Free The Immortal Game by David Shenk

finances, and instigated the Spanish Inquisition. It simply cannot have been happenstance, argues historian Marilyn Yalom, that in the same country at the exact same time several influential chess authors proposed a new chess Queen with unprecedented powers on the board. “A militant Queen more powerful than her husband had arisen in Castile; why not on the chessboard as well?” Yalom writes in her book
Birth of the Chess Queen
. “This may have been the thinking of those players from Valencia who endowed the chess Queen with her extended range of motion. Perhaps they even hoped to win favor from the Queen by promoting the chess Queen. Yet it is just as likely that those Valencian players
unconsciously
redesigned the Queen on the model of the all-powerful Isabella.”
    Such was the dynamic, symbiotic relationship between chess and its adopted continent—game and society reflected and influenced one another, like a painted portrait and its subject. The new, faster, more intellectually challenging chess echoed not just the rise of female power, but also a culture in transformation. A renaissance was taking place. Europe was slowly becoming a more frenetic, curious society.
    It was the age of humanism, the printing press, Leonardo da Vinci, and Erasmus. “This Century, like a golden age,” declared Italian philosopher Marsilio Ficino in 1492, “has restored to light the liberal arts, which were almost extinct: grammar, poetry, rhetoric, painting, sculpture, architecture, music…has joined wisdom with eloquence, and prudence with the military art…. [and] invented the instruments for printing books.” Echoing these changes, the new chess was a much quicker game, giving it a higher-octane feel and making it an emblem of the emerging age of knowledge. Whether by accident or design, the Renaissance itself was reflected in the new, more engaging format of the game, which quickly became the universal standard. Modern chess was born.
    Just looking at static pieces on the board, the enormity of the shift would have been impossible for a casual observer to appreciate. The chessboard, after all, was exactly the same. The pieces were exactly the same. Their arrangement was exactly the same. Looking at the board through a snapshot, there was no indication that anything at all had changed. But in animated motion and in the mind’s eye of the player, it was a different matter. Seasoned players realized all too well that with the tweaking of a few pieces’ powers of motion, it was an entirely new game. It was much faster and more aggressive in that the Queen and the Bishops could now move into threatening positions within just a few moves. (One opening sequence emerged which allowed Black to checkmate White in two moves.) *10 And it was vastly more complex because at any given time, each player had many more move choices—and had to anticipate more responses from the opponent. Suddenly, there were vastly more possibilities of play from the very start. Now the game was not only fast, it was also nearly infinite.
    Nearly infinite?
There’s a suspicious phrase, to be sure. How could something be
nearly
infinite? It’s like calling a tumor
almost
malignant. But such is the deceptive power of geometric progression, a method of numerical increase that leaps forward not by addition (10 + 10 + 10 =30) but by multiplication (10 × 10 × 10 = 1,000). Geometric progression is one of the foundational principles of all mathematics, helping to advance understanding of everything in nature that grows or spreads, from human population to financial investments to nuclear fission. Its manifestation in chess, which can be easily explained but is not ordinarily intuited, is one of the particulars that make the game so fascinating to mathematicians—and so intriguing to players.
    It all starts out so simply: In the first move, White is limited to twenty options:

    Each Pawn can move either one or two squares on its first move. 8 x 2 = 16 possible