Time, sequence, determinism
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From: huge on 18 Apr 2010 08:59 John Jones : > huge wrote: >> Rick : >> >>> huge wrote: >>>> Rick : >>>> >>>>> John Jones wrote: >>>>>> huge wrote: >>>>>> >>>>>>>>>>> Scientific thinking has led to the Hubble space telescope and >>>>>>>>>>> heart transplants. Now, don't you think that deserves some >>>>>>>>>>> kind of response to explain why you persist in this >>>>>>>>>>> obscurantism? >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>> The definition you were working to. >>>>>>> Non-response again noted. >>>>>>> >>>>>>> >>>>>>> >>>>>> The definition you were obviously working to and rejecting. HERE IT >>>>>> IS AGAIN: >>>>>> "I don't know of any mathematical definitions of a sequence that >>>>>> **DO** use time." >>>>> distance = time * velocity >>>> That is the definition of *distance.* It is not the definition of >>>> "sequence" itself. >>>> >>>> You want a definition of sequence like this one from Planet Math: >>>> http://planetmath.org/?op=getobj&from=objects&id=397 >>>> ___________________________ >>>> Sequences >>>> Given any set X , a sequence in X is a function f:X from the set of >>>> natural numbers to X . Sequences are usually written with subscript >>>> notation: x0x1x2 , instead of f(0)f(1)f(2) . Generalized sequences >>>> One can generalize the above definition to any arbitrary ordinal. For >>>> any set X , a generalized sequence or transfinite sequence in X is a >>>> function f:X where is any ordinal number. If is a finite ordinal, >>>> then we say the sequence is a finite sequence. >>>> ___________________________ >>>> >>>> That is only one among several ways to define a sequence. >>> Time is a sequence then: >>> authors.library.caltech.edu/3523/01/FEYpr49c.pdf >> >> Correct, time is a sequence. >> But you cannot define a sequence by that, in the same way you can't >> define the set of animals by noting that a dog is an animal. > > That's the only way you can define a sequence. By referencing time. False. -- huge: Not on my time you don't.
From: John Stafford on 18 Apr 2010 09:49 John Jones : > That's the only way you can define a sequence. By referencing time. Why is the task of definition so important? Defining does not make a thing, nor affirm its existence. Now Mr. Jones, imagine an aluminum can found on the road. It is dented, beat up. Its topography indicates a history which necessitates time.
From: huge on 18 Apr 2010 16:28 John Stafford : > John Jones : > >> That's the only way you can define a sequence. By referencing time. > > Why is the task of definition so important? Defining does not make a > thing, nor affirm its existence. Jones has repeatedly shown that he believes it does. Very medieval, and ignorant in a way that hamstrings his every thought. > > Now Mr. Jones, imagine an aluminum can found on the road. It is dented, > beat up. Its topography indicates a history which necessitates time. -- huge: Not on my time you don't.
From: Tim Golden BandTech.com on 19 Apr 2010 12:32 On Apr 17, 10:12 pm, John Jones <jonescard...(a)btinternet.com> wrote: > huge wrote: > > Rick : > > >> huge wrote: > >>> Rick : > > >>>> John Jones wrote: > >>>>> huge wrote: > > >>>>>>>>>> Scientific thinking has led to the Hubble space telescope and > >>>>>>>>>> heart transplants. Now, don't you think that deserves some kind > >>>>>>>>>> of response to explain why you persist in this obscurantism? > > >>>>>>> The definition you were working to. > >>>>>> Non-response again noted. > > >>>>> The definition you were obviously working to and rejecting. HERE IT > >>>>> IS AGAIN: > >>>>> "I don't know of any mathematical definitions of a sequence that > >>>>> **DO** use time." > >>>> distance = time * velocity > >>> That is the definition of *distance.* It is not the definition of > >>> "sequence" itself. > > >>> You want a definition of sequence like this one from Planet Math: > >>>http://planetmath.org/?op=getobj&from=objects&id=397 > >>> ___________________________ > >>> Sequences > >>> Given any set X , a sequence in X is a function f:X from the set of > >>> natural numbers to X . Sequences are usually written with subscript > >>> notation: x0x1x2 , instead of f(0)f(1)f(2) . Generalized sequences > >>> One can generalize the above definition to any arbitrary ordinal. For > >>> any set X , a generalized sequence or transfinite sequence in X is a > >>> function f:X where is any ordinal number. If is a finite ordinal, then > >>> we say the sequence is a finite sequence. ___________________________ > > >>> That is only one among several ways to define a sequence. > >> Time is a sequence then: > >> authors.library.caltech.edu/3523/01/FEYpr49c.pdf > > > Correct, time is a sequence. > > But you cannot define a sequence by that, > > in the same way you can't define the set of animals by > > noting that a dog is an animal. > > That's the only way you can define a sequence. By referencing time. Now JJ you've directly contradicted yourself, for your OP states: "I have argued that sequenced events can be ordered by association: we do not need Time as an ordering medium. For example, rather than say "A comes before B" we can, without losing information, say "that A, rather than B, is associated with C, says that A comes before B"." I don't mean to shove words into your mouth, but if you are proposing a coherent concept you'll be happy to disambiguate this contradiction cleanly. It is your own construction. Construct cleanly. Definition is fine, even loose definition, but you have the word 'association' mixed up with 'sequence' whereas I do not believe that any ordering is implied by association. That word is nondirectional. It is less structured than sequence. If A is associated with B then so is B associated with A. If we investigate the associativity property of an algebra we see the behavior ( x y ) z = x ( y z ) which is nearly the deletion of ordering of a sequence. Still, the expression reads as a sequence as does all of our text. You may be onto something, but it may be that you need to communicate more clearly. This is a matter of construction and interpretation into terms that the existing language can handle. Keep going, but time is an ill defined concept and the discrete/continuous quality of your own assumption has to be resolved. I'd argue that time is continous and that sequence is strictly discrete. Functions are nearby. - Tim
From: John Jones on 20 Apr 2010 20:29
John Stafford wrote: > John Jones : > >> That's the only way you can define a sequence. By referencing time. > > Why is the task of definition so important? Defining does not make a > thing, nor affirm its existence. > > Now Mr. Jones, imagine an aluminum can found on the road. It is dented, > beat up. Its topography indicates a history which necessitates time. Yes, but the history doesn't refer to just the can. |