On 10.01.2016 20:06, "Ingo Althöfer" wrote:
it seems that different people are using the name "influence"
for different objects/properties.
In the computer go scene, 1-dimensional use goes back to
Albert Zobrist in his doctoral dissetation from 1970.
Where does your framework for "multi-dimensional" influence comes from?
Influence is a well-known term among players but its clear meaning
remained a mystery until I described in 2011. Before influence was so
unclear that it was hard, as a player, to know its difference from the
other related term thickness. Early player understanding of influence
was as naive as black / white influence light decreasing by distance
(i.e., it is not really influence but proximity multiplied by some
radiation function such as 1 or 1/x^2 or Manhattan distance and negative
for white light and maybe visually blocked by the disks of stones) but
everybody knew that that was wrong because dead stones do not create as
much influence as live stones. Early expert system programs used the
same naive concept, and every programmer would use his own
implementation of distance and intensity of light. Such light maps give
colourful maps that are impressive as paintings but close to useless
because of containing both correct and false information.
Stronger players know that influence and thickness are related to
strength of the stones creating the influence and solidity of the groups
of thickness. But what is strength? From traditional Asian go theory, it
was known that there is some relation between strength and strategic
concepts such as (little) aji, development directions, board
partitioning lines, potential for further territory etc. However, a
systematic assessment of strength was missing.
So I studied the fundamentals of the traditional go theory and noticed
that several strategic concepts (such as aji) used for thickness and
influence were just implications of the more basic strategic concepts of
connection, life and territory. I invented / (for 'life') rediscovered
degrees of connection, life and territory, distinguished influence (the
property of affecting other intersections) from thickness / thick shape
stones (the property of the "strong" stones creating the influence) and
defined both in terms of degrees of connection, life and territory.
Territory is optional in the definition and can also be studied
independently. Territory as a propery makes sense because it makes a
difference whether influence cannot be used because of being in a
neutral region or whether it is / can be used for protecting existing /
making additional territory.
Study a few simple examples of groups of strong stones with a few or
more opposing stones in the neighbourhood, and you notice that degrees
of connection and degrees of life can differ from each other. So
influence / thickness must be described at least by these two degrees.
Furthermore, the values differ for Black and White, so at least four
parameters are necessary for a complete description.
You find my informal definitions here
http://senseis.xmp.net/?Influence
http://senseis.xmp.net/?Thickness
or more carefully in my books. For the precise parameters of connection
and life see
http://senseis.xmp.net/?NConnection
http://senseis.xmp.net/?NAlive
Concepts of proximity should be called 'proximity' while concepts of
influence should be called 'influence'. Proximity maps / functions do
not explain influence except for the simplest examples in which all
stones are alive and the view is clear in every direction.
Computer go can have various study purposes (such as training neural
nets or predicting the final colour control in a scoring position) and
some sort of function over all intersections assigning them a single
number may be convenient for fast numerical training, but do not forget
that such a simplication trains both correct and false information
without distinguishing them properly. If we want to become stronger
players or create stronger programs, we must distinguish correct from
false information. Therefore, replace 1-dimensional by multi-dimensional
values if the task is to assess current positions rather than final
scoring positions, in which one value is sufficient.
--
robert jasiek
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