Quantitation in This is the first of two parts of an article on Quantitation in Elemental Analysis which grew out of Professor Kaiser's participation as a speaker at the 22nd Annual Summer Symposium on Analytical Chemistry. This meeting was held June 11 to 13, 1969, at the University of Georgia. The second part of the article will appear in the April issue of ANALYTICAL CHEMISTRY
H. Kaiser Institut fur Spektrochemie Dortmund,
und Angewandte
Spektroskopie
Germany
I was asked by Prof. G. H. Morrison to give a 40-minute talk about "Quantitation in Elemental Analysis" during the ACS Symposium on Analytical Chemistry at Athens, Ga., in June 1969. Since I did not know, what "quantitation" exactly meant, I started thinking about the general role of numbers in chemical analysis. As we know from Shakespeare's "Julius Caesar," thinking is dangerous and Prof. Morrison may not have been aware what he did to me by choosing such a stimulating topic. The short talk at Athens could give only the main lines and indicate the problems. It was fo//owed by lively discussions in small groups during the Symposium and thereafter. A first attempt to write a brief article for ANALYTICAL CHEMISTRY failed completely. I realized that the conventional ideas about numbers, statistics, and information, widely held among chemists, are not uniform and are not precise enough to allow a "shorthand" presentation. Basic presuppositions and implications are not generally known. The technical terms have come so much in vogue recently that the omission of a commonly accepted, precise scientific language for our field is overlooked. Hence I was forced to go through all this once more and to make it clear for myself. This is the result. There are practically no concepts, relations, and thoughts in this article which are new; most of them are at present "in the air"; I myself do not rea//y know from which person or book I was first introduced to them. For this reason, I had to abstain from giving a haphazard general selection of references from the huge literature. I wish to express my gratitude to all who have contributed to my knowledge. The only responsibility remaining with me refers to the selection and composition of the following mosaic. 24 A
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ANALYTICAL CHEMISTRY, VOL. 42, NO. 2, FEBRUARY 1970
T^OR A long time chemists have been using numbers in a rather innocent way to describe the results of their analysis. Recently, they have lost their innocence and eaten from the apple in Paradise. The Paradise is lost and lost also is—at least partly—that magic feeling of the born chemist for the transformation of matter, which may be the remainder of the mysterious practice of alchemy. What have we won? Recognition of the good and the evil? The good may be the power of abstract thinking and its success with all its delight to the human intellect. The evil on the other side may be the pitfalls of deception, the constant temptation to take abstract structures as a full picture of nature and, even worse, of human life. In chemical analysis this dangerous situation is prevalent, due to the advent of the computer, the new possibilities of data processing, and by the progressing adaptation of mathematical statistics. The blind belief in the perfection of measuring instruments, electronics, and formal mathematical relations is a real danger. All this began—slowly —33 years ago in spectrochemical analysis. The main topic of this paper will not be mass production of analysis data, computer programs, methods of numerical mathematics, or some such—all of these may be found elsewhere. I intend to consider the intellectual situation, to point out which decisions are at stake and which questions about nomenclature and presentation of results must be settled. Many people are aware of these problems. Proposals are made and often repeated independently in slightly different form. However, it is a pity to observe that a good many of these efforts are useless because the newcomers to this realm just do not know enough about the many implications and
REPORT FOR ANALYTICAL CHEMISTS
Elemental Analysis the long history of scientific think ing in this field. This is the cause of much confusion. We are in the whirlpools between Scylla and Charybdis of overbelief in formal or technical procedures and repul sion caused by misplaced erudition from the side of the missionaries. However, as soon as we have passed these uncomfortable straits, a quiet sea may be before us. The ideas are simple, the necessary formulas are simple also and should be con sidered as ready-made mental tools. For their correct use, it is not nec essary to study in detail the work of the toolmakers—in this case of generations of mathematicians. Description of Scientific Facts by Numbers
Many thousands of years ago, man made a great intellectual dis covery when he recognized that five men, five trees, five stars, five words, and five thoughts had some thing in common: the "fivehood," if such a word is allowed. Why is it possible not only to count things by numbers but to describe struc tures by using numbers? We have to consider what hap pens in the chain of communica tion between two persons or be tween an apparatus and its ob server. There are signals transfer ring the information between them. Signals are configurations in space and time—e.g., sound waves, light, letters, punch tapes. All these sig nals are finite in space and in time. This fact has a remarkable con sequence which will be explained by a simple formal example: Let us suppose that we have a signal which occurs during some time. I t may be described by a mathematical model, a time-dependent function: F(t). With some general presup positions as to the mathematical •character of such functions (which mainly are valid), we may rep resent this function by its Fourier
transform. Because the signal is finite it will have an effective dura tion time At = t2 —
