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Friday, April 10, 2015

Astronomical Numbers

Replica of the first transistor from 1947 In December 1947 there was a single transistor in the world, built at AT&T's Bell Labs by John Bardeen, Walter Brattain, and William Shockley, who would share the 1956 Nobel Prize in Physics for the discovery. The image at the right is of a replica of this first transistor.

According to an article in IEEE Spectrum, in the year 2014 semiconductor manufacturers around the world produced 2.5×1020 (250 billion billion) transistors. On average, about 8 trillion transistors were produced every second in 2014.

We speak of large numbers as "astronomical", but these numbers put astronomy to shame. There are about 400 billion (4×1011) stars in the Milky Way galaxy. In the single year 2014, humans fabricated 625 million times as many transistors as there are stars in their home galaxy. There are estimated to be around 200 billion galaxies in the universe. We thus made 1.25 billion times as many transistors as there are galaxies.

The number of transistors manufactured every year has been growing exponentially from its invention in 1947 to the present (Moore's law), and this growth is not expected to abate at any time in the near future. Let's take the number of galaxies in the universe as 200 billion and assume each has, on average, as many stars as the Milky Way (400 billion) (the latter estimate is probably high, since dwarf galaxies seem to outnumber large ones by a substantial factor). Then there would be around 8×1022 stars in the universe. We will only have to continue to double the number of transistors made per year an additional seven times to reach the point where we are manufacturing as many transistors every year as there are stars in the entire universe. Moore's law predicts that the number of transistors made doubles around every two years, so this milestone should be reached about 14 years from now.

This is right in the middle of the decade I described as the "Roaring Twenties" in my appearance on the Ricochet Podcast of 2015-02-12. It is in the 2020s that continued exponential growth of computing power at constant cost will enable solving, by brute computational force, a variety of problems currently considered intractable.

Posted at April 10, 2015 16:59