"Rationality"-New Book By Steven Pinker - Page 21 - Politics and Society -- Two Plus Two Poker Forums

I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes "999999", so that I could recite it out loud, come to those six 9's, and then impishly say, "and so on!"

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01-08-2022 , 05:11 PM

#502

d2_e4

certifiable moron

Join Date: Sep 2014 Posts: 12,408

Quote:

Originally Posted by ecriture d'adulte

So I'll sum up as clearly as possible why I don't think this is super interesting (and why I don't think any experts in number or proof theory would either). There are 2 senses in which something can be true but unproveable. One is very mundane and easy to give examples of. An example would be

This is something that can be checked integer by integer because once you define a Godel numbering every integer corresponds to a unique string of symbols via the fundamental theorem of arithmetic. Whether this integer exists or not is really more of a philosophy question. We can prove it doesn't exist, but the proof is not convincing. Basically the question is whether PA is consistent and any proof of it assumes PA is consistent. It's unclear whether this would qualify as "true but unproveable" in the sense you are talking about.

The other sense is something like

This is pretty obviously true but it's unproveable in a very different sense than the former. Our present technology just doesn't allow for us to prove things like this. It's also easy to come up with hundreds of examples of stuff like this. But unless someone places any kind of fundamental limit on why stuff like this can't be proven, it's not very interesting. And nothing you're doing comes close to that. I don't know if you talked to any actual set/proof theory experts (Joel Hamkins etc) but unless one of them finds this interesting or someone else can explain to me why it is, I'm inclined to say it isn't.

Homie literally put "convergent" in quotes when talking about his discovery of how to partition pi into a series that "decreases fast enough", like it was a word he came up with himself. You think he's talking to experts? That is what? Calc 1? High school stuff? When do kids learn the ratio test over there?

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01-08-2022 , 05:36 PM

#503

d2_e4

certifiable moron

Join Date: Sep 2014 Posts: 12,408

Quote:

Originally Posted by uke_master

Speaking of pi, 9s, and Hofstader, I love this quote:

Wonder if Dave actually owns a copy.

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01-08-2022 , 05:46 PM

#504

d2_e4

certifiable moron

Join Date: Sep 2014 Posts: 12,408

Quote:

Originally Posted by King Spew

Perhaps this derail can be switched off..... ?

Can I get some rakeback for being #1 troll or something? I'm bringing people to your forum!

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01-08-2022 , 05:48 PM

#505

washoe

Carpal \'Tunnel

Join Date: Oct 2019 Posts: 8,519

Quote:

Originally Posted by d2_e4

Wonder if Dave actually owns a copy.

Mate, real geniuses like Einstein or tesla would have never used chrome. It's privacy. Use Mozilla etc.

'Google's Chrome browser is a privacy nightmare in itself, because all you activity within the browser can then be linked to your Google account. If Google controls your browser, your search engine, and has tracking scripts on the sites you visit, they hold the power to track you from multiple angles'
https://medium.com/digitalprivacywis...tiple%20angles.

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01-08-2022 , 05:48 PM

#506

King Spew

Just average

Join Date: Apr 2006 Posts: 15,283

I'll just sign over my current mod paycheck to you. Should be more than enuf to establish value.

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01-08-2022 , 05:49 PM

#507

d2_e4

certifiable moron

Join Date: Sep 2014 Posts: 12,408

Quote:

Originally Posted by King Spew

I'll just sign over my current mod paycheck to you. Should be more than enuf to establish value.

I guess my rakeback is that I haven't been banned yet. That's good enough for me.

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01-08-2022 , 05:55 PM

#508

King Spew

Just average

Join Date: Apr 2006 Posts: 15,283

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01-08-2022 , 05:56 PM

#509

d2_e4

certifiable moron

Join Date: Sep 2014 Posts: 12,408

Actually lolled.

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01-08-2022 , 06:00 PM

#510

King Spew

Just average

Join Date: Apr 2006 Posts: 15,283

Quote:

Originally Posted by King Spew

later edit:
Iz bin bery, bery hard for me to hit the Reset button.

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01-11-2022 , 12:53 PM

#511

ecriture d'adulte

Pooh-Bah

Join Date: Jan 2017 Posts: 5,946

Quote:

Originally Posted by David Sklansky

It is also important to realize that my thoughts are not so much that sparseness could account for non provability (if such a thing actually exists regarding number theory), but rather that non sufficient sparseness guarantees provability if the conjecture is true. The main problem with my thoughts is that I offer no precise algorithm to turn a number theory conjecture into a pseudo probability problem. That is why I enlisted pi's digits to help explain.

I think the main weakness of this whole “program” is you haven’t given any examples of non proveable conjectures of the type you’re talking about to begin with. So just guessing they some subsection must have proofs, when they all seem to is boring.

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01-11-2022 , 05:33 PM

#512

rickroll

oddly catty

Join Date: Aug 2011 Posts: 23,026

Quote:

Originally Posted by David Sklansky

Can someone please read the Pinker book now?

oh david, i wish i had your optimism in life

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01-12-2022 , 08:14 PM

#513

Mathematical Dick

stranger

Join Date: Aug 2018 Posts: 9

Quote:

Originally Posted by d2_e4

Since this thread is pretty much done - dude, love your posts, but you used the symbol for the wrong function. Yours is for the Euler totient function (which, ironically, takes only positive integer values). The one you want is the one that looks like the golden ratio symbol. Thank me later.

φ and ϕ are both lower case phi, just different styles. Both are used for the same things. The classic number theory book by Hardy uses ϕ for totient, and φ gets used for golden ratio. What I typed can be properly displayed as either depending on the resident fonts, but browsers generally display φ. I can force it to display ϕ, but it's not a default key binding, and some older systems can't display it. Our Euler function can also be denoted with the q-Pochhammer (0.1)_∞, (0.1; 0.1)_∞, or even (1; 0.1)_∞.