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## Google, Data, and the Problem of the Chessboard

Last week a rather impressive statistic was used by Google CEO Eric Schmidt – Tech Crunch has the figure and the quote:

Every two days now we create as much information as we did from the dawn of civilization up until  2003, according to Schmidt. That’s something like five exabytes of data, he says.

Schmidt goes on to say that the lion's share of this new data is user-created but the implications for all of us as learners is enormous. The immediate analogue is the proverb of the wheat and the chessboard

The short version is that an ancient ruler (some say India, others China) was quite pleased with one of his scholars who invented the game of chess. The ruler goes on to let the scholar name the reward for creating the chessboard. The scholar replies that he would like to receive one grain of wheat for the first square of the board and have the total amount of wheat doubled for each subsequent square. The ruler wasn't the mathematician that the scholar was but it works out to

To solve this, observe that a chess board is an 8×8 square, containing 64 squares. If the amount doubles on successive squares, then the sum of grains on all 64 squares is:

$T_{64} = 1 + 2 + 4 + \cdots + 2^{63} = \sum_{i=0}^{63} 2^i = 2^{64} - 1 \,$

This equals 18,446,744,073,709,551,615.

To bring this back to Schmidt's quote it important to note that an exabyte is defined as

### exabyte definition

unit
2^60 = 1,152,921,504,606,846,976 bytes = 1024 petabytes or roughly 10^18 bytes.

So what we're seeing nearly daily in data creation is something akin to the wheat & chessboard scenario. Again, a sizable portion of this data can be chalked up to the effluvium of life that comes in texts, tweets, and assorted blog postings – including this one. However, if even a fraction of this information is of merit it means that a drastic shift in pedagogy is needed.

Often when people criticize education it's that recent graduates are woefully inept when it comes to remembering facts. Such a lack of memory has even been the subject of late night television segments and game-shows. With the aforementioned exponential increase in the creation and storage of data, how can something like the Common Core Standards hope to serve to prepare students for the future? Given the bureaucracy that surrounds the Common Core, and education legislation in general, keeping up with "all the facts that are needed to know" seems to be an almost foregone conclusion.

Knowledge is needed to acquire any skill; facts are an indivisible part of learning. But the intertwined nature of facts and process in learning begs some important questions. Are educators supposed to strive to prepare their students for life, or for the next test? When looking at the chessboard are we approaching education as the ruler or the scholar?