“Computational reducibility may well be the exception rather than the rule: Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be formally undecidable.”

— Stephen Wolfram

[Undecidability and intractability in theoretical physics, Physical Review Letters, 54, 8, 1985, 735–738, 10.1103/PhysRevLett.54.735, https://www.stephenwolfram.com/publications/academic/undecidability-intractability-theoretical-physics.pdf]

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Stephen Wolfram16

British-American computer scientist, mathematician, physici… 1959

James Cameron (journalist) (1911–1985) British journalist

Cameron Country, broadcast on BBC TV, July 12, 1969.

“[S]cience has become used to... using the little... pockets of computational reducibility ([A]n inevitable consequence of computational irreducibility... There have to be these pockets ...scattered around.) to be able to find those cases where you can jump ahead.”

Stephen Wolfram (1959) British-American computer scientist, mathematician, physicist, writer and businessman

Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe (Sep 15, 2020)

“Data management housekeeping is not the only problem to plague oversimplified approaches to high speed computation. The physical problems which are of practical interest tend to have rather significant complications. Examples of these complications are as follows: boundaries are likely to be irregular; interiors are likely to be inhomogeneous; computations required may be dependent on the states of the variables at each point; propagation rates of different physical effects may be quite different; the rate of convergence, or convergence at all, may be strongly dependent on sweeping through the array along different axes on succeeding passes; etc. The effect of each of these complications is very severe on any computer organization based on geometrically related processors in a paralleled processing system.”

Gene Amdahl (1922–2015) American physicist

Source: Validity of the single processor approach... (1967), p. 483

“Computers were within my sphere of attention, but only computers used as number crunchers. In spite of the "giant brain" metaphor, there is little suggestion in this 1950 talk that the most important application of computers might lie in imitating intelligence symbolically, not numerically.”

Herbert A. Simon (1916–2001) American political scientist, economist, sociologist, and psychologist

Source: 1980s and later, Models of my life, 1991, p. 199.

“People can be fooled into thinking of mathematics as logical, formal, symbolic reasoning. But this is far from reality...computers are far better at formal computation and formal reasoning, but humans are far better mathematicians.”

William Thurston (1946–2012) mathematician

Foreword to Teichmüller Theory

“[Speaking of computers] But they are useless. They can only give you answers.”

Pablo Picasso (1881–1973) Spanish painter, sculptor, printmaker, ceramicist, and stage designer

As discussed in this entry from Quote Investigator http://quoteinvestigator.com/2011/11/05/computers-useless/#more-2932, the origin seems to be the article "Pablo Picasso: A Composite Interview" by William Fifield which appeared in The Paris Review 32, Summer-Fall 1964, and collected a number of interviews Fifield had done with Picasso. <br class="br">Common later variant: "Computers are useless. They can only give you answers." This variant seems to have arisen in the 1980s, the earliest known appearance in a book is Herman Feshbach, "Reflections on the Microprocessor Revolution: A Physicist's Viewpoint", in Man and Technology (1983), ed. Bruce M. Adkins, where the attribution is described as "rumoured". http://books.google.com/books?id=9EohAQAAIAAJ&q=Picasso <br class="br">1960s

“No algorithm exists for the metaphor, nor can a metaphor be produced by means of a computer's precise instructions, no matter what the volume of organized information to be fed in.”

Umberto Eco book Semiotics and the Philosophy of Language

[3] Metaphor, 3.12. Conclusions
Semiotics and the Philosophy of Language (1984)
Context: No algorithm exists for the metaphor, nor can a metaphor be produced by means of a computer's precise instructions, no matter what the volume of organized information to be fed in. The success of a metaphor is a function of the sociocultural format of the interpreting subjects' encyclopedia. In this perspective, metaphors are produced solely on the basis of a rich cultural framework, on the basis, that is, of a universe of content that is already organized into networks of interpretants, which decide (semiotically) the identities and differences of properties. At the same time, content universe, whose format postulates itself not as rigidly hierarchized but, rather, according to Model Q, alone derives from the metaphorical production and interpretation the opportunity to restructure itself into new nodes of similarity and dissimilarity.

“Present-day computers are designed primarily to solve preformulated problems or to process data according to predetermined procedures. The course of the computation may be conditional upon results obtained during the computation, but all the alternatives must be foreseen in advance. … The requirement for preformulation or predetermination is sometimes no great disadvantage. It is often said that programming for a computing machine forces one to think clearly, that it disciplines the thought process. If the user can think his problem through in advance, symbiotic association with a computing machine is not necessary.
However, many problems that can be thought through in advance are very difficult to think through in advance. They would be easier to solve, and they could be solved faster, through an intuitively guided trial-and-error procedure in which the computer cooperated, turning up flaws in the reasoning or revealing unexpected turns in the solution. Other problems simply cannot be formulated without computing-machine aid. … One of the main aims of man-computer symbiosis is to bring the computing machine effectively into the formulative parts of technical problems.
The other main aim is closely related. It is to bring computing machines effectively into processes of thinking that must go on in "real time," time that moves too fast to permit using computers in conventional ways. Imagine trying, for example, to direct a battle with the aid of a computer on such a schedule as this. You formulate your problem today. Tomorrow you spend with a programmer. Next week the computer devotes 5 minutes to assembling your program and 47 seconds to calculating the answer to your problem. You get a sheet of paper 20 feet long, full of numbers that, instead of providing a final solution, only suggest a tactic that should be explored by simulation. Obviously, the battle would be over before the second step in its planning was begun. To think in interaction with a computer in the same way that you think with a colleague whose competence supplements your own will require much tighter coupling between man and machine than is suggested by the example and than is possible today.”

J. C. R. Licklider Man-Computer Symbiosis

Man-Computer Symbiosis, 1960

“The computer constitutes the first human construction that aspired to amplify mental rather than physical human powers.”

Yiannis Laouris (1958) Cypriot neuroscientist

mLearn International Conference (2005)

“I talk to myself through the computer. I ask myself questions, leave things to be looked at again, things that you would do with a notepad. It turns out today that it’s much better today to do with a personal computer rather than a notepad.”

Seymour Cray (1925–1996) Applied mathematician, computer scientist, and electrical engineer

Video History interview (1995)

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