Timeline for Alive dynamical system
Current License: CC BY-SA 2.5
12 events
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| Mar 8, 2010 at 17:30 | comment | added | kakaz | "Church-Turing thesis, which seems fundamental to your question" - interesting part of it, is that it is empirical theorem about computable functions. So as it is used explicite in First Gödel Theorem of Incompleteness of arithmetic, it should be concerned to be in fact empirical fact and not mathematic theorem... That's way I suppose question asked here is important but should be reformulated: is for every system in mathematic to simulate it with Turing Machine. | |
| Mar 2, 2010 at 1:08 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
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| Mar 1, 2010 at 13:39 | comment | added | Joel David Hamkins | With that interpretation (and some minor assumptions on the interpretation functions), then the shift map is dead. I have edited my answer to explain this. | |
| Mar 1, 2010 at 13:26 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
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| Mar 1, 2010 at 12:11 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
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| Mar 1, 2010 at 2:04 | comment | added | Anton Petrunin | Shift space can not do "calculations". I think instead of "computable translation" one has to have an algorithm which makes "translation" in time depending only on n. | |
| Mar 1, 2010 at 2:01 | comment | added | Anton Petrunin | One can think that in CGL you start with a random position with infinite set of points but you can change something in a bounded region. Then you can take any program for UTM and make it to work for arbitrary big number of steps. (by making free space around your "computer"). (So you do not need to choose exact point but can make it approximately). This way there is no real difference with shift space. | |
| Feb 28, 2010 at 23:10 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
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| Feb 28, 2010 at 23:00 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
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| Feb 28, 2010 at 22:48 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
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| Feb 28, 2010 at 22:07 | comment | added | Anton Petrunin | With this definition, can you prove say that shift space is dead? | |
| Feb 28, 2010 at 21:58 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |