Re: Is there a general solution for x = A + Not A ???

From: Zim Olson (zimmathematics_at_yahoo.com)
Date: 02/14/05 

Date: Mon, 14 Feb 2005 16:32:32 +0000 (UTC)

On 14 Feb 2005, Justin Davis wrote:
>
>"Zim Olson" <zimmathematics@yahoo.com> wrote in message
>news://200502141117.j1EBHi231491@proapp.mathforum.org...
>> Hello:
>>
>> According to my mathematics, there is always a solution for some
>> similiar expression to x = A + Not A.
>>
>> I do this my looking at the Universe as some sort of Computer Sytem
>> and us as some part of it's Information System(s).
>>
>> Note: Mathematics cannot deal well with Apple + Orange = x. Where in
>> my Mathematics x = 2 fruit.
>>
>> But as an exercise in my theory, I am trying to find a solution to the
>> expression Life + Not Life = X. Does anybody have a solution for
>> this??
>>
>
>Your terms here are a bit loose from a mathematical standpoint. Since you
>want to bring it into those terms, it would be useful to clarify a bit.
>
>Your A, the way it is written, usually implies a set in mathematics, and
>viewing it this way will shed a lot of light on the subject. In other words,
>A is not equal to an apple, but A is equal to a basket holding an apple,
>{apple}.
>
>Viewing it this way, your use of Not is a bit loose. With your apple and
>orange statement, you imply that Not {x} is equal to {some one particular
>thing which is not x}. This is not the usual usage and is in fact not what
>you're asking when you consider Life and Not Life, since neither of these
>represents a single element. After all, my life and your life are separate
>things, but both fall under the aegis of Life. And a corpse is Not Life
>under most any reasonable definition, as well as is a TV remote, so Life =
>{my life, your life, ...} and Not Life = {corpse, TV remote, ...}. If A =
>{apple}, for instance, it is usually the case that Not A = {orange, kiwi,
>dog, cat, Truth, beauty, ...}. In other words, Not A takes the universe and
>subtracts from it A, returning what's left.
>
>What about +? This is just the union of sets. {apple} + {orange} = {apple,
>orange}. If there is a more succinct, yet still precise, way of describing
>this new set, that's great, but that is a question of representation, not
>substance. Your "two fruits" doesn't work, because {apple, orange} is not
>equal to {guava, orange}, though that second set satisfies your new
>definition. There is no force that implies that simplification is absolutely
>necessary, and to do so when it is not necessary or useful is to make a
>mistake. There is nothing wrong with a basket, a set, with two elements.
>
>To repeat - A is not a single element but a set, sometimes with only one
>element. Not A returns the complement of a set, everything in the universe
>that is not contained in the set, and + is just adding up the elements of
>the two sets.
>
>Where does that leave us? A + Not A = A union A's complement = everything in
>the universe we're considering. This is not, I should note, a deep answer to
>your question, as {Ice Cream} + Not {Ice Cream} too = everything. Reasonably
>defined, your terms leave us with a trivial exercise in set theory.
>
>Where does the problem come in? There are two things I'd bring up. The first
>is that signifiers, the way you are using them, usually imply sets, not
>single elements, unless they are given much more precisely. The rest of your
>usage pretty easily drops into normal set theory.
>
>Second, you are mixing the vagueries and biases of linguistics with math.
>Your concern with succinct categories is seen, I believe, as superficial in
>math, because if two descriptions of something suffice to pin down what
>we're talking about, they are functionally equivalent and there's no real
>use wrangling over that fact (though its initial discovery is often quite
>satisfying and simplifies a lot of work). Your drive to create new
>linguistic categories is often not only unnecessary but also not helpful.
>Take again the example of two fruits; there is nothing wrong with "apple and
>orange," but you obliterate the precision of that description by moving to
>"two fruits." This adds nothing, yet subtracts a lot from our understanding
>of what we've just done, for it pretends that any baskets containing two
>fruits are equivalent. Why? Because you fail to use the painfully more
>obvious and useful linguistic structure - the word "and" exists to be used
>and ought not be shunned because it creates compounds.
>
>I won't say that this discussion is inappropriate for a mathematics group,
>because I don't believe it is, but I will say that it is far better dealt
>with by philosophers, particularly those working, if there are still any,
>for I do not know the state of it, in the theory of linguistic analysis; the
>interest you reveal in categories would be well served by the precision they
>have historically applied to language. I hesitate to recommend it, but
>perhaps you could look in addition at the idea of dialectics, whose central
>operation, I believe, is the merging of thesis and antithesis into
>synthesis; i.e. idea + an opposite of the idea = something new.

Explanation of Terms:

A - Is any Item(s)/Event(s) perceived. That functionality is possibly
determineable is a given.
Not A - Any value, or function that is Not "A" function.
Apple - Some determineable function of a "Apple"
Orange - Same as "Apple" but different function.
Apple + Orange =2 Fruit
  ...Is non trivial example. It gives additional information. And
possible meaningful function. Fruit can be seen as a possibly
determineable function. Or Linear Transformation in Matrix Algebra as:
  [Fruit] * [Apple + Orange].

My contributions to Math. Is I say there must be some "Fruit" for any
"Apple + Orange". And I am trying to prove this by proving I can find
a "Fruit" or Linear Transformation for [Life + Not Life] a matrix of
Life Functionality and Non Life Functionality. Or meaning for "Life
after Death" I feel the Linear Transformation could be described as
a Informational Component of a Universal Information System(s) run by
a "Universal Computer System" model. This makes things workable , you
 will know, maybe, if you deal with information systems much.

Thank you for your interest. I hope I have clarified things some what.

Zim Olson
http://www.zimmathematics.com

>
>> I have a poem on this subject to get you thinking at :
>>
>> http://www.zimmathematics.com/htm/LifeDeath.htm
>>
>> We have been talking about this at a different forum at:
>>
>> http://www.createforum.com/phpbb/index.php?mforum=geproject under the
>> "Axiom" topic.
>>
>> Zim Olson
>> http://www.zimmathematics.com
>>
>

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