Part of what makes terrorism terrifying is its randomness, said Joshua A.
Plantinga suggests that randomness is a physicalist interpretation of the evidence.
When the randomness is strong enough, solutions to the equations get out of control.
There is no succour to be found for defenders of RCT in this conception of randomness.
ΩTFT plays TFT unless its measures of deadlock or randomness exceed specified thresholds.
This definition overlaps considerably with those definitions of randomness canvassed in §2.
Schnorr’s theorem is evidence that we really have captured the intuitive notion of randomness.
If we are to accept this argument, then, we shall have to take P2 as an independent truth about randomness.
The problems for RCT arise fundamentally because of the split between product randomness and process chance.
Randomness, as we ordinarily think of it, exists when some outcomes occur haphazardly, unpredictably, or by chance.
Prefix-free encodings are useful for a number of practical purposes, and they turn out to be useful in defining randomness also.
Both plain and prefix-free Kolmogorov randomness provide satisfactory accounts of the randomness of finite sequences.
To get clear on the connections and differences between chance and randomness, it would be good first to have some idea of what chance and randomness amount to.
The most popular such approach is to connect randomness with indeterminism, and to defend RCT by arguing directly that indeterminism yields both chance and randomness.
In §4 we will see a number of cases where there are apparently chancy outcomes without randomness, while in §5 we will see cases of apparent randomness where there is no chance involved.
Eagle (2005) further argues that the unpredictably generated sequences are a better fit to the theoretical role of randomness, and claims on that basis that randomness is unpredictability.
Quantum theory introduced an element of randomness standing out against the previous deterministic worldview preceding it, in which randomness expresses our ignorance of a more detailed description (as in statistical mechanics).
As has become clear, the existence of other notions of randomness—incluing Schnorr randomness, as well as a number of other proposals (Li and Vitányi 2008: §2.5; Porter 2016: 464–6)—shows that we should be somewhat cautious in yielding to its suggestion.
However a number of technical and philosophical advances in our understanding of both chance and randomness open up the possibility that the easy slide between chance and randomness in ordinary and scientific usage—a slide that would be vindicated by the truth of the Commonplace Thesis—is quite misleading.
For one, there is quite a bit of intuitive support for accounts of randomness which do not make it primarily a property of sequences, and those other accounts are no less able to be made mathematically rigorous (see especially the ‘epistemic’ theories of randomness discussed in §6.2, as well as theories of randomness as indeterminism discussed in §7.2).
- (thermodynamics) a thermodynamic quantity representing the amount of energy in a system that is no longer available for doing mechanical work
- the quality of lacking any predictable order or plan
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For one there is quite a bit of intuitive support for accounts of randomness which do not make it primarily a property of sequences and those other accounts are no less able to be made mathematically rigorous see especially the epistemic theories of randomness discussed in §62 as well as theories of randomness as indeterminism discussed in §72