The Equivalent of a Written Signature - Burdens of Proof - page 87

(elementary) classroom. 72 Such models, he argues, pointed to a certain
ontological ambiguity of mathematics, an ambiguity that was resolved
with the embrace of modern conceptual mathematics, whose purism
“excluded corporeality and visuality from the discursive universe of math-
ematics.” The disappearance of three-dimensional models, and the trou-
bled epistemological status of diagrams in contemporary mathematical
practice is, according to Mehrtens, “closely related to the dominance of
mathematical modernism with its preference for general theory, symbolic
formalism, and the treatment of mathematical theories as worlds of their
own without any immediate relation to the physical world around us.” 73
The switch to axiomatic mathematics thus enforced, among other
things, a strict demarcation between applied and pure mathematics: “If
mathematics rests in itself, no other science can legitimately discuss the
mathematical principles of truth, existence, and value. A mathematics that
takes Anschauung or intuition as essential will have to face questions from
philosophers, psychologists, and maybe neurologists. Modernist purism
restricted mathematics to the construction of strictly regulated worlds of
meaning made from formal typographical sign systems. For other tasks
there is the applied mathematician.” 74
It should then come as no surprise that in adopting the ideals, meth-
odologies, and standards of a modern, theory-oriented mathematical dis-
cipline, cryptographers found few available concepts from which to engage
with the possibilities and constraints of modeling real-world systems. No
language presented itself that might have provided some reflexive aware-
ness of this inescapable dimension of their practice. For example, as noted
earlier, Goldreich has argued cryptographic practice proceeds through “the
identification, conceptualization and rigorous definition of cryptographic
tasks which capture natural security concerns .” 75 Di Crescenzo, another foun-
dationalist, argues that modern cryptography is based on “mathematically
rigorous design requirements.” 76 But where do these requirements come
from? How does one identify such “natural security concerns”? On these
questions, the literature remains silent. Furthermore, neither of these
approaches provide a rationale for the definitions of the “mutant” signa-
tures described in the preceding section, which can hardly be accounted
for on the basis of “natural requirements.”
It is one argument of this topic that the inability to discuss models as
models , as necessary and inevitable components of scientific practice, has