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Reworked discussion of Merkle patricia dag

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Got a lot shorter as copious half formed thoughts were deleted
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2
docs/block_chain_scaling.md
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@ -16,7 +16,7 @@ state. Or some of them could throw away all the transactions, while others
transfer them to distributed and slow storage. transfer them to distributed and slow storage.
But this creates the opportunity to inject a fake history with no past But this creates the opportunity to inject a fake history with no past
through a fifty one attack. through a fifty one percent attack.
At scale you have a lot of transactions, a lot of clients, and considerably At scale you have a lot of transactions, a lot of clients, and considerably
fewer peers, so you worry about peers conspiring to quietly introduce new fewer peers, so you worry about peers conspiring to quietly introduce new

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docs/merkle_patricia_dag.md
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docs/writing_and_editing_documentation.md
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@ -216,6 +216,10 @@ an odd number of control points.
What it does instead is complicated and mysterious. What it does instead is complicated and mysterious.
Construct a series of straight lines M point L point L point.
To mark a point in the sequence h 2 h -4 h 2 v 2 v -4 v 2
To convert a sequence of straight lines into a smooth curve, you encounter To convert a sequence of straight lines into a smooth curve, you encounter
much grief matching the end of one bezier to the start of the next.\ much grief matching the end of one bezier to the start of the next.\
And if you do not match them, you get corners between beziers. And if you do not match them, you get corners between beziers.
@ -238,16 +242,13 @@ And if you do not match them, you get corners between beziers.
* Or starts at midpoint of first edge then:\ * Or starts at midpoint of first edge then:\
Q vertex midpoint T midpoint T midpoint ....\ Q vertex midpoint T midpoint T midpoint ....\
But the Q T T T chain is apt to act weird unless your midpoints are The Q T T T chain guaranteed to be smooth. This is a huge
near the middle, because the implied vertex is the mirror of the advantage, but each T curve has a mystery surprising control
preceding vertex, which may not be the vertex that you intended if point. You cannot see where it is, and the only way to
your midpoint is not near the centre of the line segment to that vertex. controllably adjust its position is to adjust the first Q point at
the start of the chain.\
Using S and T has the enormous advantage that if your midpoint is a bit If it is a nasty place, it is a bitch, you can get very sharp turns
off to one side of the line segment or the other, you still get a smooth in your curve
curve, no kinks between beziers But if it is too far off from the centre,
your curve will be off from the line segments, often in weird, surprising,
and complicated ways.
On the other hand, if you have a C or a Q bezier following a previous C On the other hand, if you have a C or a Q bezier following a previous C
or Q bezier, getting the join smooth is a bitch. or Q bezier, getting the join smooth is a bitch.