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During that year in Aarau the question came to me: If one runs after a light wave with [a velocity equal to the] light velocity, then one would encounter a time-independent wavefield. However, something like that does not seem to exist! This was the first juvenile thought experiment which has to do with the special theory of relativity. Invention is not the product of logical thought, even though the final product is tied to a logical structure.
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From his "Autobiographische Skizze" (18 April 1955), original German version here. Translation from Subtle is the Lord: The Science and the Life of Albert Einstein by Abraham Pais (1982), p. 131. Pais notes that when he said "during that year", he was referring to some time between October 1895 and early fall 1896.
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Variant: "Innovation is not the product of logical thought, even though the final product is tied to a logical structure."
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Original German version: Während dieses Jahres in Aarau kam mir die Frage: Wenn man einer Lichtwelle mit Lichtgeschwindigkeit nachläuft, so würde man ein zeitunabhängiges Wellenfeld vor sich haben. So etwas scheint es aber doch nicht zu geben! Dies war das erste kindliche Gedanken-Experiment, das mit der speziellen Relativitätstheorie zu tun hat. Das Erfinden ist kein Werk des logischen Denkens, wenn auch das Endprodukt an die logische Gestalt gebunden ist. ("Autobiographische Skizze", p. 10)

 

Albert Einstein

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...the principle of the limiting character of the velocity of light. This statement... is not an arbitrary assumption but a physical law based on experience. In making this statement, physics does not commit the fallacy of regarding absence of knowledge as evidence for knowledge to the contrary. It is not absence of knowledge of faster signals, but positive experience which has taught us that the velocity of light cannot be exceeded. For all physical processes the velocity of light has the property of an infinite velocity. In order to accelerate a body to the velocity of light, an infinite amount of energy would be required, and it is therefore physically impossible for any object to obtain this speed. This result was confirmed by measurements performed on electrons. The kinetic energy of a mass point grows more rapidly than the square of its velocity, and would become infinite for the speed of light.

 

Hans Reichenbach

 

The general equations are next applied to the case of a magnetic disturbance propagated through a non-conductive field, and it is shown that the only disturbances which can be so propagated are those which are transverse to the direction of propagation, and that the velocity of propagation is the velocity v, found from experiments such as those of Weber, which expresses the number of electrostatic units of electricity which are contained in one electromagnetic unit. This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.

 

James Clerk Maxwell

 

One thing leads to another, and soon you are searching for answers to basic questions.
Another time during lectures on Classical Logic, we were introduced to an “experimentum crucis”. It was illustrated by the deciding experiment of Fizeau on the speed of light in water as compared to its speed in air. Since wave theory predicts that speed in water is less, and corpuscular theory (with point particles) predicts it would be faster, this is supposed to have selected the wave theory is correct. But then how would one accommodate the photoelectric effect? Then it turns out that if the “corpuscle” of light had a finite size, corpuscular theory also predicts lower speed of light in water. But then one can ask how come photoelectric emission being prompt even in feeble light, how could the energy of a photon spread over ?(?/2)2 act as a whole and liberate a single photoelectron! This leads us to question the square of the amplitude being interpreted as the probability of the particle being formed in the immediate vicinity. How do probabilities enter quantum mechanics? Thus the questions (and the quest) go on.

 

George Sudarshan

 

Classical science was based upon the belief that it is possible to formulate both the position and velocity at one time of any given particle. It followed that knowledge of the position and velocity of a given number of particles would enable the future behavior of the whole collection to be accurately predicted. The principle of Heisenberg is that given the determination of position, its velocity can be stated only as of a certain order of probability, while if its velocity is determined the correlative factor of position can be stated only as of a certain order of probability. Both cannot be determined at once, from which it follows necessarily that the future of the whole collection cannot possibly be foretold except in terms of some order of probability.

 

John Dewey

 

Whenever logical processes of thought are employed— that is, whenever thought for a time runs along an accepted groove— there is an opportunity for the machine. Formal logic used to be a keen instrument in the hands of the teacher in his trying of students' souls. It is readily possible to construct a machine which will manipulate premises in accordance with formal logic, simply by the clever use of relay circuits. Put a set of premises into such a device and turn the crank, and it will readily pass out conclusion after conclusion, all in accordance with logical law, and with no more slips than would be expected of a keyboard adding machine.

 

Vannevar Bush