... defined¹

By that time the determinations had so little variability that it was considered known to 1 part in 10⁹, and the standard metre could not be measured to that great a precision. The second is similarly defined; it is the time taken for 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the atom Cesium-133. Now the metre is defined to be the distance travelled by light through a vacuum in 1/299792458 second! See [10].

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... defined²

By that time the determinations had so little variability that it was considered known to 1 part in 10⁹, and the standard metre could not be measured to that great a precision. The second is similarly defined; it is the time taken for 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the atom Cesium-133. Now the metre is defined to be the distance travelled by light through a vacuum in 1/299792458 second! See [10].

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... century.³

C.D. Lindberg presents preliminary evidence of the debate in medieval Europe [35].

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... Bacon⁴

Bacon had doubts about the infinite speed when considering the great distances that light must travel from the stars to Earth but found such speed easier to swallow given the already fantastic speeds at which stars must travel in their daily orbit about the Earth! See Aphorism 46 of Book II of the Novum Organum e.g. [7]

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... refuted!⁵

From [45] page 307: ``Contra ego, si quae talis mora sensu perciperetur, totam meam Philosophiam funditus eversam fore inquiebam.'' A rough translation, due to our classically trained colleague G.W. Bennett, is ``On the contrary, I would be worried that my entire Philosophy would be on the point of being completely overturned if any delay of this sort were to be perceived by the senses.''

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... issue.⁶

It is doubtful that Beeckman's 1629 experiment [9] was successful. The experiment involved firing a mortar and observing its' flash in a mirror situated some 1851.85 metres away; the movement of a clock situated at the side of the mortar would measure the time elapsed. With today's value, the time for the flash to reach the mirror and return would be about $\frac{1}{100,000}$ of a second! Descartes argues that even if Beeckman could detect a delay of $\frac{1}{24}$ of a pulse beat (or about $\frac{1}{24}$ of a second yielding a speed of only around 89 km/s), then it should be possible to detect a delay between the occurrence and perception of a lunar eclipse of about one hour. The flaws in this argument are discussed in detail in [45].

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... century.⁷

C.D. Lindberg presents preliminary evidence of the debate in medieval Europe [35].

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... Bacon⁸

Bacon had doubts about the infinite speed when considering the great distances that light must travel from the stars to Earth but found such speed easier to swallow given the already fantastic speeds at which stars must travel in their daily orbit about the Earth! See Aphorism 46 of Book II of the Novum Organum e.g. [7]

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... refuted!⁹

From [45] page 307: ``Contra ego, si quae talis mora sensu perciperetur, totam meam Philosophiam funditus eversam fore inquiebam.'' A rough translation, due to our classically trained colleague G.W. Bennett, is ``On the contrary, I would be worried that my entire Philosophy would be on the point of being completely overturned if any delay of this sort were to be perceived by the senses.''

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... issue.¹⁰

It is doubtful that Beeckman's 1629 experiment [9] was successful. The experiment involved firing a mortar and observing its' flash in a mirror situated some 1851.85 metres away; the movement of a clock situated at the side of the mortar would measure the time elapsed. With today's value, the time for the flash to reach the mirror and return would be about $\frac{1}{100,000}$ of a second! Descartes argues that even if Beeckman could detect a delay of $\frac{1}{24}$ of a pulse beat (or about $\frac{1}{24}$ of a second yielding a speed of only around 89 km/s), then it should be possible to detect a delay between the occurrence and perception of a lunar eclipse of about one hour. The flaws in this argument are discussed in detail in [45].

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... review¹¹

E.g. ``... his fashion of writing in dialogues, where he introduces three persons who do nothing but exalt each of his inventions in turn, greatly assists in [over]pricing his merchandise.'' Page 388 of [16]. The substantive criticisms are generally directed at Galileo's not having identified the causes of the phenomena he investigated. For most scientists at this time, and particularly for Descartes, that is the whole point of science.

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... earth.''¹²

Page 389 of [16]. This refutation appears to be based on the argument he gave to Beeckman as described in note 5.

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... telescope.¹³

According to Stillman Drake ([24] page 29), Hans Lipperhey a lens grinder from the Netherlands is generally assigned credit for the telescope's invention and applied for its patent in 1608.

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... work.¹⁴

Today's visitor to Florence's Museum of Science can find a glass and ivory case displaying an ironic relic - Galileo's bony middle finger pointing heavenward.

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... sea.¹⁵

The problem remained unsolved for more than 150 years until the development of accurate portable clocks by the English inventor John Harrison. For a popular account, see [46]

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... second.¹⁶

For more on Römer see [32]. For more detail on this study see [13].

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... (1693-1762)¹⁷

See [2] and [32].

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... km/sec.¹⁸

The time here is as reported in [42]. To calculate the speed, the distance between the Earth and sun must be known. In the estimate reported here, the distance used was 148,092,000 km as derived from Bradley's figures above.

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... km/s.¹⁹

Again, using Bradley's Earth to sun distance.

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... light.²⁰

This is essentially the experiment proposed by Isaac Beeckman to Descartes in 1629. See footnote 5.

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... father-in-law²¹

Referred to in [39] only as a ``private gentleman''.

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... diagram.²²

According to Newcomb (page 117) this had been suggested much earlier by Charles Wheatstone (1802-1875) and tried without success by Dominique Francois Jean Arago (1786-1853) in 1838.

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... 3²³

See our Figure 6 which reproduces Michelson's Fig. 3

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... theodolite²⁴

A land surveying instrument used to measure angles.

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... adjustment²⁵

to the telescope.

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... control²⁶

Ibid figures 11 and 12, page 124

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... SIZE="-1">,²⁷

Names of variates, like ``radius,'' whose values Michelson recorded are italicized here when first mentioned.

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... produced.²⁸

Ibid figure 13, page 124

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... observed.''²⁹

Ibid.

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... mirror.''³⁰

Ibid, page 124

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... aspect.³¹

As in the famous Michelson and Morley experiment [38].

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... vacuum.³²

Even as he was dying, Michelson directed a study to measure the speed of light in a mile long tube that was evacuated to a near vacuum [1]

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... review³³

E.g. ``... his fashion of writing in dialogues, where he introduces three persons who do nothing but exalt each of his inventions in turn, greatly assists in [over]pricing his merchandise.'' Page 388 of [16]. The substantive criticisms are generally directed at Galileo's not having identified the causes of the phenomena he investigated. For most scientists at this time, and particularly for Descartes, that is the whole point of science.

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... earth.''³⁴

Page 389 of [16]. This refutation appears to be based on the argument he gave to Beeckman as described in note 5.

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... telescope.³⁵

According to Stillman Drake ([24] page 29), Hans Lipperhey a lens grinder from the Netherlands is generally assigned credit for the telescope's invention and applied for its patent in 1608.

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... work.³⁶

Today's visitor to Florence's Museum of Science can find a glass and ivory case displaying an ironic relic - Galileo's bony middle finger pointing heavenward.

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... sea.³⁷

The problem remained unsolved for more than 150 years until the development of accurate portable clocks by the English inventor John Harrison. For a popular account, see [46]

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... second.³⁸

For more on Römer see [32]. For more detail on this study see [13].

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... (1693-1762)³⁹

See [2] and [32].

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... km/sec.⁴⁰

The time here is as reported in [42]. To calculate the speed, the distance between the Earth and sun must be known. In the estimate reported here, the distance used was 148,092,000 km as derived from Bradley's figures above.

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... km/s.⁴¹

Again, using Bradley's Earth to sun distance.

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... light.⁴²

This is essentially the experiment proposed by Isaac Beeckman to Descartes in 1629. See footnote 5.

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... father-in-law⁴³

Referred to in [39] only as a ``private gentleman''.

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... diagram.⁴⁴

According to Newcomb (page 117) this had been suggested much earlier by Charles Wheatstone (1802-1875) and tried without success by Dominique Francois Jean Arago (1786-1853) in 1838.

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... 3⁴⁵

See our Figure 6 which reproduces Michelson's Fig. 3

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... theodolite⁴⁶

A land surveying instrument used to measure angles.

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... adjustment⁴⁷

to the telescope.

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... control⁴⁸

Ibid figures 11 and 12, page 124

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... radius,⁴⁹

Names of variates, like ``radius,'' whose values Michelson recorded are italicized here when first mentioned.

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... produced.⁵⁰

Ibid figure 13, page 124

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... observed.''⁵¹

Ibid.

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... mirror.''⁵²

Ibid, page 124

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... aspect.⁵³

As in the famous Michelson and Morley experiment [38].

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... vacuum.⁵⁴

Even as he was dying, Michelson directed a study to measure the speed of light in a mile long tube that was evacuated to a near vacuum [1]

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... process.⁵⁵

And no wonder since so little attention is paid to the measuring process in the teaching of statistics. Consider the advice of Moore and McCabe [40] page 223 ``But, by and large, questions of measurement belong to the substantive fields of science, not the methodological field of statistics. We will therefore take for granted that all variables we work with have specific definitions and are satisfactorily measured.'' Two useful references are Youden [53] and Wheeler and Lyday [52].

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... steady''⁵⁶

p. 124 of [39]

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... processes⁵⁷

Here is an instance where it is more natural to describe the process that generates the units rather than the collection of units of interest and so target process is preferred to target population.

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... method⁵⁸

Tukey [51] names the stages as Question, Design, Collection, Analysis Answer.

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... again.⁵⁹

John Losee's book [36] provides a reasonable starting point.

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... experience.''⁶⁰

[44], page 41.

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... falsifiable;⁶¹

In a paper meant to be a general resource [26], I.J. Good gives partial prior credit to R.A. Fisher since tests of significance [20] predate Popper. This credit seems misplaced - Popper uses falsifiability as a demarcation criterion for science, Fisher does nothing of the sort.

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... theory.⁶²

See [34] pages 71 - 90 for further examples and discussion.

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... Anaxagoras⁶³

[4] 270^b20-25.

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... light!⁶⁴

See [5] 418^a26 to 419^b2 for most of the points made here.

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... observations.⁶⁵

See chapter 9 of [19].

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... statistics.⁶⁶

A notable exception is Pearson's The Grammar of Science [43].

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... statistics.⁶⁷

Indeed, John Tukey's long battle for the legitimacy of exploratory data analysis might have been easier if there had been greater sympathy in the statistical research community for separate contexts for discovery and for justification in science. E.g. see [51].

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... say.⁶⁸

This does not preclude further statistical studies being carried out to address some of these problems (e.g. further investigation of study error).

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... method.⁶⁹

For those who wish to explore this point further, a confirmatory view can be found in [51].

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