Studying Microendgame and Infinitesimals
Posted: Mon Sep 25, 2017 10:52 am
This thread is for our study of microendgame and infinitesimals, as introduced in Mathematical Go Endgames, other texts or sources. I have made several attempts to understand infinitesimals and think others share the frustration. Rather soon one meets a wall when something essential remains unclear and deeper learning is blocked. I start with my current difficulties of understanding, will add more later and invite you to do alike or clarify.
***
QUESTION 1
Why is the chilled count of the following position 2UP * ?
This has the chilled count 0.
This game is a chilled {0|*}, which is defined to be UP.
From the followers, it follows that the initial position has the chilled count {0 | {0|*}} = {0|UP}.
However, I do not understand how we get 2UP *.
***
QUESTION 2
Mathematical Go Endgames distinguishes incentive and temperature. I have not really tried to understand the mathematical definitions but wonder what is the practical difference between the two terms as used in the book?
***
QUESTION 3
Now I study table E11, example 3.
The book specifies the chilled count as 0, adds one black chilling mark in the diagram and mentions the incentive -1. I do not care about the incentive yet but first try to understand: Why is the chilled count 0?
In unchilled go, the count is B = 0.5 + 0.75 = 1.25 and the move value is 0.75.
In unchilled go, the count is W = 0.5.
From the counts of the followers, we get the initial position's tentative gote move value (B - W) / 2 = (1.25 - 0.5) / 2 = 0.75 / 2 = 0.375. The move values from the initial position to the black follower increase so the initial position is a local sente. This means its move value is the sente move value but we first need to consider the sente follower:
The unchilled count of the sente follower is S = 0.5 + 0.5 = 1.
The white follower's count is the reverse sente follower's count R = W = 0.5.
The initial position's sente move value is S - R = 1 - 0.5 = 0.5.
However, I am more interested in the initial position's unchilled count C, which is the inherited count of the sente follower C = S = 1.
Now, I recall that the book added a tax mark in the diagram, so the chilled count C1 (chilled by 1) of the initial position is C1 = 0.
Ok, if I did it right, I seem to have answered my own question but - did I do everything right? What bugs me even more is infinitesimals: why do infinitesimals not occur in the chilled count of the initial position? Do they occur in the unchilled count of the initial position?
***
QUESTION 1
Why is the chilled count of the following position 2UP * ?
This has the chilled count 0.
This game is a chilled {0|*}, which is defined to be UP.
From the followers, it follows that the initial position has the chilled count {0 | {0|*}} = {0|UP}.
However, I do not understand how we get 2UP *.
***
QUESTION 2
Mathematical Go Endgames distinguishes incentive and temperature. I have not really tried to understand the mathematical definitions but wonder what is the practical difference between the two terms as used in the book?
***
QUESTION 3
Now I study table E11, example 3.
The book specifies the chilled count as 0, adds one black chilling mark in the diagram and mentions the incentive -1. I do not care about the incentive yet but first try to understand: Why is the chilled count 0?
In unchilled go, the count is B = 0.5 + 0.75 = 1.25 and the move value is 0.75.
In unchilled go, the count is W = 0.5.
From the counts of the followers, we get the initial position's tentative gote move value (B - W) / 2 = (1.25 - 0.5) / 2 = 0.75 / 2 = 0.375. The move values from the initial position to the black follower increase so the initial position is a local sente. This means its move value is the sente move value but we first need to consider the sente follower:
The unchilled count of the sente follower is S = 0.5 + 0.5 = 1.
The white follower's count is the reverse sente follower's count R = W = 0.5.
The initial position's sente move value is S - R = 1 - 0.5 = 0.5.
However, I am more interested in the initial position's unchilled count C, which is the inherited count of the sente follower C = S = 1.
Now, I recall that the book added a tax mark in the diagram, so the chilled count C1 (chilled by 1) of the initial position is C1 = 0.
Ok, if I did it right, I seem to have answered my own question but - did I do everything right? What bugs me even more is infinitesimals: why do infinitesimals not occur in the chilled count of the initial position? Do they occur in the unchilled count of the initial position?
, costs one point. So the local count is 4 - 1 = 3.
QED.