What makes a trivial operator trivial ?
in [Math]
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From: Huang on 3 Feb 2010 09:37 > I should add a small correction. I wrote that > > ".......the only difference being the philosophical consideration of > precisely what is the difference between that which is "given" and > that which is "presumed".- .........." > > This could be worded a little better. It is better to say that there > is a difference between "that which is a given", and "that which might > be a given". And that is heart of the matter. Your position is that > you will make models _only_ with "givens", and I would allow modelling > of "might be givens". That is the difference. There is no numerical or > quantitative difference in the results which would derive from either > approach - none. And this fact makes the two approaches completely, > totally and seamlessly interchangeable. > > One direct result of this is that it becomes a formal scientific fact > that : "It cannot be known whether the universe is deterministic or > not." > > This is a very strange and useful thing. Consider - some hold the view > the G_d is law. Some say G_d is love, but others say G_d is "law". > G_d's law may be seen as being manifest in nature by virtue of the > fact that nature is modellable with mathematics. A very beautiful idea > when you think about it, but without getting too deep into religious > views - let me say that if physics is unifiable using math and math > alone, then G_d will have revealed himself to man in the form of this > system of laws. > > But G_d is under no obligation to do so. G_d is under no obligation to > reveal himself to man. > > The universe may be modelled as being based exclusively on the "law" > of mathematics, or it may be modellable using Conjecture which is > completely "lawless". Both approaches work. G_d remains a mystery to > man, and the question between agnosticism and ultra orthodoxy will not > be resolveable by any logical or science based formalism. > > Do you see where this is going ?- Hide quoted text - > > - Show quoted text - Do you suppose that you can win a debate by muzzling your opponent ?
From: Huang on 3 Feb 2010 22:35 To compose the existent with the nonexistent a non-trivial operator simply wont do the trick. Nor would we want to use an operator which is strictly nonexistent because that would be nonsense. To compose the existent with the nonexistent we must employ a "trivial operator", an operator which posseses some of the properties of the exsitent, and also some properties of the nonexistent. That is how it must be done. And the reward is being increased to anyone who can find a counterexample to this one simple claim: "Any probabilistic problem can be reworded in terms of existential indeterminacy, and conservation of existential potential." Im raising the REWARD to $2000 cash, a date with a hot chick ( http://photo.net/photodb/photo?photo_id=10413431 ), one slightly used Canon 5D and a middle aged dog.
From: Huang on 4 Feb 2010 21:59 On Feb 3, 9:35 pm, Huang <huangxienc...(a)yahoo.com> wrote: > To compose the existent with the nonexistent a non-trivial operator > simply wont do the trick. > > Nor would we want to use an operator which is strictly nonexistent > because that would be nonsense. > > To compose the existent with the nonexistent we must employ a "trivial > operator", an operator which posseses some of the properties of the > exsitent, and also some properties of the nonexistent. That is how it > must be done. > > And the reward is being increased to anyone who can find a > counterexample to this one simple claim: > "Any probabilistic problem can be reworded in terms of existential > indeterminacy, and conservation of existential potential." > > Im raising the REWARD to $2000 cash, a date with a hot chick (http://photo.net/photodb/photo?photo_id=10413431), one slightly used > Canon 5D and a middle aged dog. Cowards.
From: Ostap S. B. M. Bender Jr. on 4 Feb 2010 22:54 On Jan 31, 6:43 am, "Androcles" <Headmas...(a)Hogwarts.physics_u> wrote: > "Huang" <huangxienc...(a)yahoo.com> wrote in message > > news:f0df5ca3-4dbb-4c7c-91e9-e1f1adbc4b99(a)a32g2000yqm.googlegroups.com... > > > > > If you consider the empty set by itself it is nonsensical. It needs > > set theory to make sense. Nullity is nonsensical when it stands alone > > without all of the other apparatus which allows it to make sense. It > > is very much like the number zero in many respects. > > > And the number zero would be nonsensical if it were considered alone, > > without all of the other mathematics which allows it to make sense. > > > Zero apples is the same thing as zero oranges. It is nonsense to say > > that apples are oranges, except in such trivial instances as this. If > > zero was the only number you had at your disposal, all you would be > > able to do is trivial and/or nonsensical procedures. > > > Mathematics has trivial numbers, and trivial sets, but no trivial > > operators. My position is that the reason that mathematics has no > > trivial operator is because the concept of operator is based on very > > old and time honored philosophical considerations, and mathematicians > > typically abhor philosophy. > > False. The word "Philosophy" literally means "love of wisdom". > Mathematicians typically adore philosophy. > > > They prefer to prove things. > > It would not be wise to accept opinion without proof, no self- > respecting philosopher would do so. > I reject your opinion (or "position", as you call it) and ask you > to prove "mathematicians typically abhor philosophy" or retract > your claim. > If I were you, I would sue him in court. > > > > But can you prove this ? Can you prove that when an arbitrary quantity > > is lumped together with another arbitrary quantity that the result is > > the fusion of the two quantities into a single quantity and we should > > call this addition ? Can that really be proved ? > > > When an arbitrary quantity is lumped together with an arbitrary number > > of quantities of equal magnitude to form a single quantity, that the > > result is a process called multiplication and shall be regarded as an > > operator and signified by the symbol "X" ? Is this proveable ? > > > These things are not proveable, they are definitions. > > > And so we cannot prove that there is any such thing as a trivial > > operator, we simlpy have to define it. > > > The definition is similar to zero, or the empty set, you already know > > what it does, that is all. > > Minus (-) is a unary operator, the binary operator is +. > Trivially, 3-1 = 3 + (-1). > A computer, whether human or artificial, will evaluate a+b > even when a and/or b are less than zero. > > Prove or disprove that i (symbol for sqrt(-1)) is a unary operator.
From: Androcles on 5 Feb 2010 00:08
"Ostap S. B. M. Bender Jr." <ostap_bender_1900(a)hotmail.com> wrote in message news:2d1f7140-5bdc-466c-80e2-b5d4e27a6869(a)a5g2000prg.googlegroups.com... On Jan 31, 6:43 am, "Androcles" <Headmas...(a)Hogwarts.physics_u> wrote: > "Huang" <huangxienc...(a)yahoo.com> wrote in message > > news:f0df5ca3-4dbb-4c7c-91e9-e1f1adbc4b99(a)a32g2000yqm.googlegroups.com... > > > > > If you consider the empty set by itself it is nonsensical. It needs > > set theory to make sense. Nullity is nonsensical when it stands alone > > without all of the other apparatus which allows it to make sense. It > > is very much like the number zero in many respects. > > > And the number zero would be nonsensical if it were considered alone, > > without all of the other mathematics which allows it to make sense. > > > Zero apples is the same thing as zero oranges. It is nonsense to say > > that apples are oranges, except in such trivial instances as this. If > > zero was the only number you had at your disposal, all you would be > > able to do is trivial and/or nonsensical procedures. > > > Mathematics has trivial numbers, and trivial sets, but no trivial > > operators. My position is that the reason that mathematics has no > > trivial operator is because the concept of operator is based on very > > old and time honored philosophical considerations, and mathematicians > > typically abhor philosophy. > > False. The word "Philosophy" literally means "love of wisdom". > Mathematicians typically adore philosophy. > > > They prefer to prove things. > > It would not be wise to accept opinion without proof, no self- > respecting philosopher would do so. > I reject your opinion (or "position", as you call it) and ask you > to prove "mathematicians typically abhor philosophy" or retract > your claim. > If I were you, I would sue him in court. > ============================================ If you were you, would you sue him in court? Why do you need to be me in order to do so? You are not me, therefore your perseflage is pitifully irrelevant. I am content in the knowledge that he has failed to come up to scratch. > > > But can you prove this ? Can you prove that when an arbitrary quantity > > is lumped together with another arbitrary quantity that the result is > > the fusion of the two quantities into a single quantity and we should > > call this addition ? Can that really be proved ? > > > When an arbitrary quantity is lumped together with an arbitrary number > > of quantities of equal magnitude to form a single quantity, that the > > result is a process called multiplication and shall be regarded as an > > operator and signified by the symbol "X" ? Is this proveable ? > > > These things are not proveable, they are definitions. > > > And so we cannot prove that there is any such thing as a trivial > > operator, we simlpy have to define it. > > > The definition is similar to zero, or the empty set, you already know > > what it does, that is all. > > Minus (-) is a unary operator, the binary operator is +. > Trivially, 3-1 = 3 + (-1). > A computer, whether human or artificial, will evaluate a+b > even when a and/or b are less than zero. > > Prove or disprove that i (symbol for sqrt(-1)) is a unary operator. |