Skip to content

Good Algebraic Category

December 3, 2012

Good, one fine morning, early as always, looked in the mirror and felt that he usually looked little better than the one he’s looking at.  Upon further looking into his mirror image, it became clear that there is only one word to characterize that image: evil.

Genesis 101

This is just a fractal of the first-cut: matter, anti-matter.  In any case, we inherited a set

A = {good, evil}

It has always been obvious what should happen when we have more good

good + good = good

with evil aping good

evil + evil = evil

Soon, somewhat too soon, there were sightings of dark clouds above our clear picture

good + evil = ?

Pointing to the perils of consuming poison added to good water, I say

good + evil = evil

My brother, who wouldn’t drink creamer, probably wouldn’t mind substituting it if steamed milk is not available to add to his coffee, so:

good + evil = good

adding (thamudu always had something to add) that this all sounds quite arbitrary.

We started with two entities

A = {good, evil}

and we made three combos

(good, good)

(good, evil)

(evil, evil)

only to find ourselves on cloud atlas.

You have a book with bunch of words

A = {good, evil}

and I have a book too

B = {good, evil}

with same words, I guess.  Since communication, meaning, communication of meaning (that’s enough layering) and not words per se is what’s getting on our nerves, I exchange my book

B = {even, odd}

The best part of this one is it got so many questions–questions transcending time, space, and rings of definition (now you know what lord of the rings is all about):

Q1. Is good even?

Q2. Is evil odd?

Q3. Is even evil?

Q4. Is odd good?

Troubling questions testing our faith (‘in what’ is yet to be fathomed) don’t come anywhere near exhausting the list that each one of us carry–forced to carry like IDs.  (Wearing them IDs around necks is gross.  I guess there’s no need to add that I don’t like carrying IDs.)

One of the many easy ways to solve a problem is to look away and lo and behold we see 1, 2.  Seeing that there was 1 before (don’t know for how long) 2, we recognize that it all started with me looking in the mirror–there was no evil to begin with, and state our findings succinctly

good <-> odd

evil <-> even

Every time I cry evil, you hear even; and when you point to something odd, I see good.  This honeymoon lasts however long they do, and then we freak out at the sight of Wittgenstein in the bedroom.  Why do we need this order, these middlemen

before -> after

Let’s talk–making love, peace, sense–to each other without bringing in extraneous concepts like order; we don’t need others (before, after) to arbitrate between us

A = {good, evil} and B = {odd, even}

Once you accommodate order, you can’t say no to negativity: good is not evil & evil is not good (there’s no ‘before’; no ‘after’, informs not.)

Well, it’s not really extraneous; order, not, etc. are each like one of the sides of the mushroom in wonderland.  But I see (I think) your point–why talk about a particular side be it ORDER or NOT?  Why not get it over with–talk in terms of structure in general subsuming

I. good—>evil (order)

II. not (good) = evil, not (evil) = good (unary operation)

III. good + good = good, good + evil = good, evil + evil = evil (binary operation)

.

.

.

Well, then, I guess when I translate words from the old book A = {g, e} to a new book B = {g, e}, I need to look at what you seem to be calling the structure of A given in terms of combining words into words as in

g + g = g

g + e = g

e + e = e

and then if I interpret ‘g’ in A as, say, ‘e’ in B and ‘e’ in A as ‘g’ in B

i (g) = e

i (e) = g

you would call that ‘i’ an interpretation only if it respects the combining-rule ‘+’

i (p + q) = i (p) x i (q)

It sure is a welcome relief to hear that there’s a method in the madness called meaning!

About these ads

From → Note to self

One Comment

Trackbacks & Pingbacks

  1. How to model a calculator? | Conceptual Mathematics

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

Join 1,200 other followers

%d bloggers like this: