Some of the “vague grand claims” I still find useful/insightful:
There are (roughly) four classes of ‘complexity’: ‘static’, ‘simple repetition and nesting’, ‘randomness’, and ‘history’
‘Universal computation is common and cheap’ – this seems more and more confirmed via, e.g. various ‘Turing completeness’ results
Computation is (in some important sense(s)) ‘more general’ than mathematics (particularly the parts of it that mathematicians study) – on the other hand, I’d guess ‘computation’ and ‘math’ are ‘technically’ equivalent; on the gripping hand, one of my favorite Scott Aaronson papers/essays makes me think there might be a bit more to this
A lot of natural systems really can be modeled as ‘simple programs’, and much more easily/‘naturally’ than as simple mathematical systems
Fair enough!
Some of the “vague grand claims” I still find useful/insightful:
There are (roughly) four classes of ‘complexity’: ‘static’, ‘simple repetition and nesting’, ‘randomness’, and ‘history’
‘Universal computation is common and cheap’ – this seems more and more confirmed via, e.g. various ‘Turing completeness’ results
Computation is (in some important sense(s)) ‘more general’ than mathematics (particularly the parts of it that mathematicians study) – on the other hand, I’d guess ‘computation’ and ‘math’ are ‘technically’ equivalent; on the gripping hand, one of my favorite Scott Aaronson papers/essays makes me think there might be a bit more to this
A lot of natural systems really can be modeled as ‘simple programs’, and much more easily/‘naturally’ than as simple mathematical systems