World history then led Turing to his unique role in the Enigma problem, to his becoming the chief figure in the mechanisation of logical procedures, and to his being introduced to ever faster and more ambitious technology as the war continued.
That was the triumphant message sent by then-Turing Pharmaceuticals CEO Martin Shkreli, the infamous "Pharma Bro" who jacked up the price of a life-saving drug by 5,000 percent last year, when it became clear his firm could acquire the rights to the medicine.
Turing then goes on to add that he does not think that the argument can be dismissed "quite so lightly".
Turing then proposed that this definition of 'computable' captured precisely what was intended by such words as 'definite method, procedure, mechanical process' in stating the Entscheidungsproblem.
Turing then showed that the class \(\mathcal{F}_{\mathfrak{T}}\) of functions computable by a Turing machine was extensionally coincident with \(\mathcal{F}_{\Lambda}\). CT can be understood to assign a precise epistemological significance to Church and Turing's negative answer to the Entscheidungsproblem.
Given the definition of 'computable' as 'effectively calculable', the Church-Turing thesis does entail that if a function f is not computable by Turing machine then it is not computable by any machine.
The temporal Hopf oscillations dominate first, then the Turing pattern emerges, leading to development of mixed-mode oscillations.
I speculate that materials and agent populations conceptualized through autopoietic-extended design are to be recognized first in biology, then (via Turing), expressed as digital code amenable to bioprinting and machine fabrication not currently found in design fablabs, but existing in medical, laserjet-printed skin and 3D bioprinted organs, kidneys for example.
The consensus of computer historians is that while Babbage was clearly the first to conceive of the flexible machine that foreshadowed the modern computer, his work was forgotten and was then conceptually recreated by Turing a century later.
Since then, the research of Turing patterns in chemistry has sprung up (see [4 13] and the references therein).
