Transcomputational problem
In computational complexity theory, a transcomputational problem is a problem that requires processing of more than 10 bits of information. Any number greater than 10 is called a transcomputational number. The number 10, called Bremermann's limit, is, according to Hans-Joachim Bremermann, 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. The term "transcomputational" was coined by Bremermann. Examples. Testing integrated circuits. Exhaustively testing all combinations of an integrated circuit with 309 boolean inputs and 1 output requires testing  of a total of 2 combinations of inputs. Since the number 2 is a transcomputational number (that is, a number greater than 10), the problem of testing such a system of integrated circuits is a transcomputational problem. This means that there is no way one can verify the correctness of the circuit for all combinations of inputs through brute force alone. Pattern recognition. Consider a "q"×"q" array of the chessboard type, each square of which can have one of "k" colors. Altogether there are "k" color patterns, where "n" = "q". The problem of determining the best classification of the  patterns, according to some chosen criterion, may be solved by a search through all possible color patterns. For two colors, such a search becomes transcomputational when the array is 18×18 or larger. For a 10×10 array, the problem becomes transcomputational when there are 9 or more colors. This has some relevance in the physiological studies of the retina. The retina contains about a million light-sensitive cells. Even if there were only two possible states for each cell (say, an active state and an inactive state) the processing of the retina as a whole requires processing of more than 10  bits of information. This is far beyond Bremermann's limit. General systems problems. A system of "n" variables, each of which can take "k" different states, can have "k" possible system states. To analyze such a system, a minimum of "k" bits of information are to be processed. The problem becomes transcomputational when "k" > 10. This happens for the following values of "k" and "n": Implications. The existence of real-world transcomputational problems implies the limitations of computers as data processing tools. This point is best summarized in Bremermann's own words: In fiction. In Douglas Adams's "The  Hitchhiker's Guide to the Galaxy", Earth is a supercomputer, designed to calculate the question known as the "Ultimate Question of Life, The Universe and Everything" (the answer to which is known to be 42).