual confusion it clumsily diagnosed are still taken seriously by major publishing houses and by major news orgs like NPR. And alas:

These kinds of confusion are still OK within the high professoriate. When people like Livio offer mumbo like this, no one says a world.

The most troubling point is this:

When logicians go on holiday, their intellectual squalor trickles down through the national discourse. When our smartest people write nonsense like this, what can anyone expect from the grasping clawing lesser beings who crawl all over cable news and high-end op-ed pages, building their gonzo careers?

The number 1 lives in a fairyland! Also, Al Gore said he invented the Internet, and Donald Trump sits in the Oval.

Tomorrow: "Rogers does this every year." In the winter of 68, the book was just 15 years old!

37 comments:

  1. "According to Livio, Penrose thinks this Platonic world "has an actual reality!" What kind of reality wouldn't be actual? We're left to guess about that."

    A hypothetical reality wouldn't be actual. A fictional reality wouldn't be actual. An imagined reality wouldn't be actual. The reality of a delusional, hallucinating person wouldn't be actual. An idealized reality wouldn't be actual. What is wrong with Somerby?

    And Somerby says: "According to Livio, Penrose thinks..." For anyone taking this remotely seriously, it isn't sufficient to take Livio's impression of what Penrose thinks. One would have to go to Penrose and see what he says, in order to see whether what Livio attributes to him is fairly represented by Livio.

    But this is a popular book, not scholarly work. So Somerby pretends that Penrose said what is attributed to him. And because he is playing a game of taking everything literally, he complains that readers won't understand what they mean by a mathematical reality the corresponds to physical reality.

    And then Somerby says: "Livio will be saying this..."

    When you describe something that is written in a paper or book, you always use the past tense, because it is already written there. You do not refer to the experience of the reader, who will encounter an idea in the future, if he or she hasn't gotten to that page yet. Switching tenses is majorly confusing, more so than talking about abstractions that Somerby feels the audience for Livio's book won't understand.

    It is hard to tell who Somerby disrespects more, Livio or the prospective readers of Livio's book. The latter are assumed to have all done less well in college than Somerby himself, but is that actual reality? Hard to believe that anyone benefited less from college than Somerby.

    ReplyDelete
    Replies
    1. For anyone taking this remotely seriously, it isn't sufficient to take Livio's impression of what Penrose thinks. One would have to go to Penrose and see what he says….

      Why doesn’t your head just explode, professor?

      Substitute Corby for Livio and Somerby for Penrose, and we have the perfect description of what you do in the comment section.

      When you describe something that is written in a paper or book, you always use the past tense, because it is already written there.

      Another topic about which your ignorance is abyssal. These shifted tenses are called historical, and they’re used to give immediacy to past events. Thus:

      In 1492, Columbus arrives on the island he names La Isla Española. In fifteen years, 85% of the Taínos, the native population, will be dead.

      Hard to believe that anyone benefited less from college than Somerby.

      Oh, I can think of somebody, professor. I can think of somebody.

      Delete
    2. It is bad writing.

      I believe the shift to ubiquitous present tense, which was adopted by journalists about 10 years ago, was done because there are so many non-native speakers in TV audiences these days. The present tense is the easiest for new speakers of a language to understand. The same applies to undereducated and semi-literate native speakers. Use of present tense even for things that obviously occurred in the past thus gives media a wider audience for their work. But it is bad style for serious scholarly writing.

      Since you went to the trouble of digging up your ad hominem from my Google page, and I was forced to use that nym, in fairness you should stop calling me professor and making your own digs at me on that basis. If you can't address what I say on its own merits, attacking my identity is just bullying. It is the same thing Somerby does, and to which I am objecting below. And it is very consistent with the anti-intellectualism on the right. Why would anyone want to even complete high school, if they knew they would be mocked by every online idiot that comes down the pike?

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    4. Please bear with me, while I try to explain why I criticize you. Then I urge you to abandon the undeserved role of victim and actually respond to the substance of what write.

      @8:20P you claim a rule: Description of what is written must employ the past tense because what is written is completed.

      This is not a rule. As I point out, writing of past events in tenses other than the past is well known enough to have its own term of art — the historical present (not the ubiquitous present). It’s been recognized in texts on grammar going back to at least 1848. How do I know this? Because I checked, something you never do because you live in an unevidenced world of belief. Here’s what you believe:

      1. There’s something called the ubiquitous present tense.
      2. It was adopted by journalists a decade ago.
      3. It was adopted because of the number of non-native speakers in TV audiences.
      4. The present tense is the easiest for new speakers to understand.
      5. The present tense is easiest for undereducated native speakers.
      6. The present tense gives media a wider audience.
      7. It is bad style for “serious scholarly writing.”

      Reasonable people will disregard 1-6, leaving “I believe that TDH employs bad style.” About which, there’s nothing to dispute — your beliefs are your own for reasons of your own, and there’s no accounting for taste. But your comment is like all your commentary: phrased as statements of fact, often wrong and always without evidence.

      You know almost nothing while you believe almost anything.

      For instance, you apparently believe that an ad hominem attack is something you find insulting. It’s not. An ad hominem is the claim that a person’s argument should be dismissed because of who she is. But my objection to the first six items above doesn’t arise because you’re Corby or because you’re a professor. My objection is that as is your habit, you provide no evidence for these claims.

      Is the present tense the easiest for undereducated native speakers to understand? How would we know that?

      Let me reiterate why I call you professor. It’s not attacking your identity; it’s not anti-intellectualism; it’s not because I don’t address what you say on its merits or lack thereof. I have known many admirable professors, some in my own family. My use of the title is ironic, to call you out for intellectual failings that make your academic status an embarrassment if not to you than to your profession.

      Can you acknowledge any of these criticisms honestly? Do that and then we can discuss what I should call you to express my disdain for your argumentation. Not you, but how you present an argument.

      Delete
    5. "But your comment is like all your commentary: phrased as statements of fact, often wrong and always without evidence."

      Here we see an example of your assumption that when you disagree with me, it is because I am wrong and you are absolutely right. No gray area. No possibility that you might be mistaken. No thinking about when I said. Just a flat assertion that I am wrong and you are right.

      And then, on the basis of that assumption, you assert the right to use my job title ironically.

      I will abide by my statement that Somerby's use of the present tense is bad style. If you read a selection of academic journals, you will see that no one writes that way. Since there are no rules or laws about writing, but there are preferred styles, I will stand by my statement.

      An error of fact is not an "intellectual failing". Anyone can be wrong and anyone can make a factual error, because we are human. We try to minimize such errors. You however seem to think that errors exist to batter others over, as if my entire academic status hangs on the kinds of trivialities you notice here. And my entire profession certainly doesn't hang on whatever I do or don't do. This is the same kind of idiocy Somerby engages in.

      If I said the sky was blue, you would assert that it isn't blue at night, and that I am an ignoramus and an embarrassment to humanity, but you wouldn't point out that it is blue in the day and dark at night, because that might advance civil discussion.

      Delete
    6. Here we see an example of your assumption that when you disagree with me, it is because I am wrong and you are absolutely right. No gray area. No possibility that you might be mistaken. No thinking about when I said. Just a flat assertion that I am wrong and you are right.

      And then, on the basis of that assumption, you assert the right to use my job title ironically.


      i haven’t asserted the right to use your job title ironically because I it never occurred to me that I needed to do so. It’s a simple fact that I have the absolute right to do that. I’m going to stop for purposes of this thread because otherwise it’s bound to get in the way. So let’s see how it goes. It doesn’t look good from here, but who knows?

      When I disagree with you on matters of fact it’s generally because I am right and you are wrong. That’s because I check my assertions and you don’t. Generally.

      I’m wrong often enough, and when I’m called on an error, I admit my mistake.

      I will abide by my statement that Somerby's use of the present tense is bad style. If you read a selection of academic journals, you will see that no one writes that way.

      Fine, goalposts moved. There’s no arguing with taste. This blog isn’t an academic journal, so I think it’s an odd assertion to make, but that’s as may be.

      An error of fact is not an "intellectual failing". Anyone can be wrong and anyone can make a factual error, because we are human.

      Of course. My problem with you isn’t that you make errors. It’s that you constantly make them in the face of contrary evidence that’s often posted right above you.

      You however seem to think that errors exist to batter others over, as if my entire academic status hangs on the kinds of trivialities you notice here.

      And one of your errors is your constant mind reading. Here you claim to know what I seem to think. In spite of the fact that what I actually think is that no one with authority over your “academic status” reads your comments here or would do more than snicker if they did.

      And my entire profession certainly doesn't hang on whatever I do or don't do.

      Of course not. What “entire profession” depends on a single practitioner? By and large, I think academic psychology is a box of foolishness packed by charlatans, but I don’t think the fate of the field hangs on your action or inaction. Why would you think otherwise?

      If I said the sky was blue, you would assert that it isn't blue at night,

      This is demonstrably not true. You make “sky is blue” claims all the time that I don’t dispute. Case in point: @1:00P.

      and that I am an ignoramus and an embarrassment to humanity,

      You demonstrate your ignorance and carelessness about fact virtually ever time you comment, but where do I say you’re an embarrassment to humanity? I don’t think that.

      but you wouldn't point out that it is blue in the day and dark at night, because that might advance civil discussion.

      Well, it’s a fair cop that I don’t care about civil discussion. But it would be nice if you actually discussed things I actually said. For instance, how about withdrawing your claim that you’re the object my ad hominem attacks? True, I think your profession is largely pseudo-science, but I haven’t dismissed your claims on the grounds that you’re a professor of psychology.

      How about you acknowledge that my use of your title disparages your efforts here and isn’t “attacking your identity”? I have no reason to believe that you’re not, in fact, a professor.

      Heck, I’d settle for some evidence that the present tense is the easiest for undereducated native speakers to understand.

      Delete
    7. Because you provide documentation for all of your claims? You could learn something if you had a more open mind.

      Here is a quote from an English learning page:

      "In English, verbs are often the strongest indicator of tense and they are quite difficult to master. Begin with the easy ones which are present simple, past simple and present continuous. These are the three I encourage my students to learn first."

      In the State of CA, graduates from a public university must pass a writing test, by mandate of the state legislature. The main criterion for passing is whether a student can handle verb tenses.

      In all language learning classes, including English classes for native speakers in early grades, the present tense is taught first. It is the first tense babies learn to speak. I could probably find evidence that it is most robust against brain injury, but I won't invest the time.

      No one has to provide "evidence" to back every single claim made in blog comments. I won't do it either. If you disagree, that is your problem, not mine. But your aggressive bullying is this blog's problem. I write with an authoritative voice because I am an authority. You seem to have a knee jerk reaction to authority figures, but that too is your problem. The world doesn't owe you citations, and neither do I.

      Someone who thinks psychology, an empirical science, is pseudo-science is willfully uneducated.

      Here is Wikipedia's definition of an ad hominem attack:

      "Ad hominem (Latin for "to the person"), short for argumentum ad hominem, typically refers to a fallacious argumentative strategy whereby genuine discussion of the topic at hand is avoided by instead attacking the character, motive, or other attribute of the person making the argument."

      That is the way I have been using the term. If your definition is different, that again is your problem. You have continually made such attacks against me, not my arguments (which you rarely engage except to say that I am wrong about some nitpick).

      I'm done with this. Next time you see one of my clearly identified comments, don't read it and it won't bother you and then you won't bother me.

      Delete
    8. Because you provide documentation for all of your claims?

      You’re right. I don’t. But for claims of fact, I can. Because I check.

      Here is a quote from an English learning page:

      "In English, verbs are often the strongest indicator of tense and they are quite difficult to master. Begin with the easy ones which are present simple, past simple and present continuous. These are the three I encourage my students to learn first.”


      It’s a start. This is from quora and from a soi-disant PhD in linguistics. It too is merely a claim from someone in cyberspace. I’m suspicious because verb forms are the only indicator of tense in English, although they’re not the only indicator of time.

      No one has to provide "evidence" to back every single claim made in blog comments.

      This is another of your bad habits. You keep insisting that I’m demanding that people do something. I’d be delusional to do that. I’m merely making my objections to the comments you post. How could I possibly enforce a demand for you to change your bad habits?

      I won't do it either. If you disagree, that is your problem, not mine.

      You probably shouldn’t project your problems onto me. You’re the one who posts nonsense.

      But your aggressive bullying is this blog's problem.

      This blog’s commentary section has its problems, but my comments aren’t one of them. I’m blunt, but that’s not bullying. And your accusation is distasteful considering those who face real bullies.

      I write with an authoritative voice because I am an authority.

      You do write authoritatively, and that’s part of your problem: you’re so often wrong, and so often ridiculously so. Are you an authority? On what? How could I tell, and more importantly, what difference does it make?

      You seem to have a knee jerk reaction to authority figures, but that too is your problem.

      Possibly. But how could you know that? And you’re not an authority figure. Not here anyway.

      The world doesn't owe you citations, and neither do I.

      True on both counts. But you owe it to yourself.

      Someone who thinks psychology, an empirical science, is pseudo-science is willfully uneducated.

      Little of psychology is either empirical or a science.

      Here is Wikipedia's definition of an ad hominem attack:

      "Ad hominem (Latin for "to the person"), short for argumentum ad hominem, typically refers to a fallacious argumentative strategy whereby genuine discussion of the topic at hand is avoided by instead attacking the character, motive, or other attribute of the person making the argument."

      That is the way I have been using the term. If your definition is different, that again is your problem.


      That is exactly my definition.

      You have continually made such attacks against me, not my arguments (which you rarely engage except to say that I am wrong about some nitpick).

      This is a lie, so you should probably stop saying it. I have never attacked your character. I don’t know you, and your character is irrelevant to what you post. I have never attacked your motives. Why you post here is your business and also irrelevant to your claims. I have never attacked an attribute of yours. I have criticized your sloppy thinking and careless reading. These are actions, and not attributes. If you think that my criticisms dwell on trivia, that’s another thing entirely.

      I'm done with this. Next time you see one of my clearly identified comments, don't read it and it won't bother you and then you won't bother me.

      Sorry, no. I’ll read what I want and comment how I want. You don’t “bother” me, and I have no idea why you would be “bothered” by what I say. Here’s a modest proposal: why not take any one of my criticisms and respond to it reasonably even if you think it’s wrong?

      May I return to calling you professor, now?

      Ironically, of course.

      Delete
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  2. It is very cool that mathematics describes the real world. If it didn't, engineering wouldn't work. However, our modern physics was created by doing experiments, not by extending Aristotle. So, some of the mathematics of physics comes from the physical world, so there is some interdependence and circularity. The two worlds didn't originate separately, as Somerby's quotation of Livio seems to suggest.

    There is a similar interdependence between conscious experience of physical reality and that reality because the sensations arise from interacting with the physical world. Again, no independence, so no surprise that the two are correlated (in most people).

    There is a similar correspondence between language and perception and the physical world. But when perception isn't available, people nevertheless learn about the physical world through language relationships. Roger Shepard did an experiment in which blind-from-birth subjects were asked to make similarity/difference judgments about color terms. He applied multidimensional scaling to their answers and the data produced a graph of Newton's color wheel, closely similar and circular, like the graph of data from people with normal color vision. Since these people could not see at all, their experience of color came entirely from language used by people around them. Thus Somerby's desire to abandon language as a useless or meaningless or inaccurate descriptor of experience doesn't have a lot of empirical support. Language does describe a consensual, shared experience of physical reality.

    Shepard's experiment was done after Wittgenstein's death, but it illustrates a problem with philosophy that doesn't incorporate empirical findings from other fields. I think that is a bigger challenge to philosophy than Wittgenstein's ideas about meaning and language's difficulty capturing meaning. Those problems were addressed using probabilistic (as opposed to deterministic) approaches that Somerby utterly ignores.

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  3. “According to Livio, Penrose believes that the world of Platonic forms is a motherland which has an actual reality. It's where you'll find the number 1! Can this be distinguished from madness?”

    Actually, according to Penrose, as quoted by Livio:
    “No doubt there are not really three worlds but one, the true nature of which we do not even glimpse at present.”

    Somerby is presenting the discussion in the most boneheaded way possible, so as to make it seem ridiculous.

    The point, for me, is not whether the number “1” actually “exists” separately from our experience. It is the question of whether we can discover truths about the world via mathematics.

    Just as, by looking through a microscope, we can discover things we did not previously perceive with the unaided eye, mathematics allows us to discover truths about the physical world that were otherwise unknown, and might possibly escape detection. It is in this sense that mathematicians like Penrose mean that mathematics is as much a discovery of the realities of the world as physics is. This is, I think, what Livio is trying to convey by getting the reader to imagine a world of mathematical reality where numbers and mathematical formulae actually “exist” outside our consciousness.

    I find the discussion fascinating and worthwhile, and reject Somerby’s ridicule of it.

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  4. “ This is, I think, what Livio is trying to convey by getting the reader to imagine a world of mathematical reality where numbers and mathematical formulae actually “exist” outside our consciousness.”

    Why?

    Why not say something more precise, such as:

    “Just as, by looking through a microscope, we can discover things we did not previously perceive with the unaided eye, mathematics allows us to discover truths about the physical world that were otherwise unknown, and might possibly escape detection.”

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    Replies
    1. Because the idea is this: did Newton discover the laws of motion, or invent them? Did Einstein discover the law of relativity, or invent it?

      Newton’s mathematical formulation of the laws of motion correctly described the behavior of all objects, and allowed inferences and predictions about that behavior that were otherwise unknown, but were borne out by experiment. Einstein, via purely mathematical means, extended Newton’s discoveries to different frames of reference, accessing truths about the physical world that might never have even been suspected.

      Are the laws of motion merely a way of organizing our thoughts, or are they fundamental aspects of nature that Newton discovered? It is this latter question that prompts some mathematicians to postulate that mathematics is inherent in nature, rather than a mere set of convenient descriptions of it, just as we “see” the actual way a virus looks in a microscope, we “see” that nature behaves according to mathematical principles. That is why Livio presents mathematical constructs as existing outside our consciousness to illustrate the idea of discovering truths.

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    2. Putting aside your last sentence, you just conveyed that idea very lucidly.

      You’re a genius!

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    3. You may find Livio’s presentation of mathematical Platonism silly, or childish, or “mad”, but some readers might need or appreciate a concrete example to help them grasp the abstract concepts involved in the discussion. Somerby focuses on Livio’s simplified description, but ignores the point of his discussion, which is to try to describe and understand what some prominent mathematicians in some sense believe about their subject. It doesn’t seem like madness to me.

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    4. Newton’s mathematical formulation of the laws of motion correctly described the behavior of all objects,....

      No, the problems with Mercury's orbit under Newton’s laws were known from at least 1845.

      and allowed inferences and predictions about that behavior that were otherwise unknown, but were borne out by experiment.

      Not really, even if by "experiment" in the case of astronomy, you mean observation. Kepler's laws of planetary motion predate Newton's by decades.

      Einstein, via purely mathematical means, extended Newton’s discoveries...

      Again, no. Einstein was guided by the results of scientific experiment.

      to different frames of reference, accessing truths about the physical world that might never have even been suspected.

      Hardly. David Hilbert and Marcel Grossman had more than suspicions.

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  5. To quote Einstein, as Livio does:
    “how is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?”

    The crux of the issue is the phrase “independent of experience.”

    You may agree or disagree with that, but that is what Livio is trying to explain in the passage Somerby quotes.

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  6. Oy gevalt, TDH is back on this stuff again. He's all in a dither about some book written years ago, and he doesn't think it makes sense. He has a nutty obsession about this. He seems to imply that this one book by some physicist that he can't understand is somehow relevant to the hardly new phenomenon that lots of people (maybe everyone to some degree or another), particularly the press and our pundits, aren't always that rational. As if this is something astonishing. Livio's book, whether it's absurd or brilliant or somewhere in between, doesn't illustrate anything about the current state of our national discourse. TDH, like so many, seems to see things ahistorically - illogic and irrationality are nothing new. (Though the stakes could be higher now, the more complex things seem to keep getting). TDH seems to fall into the falsity of reading one book, and assuming it is central to a lot more than it really is. There's zillions of books. One book is only a small piece of a puzzle, and these are topics where years of study are involved to really understand them. TDH has an irrational obsession, and it's painful to read this from him, and I've been reading him for close to 20 years

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    1. You are really missing Somerby's point. It is to humiliate some professor by showing him to be not as smart as professors are supposed to be.

      That is why Somerby takes such pains to tell us how smart Livio is. Because, pointing out irrationality means nothing when someone has no pretensions to be a mind worker. Calling a stone mason not bright won't hurt his feelings. But showing that Livio has messed up, after being called smart, that is Somerby's point.

      And look who is pointing out the mistakes. Somerby! So if someone as smart as Livio can be taken to task by a mere mortal such as Somerby, Somerby must be even brighter! And that is what floats Somerby's boat. He is implicitly saying -- "see, you aren't so smart, you smarty-pants Livio."

      This is a tiresome game and Somerby should be embarrassed to play it. It is the small person's trick of humbling someone they resent for reminding them of their own failings, and each of these essays leave little doubt that Somerby didn't do well at Harvard.

      At this stage in his life, Somerby should be focusing on his own accomplishments, not still wrapped up in what he didn't do very well.

      Delete
    2. Corby, you don’t have to agree with Somerby’s reasoning in his critique of Livio, but you should at least acknowledge that reasoning since you are referring to blogs where he has expressly stated his opinion and the motive behind it.

      Start there rather than doing your usual launch into a personal attack.

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    3. You are really missing Somerby's point. It is to humiliate some professor by showing him to be not as smart as professors are supposed to be.

      That's your job, professor, as you demonstrate on yourself every time you post.

      Delete
    4. Oy! indeed. TDH, once again The Slowest Boy in the Class, pretends he's Don Quixote. Instead of windmills, he jousts with those he thinks are windbags. His motto: if I can't understand it, nobody can.

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    5. Corby, you don't seem able to reason very well. This is all projection on your part. You come across as foolish, with your evidence deficient ad hominem pronouncements. TDH has a thing about those who attempt to popularize difficult scientific theories, and in fact (at least to TDH) don't clear things up very much. (He also is disturbed by critics of these books, who claim that the writers do make things clear, when they don't, at least to TDH. There is also that ahistorical approach, which you certainly seem to share.

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    6. Somerby cannot discuss Livio without ad hominems. In nearly every post, he delves into the background of the person he is criticizing, to fault them for going to this or that Ivy League college and to blame them for being born too recently.

      This isn't the way anyone discusses ideas. It is the way Somerby vents his spleen. Somerby's posts speak for themselves.

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    7. Saying that Livio, while brilliant, is "playing out of position" because he's not a logician is an ad hominem? Somerby grousing that this sort of writing is unhelpful silliness that is the result of logicians being lax at their post is a ad hominem attack? Saying this has resulted in poor reasoning skills among the rest of us lesser beings, including the people we depend upon for news analysis, is an ad hominem?

      Oh, come on, Corby.

      Delete
    8. Calling Livio smart is an ad hominem. Then implicitly "mad" is more of the same.

      Nobody got there reasoning skills, poor or otherwise, from Livio. Reporters don't reason. They report.

      Delete
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