Cryptography Reference
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Of course, the person who answers the phone has no idea who Moshe is. A
few minutes later, Moshe dials the phone number corresponding to the person
who complained to him and asks if anyone has tried to leave a message for him.”
Ibid., 81.
70. Charles Bazerman, The Languages of Edison's Light (Cambridge, MA: MIT Press,
1999), 350.
71. Ruben Hersh, “Proving Is Convincing and Explaining,” Educational Studies in
Mathematics 24, no. 4 (1993): 395-396. This is echoed by MacKenzie: “The basis
of a sociology of ordinary 'rigorous-argument' mathematical proof is thus that there
is no abstract, context-free way of demarcating what constitutes a proof; that there
is no higher criterion than the judgment of the adequacy of a putative proof by
the members of the relevant specialist community; and that the judgments can
both vary at any given time and change through time.” Donald A. MacKenzie,
Mechanizing Proof: Computing, Risk, and Trust (Cambridge, MA: MIT Press, 2001),
319.
72. For the discussions that probabilitic proof has generated in the mathematical
community, see Don Fallis, “What Do Mathematicians Want? Probabilistic Proofs
and the Epistemic Goals of Mathematicians,” Logique et Analyse 45, no. 179-180
(2002): 373-388. Rabin's explanation of the meaning of probabilistic primality
testing is itself fascinating: it “does not mean that an integer n asserted as prime
by the use of 50 random numbers is prime with probability at least 1 - ½ 100 . Such
an interpretation is nonsensical since n is either prime or not. . . . What is stated
is that n was asserted to be prime by a procedure that on average will make no
more than one mistake in 2 100 applications (even when testing the same n ).” Michael
O. Rabin, “Probabilistic Algorithm for Testing Primality,” Journal of Number Theory
12, no. 1 (1980): 129. In reference to zero-knowledge interactive proof systems,
Jacques Stern argues: “Recent methods from the theory of computational complex-
ity, without a doubt inspired by cryptography, relativize the concept of proof in
the traditional sense. They largely rehabilitate the algorithmic approach to the
concept of demonstration that parallels the more classical logical approach. Even
more, they show that, in addition to the formal and quasi biblical notion of proof,
written and intended to be read, it is possible to productively introduce the notion
of interactive proof, preferring dialogue to the simple verification of fixed text.”
Stern, La science du secret , 17 (my translation). For arguments relative to proof
through DNA computation, see Leonard M. Adleman, “Computing with DNA,”
Scientific American 279, no. 8 (1998): 34-41; and Don Fallis, “Mathematical Proof
and the Reliability of DNA Evidence,” American Mathematical Monthly 103, no. 6
(1996): 491-497.
73. Sandra D. Mitchell, Unsimple Truths: Science, Complexity, and Policy (Chicago:
University of Chicago Press, 2009), 117.
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