What's a "phantom explanation?"

THURSDAY, JUNE 10, 2021

Afternoon delights: Yesterday afternoon, in award-winning fashion, we introduced an award-winning term—"phantom explanation."

We were thinking of the phenomenon known as "phantom limb." Somehow, an arm or a leg has been lost—but it may continue to feel like the missing limb is there.

A surprising amount of high-level academic communication involves phantom explanation. The phenomenon goes like this:

After some question has arisen, an apparent explanation is offered. In fact, the matter at issue hasn't been explained at all. The apparent explanation doesn't make sense, but the person receiving the apparent explanation can't tell. 

That person believes he's received an explanation. He believes he's understood it.

In fact, that hasn't happened at all. A few simple questions will reveal the fact that the recipient of the phantom explanation actually doesn't understand the matter in question at all.

A surprising amount of high-level academic and journalistic communication involves phantom explanation. The later Wittgenstein seemed to suggest that most academic philosophy comports to this awkward model.

A collection of words is emitted. It sounds like the words make sense—like something has been explained.

Nothing resembling that has occurred. In fact, the explanation is a phantom, but the recipient can't tell.

Phantom explanation will often occur in books about physics or math aimed at the general reader. If the person writing the book is highly regarded, journalists will enthusiastically say that the work in the book is amazingly clear, even though the work in the book is basically incomprehensible.

This question arises in the case of Stephen Budiansky's new biography of Kurt Gödel, Journey to The Edge of Reason. The book is written for the general reader. The problem we face is this:

Gödel is routinely cited as "the greatest logician since Aristotle." With that in mind, what did this greatest logician discover, prove or show?

More to the point, is Budiansky able to explain what Gödel discovered, proved or showed? Beyond that, a second question may even arise:

Are we completely sure that Gödel proved anything of value at all?

The later Wittgenstein might have said no to the latter question. Regarding Budiansky's efforts in his new book, we'll also go with a no. 

(We're not suggesting that anyone else could have done any better.)

In our view, no general reader will emerge from Budiansky's book with anything like an understanding of whatever it is Gödel is alleged to have proven.  The reader may think that he understands. Our prescription?

Let the (simple) questions begin!

We'll have much more in coming weeks about this fascinating topic. Decades after the start of our journey, the pointlessness of commenting on the mainstream public discourse has at last become abundantly clear, even at long last to us!

Meanwhile, what the heck did Gödel prove? Taking a further Wittgensteinian road, do we feel completely sure that he demonstrated, proved or showed anything at all? 

For entertainment purposes only: Budiansky occasionally offers a humorous look at what preceded Gödel. In the passage shown below, he describes the problems which arose when Bertrand Russell decided, at the turn of the century, that he should do whatever it is he did:

BUDIANSKY (page 108): In deciding to take on the fourth of the challenges Hilbert had put forward at the Congress of Mathematicians in 1928, Gödel placed himself at the very center of the storm over mathematical foundations, which had broken with a deeply unnerving discovery Bertrand Russell had made at the turn of the century while working on Principia Mathematica.

Russell's idea had been to establish the soundness of mathematics by showing how it could all be reduced to principles of logic so self-evident as to be beyond doubt. Defining even the simplest operations of arithmetic in terms of what Russell called such "primitive" notions, however, was far from an obvious task. Even the notion of what a number is raised immediate problems.

The laboriousness of the methodology and notation was all too evident in the (often remarked) fact that that it took more than seven hundred pages to reach the conclusion, "1 + 1 = 2," a result which Russell and Whitehead described as "occasionally useful."

It took Russell and Whitehead more than seven hundred pages to establish the fact that 1 + 1 = 2? The amusement only deepens as Russell makes his "deeply unnerving discovery," then later as the years lead on toward the 24-year-old Gödel.

The methodology had been laborious. Are we sure this fandango made sense?


26 comments:

  1. "In fact, the explanation is a phantom, but the recipient can't tell."

    Perhaps it's because you sound like you're looking for a layperson's common sense explanation, dear Bob, while that Gödel thing (as well as the 1+1 thing) deals with formal logic.

    The latter has very little to do with the former. They're probably trying to explain it the best they can, but they also want to sell books and make money (and/or become famous), so you get what you get, and that's all there is to it.

    ReplyDelete
    Replies
    1. Uncle Vova says the United States is making the same mistakes as the Soviet Union.

      https://www.youtube.com/watch?v=z9QIAOniWf0

      Delete
  2. "A surprising amount of high-level academic communication involves phantom explanation. The phenomenon goes like this:

    After some question has arisen, an apparent explanation is offered. In fact, the matter at issue hasn't been explained at all. The apparent explanation doesn't make sense, but the person receiving the apparent explanation can't tell. "

    This is what the world looks like to someone who thinks he knows things that he does not know. Those explanations are not phantom to people with sufficient background to understand them. That apparently does not include Somerby.

    Academics would be the first ones to cry foul on each other if these so-called phantom explanations were not real; peer review and academic criticism would point out the problelms. That is what peer review is for.

    Instead, Somerby has made up an ugly term to malign academics -- again. He is not being clever. He is being ignorant. Like Trump, Somerby's ego knows no bounds, so it cannot be his problem when he cannot understand, so he makes up an impossible explanation to preserve his self esteem. It must be that all those academics are giving phantom explanations, and in fact the whole of science is just one big house of cards, waiting for someone like Somerby to bring it tumbling down.

    And who benefits when academics aren't around to tell people not to drink bleach. We all know the answer to that question.

    ReplyDelete
  3. 'More to the point, is Budiansky able to explain what Gödel discovered, proved or showed'

    Clearly not to Trumptards like Somerby, but to people with double digit and up IQs, certainly

    ReplyDelete
  4. I think Bob’s critiques of science and philosophy are sound. For example, does this explanation from the leading authority make sense?

    https://en.wikipedia.org/wiki/Redshift

    Well, maybe it does for you, if you can synthesize the generalities into something you already know about, and may even have high-level understanding of it (as I do, of course). But try to point someone ignorant of science to such a thing, especially if they’re tribally ignorant.

    Go ahead, imagine explaining red-shift to a fundie (if you could even somehow engage in such a conversation), or even a progressive! To make it coherent would be very difficult, unless you knew both how to teach, and had the patience to try to explain it in normal conversation.

    “A collection of words is emitted. It sounds like the words make sense—like something has been explained.
    Nothing resembling that has occurred. In fact, the explanation is a phantom, but the recipient can't tell.”

    That seems to be the way it goes with even simple political discourse. Especially when the recipient _can_ tell, because he doesn’t believe it, or want to believe it.

    Leroy

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    Replies
    1. The material quoted from the book stated that mathematicians were troubled by the laboriousness of Russell’s methodology and found the process and the logic less than obvious and self-evident and that this was “often” remarked upon.

      Later Godel’s theorem challenged Russell’s work.

      It’s authoritarian to suggest that it ‘s narcissistic for someone to express these thoughts, particularly in the context of critiquing a book expressly meant to make Godel’s theorem “clear”.

      Delete
    2. The book in question is a biography and its intention is to make Godel's life clear, not his theorem.

      Delete
    3. Read how the book was billed in the NYT review that was linked by Somerby:

      “...potent and entertaining ... For interested readers, Budiansky supplies an appendix that moves through Gödel’s proof, step by step, but granular knowledge of formal logic isn’t essential for anyone’s enjoyment of this moving biography. Budiansky brings a polymath’s interest to bear on a man whose life intersected with the political and philosophical upheavals of the 20th century ... Not only does Budiansky offer a clear discussion of the incompleteness theorem along with the accolades it elicited; he takes care to embed the proof in the life, avoiding the kind of gloomy interpretations that so often made Gödel feel misunderstood ...“

      Delete
    4. Read how the book was billed in the NYT review that was linked by Somerby:

      “...potent and entertaining ... For interested readers, Budiansky supplies an appendix that moves through Gödel’s proof, step by step, but granular knowledge of formal logic isn’t essential for anyone’s enjoyment of this moving biography. Budiansky brings a polymath’s interest to bear on a man whose life intersected with the political and philosophical upheavals of the 20th century ... Not only does Budiansky offer a clear discussion of the incompleteness theorem along with the accolades it elicited; he takes care to embed the proof in the life, avoiding the kind of gloomy interpretations that so often made Gödel feel misunderstood ...“

      Delete
    5. Read how the book was billed in the NYT review that was linked by Somerby:

      “...potent and entertaining ... For interested readers, Budiansky supplies an appendix that moves through Gödel’s proof, step by step, but granular knowledge of formal logic isn’t essential for anyone’s enjoyment of this moving biography. Budiansky brings a polymath’s interest to bear on a man whose life intersected with the political and philosophical upheavals of the 20th century ... Not only does Budiansky offer a clear discussion of the incompleteness theorem along with the accolades it elicited; he takes care to embed the proof in the life, avoiding the kind of gloomy interpretations that so often made Gödel feel misunderstood ...“

      Delete
    6. Do you not know what an appendix is?

      Delete
    7. Do you not know what an appendix is?

      Delete
    8. I do.

      I know what a “clear discussion of the incompleteness theorem” is too.

      Delete
    9. Material is placed in an appendix because it is ancillary to the main text.

      Delete
    10. Oh, that makes it indisputable that a clear public discussion is ever to be had in this sort of book and with this sort of material. That such a claim is ever anything more than the emperor’s new clothes. Indeed, if the field isn’t rife with that as well.

      An appendix turns a jaundiced eye into the philistine in the temple and personal insults are then levied under the aegis of a respect for knowledge, analysis, discussion, and curiosity.

      Meanwhile, you’re tackling the racial disparity in math scores and therefore in advanced math studies, with appeals to teachers to be lenient when kids don’t put answers in the right box and to look the other way when they fail at rounding up.

      Delete
  5. Also, "1 =1" or "1 + 1=2" is mathematical language, which is quite distinct from day-to-day language. What we end up with, in the case of mathematics, is whether you can actually understand it. If you cannot, should that not lead to skepticism?

    How are the lumpen (I count myself amongst them) to trust something they can't even understand it? Faith?

    The Left has their balls in a ring when it comes to right-wing propaganda, thanks to their need for PAC money. The Right, seemingly, is winning the fight of "ideas." They have no compunctions when it comes to accepting money.

    Hope like hell things go well, and we can primary Manchin, and fucks like him. The fact that his existence creates a Senate majority is weak tea indeed.

    Leroy

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    Replies
    1. "How are the lumpen (I count myself amongst them) to trust something they can't even understand it? Faith?"

      When buildings don't fall down, when your cellphone does what it's supposed to do, when drugs cure disease, etc, etc. This is pretty solid evidence that math and science are doing something right, wouldn't you say? It seems odd to mock math and science for their supposedly opaque or difficult language. The people who understand it use it to create the things I just mentioned. You can be skeptical while reaping the benefits of mathematical and scientific endeavors, I guess. Seems kind of self-centered to me, though.

      Delete
    2. "Hope like hell things go well, and we can primary Manchin, and fucks like him. "

      Jeez, what a fool you are. Taking kabuki theater, a wrestling tv show, for the comic books struggle between Good and Evil.

      If Manchin wasn't there, your liberal cult's High Priests would've assigned someone else to be The Spoiler, a-la Joe Lieberman a decade ago.

      Delete
    3. Democrats have a big tent.
      Republicans all march in goose-step to support the one thing that is important to their voters; keeping black people down.

      Delete
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