Short takes: functionality

Wed Mar 31 10:07:44 UTC 2010

Earlier, I mentioned the appearance of "functionality" in an article
that dealt with coinage of some words in the late mid-19th century.

http://bit.ly/cNQmMR
The National Teacher. Vol. 3:7. July, 1873.
http://bit.ly/b80h9l
The Ohio Educational Monthly: Organ of the Ohio Teachers' Association.
New Series, Vol. 14:7. July, 1873.
A Few Words Not in the Dictionaries. William Downs Henkle (Salem, Ohio).
p. 252
> I give below a few additional words not to be found in the last
> edition of Webster's. The authorities for the words are given :
>> /functionality/, Earle

I also mentioned that this appears to be the same reference identified
in the OED.

> functional
> Hence *functionality*, functional character; in /Math./, the condition
> of being a function.
> *1871* EARLE /Philol. Eng. Tongue/ §252 The old native Latin, whose
> vitality and functionality was all but purely flectional. *1879*
> CAYLEY in /Encycl. Brit./ IX. 818/1 Functionality in Analysis is
> dependence on a variable or variables.

I've studied Cayley before and I am quite certain that his use of
"functionality" in 1879 was by no means a coinage. In fact, Cayley was
remarkably good at developing other people's work (in mathematics), and
was quite a presence on the mathematical scene of the second half of the
19th century, but he was hardly an original theoretician (unlike, say,
Hamilton, with whom Cayley had extensive correspondence and cooperation).

Certainly, for mathematical use, 1879 seems much too late--even if the
use might have been adopted from French or German coinage, it still
would have appeared well before 1879. And if that is indeed the case,
there should be earlier use of "functionality" in general as well.

There is a cluster of publications around 1840-43 that use
"functionality" in at least two different senses. One appears to have
been introduced by William Walton. (I am using [phi] to correspond to
the lower-case Greek letter in the original.)

http://bit.ly/cutSSI
The Cambridge Mathematical Journal. Vol. 3:18. May, 1843
VI--On the Integration of Linear Partial Differential Equations by the
Methods of Monge and Lagrange. By W. Walton. p. 270-1ff
> Hence we see that from an assumption involving no sacrifice of
> generality we obtain
>         [phi](/F/, /G/) = 0
> which is consequently a relation among the three variables /x/, /y/,
> /z/, coextensive in generality with the equation (1), and therefore
> the complete integral of the proposed equation. The symbol [phi]
> evidently denotes undefined and therefore arbitrary functionality.

In this case, "functionality" means little more than a function which
has other functions (all of the same collection of variables) as inputs.
The term is used several times in the article.

This piece, however, is preceded, in the same volume, by two other
articles by Walton and by George Boole.

Vol. 3:13. November 1841
I.--Exposition of a General Theory of Linear Transformations. Part I. By
George Boole. p. 8
> Let [phi], as symbol of functionality, indicate the combinations of
> the constants in [theta](/Q/), [theta](/R/), &c., ...

Vol. 3:14. February 1842
I.--On the Motion of a Particle Along Variable and Moveable Tubes and
Surfaces. By W. Walton. p. 50
> ...hence it is evident that in addition to the equation (I.) we shall
> have, from the particular conditions of each individual problem, a
> number of equations equivalent to two of the form
>          [phi](/x/, /y/, /z/, /t/) = 0, [chi](/x/, /y/, /z/, /t/) = 0
> . . . . (II.),
> where [phi] and [chi] are symbols of functionality depending upon the
> law of the variations of the form and position of the tube.

If the word "functionality" meant the same thing to both Walton and
Boole, it is not immediately apparent.

The preceding volume also uses "functionality" in two articles (one by
Walton).

http://bit.ly/cDORpl
The Cambridge Mathematical Journal. Vol. 2:8. February, 1840
VIII.--On the General Theory of the Loci of Curvilinear Intersection. By
W. W. [William Whewell?]. p. 86
> Suppose that, to take a particular form for the symbol of
> functionality [chi], we assume
>         [chi]([alpha]) = - 1/[alpha];
> then the equation (8) will become ...

Vol. 2:9. May 1840
III.--On the General Interpretation of Equations Between Two Variables
in Algebraic Geometry. By W. Walton. p. 104
> Let the general equation between two variables, /x/ and /y/, be
>         /f/(/x/, /y/, A_1, A_2, A_3, ... A_[tau]) = 0 ... ... ... (1),
> where /f/ is a general symbol of /functionality/, and A_1, A_2, A_3,
> ... A_[tau] are arbitrary constants of the equation.

Walton also put out a volume of mechanics problems in 1842, and it too
contained the term.
http://bit.ly/d3b4ic

The term also creeps into the volume on Differential and Integral
Calculus by D. F. Gregory, 1841.
http://bit.ly/99j20B

Although there is some variation in the specific meaning of the term, if
narrowly interpreted from each article (except for the consistent usage
by Walton and Gregory), in one interpretation they are all consistent
with the broad definition by Cayley (1879) that is cited in the OED.
Given such diverse use--and the fact that none of the 1840-43 articles
even attempt to define the terminology, it seems clear that within this
narrow group of mathematicians (Walton, Gregory, Boole, De Morgan,
Whewell), the term was known for some time prior to its appearance in
early 1840. This supposition is actually strengthened by the term's
association with Cayley, who represents a continued intellectual
tradition from this group.

GB cannot be relied upon to get the precise location. I would venture a
guess that the term had been proposed by one of these five sometime
within two years of these appearance, perhaps in a work from 1838-1840
by De Morgan or Boole, who were quite notorious innovators in
mathematical language.

Interestingly, this period corresponds /exactly/ to the earliest
appearances of "functionality" in non-mathematical sense as well!

http://books.google.com/books?id=_Ms-AAAAIAAJ
Theological Criticisms, or Hints of the Philosophy of Man and Nature. In
Six Lectures. To which Are Appended Two Poetical Scraps, and Dogmas of
Infidelity. By F. W. Adams. Montpelier: 1843
p. vii
Dogmas of Infidelity.
> Nature is an uncreated, indivisible and unlimited system of matter and
> functionality ; whose eternity is no more difficult to admit, that
> that of an antecedent creator : Nor is humanity competent to acquire
> an earlier idea of things, than that which is expressed by the term,
> formation !
p. ix
> Matter may be supposed to possess an ultimate being and functionality
> ; a state it may successively resume, in imitation of its original, at
> the termination of each complete revolution of its metamorphosis ; and
> below which, it is incapable of reduction, or simplification.
> Life is a supposed principle, to whose agency organic phenomena have
> been exclusively referred ; and which may be contemplated in the
> triple character of ultimate, structural and functional.
p. xii
> Man consists of structural organism, and consequent functionality, of
> which brain and consciousness are important particulars : Nor is the
> latter, which is synonymous with soul, one whit more spiritual, than
> the elasticity of steel.
p. 120
> To speak physiologically : Man is an aggregate of complicated
> organism, which is so arranged as that whilst each individual organic
> structure possesses a specific identity and functionality, the whole
> are associated by means of vascular and nervous intercommunication,
> into an individual, living, thinking, acting machine, whose phenomena
> are either psychological or automatic, or, in other words, voluntary
> or involuntary ; with the former of which only, are we at present
> concerned.
p. 212
> The mind of man, whatever it may be, most certainly resembles
> functionality. It bears a strict analogy to muscular motivity, being
> apparently developed in a direct ratio of that of material organism,
> from its commencement to maturity ; whence its progress is inverted,
> and it marches downward, with physical dissolution.

http://bit.ly/bb5EUT
The Sankhya Karika, or Verses on the Sankhya Philosophy, by Iswara
Krishna; Translated from the Sanscrit by Henry Thomas Colebrooke, Esq.
Oxford: 1837
Comment. p. 54
> The description of the three qualities is continued in this verse.
> /Goodness is alleviating ; laghu/, 'light;' it is matter, elastic and
> elevating, generating upward and lateral motion, as in the ascent of
> flame, and the currents of the air. It is the cause of active and
> perfect functionality also in the instruments of vitality*;
> /enlightening/, /prakasakam/, 'making manifest,' the objects of the
> senses.

It is very hard to speculate here, but, it seems, the coincidence is
really not a coincidence. The mathematical coinage and the
non-mathematical coinage are closely related. Perhaps it is yet another
foreign source that is behind both. Or perhaps it is the fact that the
period in question is the height of functionalism and terminology
related to "function", but more nuanced, was sorely needed. The same
applies to functions in mathematics. Although Cauchy has dealt with the
subject of multiple variables half a century earlier, the English
mathematicians needed terminology to discuss a generalization of
functions. At that moment, the words "functionality" fit the bill (using
"functional" as a noun would have been uncouth, at that time).

Yet, I must leave this post without a definitive conclusion, as there is
an obvious gap that needs to be filled by scouring philosophical and
mathematical literature 1835-1839.

     VS-)

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