According to George Gamow, chess was invented by Sissa ben Dahir, Wazir of the court of King Shiram. King Shiram loved the game so much that he offered Sissa any reward he could name. Perhaps trying to impress the king with his mathematical skills, Sissa asked for some rice,

one grain on the first square of the chessboard, two on the second, four on the third, eight on the fourth, and so on, each square’s amount being the double of the previous square’s.

How much rice did Shiram owe Sissa?

The last square would contain 2⁶³ grains of rice. >This is a large number: 2⁶³ = 9,223,372,036,854,775,808 Suppose Shiram had tried to stack the rice of this last square in a column, each grain lying on top of the one below it. A grain of rice is about 1 mm thick. How high a column of rice would Shiram have obtained? Would it be higher than Mt. Everest? Higher than the distance to the moon? To the sun?

Here is the answer

In fact, if he could have stacked them this way, Shiram would have obtained a column of rice one light year tall, one-quarter of the way to the nearest star after the sun. Obviously, Shiram could not give Sissa the reward he requested. What do you suppose was the outcome? Let’s just say an important lesson is “Don’t be a smart-alek.”

:::.

The quickness of doubling is not just related to the history of chess. The most elementary population models postulate the growth rate is proportional to the population size (twice as many people means twice as many couples having babies, means twice as many babies). This led Thomas Malthus to predict population pressure problems, because Malthus argued populations grow more rapidly than their ability to produce food.

https://gauss.math.yale.edu/public_html/People/frame/Fractals/Chaos/Doubling/Doubling.html

The ancient Indian Brahmin mathematician Sissa (also spelt Sessa or Sassa and also known as Sissa ibn Dahir or Lahur Sessa) is a mythical character from India, known for the invention of chaturanga, the Indian predecessor of chess, and the wheat and chessboard problem he would have presented to the king when he was asked what reward he’d like for that invention.

Sissa, a Hindu Brahmin (in some legends from the village of Lahur), invents chess for an Indian king (named as Balhait, Shahram or Ladava in different legends, with “Taligana” sometimes named as the supposed kingdom he ruled in northern India) for educational purposes. In gratitude, the king asks Sissa how he wants to be rewarded. Sissa wishes to receive an amount of grain which is the sum of one grain on the first square of the chess board, and which is then doubled on every following square.

This request is now known as the wheat and chessboard problem, and forms the basis of various mathematical and philosophical questions.

Until the nineteenth century, the legend of Sissa was one of several theories about the origin of chess. Today it is mainly regarded as a myth because there is no clear picture of the origin of chaturanga (an ancient Indian chess game), and from which modern chess has developed.

The context of the mythical Sissa is described in detail in A History of Chess. There are many variations and inconsistencies, and therefore little can be confirmed historically. Nevertheless, the legend of Sissa is placed by most sources in a Hindu kingdom between 400 and 600 AD, in an era after the invasion of Alexander the Great. The myth is often told from a Persian and Islamic perspective.

However, the oldest known narrative believed to have been the basis for the legend of Sissa is from before the advent of Islam. It tells of Husiya, daughter of Balhait, a queen whose son is killed by a rebel, but of whom she does not initially hear the news. This news is subtly announced to her through the chess game that Sissa introduced to her.

https://en.m.wikipedia.org/wiki/Sissa_(mythical_brahmin)

The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + … and so forth for the 64 squares. The total number of grains can be shown to be 2⁶⁴−1 or 18,446,744,073,709,551,615 (eighteen quintillion, four hundred forty-six quadrillion, seven hundred forty-four trillion, seventy-three billion, seven hundred nine million, five hundred fifty-one thousand, six hundred and fifteen).

This exercise can be used to demonstrate how quickly exponential sequences grow, as well as to introduce exponents, zero power, capital-sigma notation, and geometric series. Updated for modern times using pennies and a hypothetical question such as “Would you rather have a million dollars or a penny on day one, doubled every day until day 30?”, the formula has been used to explain compound interest. (Doubling would yield over one billion seventy three million pennies, or over 10 million dollars: 2³⁰−1=1,073,741,823).

The problem appears in different stories about the invention of chess. One of them includes the geometric progression problem. The story is first known to have been recorded in 1256 by Ibn Khallikan. Another version has the inventor of chess (in some tellings Sessa, an ancient Indian minister) request his ruler give him wheat according to the wheat and chessboard problem. The ruler laughs it off as a meager prize for a brilliant invention, only to have court treasurers report the unexpectedly huge number of wheat grains would outstrip the ruler’s resources. Versions differ as to whether the inventor becomes a high-ranking advisor or is executed.

https://en.m.wikipedia.org/wiki/Wheat_and_chessboard_problem

Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc. How many grains total are placed on an 8×8 chessboard? Since this is a geometric series, the answer for n squares is a Mersenne number. Plugging in n=8×8=64 then gives 2⁶⁴-1=18446744073709551615.

https://mathworld.wolfram.com/WheatandChessboardProblem.html

The Death of Moore’s Law: What it means and what might fill the gap going forward

In 1965, engineer and businessman Gordon Moore observed a trend that would go on to define the unprecedented technological explosion we’ve experienced over the past fifty years. Noting that the number of transistors in an integrated circuit doubles about every two years, Moore laid out his eponymous law, which has since become the engine behind the growing computer science industry, making everything we now enjoy—cellphones, high-resolution digital imagery, household robots, computer animation, etc.—possible.

However, Moore’s Law was never meant to last forever. Transistors can only get so small and, eventually, the more permanent laws of physics get in the way. Already transistors can be measured on an atomic scale, with the smallest ones commercially available only 3 nanometers wide, barely wider than a strand of human DNA (2.5nm). While there’s still room to make them smaller (in 2021, IBM announced the successful creation of 2-nanometer chips), such progress has become prohibitively expensive and slow, putting reliable gains into question. And there’s still the physical limitation in that wires can’t be thinner than atoms, at least not with our current understanding of material physics.

https://cap.csail.mit.edu/death-moores-law-what-it-means-and-what-might-fill-gap-going-forward

Moore’s law is the observation that the number of transistors in an integrated circuit (IC) doubles about every two years. Moore’s law is an observation and projection of a historical trend. Rather than a law of physics, it is an empirical relationship. It is an experience curve effect, a type of observation quantifying efficiency gains from learned experience in production.

A semi-log plot of transistor counts for microprocessors against dates of introduction, nearly doubling every two years

Industry experts have not reached a consensus on exactly when Moore’s law will cease to apply. Microprocessor architects report that semiconductor advancement has slowed industry-wide since around 2010, slightly below the pace predicted by Moore’s law. In September 2022, Nvidia CEO Jensen Huang considered Moore’s law dead, while Intel’s then CEO Pat Gelsinger had the opposite view.

https://en.m.wikipedia.org/wiki/Moore's_law