tag:blogger.com,1999:blog-2800316528417070757.post2798414336747418965..comments2023-04-28T22:14:09.751+01:00Comments on Random Thoughts: Truth TablesJohn Lawrence Aspdenhttp://www.blogger.com/profile/02587130870181071109noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2800316528417070757.post-1526323893627961692014-02-08T21:44:21.869+00:002014-02-08T21:44:21.869+00:00Hi John,
As a fellow Clojurist I think you will ...Hi John, <br /><br />As a fellow Clojurist I think you will find the following two books interesting. I can't adequately describe my understanding of reality in a few paragraphs so I won't attempt to do so but if you read these books in order you might have the same idea as me. I would bet on the whole universe being discrete but a single universe would appear continuous.<br /><br />Regardless, if you haven't read these then I'm sure you will gain plenty of sleepless nights once you have!<br /><br />The first is online and doesn't require you to read all of it to get the idea. The second one I have read three or four times and I wish there was more.<br /><br />http://www.stephenwolfram.com/publications/a-new-kind-of-science-future-mathematics/<br /><br />http://www.amazon.co.uk/The-Beginning-Infinity-Explanations-Transform/dp/0140278168<br /><br />David Deutsch's G+ page:<br />https://plus.google.com/u/0/107125465351779394336/about<br /><br />DeneAnonymoushttps://www.blogger.com/profile/02510416715672345534noreply@blogger.comtag:blogger.com,1999:blog-2800316528417070757.post-68299015236675549422014-02-06T14:52:32.960+00:002014-02-06T14:52:32.960+00:00No, but I can produce a machine that will print ou...No, but I can produce a machine that will print out arbitrarily close approximations to any real number. <br /><br />You're right that a universe could be based on laws of physics that are continuous rather than discrete, but it's equivalent to saying that that universe is in principle incomprehensible, and quite a controversial position.<br /><br />I'd say that the real numbers are a convenient fiction that mathematicians use in order to have to deal with fiddly little details, rather than anything that exists even in the sense of mathematics. When talking about real numbers, mathematicians only ever manipulate finite strings of symbols. <br /><br />Even quantum computers are simulatable on classical computers, although there is a huge speedup factor between the models.<br /><br />And if the physical laws really are uncomputable, in the sense that there are physical processes which can't be approximated even in principle, then we should be able to make a hyper-computer that exploits them to perform uncomputable tasks, in which case the problem just recurses!<br />John Lawrence Aspdenhttps://www.blogger.com/profile/02587130870181071109noreply@blogger.comtag:blogger.com,1999:blog-2800316528417070757.post-87450039681771795222013-12-12T23:19:41.484+00:002013-12-12T23:19:41.484+00:00> The universe is computable.
Not obvious to m...> The universe is computable.<br /><br />Not obvious to me.<br /><br />> We will simulate in precise detail every possible world<br /><br />Not obvious either. Haven't you just confused countable and uncountable infinity? (I admit I didn't read all the details. Consider a simpler task: can you product a machine corresponding to every real number between 0 and 1?).William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.com