Mathematics and Religion

[stone space]

Roundtable discussion with Dominic Balestra, Loren Graham, Edward Nelson, Rebecca Newberger Goldstein, and Max Tegmark.

[struggle4progress]

1. Nelson was a good mathematician

I enjoyed his "Radically elementary probability theory" and "Predicative Arithmetic"

I always forget the exact source for "The child counts on his fingers; the mathematician counts on ?; but at least the child knows his fingers exist" -- but I think it's Nelson's "Predicative Arithmetic"

[stone space]

2. "Predicative Arithmetic" is a cool book.

I haven't seen "radically elementary probability theory".

There was some mention of it in PA. I seem to remember something about mimicked nonstandard analysis in some extension of Robinson's Q in which the totality of exponentiation fails, or something vaguely like that, but it was a long time ago.

I'm going to check it out some time.

[Lucky Luciano]

3. Don't have time to watch a one hour video...but...

The Continuum Hypothesis was always one thing I thought mathematicians took on faith - can't be proven or disproven, but I think people silently accept it as fact.

[Jim__]

4. Interesting discussion.

It will take some time to digest everything that was said. However I did question something that was said by Rebecca Goldstein and Max Tegmark:

...

Goldstein: But you as a sort of extreme Platonist seem implicitly to agree with Spinoza, I mean that the big picture, which is inaccessible to us I mean, to me it’s amazing that we know anything at all.

...

Goldstein: I mean we’re just these random products of evolution.

Tegmark: I mean we are. We evolved our brains to be able to pick bananas and throw rocks at each other [laughter], and here we are talking about Spinoza.

...

It seems to me that intelligent entities are almost a necessary result of a long-running, competitive, adaptive process.

The video seems to end somewhat mid-sentence. There is a pdf file of the discussion which does continue a little bit passed the end of the video.

[muriel_volestrangler]

5. "almost a necessary result" doesn't seem a valid conclusion to me

It only appears to have happened once (in terms of species that can discuss philosophy, as far as we can tell) on this planet, and no sign yet on other planets (there may be good reasons we can't detect that yet, but there's no evidence intelligence has developed elsewhere).

Compare that one-off to, say, the development of streamlined, tail-driven ocean predators in multiple lines, ending up with a very similar body plan (sharks, ichthyosaurs, dolphins), and it's quite a different situation. If you'd looked at the earth 10 million years ago, there'd be no sign of our kind of intelligence; but sharks developed several hundreds of millions of years ago, ichthyosaurs a couple of hundred million years ago, and dolphins a few dozen million years ago.

[stone space]

6. Our new dog is pretty stupid. I don't expect him to be able to discuss Spinoza.

"almost a necessary result" doesn't seem a valid conclusion to me

It only appears to have happened once (in terms of species that can discuss philosophy, as far as we can tell) on this planet

Hell, I can't discuss Spinoza.

But I do expect him to have enough intelligence to read our damn minds!

Now, I can't read minds myself, but I'm a human. And a "human" is just a "namuh" spelled backwords. It's unreasonable to expect a namuh to have the ability to read minds.

On the other hand, Muñeco is a dog. Just like Trosqui was. And Trosqui had enough intelligence to read our minds forwards and backwards.

Look, I get it. Muñeco's still going to get fed regardless of his IQ, and he's been fixed, so he's got no progeny to pass any mind-reading genes down to, but damn!

His life is going to be much, much happier if he learns to read our minds like Trosqui did.

Are my expectations unreasonable? Muñeco is the result of random processes, after all. Perhaps expecting him to show some intelligence is an unreasonable expectation for a product of random processes?

[stone space]

7. I'll believe this when I meet a cat with the mind-reading abilities of a dog.

It seems to me that intelligent entities are almost a necessary result of a long-running, competitive, adaptive process.

A "cat" is just a "tac" spelled backwords, and a cat can be as dull as a tac.

Sure, maybe cats can read the minds of mice, but am I supposed to be impressed by that? A "mouse" is just a "esuom" spelled backwards. How hard can the mind of an esuom be to read?



(Thanks for the pdf, btw. Takes me forever to download a video, and I was a bit annoyed when it cut off in mid-sentence.)