tag:blogger.com,1999:blog-1500584444083499721.post5672269030004905996..comments2019-11-11T00:08:07.621+01:00Comments on Claes Johnson on Mathematics and Science: Free Will and Finite Precision Computation 3Claes Johnsonhttp://www.blogger.com/profile/07411413338950388898noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-1500584444083499721.post-38056188790100181162011-05-18T13:58:23.813+02:002011-05-18T13:58:23.813+02:00Yes, you are on theright track! You can go on, if ...Yes, you are on theright track! You can go on, if you want, or decide to quit, by free will. What do you choose?Claes Johnsonhttps://www.blogger.com/profile/07411413338950388898noreply@blogger.comtag:blogger.com,1999:blog-1500584444083499721.post-8243284293722574922011-05-18T13:36:53.047+02:002011-05-18T13:36:53.047+02:00I still don't get it.
I can understand that s...I still don't get it.<br /><br />I can understand that some ways of calculating things are more precise than others. I can understand also that infinite precision is unattainable by man, and is in that sense 'unreal', and that finite precision is something that <i>can</i> be done, and is therefore 'real'. <br /><br />Suppose that I wish to find what half of some number is, but my mathematical precision is restricted to integers, because I can only count on my fingers. So if I want to find what half of 27 is, I come up with 13. In fact I'm pretty sure that it's bigger than 13, but less than 14, but I have no way of expressing this. Is this the point where I must roll a dice, and decide the matter that way? Rolling the dice, sometimes I'll find that the answer is 13, and sometimes it will be 14. And so all numbers are made up of things we are sure about (e.g. 13) and things we are not sure about (e.g. maybe it's 14). We can use our finite precision mathematics (i.e. our fingers) to work out the important bit (13), but we have to throw dice to find the less important bit that is beyond the limits of our precision.<br /><br />Am I on the right track? Or am I hopelessly lost?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1500584444083499721.post-38828034437425417632011-05-18T07:19:39.115+02:002011-05-18T07:19:39.115+02:00I view physics as a form of analog computation, ul...I view physics as a form of analog computation, ultimately based on quantum mechanics which by e g Heisenberg's uncertainty relation, has finite precision.<br /><br />Finite precision is real, infinite precision is not.Claes Johnsonhttps://www.blogger.com/profile/07411413338950388898noreply@blogger.comtag:blogger.com,1999:blog-1500584444083499721.post-10576601947296125342011-05-18T03:57:45.954+02:002011-05-18T03:57:45.954+02:00I don't get this finite precision arithmetic b...I don't get this finite precision arithmetic business.<br /><br />As best I can make out, you seem to be saying that to get the right answers, we have to use something like 16 bit floating point mathematics. And that will result (I think) in lumpy numbers as they're rounded up or down to whatever precision we're using.<br /><br />Is the universe like that? When the Sun calculates how much the Earth has to move in its orbit, does it use finite precision math? Is there an inherent 'lumpiness' in nature that results in it looking like energy comes in packets (quanta)?<br /><br />It makes sense that us humans can't calculate the numbers to infinite precision, because we don't have the time to do so. We have problems even with numbers like Pi, which can and does fill whole books. But does it make sense that the universe isn't any better than us humans, and sort of just gives up and says, 'Well, it's somewhere around there, plus or minus yet another decimal point.<br /><br />I suspect I've gotten hold of completely the wrong end of the stick here. Maybe you can point me at a bit of finite precision arithmetic which shows exactly why it's so much better than infinite precision arithmetic (apart from not taking quite as long to work out).Anonymousnoreply@blogger.com