ontolog-forum
[Top] [All Lists]

## Re: [ontolog-forum] Axiomatic ontology

 To: "[ontolog-forum] " Pat Hayes Tue, 12 Feb 2008 15:19:01 -0600
 At 12:08 PM -0600 2/12/08, Schiffel, Jeffrey A wrote: Content-class: urn:content-classes:message Content-Type: multipart/alternative;   boundary="----_=_NextPart_001_01C86DA2.342F89E4" A series of unfair coin tosses can easily be random. The distribution of the random variable will not be uniform (as is the case of a fair coin), but it may still be random. It may be a random variable in the mathematical sense, of course.  (http://en.wikipedia.org/wiki/Random_variable) But this rather begs the question, as this definition already incorporates the notion of probability. For example, a completely unfair dice which always gives '1' is a random variable in this sense. But OK, let me accede to my own strictures. You are right, any variable which incorporates a degree of chance may be called 'random'; and Sean is right that a sampling of such values may well provide statistical information about likelihoods. Nevertheless, my original point still holds. When we are talking about what is usually called a 'random sequence' of numbers or bits, as spoken of in Kolmogoroff theory, what makes such a sequence have maximal information density is that there is no way to compute any one of its values from all the others. Pat It is just that the probabilities must be described by a different distribution. Pink noise is a simple example, since the randomness compared to white noise is red-shifted.   -- Jeffrey Schiffel  From: Pat Hayes [mailto:phayes@xxxxxxx] Sent: Tuesday, February 12, 2008 11:28 AM To: Barker, Sean (UK) Cc: [ontolog-forum] Subject: Re: [ontolog-forum] Axiomatic ontology At 10:14 AM +0000 2/12/08, Barker, Sean (UK) wrote: Pat's claim "The definition of a random sequence is that no matter how much of it you have, there is no way even in principle to compute any information about the next item." is true only where you exclude probabilistic estimates (which you might do depending on how you interpret "information"). For example, if you encode the tosses of a coin as a bit stream, as you continue to observe the bit stream, you will be able to make increasing accurate estimates of the probability that the next bit will be a 1. Given the additional knowledge that this is the encoding of coin flips, you will also be able to estimate the probability that it is a fair coin. No, wait. A series of tosses of an unfair coin is not a random sequence. One gets randomness just when the actual probability of each toss being a head is 0.5 precisely. What you say above is correct, of course, but it can be translated as: if a series of bits is not random, this can be detected with increasing accuracy as the series gets longer. Also, of course, if it is random, this can also be detected (if it were previously unknown), but that does not mean that any particular toss can be predicted. Pat -- --------------------------------------------------------------------- IHMC               (850)434 8903 or (650)494 3973   home 40 South Alcaniz St.       (850)202 4416   office Pensacola                 (850)202 4440   fax FL 32502                     (850)291 0667    cell http://www.ihmc.us/users/phayes      phayesAT-SIGNihmc.us http://www.flickr.com/pathayes/collections   _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx   ```-- ``` --------------------------------------------------------------------- IHMC               (850)434 8903 or (650)494 3973   home 40 South Alcaniz St.       (850)202 4416   office Pensacola                 (850)202 4440   fax FL 32502                     (850)291 0667    cell http://www.ihmc.us/users/phayes      phayesAT-SIGNihmc.us http://www.flickr.com/pathayes/collections ``` _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (01) ```
 Current Thread Re: [ontolog-forum] Axiomatic ontology, (continued) Re: [ontolog-forum] Axiomatic ontology, Sharma, Ravi Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Message not availableRe: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Barker, Sean (UK) Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Schiffel, Jeffrey A Re: [ontolog-forum] Axiomatic ontology, Sharma, Ravi Re: [ontolog-forum] Axiomatic ontology, Schiffel, Jeffrey A Re: [ontolog-forum] Axiomatic ontology, Pat Hayes <= Re: [ontolog-forum] Axiomatic ontology, Bill Andersen Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Message not availableRe: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Rob Freeman