We scan The Atlantic's idea of deep thought!

FRIDAY, NOVEMBER 22, 2024 

The sound of zero hands clapping: Are we the humans actually capable of conducting a serious discourse? Are we built for such work?

As we noted along the way, it isn't clear that the answer is yes. This brings us to new essay for The Atlantic by Arthur Brooks.

No one with any serious "training," analytical or comedic, could have resisted its principal headline. That principal headline says this:

Three Ways to Become a Deeper Thinker

Three ways to become a deeper thinker? Who could have passed that up?

Starting in 1991, Saturday Night Live put Jack Handey in charge of that program's Deep Thoughts. In fairness, Handey was and is a humorist; Brooks is serious all the way down.

Are we wired for this sort of work? Dual headline include, the Brooks essay starts like this:

Three Ways to Become a Deeper Thinker
You don’t have to become a Buddhist monk to realize the value of contemplating hard questions without clear answers.

What is the sound of one hand clapping?

You may have encountered this cryptic question at some point. It is a koan, or riddle, devised by the 18th-century Zen Buddhist master Hakuin Ekaku. Such paradoxical questions have been used for centuries to train young monks, who were instructed to meditate on and debate them. This was intended to be taxing work that could induce maddening frustration—but there was a method to it too. The novitiates were not meant to articulate tidy answers; they were supposed to acquire, through mental struggle, a deeper understanding of the question itself—for this was the path to enlightenment.

That's the way the essay starts, beneath that dual headline.

It's possible that there's some cultural tradition within which that "cryptic / paradoxical question" might be seen as making some kind of sense, or perhaps as serving some mind of purpose. 

Here within the western world, things may not work that way. Here within the western world, when we talk about "clapping your hands," we're talking about something that's done with two hands.

It isn't obvious what you'd mean if you spoke about clapping your hand [singular]—if you spoke about "clapping" just one hand. Of course, a person could always explain what he meant by some such locution, but absent some such explanation, there would be no obvious way to know what the person might have meant, and it wouldn't make any obvious sense to try to figure it out.

This silly piddle from Zenmaster Arthur came on a glorious day. Even as post-election intellectual chaos controls the discourse on every front, we decided today to return to a more fundamental question:

Does Kurt Gödel's "incompleteness theorem" actually make any sense?

We took Stephen Budiansky's bio of Godel with us to the medical joint, which doubles as an excellent reading room. This is the volume in question:

Journey to the Edge of Reason: The Life of Kurt Gödel. W.W. Norton & Company, 2021.

Gödel's theorem is regarded as a major masterwork. Gödel himself is routinely described as "the greatest logician since Aristotle."

Is it possible that Gödel's master theorem doesn't make any sense? We dipped into Budiansky's book for the first time in several years, and we were surprised by our initial reaction:

Counterintuitive as it might seem, we'll guess that the answer ain't yes.

(Can anything linked to "Russell's paradox" actually make any sense?)

The Atlantic chose to publish the Arthur Brook piece. Regarding the question we've been asking about the way we humans are built, that decision, all by itself, along may allow us to rest our case.


5 comments:

  1. I will try one more time for Bob's benefit. I know this is a waste of time, since he doesn't read his comments.

    Consider this statement: In the decimal expansion of pi there is no sequence of 9's longer than a trillion. If this is false, it could be disproved 9 (in theory) by expanding pi to enough digits to find a sequence of 9's longer than a trillion. But suppose it's true. Could you prove that? No matter how far you expanded pi, how could you be sure that a sequence of 9's longer than a billion exists in the part you haven't looked at. Yet, the statement really is either correct on incorrect.

    There was a hypothesis that all correct theorems could be proved within the system. Godel showed that there are true theorems that cannot be proved. This statement seems paradoxical. How could you know that some theorem is true if it can't be proved? That's why Godel's achievement is so impressive.

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    1. The theory that there is a Republican voter who cares about something other than bigotry and white supremacy, can not be proven.

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  2. Somerby pretends to think by name-droping Godel. It is our signal to go do something useful, like laundry. Somerby should ask any computer scientist why Godel’s work is important and stop wasting his readers’ time.

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  3. "Godel showed that there are true theorems that cannot be proved."

    How did he show this?

    And what does it mean to say 'There was a hypothesis that all correct theorems could be proved within the system.'

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    1. Answer to your second question: Some mathematicians suggested that this might be the case.

      To fully answer your first question I would have to repeat Godel’s entire proof. Many years ago I had a general idea of how the proof worked, but haven’t reviewed it for a long time. My vague memory is that the proof involved converting statements into unique numbers. Verifying a statement could be determined by arithmetic operations on the corresponding Godel number.

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