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Jordan Peacock
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In varying degrees of progress...

Big step is that I'm now driving enough to justify audiobooks; working through The Name of the Wind (paused The Making of the Atomic Bomb, but both audiobooks are fantastic thus far).

Reading aloud Thinking the Twentieth Century with the girlfriend; we get about 10 pages of progress per session, so that one will bleed into 2017 for sure.

Voltaire's Bastards and The Use of Bodies are books where you read each chapter thrice.
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Currently reading. Also starting Pattern Recognition by William Gibson this weekend as part of a reading group.
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Icelandic inheritance law 
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I may have bitten off more than I can chew. 
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I'll just leave this here..

https://news.ycombinator.com/item?id=11803165

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Some updates.

First of all, because I'm a huge philosophy geek, I excitedly preordered these two books that I've been watching the progress of for literally years:

An English translation of Simondon's 'On the Mode of Existence of Technical Objects':
http://www.univocalpublishing.com/univocal-books/on-the-mode-of-existence-of-technical-objects

and Adam Kotsko's treatise on the devil, 'The Prince of This World':
https://itself.wordpress.com/2016/04/29/the-prince-of-this-world-is-available-for-pre-order/

The other thing was recognizing how I tend to find books, novels in particular, at all. My wife was asking me was led to the novels currently on my stack (Jo Walton's The Just City, Alvaro Enrigue's Sudden Death and Maureen F. McHugh's China Mountain Zhang).

The answer was telling: Walton was via the Crooked Timber group blog, they have been doing a symposium on it. Past symposiums have covered non-fiction such as Piketty's Capital in the Twenty-First Century and Graeber's Debt: The First 5,000 Years and novels such as Stross' bibliography and Spufford's Red Plenty. I've read Among Others by Walton, which was pretty good (although not the 6/5 stars I was hearing from other people), but the conceit of a novel in which Athena pulls Sokrates, Boethius, Proclus, Plotinus, etc. into pre-cataclysm Atlantis to build Plato's republic was pure Jordan-candy. And I just finished vol. 2 of A History of Philosophy Without Any Gaps which focused substantially on these Neoplatonists. So, there's that.

Enrigue I'd never heard of, but Warren Ellis reviewed Sudden Death in his newsletter as follows:

"SUDDEN DEATH by Alvaro Enrigue is fucking superb. The translator, Natasha Wimmer, produces a sensitive and nimble translation of what must have been a murderous enterprise. Enrigue frames the end of the Renaissance and the conquest of Mexico in... a tennis game. He achieves that marvellous thing of connecting all the moving parts of the transition of an age in a single bloody tennis game and all the threads that come off it. Very few people can pull this particular stunt off properly, and we have to add Enrigue to that short list. And Enrigue doesn't give a fuck - he sticks emails in there, stops dead to address the audience like a writer/presenter of rhetorical television, even discussing and explaining the mechanics of the book itself. It's big, audacious, smart, funny, learned, gory, occasionally lit with anger, and he spins it all together into a swirling fugue of a crescendo. I burned through it in three nights. One of the essential reads of the year, I think."

Finally, China Moutain Zhang came up not once, but three times, once with the high praise of "my favourite science fiction novel of all time" at the local science fiction convention I attended last month. Having not heard of it before, I was immediately intrigued... more so the more I learned of it.

So short answer: find people with excellent taste. Poach from them.

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Computing the uncomputable

Last month the logician +Joel David Hamkins proved a surprising result: you can compute uncomputable functions!  

Of course there's a catch, but it's still interesting.

Alan Turing showed that a simple kind of computer, now called a Turing machine, can calculate a lot of functions.  In fact we believe Turing machines can calculate anything you can calculate with any fancier sort of computer.  So we say a function is computable if you can calculate it with some Turing machine.

Some functions are computable, others aren't.  That's a fundamental fact.

But there's a loophole.

We think we know what the natural numbers are:

0, 1, 2, 3, ...

and how to add and multiply them.  We know a bunch of axioms that describe this sort of arithmetic: the Peano axioms.  But these axioms don't completely capture our intuitions!  There are facts about natural numbers that most mathematicians would agree are true, but can't be proved from the Peano axioms.

Besides the natural numbers you think you know - but do you really? - there are lots of other models of arithmetic.  They all obey the Peano axioms, but they're different.  Whenever there's a question you can't settle using the Peano axioms, it's true in some model of arithmetic and false in some other model.

There's no way to decide which model of arithmetic is the right one - the so-called "standard" natural numbers.   

Hamkins showed there's a Turing machine that does something amazing.  It can compute any function from the natural numbers to the natural numbers, depending on which model of arithmetic we use. 

In particular, it can compute the uncomputable... but only in some weird "alternative universe" where the natural numbers aren't what we think they are. 

These other universes have "nonstandard" natural numbers that are bigger than the ones you understand.   A Turing machine can compute an uncomputable function... but it takes a nonstandard number of steps to do so.

So: computing the computable takes a "standard" number of steps.   Computing the uncomputable takes a little longer.

This is not a practical result.  But it shows how strange simple things like logic and the natural numbers really are.

For a better explanation, read my blog post:

https://johncarlosbaez.wordpress.com/2016/04/02/computing-the-uncomputable/

And for the actual proof, go on from there to the blog article by +Joel David Hamkins.
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