Historical background.

The thought of Aristotle (384-322 BC) dominated western science for nearly two millenia. So powerful is his cosmology that it compels him to declare that ``$\ldots$ light is due to the presence of something, but it is not a movement'' ([6] 446^b25-447^a10). No movement, no speed. And if that were not enough, the argument for finite speed is easily dismissed:

Empedocles (and with him all others who used the same forms of expression) was wrong in speaking of light as `travelling' or being at a given moment between the earth and its envelope, its movement being unobservable to us; that view is contrary both to the clear evidence of argument and to the observed facts; if the distance traversed were short, the movement might have been unobservable, but where the distance is from extreme East to extreme West, the strain upon our powers of belief is too great.

Aristotle (384-322 BC)
On the Soul: Book II
418^b20-27 [5]

This view was echoed by many thinkers in western history: Augustine (ca 354-430), John Pecham (ca 1230-1292), Albert the Great (ca 1200-1280), Thomas Aquinas (ca 1225-1274), and Witelo (ca 1230-ca 1275) to name a few. So too, the opposite view was argued by some, notably Ibn Al-Haytham (ca 965-1040) and Roger Bacon (ca 1219-1292). But without empirical demonstration to the contrary, the case for instantaneous perception of the source could always be made. In the absence of data, arguments pro and con were forced to be based on the contemporary theory of light, or on interpretation of the conflicting views of ancient authorities, or on established religious doctrines, or on mathematical arguments that demonstrated the necessity or absurdity of one of the alternatives [35].

The debate continued into the beginning of the ``scientific revolution'' of the seventeenth century.³ Such giants as Francis Bacon⁴ (1561-1626), Johannes Kepler (1571-1630), and René Descartes (1596-1650), believed the speed to be infinite.

Descartes, for example, likened the transmission of light to that of pushing on a stiff stick - the instant one end (the source) was pushed the other end (the perception) moved (pp. 258-9 of [25]). The analogy is powerful; there is no perceptible movement anywhere along the stick, no matter how long a stick is used! Descartes strongly held this view; when his colleague and scientific mentor, Issac Beeckman (1588-1637), claimed to have performed an experiment which demonstrated the speed was finite, Descartes dismissed the claim saying that if it were true, then Descartes knows nothing of philosophy and his whole theory would be refuted!⁵ Beeckman and Descartes could not agree on an experiment to resolve the issue.⁶

Among these giants, Galileo Galilei (1564-1642) stands alone in his disagreement; he wrote

Empedocles (and with him all others who used the same forms of expression) was wrong in speaking of light as `travelling' or being at a given moment between the earth and its envelope, its movement being unobservable to us; that view is contrary both to the clear evidence of argument and to the observed facts; if the distance traversed were short, the movement might have been unobservable, but where the distance is from extreme East to extreme West, the strain upon our powers of belief is too great.

Aristotle (384-322 BC)
On the Soul: Book II
418^b20-27 [5]

This view was echoed by many thinkers in western history: Augustine (ca 354-430), John Pecham (ca 1230-1292), Albert the Great (ca 1200-1280), Thomas Aquinas (ca 1225-1274), and Witelo (ca 1230-ca 1275) to name a few. So too, the opposite view was argued by some, notably Ibn Al-Haytham (ca 965-1040) and Roger Bacon (ca 1219-1292). But without empirical demonstration to the contrary, the case for instantaneous perception of the source could always be made. In the absence of data, arguments pro and con were forced to be based on the contemporary theory of light, or on interpretation of the conflicting views of ancient authorities, or on established religious doctrines, or on mathematical arguments that demonstrated the necessity or absurdity of one of the alternatives [35].

The debate continued into the beginning of the ``scientific revolution'' of the seventeenth century.⁷ Such giants as Francis Bacon⁸ (1561-1626), Johannes Kepler (1571-1630), and René Descartes (1596-1650), believed the speed to be infinite.

Descartes, for example, likened the transmission of light to that of pushing on a stiff stick - the instant one end (the source) was pushed the other end (the perception) moved (pp. 258-9 of [25]). The analogy is powerful; there is no perceptible movement anywhere along the stick, no matter how long a stick is used! Descartes strongly held this view; when his colleague and scientific mentor, Issac Beeckman (1588-1637), claimed to have performed an experiment which demonstrated the speed was finite, Descartes dismissed the claim saying that if it were true, then Descartes knows nothing of philosophy and his whole theory would be refuted!⁹ Beeckman and Descartes could not agree on an experiment to resolve the issue.¹⁰

Among these giants, Galileo Galilei (1564-1642) stands alone in his disagreement; he wrote

Sagredo: ... I cannot believe that the action of light, however pure, can be without motion, and indeed the swiftest.

Salviati: But what and how great should we take the speed of light to be? Is it instantaneous perhaps, and momentary? Or does it require time, like other movements? Could we assure ourselves by experiment which it may be?

Galileo Galilei  (1564-1642)
Two New Sciences (1638)
page 49 of Stillman Drake's   translation of [23]

{ In the same book, Galileo proposed a demonstration to determine whether light was instantaneous. It was essentially the same that Beeckman had proposed earlier and drew similar fire from Descartes. In a letter to the great experimental scientist Marin Mersenne (1588-1647), dated 11 October 1638, Descartes gave a scathing review¹¹ of Galileo's book. Of the proposed demonstration, Descartes wrote ``His experiment to know if light is transmitted in an instant is useless, since eclipses of the moon, related so closely to calculations made of them, prove this incomparably better than anything that could be tested on earth.'' ¹² Nevertheless, the demonstration was tried in 1667 by members of the Florentine Academy, but without success. [13] Light's movement was either instantaneous or near enough so as to be too fast to measure successfully.

In 1676 the first empirical evidence of a finite speed was presented. The Danish astronomer Ole Römer (1644-1710), while investigating an entirely different matter, gathered data and found a discrepancy which led to the discovery. Interestingly, this important and purely scientific discovery came about while Römer was working on what we would today call a very applied problem.