finally figured out how to social network lookups

docs/recognizing_categories_and_instances.md

@@ -90,7 +90,7 @@ The optimal instance recognition algorithm, for normally distributed
 attributes, and for already existent, already known categories, is Mahalanobis
 distance
 
-Is not the spam characteristic of an email just its $T.(S-G)$, where $T$ is
+Is not the spam probability of an email just its $T.(S-G)$, where $T$ is
 the vector of the email, and $S$ and $G$ are the average vectors of good
 email and spam email?
 
@@ -103,9 +103,18 @@ normal.
 But variance is, approximately, the log of probability, so Mahalanobis is
 more or less Bayes filtering, or at least one can be derived in terms of the other.
 
-So we can reasonably reduce each email into twenty questions space, or, just
+So we can reasonably reduce each email into twenty questions space, albeit in practice, a great deal more than twenty.  Finding far from random
-to be on the safe side, forty questions space. (Will have to test how many
+dimensions that reduce it to a mere twenty or so is an artificial intelligence
-dimensions empirically retain angles and distances)
+hard problem.  If random dimensions, need $\bigcirc20\log{(n)}$ dimensions
+where $n$ is the number of things.  And $n$ is apt to be very large.
+
+Finding interesting and relevant dimensions, and ignoring irrelevant and
+uninteresting dimensions, is the big problem.  It is the tie between
+categorizing the world into natural kinds and seeing what matters in the
+perceptual data while ignoring what is trivial and irrelevant.  This requires
+non trivial non local and non linear combinations of data, for example
+adjusting the perceived colour of the apple for shadow and light colour, so
+see the ample, rather than merely the light scattered by the apple into the eye.
 
 We then, in the reduced space, find natural groupings, a natural grouping
 being an elliptic region in high dimensional space where the density is

docs/social_networking.md

@@ -363,6 +363,34 @@ way hash, so are not easily linked to who is posting in the feed.
 
 This handles public posts.
 
+### Kademlia in social space
+
+The vector of each identity is a sequence ones and zeros of unbounded
+length, unboundedly large dimension, but in practice you will not need
+anything beyond the first few hundred.
+
+We deterministically generate the vector by hashing the public key of the identity.
+
+We do not have, and do not need, an exact consensus on how much of the
+vector to actually use, but everyone needs to use roughly the same amount
+as everyone else.  The amount is adjusted according to what is, over time,
+needed, by each identity adjusting according to circumstances, with the
+result that over time the consensus adjusts to what is needed.
+
+Each party indicates what entities he can provide a direct link to by
+publishing the sum of the vectors of the parties he can link to - and also
+the sum of the their sums, and also the sum of their ...  to as many deep as
+turns out to be needed in practice, which is likely to  two or three such
+vector sums, maybe four or five.
+
+When someone is looking to find how to connect to an identity, he goes
+through the entities he can connect to, and looks at the dot product of
+their sum vectors with target vector.
+
+He contacts the closest entity, or a close entity, and if that does not work
+out, contacts another.  The closest entity will likely be able to contact
+the target, or contact an entity more likely to contact the target.
+
 ##   Private messaging
 
 Private messaging is trivial.  There is no end of excellent existing software

docs/writing_and_editing_documentation.md

@@ -307,13 +307,15 @@ In this table, edited in a fixed font, you are using whitespace and blank lines
 
 ### Grid tables
 
-Allows multiline, and alignment, but visual studio does not like it, and you still have to count those spacees
+Allows multiline, and alignment, but visual studio does not like it, and you still have to count those spaces
 
 +---------------+---------------+--------------------+
 | Fruit         | Price         | Advantages         |
 +===============+==============:+====================+
-| Bananas       | $1.34         | - built-in wrapper |
+| Bananas       | $1.34         | Mary had a little lamb whose fleece was white as snow, and everywhere that |
-|               |               | - bright color     |
+|               |               |            Mary went the lamb was sure to go          |
+|               |               |                                 |
+|               |               | bright color     |
 +---------------+---------------+--------------------+
 | Oranges       | $2.10         | - cures scurvy     |
 |               |               | - tasty            |
@@ -479,7 +481,16 @@ defined by very small source code.
 		font-weight="400"
 		stroke-width="2"
 		style="text-decoration:underline; cursor:pointer;" >
-		<line x1="22" y1="70" x2="28" y2="100" stroke="lightgrey"/>
+		<path fill="none" stroke="#800000"
+			d="M45 100,  c100 -50, -40 -50, 60 0" />
+		<line x1="22" y1="70" x2="28" y2="100" stroke="grey"/>
+	<rect x="60" y="64" width="20" height="20">
+		<animate attributeType="XML" attributeName="y"
+			from="64" to="120"
+			dur="3s" repeatCount="5" restart="whenNotActive"/>
+		<animate attributeType="XML" attributeName="x"
+			from="60" to="0"
+			dur="3s" repeatCount="5" restart="whenNotActive"/></rect>
 		<rect style="fill:#FFFF00;"
 			x="12" y="64" width="36" height="20">
 			<animate attributeType="XML" attributeName="y"
@@ -493,19 +504,12 @@ defined by very small source code.
 			start animation
 		</text>
 	</g>
-	<rect x="60" y="64" width="20" height="20">
-		<animate attributeType="XML" attributeName="y"
-			from="64" to="120"
-			dur="3s" repeatCount="5" restart="whenNotActive"/>
-		<animate attributeType="XML" attributeName="x"
-			from="60" to="0"
-			dur="3s" repeatCount="5" restart="whenNotActive"/></rect>
 	<g
 		font-family="'Times New Roman'" font-size="5"
 		font-weight="400"
 		stroke-width="2">
 		<path fill="none" stroke="#00f000"
-			d="M14 101,  c40 -20, 30 -56, 54 -18,  s60 15, 40 15  c -20,0  -10,-20  0,-20 q 5,0 10,10" />
+			d="M14 101,  c40 -20, 30 -56, 54 -18 s60 15, 40 15  c -20,0  -10,-20  0,-20 q 5,0 10,10" />
 		<ellipse cx="60" cy="85" rx="12" ry="5" style="fill:red" />
 		<text  x="60" y="82" text-anchor="middle"  style="fill:#A050C0;" >
 			A simple scalable vector graphic