yyGrams logoyyGrams > yyGrams logoworked > example

zang: (( ))=    

fu: ( )( )=( )

Puzzle example: One active name, pool of two names

<#yypuz 5><e,g 1-2><n: {e,g}{e} ><y: {g}{ }>demo 1of2</yy>

Put the outcome catalog into the columns indicated. The pool of two names—e,g—has 22 = 4 combinations; those yielding yiN on evaluating the hidden yy-gram are given in the puzzle tweet explicity, tagged <n: > as are those yielding Yang, tagged <y: >.

—some unseen yy-gram—

yy col heads
—whole-pool catalog of outcomes—

{e,g}
{e}

{g}
{ }

Names that never affect the outcome when the yy-gram is evaluated we call "inactive" or "bogus" names.

A yy-gram where all the names are bogus is easy to construct. Enclose as many names as you like, and among them plant Yang, ( ):

(a b c  ( )  d e) =

Demo yy-gram illustrating "cloak" shortcut (theorem)

Satisfy yourself with some experimental valuations (there-lists) that zang-fu disappearance moves always let you reduce the "cloak" demo yy-gram all the way to nothing—yiN.

Group the outcomes into pairs of there-list valuations that differ by exactly one name.

This makes it easy to spot names that are either pretty deeply enclosed in a yy-gram or that make no difference in any case:

—some unseen yy-gram—

yy col heads
—catalog grouped in differ-by-one pairs—

{e,g}, {e}

{g},{ }

This differ-by-one pairing discloses that g never affects the outcome. Whether or not g is present, pairs stay in one column or the other.

Since g makes no difference ever, we clarify the catalog by dismissing all there-lists that mention g:

—some unseen yy-gram—

yy col heads
—re-catalog to dismiss g

{e}

{ }

The clarified catalog lets us state the necessary and sufficient condition for a Yang outcome on evaluation:

e not there—that is, not Yang.

In formal logic terms this is said,

NOT e

The yy-gram that negates the yy-value of a name is an enclosure around the name:

(e)

The solution yy-gram might appear in tweet format as

<#yygram 5> <ans: (e) >demo 1of2</yy>



©2012 David Zethmayr
2012.4.11 - 12gb