diff --git a/docs/recognizing_categories_and_instances.md b/docs/recognizing_categories_and_instances.md
index c2b6346..92ef18b 100644
--- a/docs/recognizing_categories_and_instances.md
+++ b/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
-to be on the safe side, forty questions space. (Will have to test how many
-dimensions empirically retain angles and distances)
+So we can reasonably reduce each email into twenty questions space, albeit in practice, a great deal more than twenty. Finding far from random
+dimensions that reduce it to a mere twenty or so is an artificial intelligence
+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
diff --git a/docs/social_networking.md b/docs/social_networking.md
index ef60daf..a5ce97c 100644
--- a/docs/social_networking.md
+++ b/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
diff --git a/docs/writing_and_editing_documentation.md b/docs/writing_and_editing_documentation.md
index 2e817f0..cab51ac 100644
--- a/docs/writing_and_editing_documentation.md
+++ b/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 |
-| | | - bright color |
+| Bananas | $1.34 | Mary had a little lamb whose fleece was white as snow, and everywhere that |
+| | | 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;" >
-
+
+
+
+
+
-
-
-
+ 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" />
A simple scalable vector graphic