Deus Ex Digita?

© 2001 Robert A. Freitas Jr.

May 2001

Recent discussions with Nick Bostrom (e.g., the Simulation Argument) have prompted this commemoration of some previous thoughts. The magnitudes of the following simple numerical estimates appear nonsensitively to imply that humanity is a digital simulation ("sim"). Detecting the computational error which must surely lurk herein is left as an exercise for the reader.


I. Some Assumptions

Total bits processed by all human brains, ever, is ~1034 bits.
Physical volume of nanomechanical computronium to store all human thoughts that have ever been thought, to date, is ~107 m3 (a ~215-meter cube).
Physical volume of computronium to compute all current human thought is ~10-7 m3.
Computronium power required to compute all human thought is ~108 W (vs. ~1011 W for all biological human brains currently alive).

~1030 bits must be processed to simulate all human sensory data ever received by all human sensoria, up to the present.


II. Some Arguments

Computation Power arguments:

Probability we live in a sim is ~(1 - 10-7) = 99.999 99%.
Probability we live in a sim is ~(1 - 10-18)= 99.999 999 999 999 999 9%.
Probability we live in a sim ranges from ~(1 - 10-6) = 99.999 9% to ~(1 - 10-17) = 99.999 999 999 999 999%.

Computation Volume argument:

Probability we live in a sim ranges from ~(1 - 10-19) to ~(1 - 10-31).

Sensory Simulation argument:

III. A Conservative Conclusion

These estimates assume only the existence of the most primitive conventional nanomechanical computation and data storage technologies, and entirely ignore nanoelectronics, quantum computing, Bekenstein-bounded computing, and so forth. The estimates also leave aside scenarios involving a possible "aggressive" Type II civilization (a scenario virtually everyone ignores) that throttles its home star intelligently, thus obtaining ~104 times more available mass or volume and up to ~108 times more available power (albeit for vastly shorter durations).

So even if these estimates err by many orders of magnitude in the contrary direction, perhaps because only a small fraction of the maximum possible number of sims are actually being run, the overall conclusion should remain essentially unchanged. The probability that we live in a simulation, rather than the reality, may range from (1 - 10-6) to (1 - 10-31).


Last updated on 2 November 2002