On Saturday, July 27, 2019 at 2:14:26 PM UTC-5, Philip Thrift wrote: > > > > On Saturday, July 27, 2019 at 1:42:43 PM UTC-5, Lawrence Crowell wrote: >> >> On Saturday, July 27, 2019 at 8:38:12 AM UTC-5, John Clark wrote: >>> >>> All that assumes that infinity exists for any meaningful use of the word >>> “exists” and as far as I know nobody has ever found a infinite number of >>> anything. Mathematics can write stories about the infinite in the language >>> of mathematics but are they fiction or nonfiction? >>> >>> John k Clark >>> >>> >> Infinity is not a number in the usual sense, but more a cardinality of a >> set. Infinity has been a source of trouble for some. I work with Hilbert >> spaces that have a form of construction that is finite, but where the >> finite upper limit is not bounded ---- it can always be increased. This is >> because of entropy bounds, such as the Bekenstein bound for black holes and >> Bousso bounds on AdS, that demands a finite state space for local physics. >> George Cantor made some set theoretic sense out of infinities, even a >> hierarchy of them. This avoids some difficulties. However, I think that >> mathematics in general is not as rich if you work exclusively in finitude. >> Fraenkel-Zermelo set theory even has an axiom of infinity. The main point >> is with axiomatic completeness, and mathematics with infinity is more >> complete. >> >> Richard Feynman talked about Greek mathematics, the axiomatic formal >> systems of mathematics, and Babylonian mathematics that is set up for >> practical matters. I have no particular preference for either, and think it >> is interesting to switch hats. >> >> LC >> >> >>> >>> On Sat, Jul 27, 2019 at 7:36 AM Lawrence Crowell < >>> goldenfield...@gmail.com> wrote: >>> >>>> On Thursday, July 25, 2019 at 10:02:39 PM UTC-5, Bruce wrote: >>>>> >>>>> On Fri, Jul 26, 2019 at 12:48 PM John Clark <johnk...@gmail.com> >>>>> wrote: >>>>> >>>>>> When I was younger I read a lot of science fiction, I don't do it so >>>>>> much anymore and technically I didn't do it this time either but I did >>>>>> listen to a audio book called "We Are Legion We Are Bob" it's the first >>>>>> book of the Bobiverse trilogy and I really enjoyed it. You can get a >>>>>> free 5 >>>>>> minute sample of the book here: >>>>>> >>>>>> We Are Legion (We Are Bob): Bobiverse, Book 1 >>>>>> <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8&qid=&sr=> >>>>>> >>>>>> It tells the story of Bob, a young man who has just sold his >>>>>> software company for a crazy amount of money and decides that after a >>>>>> decade of hard work he's going to spent the rest of his life just >>>>>> goofing >>>>>> off. On a whim he signs with a Cryonics company to have his head frozen >>>>>> after his death and then just hours later while crossing the street >>>>>> to go to a science fiction convention is hit by a car and dies. Five >>>>>> subjective seconds later he wakes up and finds that a century has >>>>>> passed and he's been uploaded into a computer. This is all in the >>>>>> opening chapter. >>>>>> >>>>>> Parts of the story are unrealistic but parts of it are not, I think >>>>>> it was Isaac Asimov who said it's OK for a science fiction writer to >>>>>> violate the known laws of physics but only if he knows he's doing it, >>>>>> and >>>>>> when Dennis Taylor, the creator of Bob universe, does it at one point >>>>>> with >>>>>> faster than light communication it's obvious that he knowns it. And I >>>>>> can't >>>>>> deny it makes for a story that is more fun to read. I have now read >>>>>> (well >>>>>> listened) to all 3 Bob books and, although parts are a little corny and >>>>>> parts a little too Star Trek for my taste, on the whole I greatly >>>>>> enjoyed >>>>>> them all. They're a lot of fun. >>>>>> >>>>>> The only other novel I can think of that treats the subject of >>>>>> uploading with equal intelligence is "The Silicon Man". >>>>>> >>>>>> The Silicon Man by Charles Platt >>>>>> <https://www.amazon.com/Silicon-Man-Cortext-Charles-Platt/dp/1888869143> >>>>>> >>>>>> John K Clark >>>>>> >>>>> >>>>> Consider any of the earlier novels by Greg Egan, the Australian hard >>>>> science fiction write based in Perth, WA: particularly "Permutation City" >>>>> (1994). >>>>> >>>>> Bruce >>>>> >>>> >>>> I had this idea of a science fiction story of where minds are stored in >>>> machines in order to "eternally" punish them. The idea is that if a >>>> million >>>> seconds in the simulated world is a second in the outer world then one can >>>> in effect construct a near version of eternal hell-fire. The setting is a >>>> world governed by complete terror. Then Egan came out with Permutation >>>> city, which explores a similar set of ideas. >>>> >>>> The problem with the idea of putting minds into machines is that >>>> machines can run recursive functions or algorithms, but in a number system >>>> such as Peano's we make the inductive leap that the successor of any >>>> number >>>> can't be the same number or zero in all (infinite number) cases. We can >>>> make an inference from a recursively enumerable set. I would then think >>>> that the idea of putting minds into machines, or robotic consciousness, is >>>> at this time an unknown, maybe an unknowable, proposition. >>>> >>>> LC >>>> >>>> >>>> > > > > If an actual "black hole" (relativistic) computer existed, it would > effectively compute an infinite number of operations in finite time. > > One could have, in effect, an *infinite-time Turing machine*. > > https://arxiv.org/abs/math/9808093 > <https://www.google.com/url?q=https%3A%2F%2Farxiv.org%2Fabs%2Fmath%2F9808093&sa=D&sntz=1&usg=AFQjCNEmfCZe-55X9cBWq8Bcsq11vVN6nA> > > We extend in a natural way the operation of Turing machines to infinite > ordinal time. > > But all this is fiction. >
Black holes are limited to the amount of information they contain by the Bekenstein bound. Also the duration of a black hole is T ~ M^3. So an observer of the outside world would not encounter an infinite Cauchy sequence of null rays at the inner event horizon. The idea of the infinite task or hyper-Turing machine is interesting, but it may only adjust the Chaitin halting probability for any given algorithm closer to 0 or 1, but not absolutely determine halting or non-halting status. LC > > > "In the 1980s, Hartry Field started a project in the philosophy of > mathematics discussing mathematical fictionalism, the doctrine that all > mathematical statements are merely useful fictions, and should not be taken > to be literally true. More precisely, Field holds that the existence of > sets may be denied, in opposition to Quine and Putnam." [Wikipedia] > > @philipthrift > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/e4351752-f43c-41ab-b3db-fae4df0d89de%40googlegroups.com.
