Addressing the Observable Universe

Developments in microprocessor technology have seen address buses increase in width from 8 to 16, 24, 32, to 64 bits. IPv6 uses 128 bits to address network nodes – but how many bits does it take to address the universe?

To address the universe, we need to be able to specify four dimensions 1) a point in time since the beginning of the known universe and 2) a 3-D point in space.

Lets take a point of time as having the duration of a Planck Time. One second is about 1.9×1043 Planck times.

The age of the known universe is approximately 13.7 billion years or 8 x 1060 Planck Times. This number is in the order of 2203 so we will need 203 bits to specify a point in time since the beginning of the known universe.

Lets take points in space as having dimensions of the Planck Length. There are approximately 1.6 × 1035 Planck Lengths in a metre, and 1.51×1051 Planck Lengths in a Light Year.

The radius of the observable universe is approximately 46.5 billion light-years or 7.04×1061 Planck Lengths. This gives a volume of the observable universe of 4.65×10185 Cubic Planck Lengths. This number is in the same order as 2617 and so we need 617 bits to specify a point in the observable universe.

Taking the time and space dimensions together we need 820 bits to specify a unique point in space at a unique point in time.

[[Update: I just noticed that the Age of the Universe in Planck Times (8 x 1060) and the Radius of the Universe in Planck Lengths (7.04×1061) are almost identical. I bet this is no coincidence!]]

The number 2820 is also a generous upper bound on the number of computer instructions that could possibly have been performed since the beginning of the known universe. How so? If we assume that every Cubic Planck Length in the universe contains a computing element that performs one instruction every Planck Time then the number of instructions processed would be 2203 Planck Times * 2617 computing elements = 2820 Instructions performed.

Another Factoid
This is a random pattern of 841 bits generated courtesy of . If my calculations above are correct, then there are more variations of this pattern than there have been unique points in space and time!

  • BTW this means that only a minute fraction of the possible combinations of 841 bits have ever existed in all the Petabytes of data generated by the Googleplex and all the rest of the computers in the world!
  • It also means that unless this pattern is saved it will never ever be seen again by any observer wholly inside the observable universe.

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