Intro / Background / Definitions
What is Fluid Intelligence?Cattell defined fluid intelligence as "…the ability to perceive relationships independent of previous specific practice or instruction concerning those relationships."
Fluid intelligence involves being able to think and reason abstractly and solve problems. This ability is considered independent of learning, experience, and education. Examples of the use of fluid intelligence include solving puzzles and coming up with problem-solving strategies.
While many people claim that their intelligence seems to decline as they age, research suggests that while fluid intelligence begins to decrease after adolescence, crystallized intelligence continues to increase throughout adulthood.
( http://psychology.about.com/od/cognitivepsychology/a/fluid-crystal.htm )
is the system that actively holds multiple pieces of transitory information in the mind, where they can be manipulated
Working memory is generally considered to have limited capacity. The earliest quantification of the capacity limit associated with short-term memory was the "magical number seven" suggested by Miller in 1956. He noticed that the memory span of young adults was around seven elements, called chunks, regardless whether the elements were digits, letters, words, or other units.
Measures of working-memory capacity are strongly related to performance in other complex cognitive tasks such as reading comprehension, problem solving, and with any measures of the intelligence quotient. Some researchers have argued that working memory capacity reflects the efficiency of executive functions, most notably the ability to maintain a few task-relevant representations in the face of distracting irrelevant information. The tasks seem to reflect individual differences in ability to focus and maintain attention, particularly when other events are serving to capture attention. These effects seem to be a function of frontal brain areas.
( http://en.wikipedia.org/wiki/Working_memory )
The ability to quickly and accurately recognize where all
the pieces are and assess what they are doing in the present chess position
( http://www.chesscafe.com/text/heisman89.pdf )
I was watching myself solving this tactical problem.
De Pauw, S.-Paci, Cedric 1997
1k4r1/1p2n3/p7/5r1p/1Qp2q2/P3B3/2P2PPP/R4RK1 b - - 0 30
Black to move
I did recognise several elements, some of them:
- Qb4-d6 +
- Qf4xh2 is nonsense
- Rooks at f2 and a1 are doing nothing and cant be won
- Ne7 is uninteresting
- strong local majority of the black pieces at the wing of the white King
- black can hardly use the f- file
Now i did start to search the concrete solution ( calculation ) with series of checks.
The white King HAS to take or Qh2#
and now Qf3+ ( usually you move the strongest piece as close as possible to the opponents King ) and then Rg5? OOps don't work there is the Bishop at e3. Hmmm..
Qg4+? ... don't work either. Insight: I need the Rook f5 at the g-file to mate. And so i found the solution
A more structured method to solve that problem would start with material count first and would focus on the king safety next.
Kramnik, Vladimir - Hertneck, Gerald 1994
6k1/5p1p/3p2pb/2pP4/4n3/7P/1PQN1PP1/r1Bn2K1 w - - 0 25
White to move
Many tactical elements to see
- weak white back rank
- Ra1 already x-raying at the white king
- Black king is save
- Nd2 is pinned
- Nd1 and Ne4 are forked by the Qc2
- material: White has more material
- black threatens to play Nxd2 and win a piece
So what is necessary to solve chess problems?
- recognising the (possible) tactical elements
- correct judgement of these elements
- combining these elements to an Idea
- "logical" reasoning with the elements to make the Idea work
The number of ( possible/interesting/relevant ) tactical elements is high and will usually exceed ( by far ) the capacity of the working memory. So we have to load and unload these elements permanently. "Board Vision" is the Cache memory of the Tactician, the Tactician does not have to look at the Board and check, he "knows" where the pieces are and what they are doing. Things we don't have in our internal board have to be "read" from the board. That the slowest process, equivalent to the reading from the hard drive.