All 4 books by Edward Tufte now in
paperback editions, $100 for all 4
Visual Display of Quantitative Information
Beautiful EvidencePaper/printing = original clothbound books.
Only available through ET's Graphics Press:
catalog + shopping cart
All 4 clothbound books, autographed by the author $150
catalog + shopping cart
Edward Tufte e-books
Immediate download to any computer:
Visual and Statistical Thinking $2
The Cognitive Style of Powerpoint $2
Seeing Around + Feynman Diagrams $2
Data Analysis for Politics and Policy $2catalog + shopping cart
Edward Tufte one-day course,
Presenting Data and Information
Washington DC, June 12
Arlington VA, June 13
Bethesda MD, June 15
Seattle WA, July 23, 24
Portland OR, July 26
Denver CO, July 30
Minneapolis MN, August 21
This superb display from The New York Times shows complex narratives with good text/image integration and a precise use of color. The informative and vivid writing is by Paul Hoffman; the excellent work of the analytical designer, however, is not credited.
-- Edward Tufte
Computer and Human Chess Masters
Some excellent work -- and one obvious design flaw.
The standard way to indicate which player is playing which color pieces is to put the player's name on their side of the board. So in the first example, where the human was playing black, the word "Human" would have appeared just above the board, and "Computer" just below it.
This would have been much better than using what amounds to a chart legend, which requires you to look away from the board, memorize the data, then look back to the board.
It's particularly surprising to see this mistake, since the preferred approach is overwhelmingly standard in the thousands of books devoted to chess.
-- Pete McCabe (email)
The minor defects in this graphic result from ignoring the traditional and well-tested practices of standard chess diagrams.
-- Edward Tufte
One disorienting factor is that color is inconsistently applied to the players - for example, Human switches from black to white.
-- Anthony Edward Martinez (email)
These are examples from real games. The colors listed were the colors the players actually had.
-- Jeffery Sellers (email)
Not relevant to chess, but might be interesting: while I'm sure chess has its own display traditions where the players keep their colors when games are discussed in books or newspapers, bridge (the other daily newspaper game) does it a little differently. No matter what the original positions at the table, newspaper columns always place the player who ends up as dealer at the South (bottom) position of the table display.
-- Sean Owens (email)
In chess, the color of each player's pieces can have an impact on the outcome. Since white always moves first, the player controlling the white pieces has a slight, although statistically significant, advantage.
Consequently players in a two-person, multi-game tournament will alternate playing the white pieces. Furthermore, most (if not all) tournaments consist of an even number of games so that each player controls the white pieces an equal number of times.
The association of player and piece color is therefore important in representations of a game.
-- J. E. Ivancich
I have many books on chess and have never seen the names of the players above and below the board.
These diagrams are better than most, although they have the advantage that they are describing a handful of moves. Longer games present more problems. All chess books and articles suffer from the same difficulty: you have to memorise the moves, or play them out on a board as you go along, flicking between text and diagram/board.
Chess is much better represented online, where the moves can be made dynamically, ideally with a lecturer's voice commentary, so you can keep your eyes on the board. Chess.fm has some nice examples of this, though their presentation lack a "pause" or "rewind button", so you have to make sure you've been to the bathroom before you press play.
-- brian millar (email)
I'll have to check my library at home to see where I've seen boards with names above and below. I can say that all my book are 10-20 years old (they're all in descriptive notation, if you can imagine).
Even if it turns out that I'm hallucinating and this was never a standard, it should be.
[links updated January 2005]
-- Pete McCabe (email)
Consideration of the spatial relationships between the pieces aside, there is also a temporal aspect to the game. It would be interesting, I think, to convey the amount of time taken for the moves under consideration. This might give us a clearer understanding of the realities faced by the human player sitting across the board from a machine.
-- Ted Buenz (email)
A close look at the game in the left hand column reveals that both queens are black; good design but an error in detail that could cause confusion.
-- Prem Thomas (email)
Adjust screen brightness.
-- Edward Tufte
Actually, the designer needed to take the weight of the stroke into more consideration at this size... the queen is a detailed piece. It is nice work overall though, and none of those annoying diagonal fills. Perhaps a letter H or C at either end of the board?
-- Michael Anderson (email)
Many books on Go use an interesting convention for added clarity when describing gameplay in text. White is always referred to with female pronouns and black with male pronouns (e.g. she runs at two and he counters with...)
Interesting, in any case.
-- PJ Doland (email)
One other point on the graphic. It is also the standard practice to indicate who's turn it is to move beside the diagram. Without that information, the diagram itself is useless. In many chess positions it is possible for both sides to win -- if only it was their move (yours truely included). Below the player who's turn it is to move, would be either the words "White to Move" or "Black to Move". Additionally, that text might be expand if there is a tactical element: "White to Move and Win" or "Black to Mate in 3", etc. Also, in order to aid the reader in analyzing the position, the board is often oriented so that the side who's turn it is to move is at the bottom.
-- Mike Miller (email)
Also, in order to aid the reader in analyzing the position, the board is often oriented so that the side who's turn it is to move is at the bottom.
Really? I believed until now that convention puts White at the bottom; are there respected counter-examples?
-- Michael Bolton (email)
Good Point. I need to stand corrected on board-orientation, as there does appear to be a standard of white at the bottom. However, I was able to find, rather quickly, an exception to this in my limited chess collection. The exception was where the author displayed two diagrams for each position, one from Black's point of view and one from White's point of view. Other than the "white at bottom" standard, there does not appear to be any other standards. From the quick sampling I did, the diagrams vary greatly in configuration and style. Again this was a very cursory review of some classic and more modern chess texts. Here is what I found:
My Best Games of Chess 1908-1937, Alexander Alekhine Diagrams are oriented with White at bottom. The diagrams have no other notation than the simple text, "Position after Black's 22nd move" preceeding the diagram in the text. The inside cover of this book says it is an unabridged and unaltered reproduction in one volume of My Best Games of Chess 1908-1923 first published by G.Bell & Sons, London, in 1927 and My Best Games of Chess 1924-1937, published by G. Bell & Sons in 1938.
Opening Systems for Competitive Chess Players, John Hall 1992 This book is an opening repertoire for White playing the Torre Attack and Black the Tartakower and Caro Kann. The author uses a technique of showing each position as two diagrams. One from White's point of view and one from Black's. I believe this very useful when studying openings, as it helps the student better recognize the placement of pieces on the board. The diagrams have no other annotation than White's View and Black's view listed at the bottom of each.
Plan Like a Grandmaster, Alexei Suetin 1988 The diagrams are oriented with White at the bottom and are sequentially numbered on the upper left hand side. The numbers are used to refer to the diagrams in the text.
My System, Aron Nimzovich 1930 The diagrams are oriented with White at the bottom and are sequentially numbered at the top with "Diagram 23", for example. At the bottom of the diagram are comments explaining the position, such as "Here the right procedure for Black is to attack the chain by ... P-Kt4-5 in order to provoke BPXP. ...P-B3 would be wrong".
How to Reassess Your Chess, Jeremy Silman 1993 The diagrams are oriented with White at the bottom and are sequentially numbered on the upper left hand side, as in Suetin. At the bottom of the diagrams are the player's names, where and when the played, and whose turn it is to move.
That's a quick summary. In terms of board orientation, I would make the following observations.
Where the subject is annotation of a game, it makes sense to adhere to the "White" at bottom standard. It is what most readers will expect as it shows the flow of the game through a series of small-multiples. Flipping the orientation of the board on opposite turns would be distracting, to say the least.
Where the book is a treatment of an opening repertoire, the style that John Hall used is extremely helpful in showing the view from both sides of the board. This style aides the reader in being able to recognize the position, whether they are playing the opening from the Black or White side.
Puzzle/Problem Books I reviewed two books of chess problems (not listed above). They also followed the "white at bottom" standard. Here, I think it would be helpful to discard this standard and orient the position depending on the move. When using this type of book, the student is attempting to solve the problem and compare it with an answer in the back of the book. I've solved these problems before by setting up the position on the chessboard. The first thing I do is turn the board around so that it is oriented as if I was player with the move. Why not go ahead and do that for the reader in the book?
-- Mike Miller (email)
Mike Miller's research is remarkable. The idea of seeing the board from the side of the next move is intriguing; perhaps the reason I can't solve many chess problems (white to mate in 3) is that the board is facing the wrong way half the time!
For a news report in The New York Times, which is the example here, better to follow conventions rigorously (white's point-of-view, up is north in maps, and so on) than to have a rotating chess board or north some other direction than up on a map.
Is the game of go symmetric with respect to colors?
-- Edward Tufte
With Go black always goes first and is always the weaker of the two players. The board itself is not exactly square with the narrower edges facing the players. The squares are 29/32in by 27/29in. With the (up to) nine handicap stones that black can receives they are placed on given points on the board with a bias towards the outer edges.
In the book by Edware Lasker, GO and GO-MOKU, Dover, 1934. The boards are all presented with black at the bottom.
As the game is not 'played away from you' like chess, I have always pictured the game as looking from above. More like reading a map. Play can move in any direction. You are visualising in which direction your opponent is going next.
-- Andrew Nicholls (email)
While looking over my new Mac tonight, I played a game of chess which allowed rotating the chess board in 3 dimensions (yaw, roll, and pitch). Didn't help, the computer still wiped me out (even when I peeked at the "hints") never relenting after my poor opening which yielded doubled-up pawns. But the pieces were very vivid on the 23" monitor.
-- Edward Tufte
The NYT display is beautiful because of the neat layout employing dividing lines and subheads and the pairing of each paragraph with an accompanying diagram, augmented with red arrows and circles. In spite of the visual merit, the article is less than superb: the text is frequently imprecise, the graphic language is used loosely, and the visualization method systematically misplaces the emphasis.
The intent of the first two examples is to illustrate the contrasting strengths of machine and man, yet the text for both is introduced with the same subject: Vladimir Kramnik. Example 1 (Advantage: Silicon) talks about the computer, so the introductory paragraph should be recast with Deep Fritz as the subject: "Deep Fritz played an eight-game match against current world champion Vladimir Kramnik in 2002. In the fifth game the computer had the white pieces. After its 33rd move its queen was threatening Black's knight."
The second paragraph explains a queen move, the biggest blunder of Kramnik's career, yet the accompanying diagram fails to depict the move. It shows the position reached after that move and distracts us with two other moves -- potential next moves indicated by arrows. Where is the queen move? We must compare Diagrams 1 and 2 to imagine it. In fact, we must refer to previous diagrams to imagine the key moves in four of the six diagrams in the first two examples.
The designer's essential problem is that the board can show a position but not a move; hence the use of arrows (explicit display of information). The designer here chose to use an additional method of "showing" moves — by jumping to the next board position (implicit display) — and furthermore chose to alternate between the two methods. The methods differ in that arrows emphasize moves whereas new board positions "swallow" the moves. Problem is, key moves discussed in the text are represented implicitly while the potential following moves are depicted explicitly. In short — the graphics emphasize the wrong moves.
Emphasizing the actual move plus showing the potential next moves requires expanding the graphic vocabulary. Diagram 2 should show Kramnik's infamous queen move by a solid arrow from a2 to c4 (x-axis alphabetic, y-axis numeric). (Incidentally, algebraic notation is a chief reason White is normally placed at the bottom in chess diagrams.) The shafts of the two solid arrows in Diagram 2 could be changed to dotted lines, indicating threats or potential next moves. This graphic vocabulary explicitly shows every move, distinguishes between previous move and potential next move, and emphasizes the actual moves. It clearly displays the logical connection between consecutive moves.
The graphics are loose in Example 2 (Advantage: Human). The first paragraph tells that the white rook threatens two pawns but the diagram shows only one. The third diagram can be easily misinterpreted where the arrows cross. To add clarity one might consider using e.g. red arrows for Black moves and green arrows for White moves. Why is the black rook circled? This careless use of the circle is inconsistent with the effective use in Example 1.
The first case in Example 3 (Outthinking the Computer) is poorly explained. Exchanging queens deprives both sides of their strongest attacking piece, so where's the advantage? The diagram shows the position after White's eighth — not ninth — move. With the pawn on c5 obviously en prise the question of whose turn it is becomes a point of distraction that the writer should allay with three words: Black to move.
In the last case, the pawn phalanx known as the Alterman Wall looks deliberate but Grandmaster Boris Alterman did not intend it. During the game he did not even notice it. Of his strategy he says "White's main objective is to keep all the pieces on the board, since the more pieces remaining on the board, the more calculations are required for the computer after each move, decreasing its ability to focus on the crucial lines. The calculations become very complicated for the computer under such conditions." This is not the strategy Paul Hoffman claims the example illustrates. (Interestingly, this strategy also seems to be at odds with the strategy Kramnik adopted in the previous example.) Alterman's Internet page http://balterman.freeservers.com/altermanwall.html discusses the strategy and includes three diagrams — one of which is his graphic version of this freak position.
The title of the piece "When the Computer is a Chess Master" misses the mark. Edward Tufte replaced it with an apropos title for his Graphic of the Day: "Computer and Human Chess Masters."
-- Daniel Wentz (email)
I have played enough Chess that the orientation of the board while I am playing is not really a factor. (The real challenge is playing blindfolded.)
The comments about orientation made me think of sports coverage. For a game like hockey, 95% of the game is shown from cameras on one specific side of the rink. This makes sense as a viewer would not have to continuously try to determine which end is which.
This is why White is typically on the bottom in Chess diagrams. It saves the viewer the challenge of reorienting.
-- Gord Schmidt (email)
As a long time chess player (learned when I was 4, am now just over 30 as I write this) a few comments.
First one of the earlier ocmmentors talked about visual presentations online where the potential moves were animated etc. This is, I would argue, not so useful in terms of teaching you to play chess, at least tournement competitive chess well. It is a common habit for many people to move pieces around while analyzing a position - but in tournement conditions if you touch one of your pieces you MUST (unless moving it were no legal) move that piece, likewise if you touch an opponent's piece you MUST capture it (if a legal capture is available). As a result of this, as well as general politeness in non-tournement chess chess players have to develop an ability to visualize board positions and moves many moves into the future - without, ideally, the aid of moving pieces around.
Historically (and even today) a common demonstration by grandmasters is to play "blindfold" chess - that is, to play the entire game without ever seeing the board (against other grandmasters entire games may be played this way with neither player seeing the board, against regular players the grandmaster does not see the board, the players do). Usually when grandmasters do this, they play many of these games at the same time - i.e. they have the ability to play 10, 20, even more games, simultanously without ever seeing any of the boards.
To get to the issue of illustrations. There are a number of competing standards for chess illustrations. One very popular, but not completely dominant format is the "informant" format - the Informant series of books would actually make a great case study. They are a very long running series of chess books, with 1000's of games from around the world, published with nearly no words - just moves, limited graphics, and universial symbols to cross languages and share the games (and commentary on the moves). An entire set of conventions about how to mark good, great, questionable moves has arisen, as well as multiple conventions for record the moves of the game.
The convention of noting the players at the top/bottom of the illustration is used in some books, but only rarely. Again, in part it is part of the training of a chess player to remember these things - in a position such as the one on the far right bottom I (and most other chess players) could probably identify the human player and the computer without anything other than the illustration - the position of the pawns in a row across the 4th rank is one that only a human would concieve of or make.
Likewise many chess problems and puzzles are designed to help stretch and teach chess players to recall and remember positions. Challenges such as working out what the previous moves of a game, playing games blindfolded, doing anlysis without moving pieces on a board, playing games following a strict "touch move" rule, etc all help teach good chess habits.
And a final note - advice for anyone wishing to get better at chess. Start at the endgame and work back to the opening. First, learn how games are won (and lost or drawn) in the endgame. Ruben Fine's classic book on endgames is a great starting point. Second, learn the tactics, positional play, exchanges, and various tactical and as well as strategic aspects of the middlegame. Here there are countless options but collections of middlegame puzzles are a great starting point, learn to analyze a position, consider how the game might be won or lost, but even more consider how long term advantage (such as what you learned in your endgame studies) might be gained over the next few moves.
Going over complete games will also help.
Only then would I recommend looking at the opening - by then you'll have an idea of how to win in various tactical situations (and how to avoid them) and finally how to "close the deal" and win in the endgame.
Against a computer opponent one further point - do practice a set of openings, perhaps with the help of an opening book to avoid known tricks/traps (which you can usually assume a computer will know/discover). Against humans, also look to learn openings that do not rely on the opponent "not seeing/not knowing" the problem - but which reflect the style and type of game you enjoy (open vs. closed, tactical vs. longterm etc).
Hope this helps!
-- Shannon Clark (email)
The mention of Lasker and his 1934 book on Go charmed my heart but I hasten to point out that Lasker himself always played black -- he was without fail the weaker player in any contest. Mindful of his ability at chess, at Go he was nevertheless a bare amateur. Modern go books, whether from China, Japan or Korea, do not favor any one orientation in the placement of board on paper -- with one common exception: in an even game (ie: no handicap) a traditionally-taught player would not place the first stone in the opponent's right hand corner. It would appear discourteous.
As for adding a sense of time to game records such as Chess or Go, I've never seen the duration between plays presented in a graphical manner. Chess programs in general, and some of the newer chess books, offer a wealth of symbols to annotate the 2-dimentional board. But time isn't one of them. On the other hand, in the detailed narrative records of certain famous games, the times between moves are often given. It seems that someone is recording the times -- at least for some pretigeous games -- and this data is considered enlightening for close tournament followers. For example, the 1971 Honinbo Tournament, Ishi Press, gives frequent references to the time given for a certain play. Odd how the detail is considered worth saving and occastionally reporting, but never in the standard graphical versions. The audience is surely the same; yet the mere change in style (text v. graphical) affects which data are given.
-- Jeffry Finer (email)
A recent innovation, I believe, in Go books is the use of symbols in text to refer to moves. The effect is to mimic in the text the look of the black and white moves shown in the board diagram, where moves are shown as numbered black and white disks. Rather than saying "attacking with Black 3" the text says "attacking with (3)" where (3) is a picture of a black stone with a 3 on it. This greatly speeds the mental process of coordinating the text with the diagrams. An example can be found at the online go repository, Sensei's Library. See http://senseis.xmp.net/?path=GoProverbs&page=IkkenTobiIsNeverWrong I wonder if this is done in chess books. I suspect it might be less effective in chess because the names of the pieces are more meaningful and because the small shapes might be harder to distinguish uprooted from the board diagram.
-- John Pinkerton (email)
A discussing chess computer.
At http://turbulence.org/spotlight/thinking/chess.html is a chess computer which reveals what moves it is considering in a nice way. In this image from the gallery, each side is down to king (cross, black obscured on b8) plus one pawn; the original caption was "The machine foresees that white's pawn will become a queen, and dominate the board as the black king flees." Each line is a move in a considered sequence. Brighter lines are considered better moves for white.
In the stills unfortunately the pieces have not been redrawn in front of the moves. But during play, watching the lines appear, that is not so much of an obstacle. In fact watching potential moves pile on almost makes it easier to see the board than just looking at the (abstract, nonstandard) representations of the pieces.
-- Rob Mahurin (email)
After one has moved, it is a bit intimidating to watch all the lines of movement under consideration by one's computer opponent.
But the move choices surely are not sophisticated; I played it to a stalemate the second try, and although it found some clever knight moves, my doubled-up bishops lasted well into the end game insuring a stalemate. I have now retired from chess.
[Further research reveals the modesty of my stalemate: "The chess playing engine is designed to be at the same level as the average viewer. If you're a tournament chess player, you would clobber most casual players--and you'll clobber Thinking Machine 4 too. If you barely remember the rules of the game, the artwork may clobber you instead. The chess engine we built is simple and uses only basic algorithms from the 50s (alpha-beta pruning and quiescence search). The program's unconventional initial moves may raise eyebrows among experts: we did not give it an 'opening book' of standard lines since we wanted it to think through every position."]
-- Edwrd Tufte
With regard to Chess and cognition in board displays, Scientific America published an interesting article called "The Expert Mind." It discusses a theory in human cognition based on studies of chess grand masters. Not only does it give interesting insight into cognitive science but might reveal a visual perspective on how chess can be represented. The link is http://scientificamerican.com/print_version.cfm?articleID=00010347-101C-14C1-8F9E83414B7F4945
-- Lance Brown (email)
Here is a site on information display in board games:
-- Paul M. Boos
Excellent sequential chess display
The New York Times report on the death of Bobby Fischer also depicts (in a sidebar) two excellent sequential game histories, including the elegant game 6 of Fischer v. Spassky.
The virtue of the sequential animated display is that it enables those, such as myself, who are are unable to track beyond a few moves in the traditional still-land chessboard + the encoded game history. By staying close to the actual chess events, the visual animation replaces the traditional programmer model of chess game history.
-- Edward Tufte
David Gerrold wrote at some length on 'fairy' chess, in his (not particularly excellent) science-fiction novel 'A Day for Damnation', 1985. The protagonist, in this flashback, recalls his teenage fascination with variant computer chess, for which he invented bizarre pieces like the Magician, the Troll, Ghouls and Vampires and Zombies. Below I quote some of the build-up for the sake of context; the visualization method comes toward the end.
In order to play a game with all these new pieces, I had to redesign the chessboard. I invented a gigantic spherical playing field with the opposing armies starting the game at opposite poles. I found I had to put in oceans then, blank areas that no piece could move through, to allow for edge strategies. Very quickly, I reached the point that the game could only be played on multiple high-resolution terminals. It was the only way to keep track of what was happening on all sides of the globe at once.
[the protagonist writes his own version of the computer-chess program he started with, to present all this complexity on his super-duper science-fictional fifty-years-in-the-future Cray-9000: a 256-bit machine running at 2 gigaherz]
When I finally sat down to actually *play* the game, I realized that something very interesting had happened. My perception of chess had shifted.
I no longer saw the game as a board with a set of pieces moving around on it. Rather, I saw it as a set of arrays and values and overlapping matrices of shifting dimensions &ndash and the pieces merely represented the areas of influence and control. The game was not about tactics and strategy any more; it was about options and relationships.
I had a bizarre experience of looking at a chessboard and realizing that it and the pieces were actually unnecessary. They didn't need to exist at all. They were only place-holders in the physical universe, something with which to annotate the actual relationships which the game was truly about.
The pieces weren't the pieces any more &ndash they were their move patterns. A King was a square block, three squares by three. A queen was a star-shaped radius [sic] of power. A rook was a sliding cross. A bishop was an X- shape. And I didn't play chess by just studying the pieces any more. I looked instead at the overlapping relationships.
I rewrote my program one more time.
I added an option to display the relative strength of the opposing sides. The pieces were black and white; the areas they controlled were coloured red and green. The more a square was under the black control, the redder the square was shown. The more a square was under white's influence, the greener it was displayed. Squares that were equally contested showed up yellow. It became possible to look at the sphere and see all the strong and weak points at once.
The game was no longer chess. It had become something else. You didn't move your pieces to move pieces, but to change the colouring of the board &ndash to control space. Controlling space was more important than capturing it. Capturing a piece tended to decrease the amount of space controlled. The game was won by juggling threats, not actions."
I could certainly question the author's ideas about chess in that last paragraph, but I think the visualization technique could be quite interesting. Personally, I'd have used yellow and blue tints, so equally-contested squares would show up green, yellowness* or blueness would represent relative advantage, and saturation would represent intensity of coverage &ndash there's a big difference between a square 'equally contested' between one piece on each side, and one 'equally contested' between four pieces on each side.
*Humans, it turns out, are exquisitely sensitive to subtle colour variations in the yellow-to-green range. As the waggish marine biologist N. Justin Marshall put it: 'We're very good at bananas.'
-- Dominic Brown (email)
I would like to comment on Mr. Owens post of January 26, 2003 in which he states:
"No matter what the original positions at the table, newspaper columns always place the player who ends up as dealer at the South (bottom) position of the table display."
I believe Mr. Owens meant to say that the "player who ends up as DECLARER" is portrayed in the South position, so that it is easier for the reader to follow the play of the cards, rather than the bidding.
-- Gregory LaMothe (email)
Much to be recommended is Gary Kasparov's 'How Life Imitates Chess' (ISBN 978-0-099-48986-3). A few of the analogies between Chess and Life seem a trifle forced, but nevertheless it is an excellent analysis of the connection between strategy and operational events. A difference between normal data analysis and chess analysis is that the player cannot work on the full dataset because it is too large - far more possible moves than there are atoms in the universe. Accordingly, there needs to be a preliminary pattern-recognition exercise which is essentially synthesis rather than analysis. The hypothesis that follows the synthesis will lead to the discarding of nearly all the data so that analysis can focus on what is perceived to be relevant. In chess of course the 'rage to conclude' is paramount: again somewhat different from the virtues of scientific analysis.
-- Martin Ternouth (email)