#goldreich

[vsevolod7c8]

peter goldreich

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[curiousaboutcreativity]

[T]he randomness of an event is relative to the information and computing resources at our disposal. At the extreme, even events that are fully determined by public information may be perceived as random events by an observer that lacks the relevant information and/or the ability to process it. (286)

Goldreich O. 2008. Computational Complexity: A Conceptual Perspective. New York: Cambridge University Press.

[curiousaboutcreativity]

Pseudorandom generators are efficient deterministic procedures that stretch short random seeds into longer pseudorandom sequences. (284)

Goldreich O. 2008. Computational Complexity: A Conceptual Perspective. New York: Cambridge University Press.

[curiousaboutcreativity]

What matters is how the world looks to us and to various computationally bounded devices. That is, if some phenomenon looks random, then we may just treat it as if it were random. (284)

Goldreich O. 2008. Computational Complexity: A Conceptual Perspective. New York: Cambridge University Press.

[curiousaboutcreativity]

[T]he notion of computation can be used to model the 'mechanical' aspects of the natural reality, that is, the rules that determine the evolution of the reality (rather than the specific state of the reality at a specific time). In this case, the starting point of the study is the actual evolution process that takes place in the natural reality, and the goal of the study is finding the (computation) rule that underlies this natural process. In a sense, the goal of science at large can be phrased as finding (simple) rules that govern various aspects of reality (or rather one's abstraction of these aspects of reality). (21)

Goldreich O. 2008. Computational Complexity: A Conceptual Perspective. New York: Cambridge University Press.

[curiousaboutcreativity]

A computation is a process that modifies an environment via repeated applications of a predetermined rule. The key restriction is that this rule is simple: In each application it depends on and affects only a (small) portion of the environment, called the active zone. (21)

Goldreich O. 2008. Computational Complexity: A Conceptual Perspective. New York: Cambridge University Press.

[curiousaboutcreativity]

The concept of randomness has puzzled thinkers for ages. Their perspective can be described as ontological. They asked 'what is randomness' and wondered whether it exists at all (or is the world deterministic). The perspective of Complexity Theory is behavioristic. It is based on defining objects as equivalent if they cannot be told apart by any efficient procedure. That is, a coin toss is (defined to be) 'random' (even if one believes that the universe if deterministic) if it is infeasible to predict the coin's outcome. Likewise, a string (or a distribution of strings) is 'random' if it is infeasible to distinguish it from the uniform distribution (regardless of whether or not one can generate the latter). (4)

Goldreich O. 2008. Computational Complexity: A Conceptual Perspective. New York: Cambridge University Press.