Showing posts with label science. Show all posts
Showing posts with label science. Show all posts

Wednesday, July 3, 2013

Andrew Barker on Ptolemy and experimental science

Here is an excerpt from the Introduction to Andrew Barker's book Scientific Method in Ptolemy's Harmonics:

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"The task I have set myself in this book is to explore the Harmonics from a methodological point of view. Its own pronouncements on these matters are of great interest in their own right, and demand close analysis. But it will also be necessary to ask how far the treatise is faithful to the principles it advertises, in the actual conduct of its investigations. There are grounds for some scepticism here, and special reasons why the issue should be thought important. The complex combination of rationalism and empiricism which Ptolemy professes to adopt insists, among other things, on a crucial role for experimental tests of provisional, theorybased results. Here, as we shall see, the word ‘experimental’ is to be construed in a strict sense that will seem surprisingly modern. I hope to show beyond reasonable doubt that Ptolemy understood very well what conditions must be met if experimental tests are to be fully rigorous, and that he had a clear and persuasive conception of the roles they should be assigned in a well conducted scientific project. I do not think that these ideas are so fully worked out and so lucidly expressed in any other surviving Greek source. What is much harder to decide is whether the experimental equipment he meticulously describes was ever actually built, whether his carefully designed and controlled experiments were ever conducted, and if they were, whether he allowed their results genuinely to modify or to put at risk the theoretically grounded conclusions which they purported to test. Greek science in general is not renowned for its adherence to experimental methods.Harmonic scientists in particular often claim that their theoretical results are confirmed ‘by perception’, sometimes offering geometrically conceived descriptions of instrumental devices through which (they allege) these results can be presented to the ear. But their remarks seldom inspire much confidence in the supposition that the instruments were actually built and used, still less that they were used in an experimental spirit; they seem to have been thought of, at the most, as making manifest ‘rationally’ excogitated truths to the senses, rather than as putting them to the test. If we are to conclude that Ptolemy not only represented the use of strict experimental techniques as an essential element in a well conducted scientific project, but also carried his programme through in practice, the case will have to be argued in detail and with the greatest caution. Certainly the author’s explicit statements about his own procedures should not be taken at face value without a good deal of supporting evidence.

"To anticipate the book’s conclusions on this issue, I believe that a very strong case can be made in Ptolemy’s favour, and I shall do my best to provide it. If it can indeed be shown that when he wrote the Harmonics, Ptolemy not only had a well honed understanding of experimental methods but was also seriously committed to their use, that fact should obviously provoke the question whether this treatise is merely a freakish anticipation of later concepts of science, or whether once these methods have been drawn to our notice, we shall be able to find convincing traces of comparable procedures in other Greek works in the ‘exact’ or ‘mathematical’ sciences. Such questions have of course been asked before; but it may be that a starting-point in the Harmonics, where the issues are brought so insistently to our attention, will place them in a fresh perspective. My business in this book is only to provide the necessary point of departure. No doubt the wider questions are the more important, but they must be reserved for a different book and probably for a different writer. Here I intend to keep the focus as sharp as possible, restricting myself to an examination of this single text, without drawing elaborate comparisons or attempting to generate large conclusions about Greek science in general.

"Ptolemy’s treatment of the strictly ‘rational’ or ‘theoretical’ phases of his enquiry also raises issues relevant to the other sciences, particularly, perhaps, to astronomy. He proposes that what the ear perceives as musically admirable relations between pitched sounds are manifestations of mathematically intelligible and elegant form; and their complex and various structures can be derived, through orderly mathematical procedures, from principles of ‘reason’ whose credentials are accessible to the mind. This is all very fine and inspiring. But given that our initial data are simply patterns of sound which are perceived as musically satisfactory, we must plainly ask, first, how we are to represent them in ways that express their mathematical form and make them amenable to ‘rational’ (that is, mathematical) manipulation.We must also ask how we are to move from our initial perceptions to a grasp on the principles which govern their orderly relationships; why it is that these rational principles and no others are the appropriate ones for the task; why it is that some mathematically describable patterns are ‘better’ and correspond to ‘finer’ musical relations than others; by what procedures well formed musical systems are to be derived from the initial principles, and why (since different methods of derivation will yield different results); and so on. All these questions have their counterparts in astronomy, at least as Ptolemy conceived it, and the answers offered in the Harmonics may shed some light on the character of his reasoning in the Syntaxis, perhaps on that of other ancient astronomers too. But those issues, once again, will not be addressed in this book.

"From time to time in the course of this study it will be necessary to examine rather closely some of the finer details of Ptolemy’s arguments, partly for the light they shed on the nature and application of his method, and partly for their own intrinsic interest. The procedure of the Harmonics depends to a high degree on rigorous reasoning, and its sophisticated intricacies can on occasion provide matter for serious philosophical reflection. I shall also suggest, on the other hand, that some of his arguments fail to pass muster by the standards he purports to accept. Some of his constructive strategies seem to break down in their applications; and his criticisms of his predecessors are sometimes more rhetorically than rationally persuasive. It is not always possible to judge whether Ptolemy is merely being too hasty, or whether on some occasions he is deliberately seeking to mislead. This book is a discussion of procedures and the principles governing them, not primarily of the substance of Ptolemy’s conclusions or those of other writers in this field; but it would hardly be possible to explore the issues at which I have gestured, at least in any depth, without introducing some musicological technicalities. I shall expound them, however, only to the extent that seems necessary for my main purposes, and a good deal of detail will be ignored. I shall also do my best to introduce them in ways that will be accessible to readers unversed in the conundrums of Greek harmonics, and digestible by those for whom the subject is not itself of special interest."

Tuesday, September 18, 2012

My Beliefs Don't Stink! (Part One)

"But Thomas, one of the twelve, called Didymus, was not with them when Jesus came.

"The other disciples therefore said unto him, We have seen the LORD. But he said unto them, Except I shall see in his hands the print of the nails, and put my finger into the print of the nails, and thrust my hand into his side, I will not believe.

"And after eight days again his disciples were within, and Thomas with them: then came Jesus, the doors being shut, and stood in the midst, and said, Peace be unto you.

"Then saith He to Thomas, Reach hither thy finger, and behold my hands; and reach hither thy hand, and thrust it into my side: and be not faithless, but believing.

"And Thomas answered and said unto him, My LORD and my God.

"Jesus saith unto him, Thomas, because thou hast seen Me, thou hast believed: blessed are they that have not seen, and yet have believed."


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As the story of doubting Thomas in the Gospel of John makes quite clear, in the English language the verb "to believe" does not imply believing without evidence. This simple fact is also communicated by the well-known proverb "Seeing is believing", which, as a matter of fact, strongly implies the opposite, and which has been in circulation in the English language at least since the early 17th century (it appears in a collection of proverbs compiled by John Clarke published in 1639, but is even older than that).

The word "believe" appears well over 200 times in the works of Shakespeare, and 18 times in Hamlet alone, where it is first uttered by Horatio in Act One, Scene One:
"Before my God, I might not this believe
Without the sensible and true avouch
Of mine own eyes."
Obviously, then, the English word "believe" can mean either belief based on evidence or belief without evidence. To remove this ambiguity it is necessary to explicitly state whether or not there is evidence, and/or making this clear through the context.

Moreover, the English word "believe" can be used to denote a belief that is based on scientific evidence. Take, for example, this sentence from a January, 2000 NASA press release (link) quoting Yale University researcher David L. Rabinowitz:
"We now believe there are between 500 and 1,000 near-Earth asteroids larger than one kilometer (about 0.6 miles) in diameter."
Similar examples are easy to find if one searches the scientific literature for the phrase "we now believe".

At the risk of belaboring this point, let us ask why Rabinowitz says (above) that scientists "now believe there are between 500 and 1,000 near-Earth asteroids" etc., etc.? Is it because these scientists have prayed to their Gods and in answer to their prayers the truth has been revealed unto them? No. (Although it must be allowed parenthetically that a great many working scientists have tried this and will admit to it if they are honest!) Rather, it is because these scientists have examined the evidence and have come to a scientific conclusion based on that evidence.

Moreover, like all scientific conclusions, this conclusion about asteroids contains some (in this case fairly significant) amount of uncertainty. An alternative way of stating "between 500 and 1,000" makes the measure of uncertainty more explicit: "750 plus or minus 250".

Not only do all scientific conclusions involve uncertainty, but all scientific meaurements (aka "data") involve uncertainty. One thing that lay people are often completely ignorant about is the fact that data and uncertainty always go hand in hand, and this even to the extent that any data worth a scientist's attention must include, as an integral part of the data, an estimate (for, quite naturally, there is unavoidable uncertainty when it comes to quantifying uncertainty itself) of the error involved in the data.

To briefly summarize:

1. Belief can be based on evidence, and often is. In fact, the word "belief" often comes up in the context of arguments to the effect that evidence should always be required as a basis for belief.

2. All scientific data, and, necessarily so, all scientific conclusions based upon the analysis and interpretation of data, involve uncertainty.


Friday, October 23, 2009

Happy Mole Day

The mole is much more than just a geeky Chemistry concept, although it is that. It is also an initiatory gateway that one must pass through. It's very much like a Zen koan. Once you "get it", well, you know for certain that you have gotten it. It might take a few (or even several) false starts. You might try to fake it, but you can't fool anyone who really knows what a mole is.

I can think back over my years of (over) educating myself and identify several other terms/concepts/phenomena that, at least for me, provided the same kind of "AHA!" experience that can accompany learning about the Great Mystery of the Mole.

In phonology there is the phoneme.

In calculus there is the limit.

In computer science there is recursion.

In marxist economics there is value (surplus, use and exchange).

In magic there is sympathy.

In unix there is the file.

In european history there is Charlemagne.

In chaos there is sensitive dependence on initial conditions.

In protein x-ray crystallography there is anomalous scattering.