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Computational Universality, Chaos, and Computing with Real Numbers
Published on Jul 10, 20124996 Views
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Chapter list
Computational universality, chaos, and computing with real numbers00:00
The big question00:26
The mathematical abstraction of "everything": dynamical systemsynamical systems01:00
Dynamical systems (1)01:44
Dynamical systems (2)02:49
Examples of prediction questions04:25
The big question – refined05:21
A "dream box" of Applied Mathematics05:39
Obstacles to "predicting everything"06:03
Obstacle #1: Computation and continuous systems07:11
Obstacle #2: Chaotic behavior08:02
Chaotic ≠ hard!08:37
Obstacle #3: Computational universality and undecidability10:28
Other shattered dreams10:59
The Halting Problem11:46
Other examples12:30
The computer as a dynamical system12:57
Computational universality (1)13:56
Computational universality (2)14:13
Computational undecidability vs. computational universality15:02
Undecidable = hard!15:37
Universality is there ...15:56
Universality is there ... but is it relevant in practice?17:07
Robust universal systems do exist18:00
Universality in "simple" systems18:40
An example of a "simple" system19:02
Julia sets (1)20:00
Julia sets (2)20:11
Julia sets (3)20:42
Julia sets (4)21:15
Julia sets (5)21:16
There are non-computable Julia sets21:18
But ...21:53
The map of parameters22:24
(Non)-Computability in dynamics (1)23:24
(Non)-Computability in dynamics (2)23:52
(Non)-Computability in dynamics (3)24:12
The road ahead24:26
Thank You!25:40