What makes a trivial operator trivial ?
in [Math]
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From: Huang on 5 Feb 2010 07:22 > > > 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. > Saying that mathematicians "typically abhor philosophy" is incorrect - I concede that specific point, there are some who hate it and others who love it. Fine. Whatever. I have met mathematicians who loathed philosophy because it is based on a bunch of loose justifications, many crazy ideas are possible, and it lacks the rigor of pure math. That is why some people hate it. As far as this is concerned : > I am content in the knowledge that he has failed to come up to scratch. There are things that are proveable and things that are not. Just because something is non-proveable does not automatically imply that it is BS. I disagree that Conjetural modelling is BS. Mathematics is consistent, and it is rigorously proveable throughout. If Conjecture is consistent with mathematics, then to some extent it must inherit the rigor even if nothing is proveable using the traditional methods of PROOF. I have already stated elsewhere that Conjecture does not care to demonstrate proof of anything, but merely CONSISTENCY with mathematics, and there should be as many ways to rigorously demonstrate that consistency as there are to actually prove something if one were doing math. The overall procedure is similar but you are merely doing something completely different. There are NO GIVENS in conjecture - nothing is "known to exist". You cannot have proof of anything in such a system. But it does not mean that this is inconsistent with math.....the lack of proveability is not a death sentence. Demonstrating consistency is all that you need to do, Conjectures must be consistent with respect to each other, and also to mathematics. THIS IS VERY SIMPLE. The criticism keeps me alive because it keeps me laughing. Lately it is your silence that makes me laugh. I have given you a million places where you could attack what I say, and you cannot make a dent - anywhere- . It is my turn to grade you - and I give you all an F. I give you an F for inhabiting a world where you have a unified reality and thus far have failed to unify the tools which you use to model it. I give science an F, I give humanity an F. You can laugh at what I say - but the failure is YOURS. I'd like to hear some clever person plonk me now :)
From: Huang on 6 Feb 2010 10:33 > It is my turn to grade you - and I give you all an F. I give you an F > for inhabiting a world where you have a unified reality and thus far > have failed to unify the tools which you use to model it. I give > science an F, I give humanity an F. You can laugh at what I say - but > the failure is YOURS. I'd like to hear some clever person plonk me > now :)- Hide quoted text - > > - Show quoted text - Silly persons - I demand the immediate and unconditional surrender of this debate to ME - because I have won it.
From: Huang on 12 Feb 2010 07:06 There are other ways to play with existence as if one were a programmer. Consider the unit cube and define it s.t. Unit cube exists for all t s.t. INT( t ) mod 2 = 1 Otherwise cube does not exist. This gives us a cube which is blinking in and out of existence at 1 second intervals. This is a PERFECTLY VALID thing to do in mathematics because it does NOT violate the laws of logic. You dont see these kinds of things in physics, but there is nothing wrog with this as a mathematical construct.
From: Frisbieinstein on 12 Feb 2010 07:24 On Feb 1, 4:22 pm, "Androcles" <Headmas...(a)Hogwarts.physics_u> wrote: > "Frisbieinstein" <patmpow...(a)gmail.com> wrote in message > > news:6359a960-c4fa-4c0e-a759-b9d72c31ec17(a)u19g2000prh.googlegroups.com... > On Jan 31, 9:48 pm, Huang <huangxienc...(a)yahoo.com> wrote: > > > > > 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. They prefer to prove things. > > > 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. > > For logic to work all empty sets are equal. > > An empty apple barrel is not the same as an empty oil barrel. But > neither is an empty set. Each is a member of the set of barrels. > > ========================================== > An empty oil barrel is NOT a dog's breakfast. > An empty oil barrel is NOT the 8:30 to London on platform 2. > An empty oil barrel is NOT an apple. > One can construct an infinite list of what things are not and the list > contains (useful information) NOT. > Tell us what an empty oil barrel IS and how to distinguish it from > an empty apple barrel. > > An empty apple barrel IS the same as an empty oil barrel until > you write "Apples" on the staves to make it different. I dare say you don't know much about barrels.
From: Androcles on 12 Feb 2010 08:46
"Frisbieinstein" <patmpowers(a)gmail.com> wrote in message news:856c18a6-8bfe-4e8f-9427-015dd5d69034(a)k6g2000prg.googlegroups.com... On Feb 1, 4:22 pm, "Androcles" <Headmas...(a)Hogwarts.physics_u> wrote: > "Frisbieinstein" <patmpow...(a)gmail.com> wrote in message > > news:6359a960-c4fa-4c0e-a759-b9d72c31ec17(a)u19g2000prh.googlegroups.com... > On Jan 31, 9:48 pm, Huang <huangxienc...(a)yahoo.com> wrote: > > > > > 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. They prefer to prove things. > > > 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. > > For logic to work all empty sets are equal. > > An empty apple barrel is not the same as an empty oil barrel. But > neither is an empty set. Each is a member of the set of barrels. > > ========================================== > An empty oil barrel is NOT a dog's breakfast. > An empty oil barrel is NOT the 8:30 to London on platform 2. > An empty oil barrel is NOT an apple. > One can construct an infinite list of what things are not and the list > contains (useful information) NOT. > Tell us what an empty oil barrel IS and how to distinguish it from > an empty apple barrel. > > An empty apple barrel IS the same as an empty oil barrel until > you write "Apples" on the staves to make it different. I dare say you don't know much about barrels. =================================== I dare say what you know about mathematics is contained in the empty space between your ears. Answer the question: How do I distinguish an empty oil barrel from an empty apple barrel, you anencephalous cretin? |