Uncertainty-based Information

(George J. Klir, Mark J. Wierman)

(...) it was the common belief of many scientist that the level of complexity we can handle is basically a matter of the level of the computational power at our disposal. Later, in early 1960s, this belief was replaced with a more realistic outlook. We began to undestand that there are definite limits in dealing with complexity, which neither our human capabilities nor any computer technology can overcome. One such limit was determined by Hans Bremermann [1962] by simple considerations based on quantum theory. The limit is expressed by the proposition: "No data processing system, whether artificial or living, can process more than 2x10^47 bits per second per gram of its mass." (...)

Using the limit of information procssing obtained for one gram of mass and one second of processing time, Bremermann then calculates the total number of bits processed by a hypothetical computer the size of the Earth within a time period equal to the estimated age of the Earth. Since the mass and age of the Earth are estimated to be less than 6x10^27 grams and 10^10 years, respectively, and each year contains approximately 3.14 x 10^7 seconds, this imaginary computer would not be able to process more than 2.56 x 10^92 bits or, when roimding up to the nearest power of ten, 10^93 bits. The last number — 10^93 — is usually referred to as Bremermann's limit
and problems that require processing more than 10^93 bits of information
are called 'transcomputational problems'.