The widespread a priori claim that any analogue process can always be digitally represented illegiti… — Hubert L. Dreyfus

The widespread a priori claim that any analogue process can always be digitally represented illegitimately borrows its plausibility from the much weaker claim that analogue devices can be digitally simulated at the level of input-output behavior; genuine representation would require simulating the inner operations and components of the analogue device, which is often impossible or explanatorily irrelevant, so digital simulability does not justify assuming full digital representability or explanatory adequacy.

By Hubert L. Dreyfus, from What Computers Can't Do

Key Arguments

Dreyfus distinguishes 'simulation' from 'representation' by examples: a slide rule’s division function is simulated by 'any algorithm which yields appropriate quotients' but is represented 'only if the quotients are obtained in a sliderulelike manner in which the steps correspond to comparing lengths.'
He generalizes with analogue computers: 'one can simulate any multiply coupled harmonic system (such as most commercial analogue computers) by solving their characteristic differential equations,' whereas a representation 'would require a simulation of each electronic component (resistors, capacitors, wires, etc.), their effects on one another, and thence their variations iterated through time.'
He points out that 'Some analogues are not composed of identifiable parts, e.g., a soap film "computing" the minimum surface which is bounded by an irregularly shaped wire, and hence are not representable in anything like the above fashion,' directly challenging the idea that all analogues admit part‑by‑part representation.
Against the move to invoke microphysics, he notes that although one might claim that a soap bubble 'can still always be represented in principle by working out an immense (!) amount of quantum mechanics,' it is 'at best very dubious that such a mountain of equations would or could amount to an explanation of how something works, or in the case of the brain, have any relevance at all to psychology.'
He uses the example of an adding machine made of wheels and cogs to argue that our conviction that it is representable as a mechanism 'is not in the least based on the fact that it is made of atoms'; even if made of 'some totally mysterious, indivisible substance' we would still regard a representation in terms of wheels and cogs as the relevant explanation, showing that appeal to atomic constitution is a red herring.
He extends this point to 'electronic analogue computers, slide rules, and so on,' saying that the same reasoning applies: the explanatory representation concerns their macroscopic organization, not microphysical reducibility.
He concludes that 'the plausibility of the a priori position that an analogue can always be digitally represented is illegitimate, only borrowed, so to speak, from the plausibility of the much weaker and irrelevant claim of mere simulability,' explicitly identifying the fallacy as a transfer of credibility from one claim to another.

Source Quotes

The flaw in this alternative, however, is difficult to grasp until a few examples have clarified the distinction between simulation and representation. The division function of a slide rule is simulated by any algorithm which yields appropriate quotients; but it is represented only if the quotients are obtained in a sliderulelike manner in which the steps correspond to comparing lengths. On a computer this would amount to assigning (colinear) spatial coordinates to the mantissas of two log tables, and effecting a "translation" by subtracting.

On a computer this would amount to assigning (colinear) spatial coordinates to the mantissas of two log tables, and effecting a "translation" by subtracting. To treat a more general case, one can simulate any multiply coupled harmonic system (such as most commercial analogue computers) by solving their characteristic differential equations. On the other hand, a representation, roughly a simulation of the inner operation as well as the end result, would require a simulation of each electronic component (resistors, capacitors, wires, etc.), their effects on one another, and thence their variations iterated through time.

To treat a more general case, one can simulate any multiply coupled harmonic system (such as most commercial analogue computers) by solving their characteristic differential equations. On the other hand, a representation, roughly a simulation of the inner operation as well as the end result, would require a simulation of each electronic component (resistors, capacitors, wires, etc.), their effects on one another, and thence their variations iterated through time. Each of these analogues happens to be both simulable and representable, but this is not always the case.

Each of these analogues happens to be both simulable and representable, but this is not always the case. Some analogues are not composed of identifiable parts, e.g., a soap film "computing" the minimum surface which is bounded by an irregularly shaped wire, and hence are not representable in anything like the above fashion. Now it might be claimed that since a soap bubble (or any other material object) is made of atoms it can still always be represented in principle by working out an immense (!) amount of quantum mechanics.

Essentially the same point could be made about electronic analogue computers, slide rules, and so on. Thus, the plausibility of the a priori position that an analogue can always be digitally represented is illegitimate, only borrowed, so to speak, from the plausibility of the much weaker and irrelevant claim of mere simulability. 12.

Key Concepts

The division function of a slide rule is simulated by any algorithm which yields appropriate quotients; but it is represented only if the quotients are obtained in a sliderulelike manner in which the steps correspond to comparing lengths.
To treat a more general case, one can simulate any multiply coupled harmonic system (such as most commercial analogue computers) by solving their characteristic differential equations.
On the other hand, a representation, roughly a simulation of the inner operation as well as the end result, would require a simulation of each electronic component (resistors, capacitors, wires, etc.), their effects on one another, and thence their variations iterated through time.
Some analogues are not composed of identifiable parts, e.g., a soap film "computing" the minimum surface which is bounded by an irregularly shaped wire, and hence are not representable in anything like the above fashion.
Thus, the plausibility of the a priori position that an analogue can always be digitally represented is illegitimate, only borrowed, so to speak, from the plausibility of the much weaker and irrelevant claim of mere simulability.

Context

Long note 11 in Chapter 4 ('The Psychological Assumption'), where Dreyfus attacks the common assumption in cognitive science and AI that any analogue process (including brain activity) can in principle be digitally represented, by carefully distinguishing input‑output simulation from structurally faithful representation and highlighting the irrelevance of microphysical reducibility to psychological explanation.