![demonstration: which is not limited to the idea of extension, figure,
number, and their modes.—Locke, John.
An Essay concerning Human
Understanding, Bk. 4, chap. 2, sect. 9.
1442. Now I shall remark again what I have already touched upon
more than once, that it is a common opinion that only mathematical
sciences are capable of a demonstrative certainty; but as the
agreement and disagreement which may be known intuitively is not
a privilege belonging only to the ideas of numbers and figures, it is
perhaps for want of application on our part that mathematics alone
have attained to demonstrations.—Leibnitz.
New Essay concerning Human
Understanding, Bk. 4, chap. 2, sect. 9
[Langley].](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-31-320.jpg)
![CHAPTER XV
MATHEMATICS AND SCIENCE
1501. How comes it about that the knowledge of other sciences,
which depend upon this [mathematics], is painfully sought, and that
no one puts himself to the trouble of studying this science itself? I
should certainly be surprised, if I did not know that everybody
regarded it as being very easy, and if I had not long ago observed
that the human mind, neglecting what it believes to be easy, is
always in haste to run after what is novel and advanced.—Descartes.
Rules for the Direction of the Mind;
Philosophy of Descartes [Torrey], (New
York, 1892), p. 72.
1502. All quantitative determinations are in the hands of
mathematics, and it at once follows from this that all speculation
which is heedless of mathematics, which does not enter into
partnership with it, which does not seek its aid in distinguishing
between the manifold modifications that must of necessity arise by a
change of quantitative determinations, is either an empty play of
thoughts, or at most a fruitless effort. In the field of speculation
many things grow which do not start from mathematics nor give it
any care, and I am far from asserting that all that thus grow are
useless weeds, among them may be many noble plants, but without
mathematics none will develop to complete maturity.—Herbart, J. F.
Werke (Kehrbach), (Langensalza, 1890),
Bd. 5, p. 106.](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-32-320.jpg)
![1503. There are few things which we know, which are not capable
of being reduc’d to a Mathematical Reasoning, and when they
cannot, it’s a sign our knowledge of them is very small and confus’d;
and where a mathematical reasoning can be had, it’s as great folly
to make use of any other, as to grope for a thing in the dark, when
you have a candle standing by you.—Arbuthnot.
Quoted in Todhunter’s History of the
Theory of Probability (Cambridge and
London, 1865), p. 51.
1504. Mathematical Analysis is ... the true rational basis of the
whole system of our positive knowledge.—Comte, A.
Positive Philosophy [Martineau], Bk. 1,
chap. 1.
1505. It is only through Mathematics that we can thoroughly
understand what true science is. Here alone we can find in the
highest degree simplicity and severity of scientific law, and such
abstraction as the human mind can attain. Any scientific education
setting forth from any other point, is faulty in its basis.—Comte, A.
Positive Philosophy [Martineau], Bk. 1,
chap. 1.
1506. In the present state of our knowledge we must regard
Mathematics less as a constituent part of natural philosophy than as
having been, since the time of Descartes and Newton, the true basis
of the whole of natural philosophy; though it is, exactly speaking,
both the one and the other. To us it is of less use for the knowledge
of which it consists, substantial and valuable as that knowledge is,
than as being the most powerful instrument that the human mind
can employ in the investigation of the laws of natural phenomena.—
Comte, A.
Positive Philosophy [Martineau],
Introduction, chap. 2.](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-33-320.jpg)
![view of the fact that the degree of approximation necessary for
various purposes is very different, and thus that unassigned grades
of approximation would have to be provided for. Moreover, the
mathematician working on these lines would be cut off from the
chief sources of inspiration, the ideals of exactitude and logical
rigour, as well as from one of his most indispensable guides to
discovery, symmetry, and permanence of mathematical form. The
history of the actual movements of mathematical thought through
the centuries shows that these ideals are the very life-blood of the
science, and warrants the conclusion that a constant striving toward
their attainment is an absolutely essential condition of vigorous
growth. These ideals have their roots in irresistible impulses and
deep-seated needs of the human mind, manifested in its efforts to
introduce intelligibility in certain great domains of the world of
thought.—Hobson, E. W.
Presidential Address British Association
for the Advancement of Science, Section
A (1910); Nature, Vol. 84, pp. 285-286.
1519. The immense part which those laws [laws of number and
extension] take in giving a deductive character to the other
departments of physical science, is well known; and is not
surprising, when we consider that all causes operate according to
mathematical laws. The effect is always dependent upon, or in
mathematical language, is a function of, the quantity of the agent;
and generally of its position also. We cannot, therefore, reason
respecting causation, without introducing considerations of quantity
and extension at every step; and if the nature of the phenomena
admits of our obtaining numerical data of sufficient accuracy, the
laws of quantity become the grand instruments for calculating
forward to an effect, or backward to a cause.—Mill, J. S.
System of Logic, Bk. 3, chap. 24, sect. 9.](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-38-320.jpg)
![1520. The ordinary mathematical treatment of any applied science
substitutes exact axioms for the approximate results of experience,
and deduces from these axioms the rigid mathematical conclusions.
In applying this method it must not be forgotten that the
mathematical developments transcending the limits of exactness of
the science are of no practical value. It follows that a large portion of
abstract mathematics remains without finding any practical
application, the amount of mathematics that can be usefully
employed in any science being in proportion to the degree of
accuracy attained in the science. Thus, while the astronomer can put
to use a wide range of mathematical theory, the chemist is only just
beginning to apply the first derivative, i.e. the rate of change at
which certain processes are going on; for second derivatives he does
not seem to have found any use as yet.—Klein, F.
Lectures on Mathematics (New York,
1911), p. 47.
1521. The bond of union among the physical sciences is the
mathematical spirit and the mathematical method which pervades
them.... Our knowledge of nature, as it advances, continuously
resolves differences of quality into differences of quantity. All exact
reasoning—indeed all reasoning—about quantity is mathematical
reasoning; and thus as our knowledge increases, that portion of it
which becomes mathematical increases at a still more rapid rate.—
Smith, H. J. S.
Presidential Address British Association
for the Advancement of Science, Section
A (1873); Nature, Vol. 8, p. 449.
1522. Another way of convincing ourselves how largely this process
[of assimilation of mathematics by physics] has gone on would be to
try to conceive the effect of some intellectual catastrophe, supposing
such a thing possible, whereby all knowledge of mathematics should
be swept away from men’s minds. Would it not be that the departure](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-39-320.jpg)
![our mathematics!... In the schools of today mathematics serves only
as a disciplinary study, a mental gymnastic; that it includes the
highest ideal value for the comprehension of the universe, one dares
scarcely to think of in view of our present day instruction.—Lindeman,
F.
Lehren und Lernen in der Mathematik
(München, 1904), p. 14.
1524. All applications of mathematics consist in extending the
empirical knowledge which we possess of a limited number or region
of accessible phenomena into the region of the unknown and
inaccessible; and much of the progress of pure analysis consists in
inventing definite conceptions, marked by symbols, of complicated
operations; in ascertaining their properties as independent objects of
research; and in extending their meaning beyond the limits they
were originally invented for,—thus opening out new and larger
regions of thought.—Merz, J. T.
History of European Thought in the 19th
Century (Edinburgh and London, 1903),
Vol. 1, p. 698.
1525. All the effects of nature are only mathematical results of a
small number of immutable laws.—Laplace.
A Philosophical Essay on Probabilities
[Truscott and Emory] (New York, 1902),
p. 177; Oeuvres, t. 7, p. 139.
1526. What logarithms are to mathematics that mathematics are to
the other sciences.—Novalis.
Schriften (Berlin, 1901), Teil 2, p. 222.
1527. Any intelligent man may now, by resolutely applying himself
for a few years to mathematics, learn more than the great Newton](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-41-320.jpg)
![1534. It is not easy to anatomize the constitution and the
operations of a mind [like Newton’s] which makes such an advance
in knowledge. Yet we may observe that there must exist in it, in an
eminent degree, the elements which compose the mathematical
talent. It must possess distinctness of intuition, tenacity and facility
in tracing logical connection, fertility of invention, and a strong
tendency to generalization.—Whewell, W.
History of the Inductive Sciences (New
York, 1894), Vol. 1, p. 416.
1535. The domain of physics is no proper field for mathematical
pastimes. The best security would be in giving a geometrical training
to physicists, who need not then have recourse to mathematicians,
whose tendency is to despise experimental science. By this method
will that union between the abstract and the concrete be effected
which will perfect the uses of mathematical, while extending the
positive value of physical science. Meantime, the use of analysis in
physics is clear enough. Without it we should have no precision, and
no co-ordination; and what account could we give of our study of
heat, weight, light, etc.? We should have merely series of
unconnected facts, in which we could foresee nothing but by
constant recourse to experiment; whereas, they now have a
character of rationality which fits them for purposes of prevision.—
Comte, A.
Positive Philosophy [Martineau], Bk. 3,
chap. 1.
1536. It must ever be remembered that the true positive spirit first
came forth from the pure sources of mathematical science; and it is
only the mind that has imbibed it there, and which has been face to
face with the lucid truths of geometry and mechanics, that can bring
into full action its natural positivity, and apply it in bringing the most
complex studies into the reality of demonstration. No other discipline
can fitly prepare the intellectual organ.—Comte, A.](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-44-320.jpg)
![Positive Philosophy [Martineau], Bk. 3,
chap. 1.
1537. During the last two centuries and a half, physical knowledge
has been gradually made to rest upon a basis which it had not
before. It has become mathematical. The question now is, not
whether this or that hypothesis is better or worse to the pure
thought, but whether it accords with observed phenomena in those
consequences which can be shown necessarily to follow from it, if it
be true. Even in those sciences which are not yet under the
dominion of mathematics, and perhaps never will be, a working copy
of the mathematical process has been made. This is not known to
the followers of those sciences who are not themselves
mathematicians, and who very often exalt their horns against the
mathematics in consequence. They might as well be squaring the
circle, for any sense they show in this particular.—De Morgan, A.
A Budget of Paradoxes (London, 1872),
p. 2.
1538. Among the mere talkers so far as mathematics are
concerned, are to be ranked three out of four of those who apply
mathematics to physics, who, wanting a tool only, are very impatient
of everything which is not of direct aid to the actual methods which
are in their hands.—De Morgan, A.
Graves’ Life of Sir William Rowan
Hamilton (New York, 1882-1889), Vol. 3,
p. 348.
1539. Something has been said about the use of mathematics in
physical science, the mathematics being regarded as a weapon
forged by others, and the study of the weapon being completely set
aside. I can only say that there is danger of obtaining untrustworthy
results in physical science, if only the results of mathematics are
used; for the person so using the weapon can remain unacquainted](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-45-320.jpg)
![with wires which transmit messages from Madrid to St. Petersburg
with the rapidity of lightning, by means of the same principle whose
first manifestations this anatomist then observed!...
He who seeks for immediate practical use in the pursuit of
science, may be reasonably sure, that he will seek in vain. Complete
knowledge and complete understanding of the action of forces of
nature and of the mind, is the only thing that science can aim at.
The individual investigator must find his reward in the joy of new
discoveries, as new victories of thought over resisting matter, in the
esthetic beauty which a well-ordered domain of knowledge affords,
where all parts are intellectually related, where one thing evolves
from another, and all show the marks of the mind’s supremacy; he
must find his reward in the consciousness of having contributed to
the growing capital of knowledge on which depends the supremacy
of man over the forces hostile to the spirit.—Helmholtz, H.
Vorträge und Reden (Braunschweig,
1884), Bd. 1, p. 142.
1546. When the time comes that knowledge will not be sought for
its own sake, and men will not press forward simply in a desire of
achievement, without hope of gain, to extend the limits of human
knowledge and information, then, indeed, will the race enter upon
its decadence.—Hughes, C. E.
Quoted in D. E. Smith’s Teaching of
Geometry (Boston, 1911), p. 9.
1547. [In the Opus Majus of Roger Bacon] there is a chapter, in
which it is proved by reason, that all sciences require mathematics.
And the arguments which are used to establish this doctrine, show a
most just appreciation of the office of mathematics in science. They
are such as follows: That other sciences use examples taken from
mathematics as the most evident:—That mathematical knowledge is,
as it were, innate to us, on which point he refers to the well-known
dialogue of Plato, as quoted by Cicero:—That this science, being the](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-48-320.jpg)
![phenomena, met with success. To do this two things are necessary:
First, simple fundamental concepts with which to construct; second,
some method by which to deduce, from the simple fundamental laws
of the construction which relate to instants of time and points in
space, laws for finite intervals and distances, which alone are
accessible to observation (can be compared with experience).”
[Riemann.]
The first of the two problems here indicated by Riemann
consists in setting up the differential equation, based upon physical
facts and hypotheses. The second is the integration of this
differential equation and its application to each separate concrete
case, this is the task of mathematics.—Weber, Heinrich.
Die partiellen Differentialgleichungen der
mathematischen Physik (Braunschweig,
1882), Bd. 1, Vorrede.
1550. Mathematics is the most powerful instrument which we
possess for this purpose [to trace into their farthest results those
general laws which an inductive philosophy has supplied]: in many
sciences a profound knowledge of mathematics is indispensable for a
successful investigation. In the most delicate researches into the
theories of light, heat, and sound it is the only instrument; they have
properties which no other language can express; and their
argumentative processes are beyond the reach of other symbols.—
Price, B.
Treatise on Infinitesimal Calculus
(Oxford, 1858), Vol. 3, p. 5.
1551. Notwithstanding the eminent difficulties of the mathematical
theory of sonorous vibrations, we owe to it such progress as has yet
been made in acoustics. The formation of the differential equations
proper to the phenomena is, independent of their integration, a very
important acquisition, on account of the approximations which
mathematical analysis allows between questions, otherwise](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-50-320.jpg)
![heterogeneous, which lead to similar equations. This fundamental
property, whose value we have so often to recognize, applies
remarkably in the present case; and especially since the creation of
mathematical thermology, whose principal equations are strongly
analogous to those of vibratory motion.—This means of investigation
is all the more valuable on account of the difficulties in the way of
direct inquiry into the phenomena of sound. We may decide the
necessity of the atmospheric medium for the transmission of
sonorous vibrations; and we may conceive of the possibility of
determining by experiment the duration of the propagation, in the
air, and then through other media; but the general laws of the
vibrations of sonorous bodies escape immediate observation. We
should know almost nothing of the whole case if the mathematical
theory did not come in to connect the different phenomena of
sound, enabling us to substitute for direct observation an equivalent
examination of more favorable cases subjected to the same law. For
instance, when the analysis of the problem of vibrating chords has
shown us that, other things being equal, the number of oscillations
is in inverse proportion to the length of the chord, we see that the
most rapid vibrations of a very short chord may be counted, since
the law enables us to direct our attention to very slow vibrations.
The same substitution is at our command in many cases in which it
is less direct.—Comte, A.
Positive Philosophy [Martineau], Bk. 3,
chap. 4.
1552. Problems relative to the uniform propagation, or to the varied
movements of heat in the interior of solids, are reduced ... to
problems of pure analysis, and the progress of this part of physics
will depend in consequence upon the advance which may be made
in the art of analysis. The differential equations ... contain the chief
results of the theory; they express, in the most general and concise
manner, the necessary relations of numerical analysis to a very
extensive class of phenomena; and they connect forever with](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-51-320.jpg)
![mathematical science one of the most important branches of natural
philosophy.—Fourier, J.
Theory of Heat [Freeman], (Cambridge,
1878), Chap. 3, p. 131.
1553. The effects of heat are subject to constant laws which cannot
be discovered without the aid of mathematical analysis. The object
of the theory is to demonstrate these laws; it reduces all physical
researches on the propagation of heat, to problems of the integral
calculus, whose elements are given by experiment. No subject has
more extensive relations with the progress of industry and the
natural sciences; for the action of heat is always present, it
influences the processes of the arts, and occurs in all the
phenomena of the universe.—Fourier, J.
Theory of Heat [Freeman], (Cambridge,
1878), Chap. 1, p. 12.
1554. Dealing with any and every amount of static electricity, the
mathematical mind has balanced and adjusted them with wonderful
advantage, and has foretold results which the experimentalist can do
no more than verify.... So in respect of the force of gravitation, it has
calculated the results of the power in such a wonderful manner as to
trace the known planets through their courses and perturbations,
and in so doing has discovered a planet before unknown.—Faraday.
Some Thoughts on the Conservation of
Force.
1555. Certain branches of natural philosophy (such as physical
astronomy and optics), ... are, in a great measure, inaccessible to
those who have not received a regular mathematical education....—
Stewart, Dugald.
Philosophy of the Human Mind, Part 3,
chap. 1, sect. 3.](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-52-320.jpg)
![1558. You know that if you make a dot on a piece of paper, and
then hold a piece of Iceland spar over it, you will see not one dot
but two. A mineralogist, by measuring the angles of a crystal, can
tell you whether or no it possesses this property without looking
through it. He requires no scientific thought to do that. But Sir
William Roman Hamilton ... knowing these facts and also the
explanation of them which Fresnel had given, thought about the
subject, and he predicted that by looking through certain crystals in
a particular direction we should see not two dots but a continuous
circle. Mr. Lloyd made the experiment, and saw the circle, a result
which had never been even suspected. This has always been
considered one of the most signal instances of scientific thought in
the domain of physics.—Clifford, W. K.
Lectures and Essays (New York, 1901),
Vol. 1, p. 144.
1559. The discovery of this planet [Neptune] is justly reckoned as
the greatest triumph of mathematical astronomy. Uranus failed to
move precisely in the path which the computers predicted for it, and
was misguided by some unknown influence to an extent which a
keen eye might almost see without telescopic aid.... These minute
discrepancies constituted the data which were found sufficient for
calculating the position of a hitherto unknown planet, and bringing it
to light. Leverrier wrote to Galle, in substance: “Direct your
telescope to a point on the ecliptic in the constellation of Aquarius,
in longitude 326°, and you will find within a degree of that place a
new planet, looking like a star of about the ninth magnitude, and
having a perceptible disc.” The planet was found at Berlin on the
night of Sept. 26, 1846, in exact accordance with this prediction,
within half an hour after the astronomers began looking for it, and
only about 52′ distant from the precise point that Leverrier had
indicated.—Young, C. A.
General Astronomy (Boston, 1891), Art.
653.](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-54-320.jpg)
![1560. I am convinced that the future progress of chemistry as an
exact science depends very much indeed upon the alliance with
mathematics.—Frankland, A.
American Journal of Mathematics, Vol. 1,
p. 349.
1561. It is almost impossible to follow the later developments of
physical or general chemistry without a working knowledge of higher
mathematics.—Mellor, J. W.
Higher Mathematics (New York, 1902),
Preface.
1562.
... Mount where science guides;
Go measure earth, weigh air, and state the tides;
Instruct the planets in what orb to run,
Correct old time, and regulate the sun.
—Thomson, W.
On the Figure of the Earth, Title page.
1563. Admission to its sanctuary [referring to astronomy] and to
the privileges and feelings of a votary, is only to be gained by one
means,—sound and sufficient knowledge of mathematics, the great
instrument of all exact inquiry, without which no man can ever make
such advances in this or any other of the higher departments of
science as can entitle him to form an independent opinion on any
subject of discussion within their range.—Herschel, J.
Outlines of Astronomy, Introduction,
sect. 7.
1564. The long series of connected truths which compose the
science of astronomy, have been evolved from the appearances and
observations by calculation, and a process of reasoning entirely](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-55-320.jpg)
![Edinburgh Review, Vol. 58 (1833-1834),
p. 169.
1566. With an ordinary acquaintance of trigonometry, and the
simplest elements of algebra, one may take up any well-written
treatise on plane astronomy, and work his way through it, from
beginning to end, with perfect ease; and he will acquire, in the
course of his progress, from the mere examples put before him, an
infinitely more correct and precise idea of astronomical methods and
theories, than he could obtain in a lifetime from the most eloquent
general descriptions that ever were written. At the same time he will
be strengthening himself for farther advances, and accustoming his
mind to habits of close comparison and rigid demonstration, which
are of infinitely more importance than the acquisition of stores of
undigested facts.
Edinburgh Review, Vol. 58 (1833-1834),
p. 170.
1567. While the telescope serves as a means of penetrating space,
and of bringing its remotest regions nearer us, mathematics, by
inductive reasoning, have led us onwards to the remotest regions of
heaven, and brought a portion of them within the range of our
possibilities; nay, in our own times—so propitious to the extension of
knowledge—the application of all the elements yielded by the
present conditions of astronomy has even revealed to the intellectual
eyes a heavenly body, and assigned to it its place, orbit, mass,
before a single telescope has been directed towards it.—Humboldt, A.
Cosmos [Otte], Vol. 2, part 2, sect. 3.
1568. Mighty are numbers, joined with art resistless.—Euripides.
Hecuba, Line 884.](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-57-320.jpg)
![1569. No single instrument of youthful education has such mighty
power, both as regards domestic economy and politics, and in the
arts, as the study of arithmetic. Above all, arithmetic stirs up him
who is by nature sleepy and dull, and makes him quick to learn,
retentive, shrewd, and aided by art divine he makes progress quite
beyond his natural powers.—Plato.
Laws [Jowett,] Bk. 5, p. 747.
1570. For all the higher arts of construction some acquaintance with
mathematics is indispensable. The village carpenter, who, lacking
rational instruction, lays out his work by empirical rules learned in
his apprenticeship, equally with the builder of a Britannia Bridge,
makes hourly reference to the laws of quantitative relations. The
surveyor on whose survey the land is purchased; the architect in
designing a mansion to be built on it; the builder in preparing his
estimates; his foreman in laying out the foundations; the masons in
cutting the stones; and the various artisans who put up the fittings;
are all guided by geometrical truths. Railway-making is regulated
from beginning to end by mathematics: alike in the preparation of
plans and sections; in staking out the lines; in the mensuration of
cuttings and embankments; in the designing, estimating, and
building of bridges, culverts, viaducts, tunnels, stations. And similarly
with the harbors, docks, piers, and various engineering and
architectural works that fringe the coasts and overspread the face of
the country, as well as the mines that run underneath it. Out of
geometry, too, as applied to astronomy, the art of navigation has
grown; and so, by this science, has been made possible that
enormous foreign commerce which supports a large part of our
population, and supplies us with many necessaries and most of our
luxuries. And nowadays even the farmer, for the correct laying out of
his drains, has recourse to the level—that is, to geometrical
principles.—Spencer, Herbert.
Education, chap. 1.](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-58-320.jpg)
![1571. [Arithmetic] is another of the great master-keys of life. With
it the astronomer opens the depths of the heavens; the engineer,
the gates of the mountains; the navigator, the pathways of the deep.
The skillful arrangement, the rapid handling of figures, is a perfect
magician’s wand. The mighty commerce of the United States, foreign
and domestic, passes through the books kept by some thousands of
diligent and faithful clerks. Eight hundred bookkeepers, in the Bank
of England, strike the monetary balance of half the civilized world.
Their skill and accuracy in applying the common rules of arithmetic
are as important as the enterprise and capital of the merchant, or
the industry and courage of the navigator. I look upon a well-kept
ledger with something of the pleasure with which I gaze on a picture
or a statue. It is a beautiful work of art.—Everett, Edward.
Orations and Speeches (Boston, 1870),
Vol. 3, p. 47.
1572. [Mathematics] is the fruitful Parent of, I had almost said all,
Arts, the unshaken Foundation of Sciences, and the plentiful
Fountain of Advantage to Human Affairs. In which last Respect, we
may be said to receive from the Mathematics, the principal Delights
of Life, Securities of Health, Increase of Fortune, and Conveniences
of Labour: That we dwell elegantly and commodiously, build decent
Houses for ourselves, erect stately Temples to God, and leave
wonderful Monuments to Posterity: That we are protected by those
Rampires from the Incursions of the Enemy; rightly use Arms,
skillfully range an Army, and manage War by Art, and not by the
Madness of wild Beasts: That we have safe Traffick through the
deceitful Billows, pass in a direct Road through the tractless Ways of
the Sea, and come to the designed Ports by the uncertain Impulse of
the Winds: That we rightly cast up our Accounts, do Business
expeditiously, dispose, tabulate, and calculate scattered Ranks of
Numbers, and easily compute them, though expressive of huge
Heaps of Sand, nay immense Hills of Atoms: That we make pacifick
Separations of the Bounds of Lands, examine the Moments of
Weights in an equal Balance, and distribute every one his own by a](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-59-320.jpg)
![Mathematical Lectures (London, 1734),
pp. 27-30.
1573. Analytical and graphical treatment of statistics is employed by
the economist, the philanthropist, the business expert, the actuary,
and even the physician, with the most surprisingly valuable results;
while symbolic language involving mathematical methods has
become a part of wellnigh every large business. The handling of pig-
iron does not seem to offer any opportunity for mathematical
application. Yet graphical and analytical treatment of the data from
long-continued experiments with this material at Bethlehem,
Pennsylvania, resulted in the discovery of the law that fatigue varied
in proportion to a certain relation between the load and the periods
of rest. Practical application of this law increased the amount
handled by each man from twelve and a half to forty-seven tons per
day. Such study would have been impossible without preliminary
acquaintance with the simple invariable elements of mathematics.—
Karpinsky, L.
High School Education (New York, 1912),
chap. 6, p. 134.
1574. They [computation and arithmetic] belong then, it seems, to
the branches of learning which we are now investigating;—for a
military man must necessarily learn them with a view to the
marshalling of his troops, and so must a philosopher with the view
of understanding real being, after having emerged from the unstable
condition of becoming, or else he can never become an apt
reasoner.
That is the fact he replied.
But the guardian of ours happens to be both a military man and
a philosopher.
Unquestionably so.](https://image.slidesharecdn.com/35909-250422081612-1386379b/85/IT-strategy-issues-and-practices-3rd-ed-Edition-Mckeen-61-320.jpg)
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- 5. Global edition Global edition This is a special edition of an established title widely used by colleges and universities throughout the world. Pearson published this exclusive edition for the benefit of students outside the United States and Canada. If you purchased this book within the United States or Canada you should be aware that it has been imported without the approval of the Publisher or Author. Pearson Global Edition Global edition For these Global Editions, the editorial team at Pearson has collaborated with educators across the world to address a wide range of subjects and requirements, equipping students with the best possible learning tools.This Global Edition preserves the cutting-edge approach and pedagogy of the original, but also features alterations, customization, and adaptation from the North American version. IT Strategy: Issues and Practices McKeen Smith IT Strategy Issues and Practices THIRD edition James D. McKeen • Heather A. Smith THIRD edition McKeen_1292080264_mech.indd 1 28/11/14 12:56 PM
- 6. IT Strategy: Issues and Practices A01_MCKE0260_03_GE_FM.indd 1 26/11/14 9:32 PM
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- 8. IT Strategy: Issues and Practices T h i r d E d i t i o n G l o b a l E d i t i o n James D. McKeen Queen’s University Heather A. Smith Queen’s University Boston Columbus Indianapolis New York San Francisco Hoboken Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo A01_MCKE0260_03_GE_FM.indd 3 26/11/14 9:32 PM
- 9. Editor in Chief: Stephanie Wall Head of Learning Asset Acquisition, Global Edition: Laura Dent Acquisitions Editor: Nicole Sam Program Manager Team Lead: Ashley Santora Program Manager: Denise Vaughn Editorial Assistant: Kaylee Rotella Assistant Acquisitions Editor, Global Edition: Debapriya Mukherjee Associate Project Editor, Global Edition: Binita Roy Executive Marketing Manager: Anne K. Fahlgren Project Manager Team Lead: Judy Leale Project Manager: Thomas Benfatti Procurement Specialist: Diane Peirano Senior Manufacturing Controller, Production, Global Edition: Trudy Kimber Cover Image: © Toria/Shutterstock Cover Designer: Lumina Datamantics Full Service Project Management: Abinaya Rajendran at Integra Software Services, Pvt. Ltd. Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on appropriate page within text. Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsonglobaleditions.com © Pearson Education Limited 2015 The rights of James D. McKeen and Heather A. Smith to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Authorized adaptation from the United States edition, entitled IT Strategy: Issues and Practices, 3rd edition, ISBN 978-0-13-354424-4, by James D. McKeen and Heather A. Smith, published by Pearson Education © 2015. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a license permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. ISBN 10: 1-292-08026-4 ISBN 13: 978-1-292-08026-0 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library 10 9 8 7 6 5 4 3 2 1 Typeset in 10/12 Palatino LT Std by Integra Software Services, Pvt. Ltd. Printed and bound in Great Britain by Clays Ltd, Bungay, Suffolk. A01_MCKE0260_03_GE_FM.indd 4 26/11/14 9:32 PM
- 10. Contents Preface 13 About the Authors 21 Acknowledgments 22 Section I Delivering Value with IT 23 Chapter 1 the IT Value Proposition 24 Peeling the Onion: Understanding IT Value 25 What Is IT Value? 25 Where Is IT Value? 26 Who Delivers IT Value? 27 When Is IT Value Realized? 27 The Three Components of the IT Value Proposition 28 Identification of Potential Value 29 Effective Conversion 30 Realizing Value 31 Five Principles for Delivering Value 32 Principle 1. Have a Clearly Defined Portfolio Value Management Process 33 Principle 2. Aim for Chunks of Value 33 Principle 3. Adopt a Holistic Orientation to Technology Value 33 Principle 4. Aim for Joint Ownership of Technology Initiatives 34 Principle 5. Experiment More Often 34 Conclusion 34 • References 35 Chapter 2 Delivering Business Value through IT Strategy 37 Business and IT Strategies: Past, Present, and Future 38 Four Critical Success Factors 40 The Many Dimensions of IT Strategy 42 Toward an IT Strategy-Development Process 44 Challenges for CIOs 45 Conclusion 47 • References 47 Chapter 3 Making IT Count 49 Business Measurement: An Overview 50 Key Business Metrics for IT 52 5 A01_MCKE0260_03_GE_FM.indd 5 26/11/14 9:32 PM
- 11. 6 Contents Designing Business Metrics for IT 53 Advice to Managers 57 Conclusion 58 • References 58 Chapter 4 Effective Business–IT Relationships 60 The Nature of the Business–IT Relationship 61 The Foundation of a Strong Business–IT Relationship 63 Building Block #1: Competence 64 Building Block #2: Credibility 65 Building Block #3: Interpersonal Interaction 66 Building Block #4: Trust 68 Conclusion 70 • References 70 Appendix A The Five IT Value Profiles 72 Appendix B Guidelines for Building a Strong Business–IT Relationship 73 Chapter 5 Business–IT Communication 74 Communication in the Business–IT Relationship 75 What Is “Good” Communication? 76 Obstacles to Effective Communication 78 “T-Level” Communication Skills for IT Staff 80 Improving Business–IT Communication 82 Conclusion 83 • References 83 Appendix A IT Communication Competencies 85 Chapter 6 Effective IT Leadership 86 The Changing Role of the IT Leader 87 What Makes a Good IT Leader? 89 How to Build Better IT Leaders 92 Investing in Leadership Development: Articulating the Value Proposition 95 Conclusion 96 • References 97 Mini Cases Delivering Business Value with IT at Hefty Hardware 98 Investing in TUFS 102 IT Planning at ModMeters 104 A01_MCKE0260_03_GE_FM.indd 6 26/11/14 9:32 PM
- 12. Contents 7 Section II IT Governance 109 Chapter 7 Effective IT Shared Services 110 IT Shared Services: An Overview 111 IT Shared Services: Pros and Cons 114 IT Shared Services: Key Organizational Success Factors 115 Identifying Candidate Services 116 An Integrated Model of IT Shared Services 117 Recommmendations for Creating Effective IT Shared Services 118 Conclusion 121 • References 121 Chapter 8 Successful IT Sourcing: Maturity Model, Sourcing Options, and Decision Criteria 122 A Maturity Model for IT Functions 123 IT Sourcing Options: Theory Versus Practice 127 The “Real” Decision Criteria 131 Decision Criterion #1: Flexibility 131 Decision Criterion #2: Control 131 Decision Criterion #3: Knowledge Enhancement 132 Decision Criterion #4: Business Exigency 132 A Decision Framework for Sourcing IT Functions 133 Identify Your Core IT Functions 133 Create a “Function Sourcing” Profile 133 Evolve Full-Time IT Personnel 135 Encourage Exploration of the Whole Range of Sourcing Options 136 Combine Sourcing Options Strategically 136 A Management Framework for Successful Sourcing 137 Develop a Sourcing Strategy 137 Develop a Risk Mitigation Strategy 137 Develop a Governance Strategy 138 Understand the Cost Structures 138 Conclusion 139 • References 139 Chapter 9 Budgeting: Planning’s Evil Twin 140 Key Concepts in IT Budgeting 141 The Importance of Budgets 143 The IT Planning and Budget Process 145 A01_MCKE0260_03_GE_FM.indd 7 26/11/14 9:32 PM
- 13. 8 Contents Corporate Processes 145 IT Processes 147 Assess Actual IT Spending 148 IT Budgeting Practices That Deliver Value 149 Conclusion 150 • References 151 Chapter 10 Risk Management in IT 152 A Holistic View of IT-Based Risk 153 Holistic Risk Management: A Portrait 156 Developing a Risk Management Framework 157 Improving Risk Management Capabilities 160 Conclusion 161 • References 162 Appendix A A Selection of Risk Classification Schemes 163 Chapter 11 Information Management: Stages and Issues 164 Information Management: How Does It Fit? 165 A Framework For IM 167 Stage One: Develop an IM Policy 167 Stage Two: Articulate the Operational Components 167 Stage Three: Establish Information Stewardship 168 Stage Four: Build Information Standards 169 Issues In IM 170 Culture and Behavior 170 Information Risk Management 171 Information Value 172 Privacy 172 Knowledge Management 173 The Knowing–Doing Gap 173 Getting Started in IM 173 Conclusion 175 • References 176 Appendix A Elements of IM Operations 177 Mini Cases Building Shared Services at RR Communications 178 Enterprise Architecture at Nationstate Insurance 182 IT Investment at North American Financial 187 A01_MCKE0260_03_GE_FM.indd 8 26/11/14 9:32 PM
- 14. Contents 9 Section III IT-Enabled Innovation 191 Chapter 12 Technology-Driven Innovation 192 The Need for Innovation: An Historical Perspective 193 The Need for Innovation Now 193 Understanding Innovation 194 The Value of Innovation 196 Innovation Essentials: Motivation, Support, and Direction 197 Challenges for IT leaders 199 Facilitating Innovation 201 Conclusion 202 • References 203 Chapter 13 When Big Data and Social Computing Meet 204 The Social Media/Big Data Opportunity 205 Delivering Business Value with Big Data 207 Innovating with Big Data 211 Pulling in Two Different Directions: The Challenge for IT Managers 212 First Steps for IT Leaders 214 Conclusion 215 • References 216 Chapter 14 Effective Customer Experience 217 Customer Experience and Business value 218 Many Dimensions of Customer Experience 219 The Role of Technology in Customer Experience 221 Customer Experience Essentials for IT 222 First Steps to Improving Customer Experience 225 Conclusion 226 • References 226 Chapter 15 Business Intelligence: An Overview 228 Understanding Business Intelligence 229 The Need for Business Intelligence 230 The Challenge of Business Intelligence 231 The Role of IT in Business Intelligence 233 Improving Business Intelligence 235 Conclusion 238 • References 238 A01_MCKE0260_03_GE_FM.indd 9 26/11/14 9:32 PM
- 15. 10 Contents Chapter 16 Technology-Enabled Collaboration 240 Why Collaborate? 241 Characteristics of Collaboration 244 Components of Successful Collaboration 247 The Role of IT in Collaboration 249 First Steps for Facilitating Effective Collaboration 251 Conclusion 253 • References 254 Mini Cases Innovation at International Foods 256 Consumerization of Technology at IFG 261 CRM at Minitrex 265 Customer Service at Datatronics 268 Section IV IT Portfolio Development and Management 273 Chapter 17 Managing the Application Portfolio 274 The Applications Quagmire 275 The Benefits of a Portfolio Perspective 276 Making APM Happen 278 Capability 1: Strategy and Governance 280 Capability 2: Inventory Management 284 Capability 3: Reporting and Rationalization 285 Key Lessons Learned 286 Conclusion 287 • References 287 Appendix A Application Information 288 Chapter 18 IT Demand Management: Supply Management is Not Enough 292 Understanding IT Demand 293 The Economics of Demand Management 295 Three Tools for Demand management 295 Key Organizational Enablers for Effective Demand Management 296 Strategic Initiative Management 297 Application Portfolio Management 298 Enterprise Architecture 298 Business–IT Partnership 299 Governance and Transparency 301 Conclusion 303 • References 303 A01_MCKE0260_03_GE_FM.indd 10 26/11/14 9:32 PM
- 16. Contents 11 Chapter 19 Technology Roadmap: Benefits, Elements, and Practical Steps 305 What is a Technology Roadmap? 306 The Benefits of a Technology Roadmap 307 External Benefits (Effectiveness) 307 Internal Benefits (Efficiency) 308 Elements of the Technology Roadmap 308 Activity #1: Guiding Principles 309 Activity #2: Assess Current Technology 310 Activity #3: Analyze Gaps 311 Activity #4: Evaluate Technology Landscape 312 Activity #5: Describe Future Technology 313 Activity #6: Outline Migration Strategy 314 Activity #7: Establish Governance 314 Practical Steps for Developing a Technology Roadmap 316 Conclusion 317 • References 317 Appendix A Principles to Guide a Migration Strategy 318 Chapter 20 Emerging Development Practices 319 The Problem with System Development 320 Trends in System Development 321 Obstacles to Improving System Development Productivity 324 Improving System Development Productivity: What we know that Works 326 Next Steps to Improving System Development Productivity 328 Conclusion 330 • References 330 Chapter 21 Information Delivery: Past, Present, and Future 332 Information and IT: Why Now? 333 Delivering Value Through Information 334 Effective Information Delivery 338 New Information Skills 338 New Information Roles 339 New Information Practices 339 A01_MCKE0260_03_GE_FM.indd 11 26/11/14 9:32 PM
- 17. 12 Contents New Information Strategies 340 The Future of Information Delivery 341 Conclusion 343 • References 344 Mini Cases Project Management at MM 346 Working Smarter at Continental Furniture International 350 Managing Technology at Genex Fuels 355 Index 358 A01_MCKE0260_03_GE_FM.indd 12 26/11/14 9:32 PM
- 18. Preface Today, with information technology (IT) driving constant business transformation, overwhelming organizations with information, enabling 24/7 global operations, and undermining traditional business models, the challenge for business leaders is not simply to manage IT, it is to use IT to deliver business value. Whereas until fairly recently, decisions about IT could be safely delegated to technology specialists after a business strategy had been developed, IT is now so closely integrated with business that, as one CIO explained to us, “We can no longer deliver business solutions in our company without using technology so IT and business strategy must constantly interact with each other.” What’s New in This Third Edition? • Six new chapters focusing on current critical issues in IT management, including IT shared services; big data and social computing; business intelligence; manag- ing IT demand; improving the customer experience; and enhancing development productivity. • Two significantly revised chapters: on delivering IT functions through different resourcing options; and innovating with IT. • Two new mini cases based on real companies and real IT management situations: Working Smarter at Continental Furniture and Enterprise Architecture at Nationstate Insurance. • A revised structure based on reader feedback with six chapters and two mini cases from the second edition being moved to the Web site. All too often, in our efforts to prepare future executives to deal effectively with the issues of IT strategy and management, we lead them into a foreign country where they encounter a different language, different culture, and different customs. Acronyms (e.g., SOA, FTP/IP, SDLC, ITIL, ERP), buzzwords (e.g., asymmetric encryption, proxy servers, agile, enterprise service bus), and the widely adopted practice of abstraction (e.g., Is a software monitor a person, place, or thing?) present formidable “barriers to entry” to the technologically uninitiated, but more important, they obscure the impor- tance of teaching students how to make business decisions about a key organizational resource. By taking a critical issues perspective, IT Strategy: Issues and Practices treats IT as a tool to be leveraged to save and/or make money or transform an organization—not as a study by itself. As in the first two editions of this book, this third edition combines the experi- ences and insights of many senior IT managers from leading-edge organizations with thorough academic research to bring important issues in IT management to life and demonstrate how IT strategy is put into action in contemporary businesses. This new edition has been designed around an enhanced set of critical real-world issues in IT management today, such as innovating with IT, working with big data and social media, 13 A01_MCKE0260_03_GE_FM.indd 13 26/11/14 9:32 PM
- 19. 14 Preface enhancing customer experience, and designing for business intelligence and introduces students to the challenges of making IT decisions that will have significant impacts on how businesses function and deliver value to stakeholders. IT Strategy: Issues and Practices focuses on how IT is changing and will continue to change organizations as we now know them. However, rather than learning concepts “free of context,” students are introduced to the complex decisions facing real organi- zations by means of a number of mini cases. These provide an opportunity to apply the models/theories/frameworks presented and help students integrate and assimilate this material. By the end of the book, students will have the confidence and ability to tackle the tough issues regarding IT management and strategy and a clear understand- ing of their importance in delivering business value. Key Features of This Book • A focus on IT management issues as opposed to technology issues • Critical IT issues explored within their organizational contexts • Readily applicable models and frameworks for implementing IT strategies • Mini cases to animate issues and focus classroom discussions on real-world deci- sions, enabling problem-based learning • Proven strategies and best practices from leading-edge organizations • Useful and practical advice and guidelines for delivering value with IT • Extensive teaching notes for all mini cases A Different Approach to Teaching IT Strategy The real world of IT is one of issues—critical issues—such as the following: • How do we know if we are getting value from our IT investment? • How can we innovate with IT? • What specific IT functions should we seek from external providers? • How do we build an IT leadership team that is a trusted partner with the business? • How do we enhance IT capabilities? • What is IT’s role in creating an intelligent business? • How can we best take advantage of new technologies, such as big data and social media, in our business? • How can we manage IT risk? However, the majority of management information systems (MIS) textbooks are orga- nized by system category (e.g., supply chain, customer relationship management, enterprise resource planning), by system component (e.g., hardware, software, networks), by system function (e.g., marketing, financial, human resources), by system type (e.g., transactional, decisional, strategic), or by a combination of these. Unfortunately, such an organization does not promote an understanding of IT management in practice. IT Strategy: Issues and Practices tackles the real-world challenges of IT manage- ment. First, it explores a set of the most important issues facing IT managers today, and second, it provides a series of mini cases that present these critical IT issues within the context of real organizations. By focusing the text as well as the mini cases on today’s critical issues, the book naturally reinforces problem-based learning. A01_MCKE0260_03_GE_FM.indd 14 26/11/14 9:32 PM
- 20. Preface 15 IT Strategy: Issues and Practices includes thirteen mini cases—each based on a real company presented anonymously.1 Mini cases are not simply abbreviated versions of standard, full-length business cases. They differ in two significant ways: 1. A horizontal perspective. Unlike standard cases that develop a single issue within an organizational setting (i.e., a “vertical” slice of organizational life), mini cases take a “horizontal” slice through a number of coexistent issues. Rather than looking for a solution to a specific problem, as in a standard case, students analyzing a mini case must first identify and prioritize the issues embedded within the case. This mim- ics real life in organizations where the challenge lies in “knowing where to start” as opposed to “solving a predefined problem.” 2. Highly relevant information. Mini cases are densely written. Unlike standard cases, which intermix irrelevant information, in a mini case, each sentence exists for a reason and reflects relevant information. As a result, students must analyze each case very carefully so as not to miss critical aspects of the situation. Teaching with mini cases is, thus, very different than teaching with standard cases. With mini cases, students must determine what is really going on within the organiza- tion. What first appears as a straightforward “technology” problem may in fact be a political problem or one of five other “technology” problems. Detective work is, there- fore, required. The problem identification and prioritization skills needed are essential skills for future managers to learn for the simple reason that it is not possible for organi- zations to tackle all of their problems concurrently. Mini cases help teach these skills to students and can balance the problem-solving skills learned in other classes. Best of all, detective work is fun and promotes lively classroom discussion. Toassistinstructors,extensiveteachingnotesareavailableforallminicases.Developed by the authors and based on “tried and true” in-class experience, these notes include case summaries, identify the key issues within each case, present ancillary information about the company/industry represented in the case, and offer guidelines for organizing the class- room discussion. Because of the structure of these mini cases and their embedded issues, it is common for teaching notes to exceed the length of the actual mini case! This book is most appropriate for MIS courses where the goal is to understand how IT delivers organizational value. These courses are frequently labeled “IT Strategy” or “IT Management” and are offered within undergraduate as well as MBA programs. For undergraduate juniors and seniors in business and commerce programs, this is usually the “capstone” MIS course. For MBA students, this course may be the compulsory core course in MIS, or it may be an elective course. Each chapter and mini case in this book has been thoroughly tested in a variety of undergraduate, graduate, and executive programs at Queen’s School of Business.2 1 We are unable to identify these leading-edge companies by agreements established as part of our overall research program (described later). 2 Queen’s School of Business is one of the world’s premier business schools, with a faculty team renowned for its business experience and academic credentials. The School has earned international recognition for its innovative approaches to team-based and experiential learning. In addition to its highly acclaimed MBA programs, Queen’s School of Business is also home to Canada’s most prestigious undergraduate business program and several outstanding graduate programs. As well, the School is one of the world’s largest and most respected providers of executive education. A01_MCKE0260_03_GE_FM.indd 15 26/11/14 9:32 PM
- 21. 16 Preface These materials have proven highly successful within all programs because we adapt how the material is presented according to the level of the students. Whereas under- graduate students “learn” about critical business issues from the book and mini cases for the first time, graduate students are able to “relate” to these same critical issues based on their previous business experience. As a result, graduate students are able to introduce personal experiences into the discussion of these critical IT issues. Organization of This Book One of the advantages of an issues-focused structure is that chapters can be approached in any order because they do not build on one another. Chapter order is immaterial; that is, one does not need to read the first three chapters to understand the fourth. This pro- vides an instructor with maximum flexibility to organize a course as he or she sees fit. Thus, within different courses/programs, the order of topics can be changed to focus on different IT concepts. Furthermore, because each mini case includes multiple issues, they, too, can be used to serve different purposes. For example, the mini case “Building Shared Services at RR Communications” can be used to focus on issues of governance, organizational structure, and/or change management just as easily as shared services. The result is a rich set of instructional materials that lends itself well to a variety of pedagogical appli- cations, particularly problem-based learning, and that clearly illustrates the reality of IT strategy in action. The book is organized into four sections, each emphasizing a key component of developing and delivering effective IT strategy: • Section I: Delivering Value with IT is designed to examine the complex ways that IT and business value are related. Over the past twenty years, researchers and prac- titioners have come to understand that “business value” can mean many different things when applied to IT. Chapter 1 (The IT Value Proposition) explores these con- cepts in depth. Unlike the simplistic value propositions often used when imple- menting IT in organizations, this chapter presents “value” as a multilayered busi- ness construct that must be effectively managed at several levels if technology is to achieve the benefits expected. Chapter 2 (Delivering Business Value through IT Strategy) examines the dynamic interrelationship between business and IT strat- egy and looks at the processes and critical success factors used by organizations to ensure that both are well aligned. Chapter 3 (Making IT Count) discusses new ways of measuring IT’s effectiveness that promote closer business–IT alignment and help drive greater business value. Chapter 4 (Effective Business–IT Relationships) exam- ines the nature of the business–IT relationship and the characteristics of an effec- tive relationship that delivers real value to the enterprise. Chapter 5 (Business–IT Communication) explores the business and interpersonal competencies that IT staff will need in order to do their jobs effectively over the next five to seven years and what companies should be doing to develop them. Finally, Chapter 6 (Effective IT Leadership) tackles the increasing need for improved leadership skills in all IT staff and examines the expectations of the business for strategic and innovative guid- ance from IT. A01_MCKE0260_03_GE_FM.indd 16 26/11/14 9:32 PM
- 22. Preface 17 In the mini cases associated with this section, the concepts of delivering value with IT are explored in a number of different ways. We see business and IT executives at Hefty Hardware grappling with conflicting priorities and per- spectives and how best to work together to achieve the company’s strategy. In “Investing in TUFS,” CIO Martin Drysdale watches as all of the work his IT depart- ment has put into a major new system fails to deliver value. And the “IT Planning at ModMeters” mini case follows CIO Brian Smith’s efforts to create a strategic IT plan that will align with business strategy, keep IT running, and not increase IT’s budget. • Section II: IT Governance explores key concepts in how the IT organization is structured and managed to effectively deliver IT products and services to the orga- nization. Chapter 7 (Effective IT Shared Services) discusses how IT shared services should be selected, organized, managed, and governed to achieve improved organi- zational performance. Chapter 8 (Successful IT Sourcing: Maturity Model, Sourcing Options, and Decision Criteria) examines how organizations are choosing to source and deliver different types of IT functions and presents a framework to guide sourc- ing decisions. Chapter 9 (Budgeting: Planning’s Evil Twin) describes the “evil twin” of IT strategy, discussing how budgeting mechanisms can significantly undermine effective business strategies and suggesting practices for addressing this problem while maintaining traditional fiscal accountability. Chapter 10 (Risk Management in IT) describes how many IT organizations have been given the responsibility of not only managing risk in their own activities (i.e., project development, operations, and delivering business strategy) but also of managing IT-based risk in all company activities (e.g., mobile computing, file sharing, and online access to information and software) and the need for a holistic framework to understand and deal with risk effectively. Chapter 11 (Information Management: Stages and Issues) describes how new organizational needs for more useful and integrated information are driving the development of business-oriented functions within IT that focus specifically on information and knowledge, as opposed to applications and data. The mini cases in this section examine the difficulties of managing com- plex IT issues when they intersect substantially with important business issues. In “Building Shared Services at RR Communications,” we see an IT organiza- tion in transition from a traditional divisional structure and governance model to a more centralized enterprise model, and the long-term challenges experi- enced by CIO Vince Patton in changing both business and IT practices, includ- ing information management and delivery, to support this new approach. In “Enterprise Architecture at Nationstate Insurance,” CIO Jane Denton endeavors to make IT more flexible and agile, while incorporating new and emerging tech- nologies into its strategy. In “IT Investment at North American Financial,” we show the opportunities and challenges involved in prioritizing and resourcing enterprisewide IT projects and monitoring that anticipated benefits are being achieved. • Section III: IT-Enabled Innovation discusses some of the ways technology is being used to transform organizations. Chapter 12 (Technology-Driven Innovation) examines the nature and importance of innovation with IT and describes a typi- cal innovation life cycle. Chapter 13 (When Big Data and Social Computing Meet) discusses how IT leaders are incorporating big data and social media concepts A01_MCKE0260_03_GE_FM.indd 17 26/11/14 9:32 PM
- 23. 18 Preface and technologies to successfully deliver business value in new ways. Chapter 14 (Effective Customer Experience) explores the IT function’s role in creating and improving an organization’s customer experiences and the role of technology in helping companies to understand and learn from their customers’ experiences. Chapter 15 (Business Intelligence: An Overview) looks at the nature of business intelligence and its relationship to data, information, and knowledge and how IT can be used to build a more intelligent organization. Chapter 16 (Technology- Enabled Collaboration) identifies the principal forms of collaboration used in orga- nizations, the primary business drivers involved in them, how their business value is measured, and the roles of IT and the business in enabling collaboration. The mini cases in this section focus on the key challenges companies face in innovating with IT. “Innovation at International Foods” contrasts the need for pro- cess and control in corporate IT with the strong push to innovate with technology and the difficulties that ensue from the clash of style and culture. “Consumerization of Technology at IFG” looks at issues such as “bring your own device” (BYOD) to the workplace. In “CRM at Minitrex,” we see some of the internal technological and political conflicts that result from a strategic decision to become more customercen- tric. Finally, “Customer Service at Datatronics” explores the importance of present- ing unified, customer-facing IT to customers. • Section IV: IT Portfolio Development and Management looks at how the IT func- tion must transform itself to be able to deliver business value effectively in the future. Chapter 17 (Managing the Application Portfolio) describes the ongoing management process of categorizing, assessing, and rationalizing the IT applica- tion portfolio. Chapter 18 (IT Demand Management: Supply Management is Not Enough) looks at the often neglected issue of demand management (as opposed to supply management), explores the root causes of the demand for IT services, and identifies a number of tools and enablers to facilitate more effective demand management. Chapter 19 (Technology Roadmap: Benefits, Elements, and Practical Steps) examines the challenges IT managers face in implementing new infrastruc- ture, technology standards, and types of technology in their real-world business and technical environments, which is composed of a huge variety of hardware, software, applications, and other technologies, some of which date back more than thirty years. Chapter 20 (Emerging Development Practices) explores how system develop- ment practices are changing and how managers can create an environment to pro- mote improved development productivity. And Chapter 21 (Information Delivery: Past, Present, and Future) examines the fresh challenges IT faces in managing the exponential growth of data and digital assets; privacy and accountability concerns; and new demands for access to information on an anywhere, anytime basis. The mini cases associated with this section describe many of these themes embedded within real organizational contexts. “Project Management at MM” mini case shows how a top-priority, strategic project can take a wrong turn when proj- ect management skills are ineffective. “Working Smarter at Continental Furniture” mini case follows an initiative to improve the company’s analytics so it can reduce its environmental impact. And in the mini case “Managing Technology at Genex Fuels,” we see CIO Nick Devlin trying to implement enterprisewide technology for competitive advantage in an organization that has been limping along with obscure and outdated systems. A01_MCKE0260_03_GE_FM.indd 18 26/11/14 9:32 PM
- 24. Preface 19 Supplementary Materials Online Instructor Resource Center The following supplements are available online to adopting instructors: • PowerPoint Lecture Notes • Image Library (text art) • Extensive Teaching Notes for all Mini cases • Additional chapters including Developing IT Professionalism; IT Sourcing; Master DataManagement;DevelopingITCapabilities;TheIdentityManagementChallenge; Social Computing; Managing Perceptions of IT; IT in the New World of Corporate Governance Reforms; Enhancing Customer Experiences with Technology; Creating Digital Dashboards; and Managing Electronic Communications. • Additional mini cases, including IT Leadership at MaxTrade; Creating a Process-Driven Organization at Ag-Credit; Information Management at Homestyle Hotels; Knowledge Management at Acme Consulting; Desktop Provisioning at CanCredit; and Leveraging IT Vendors at SleepSmart. For detailed descriptions of all of the supplements just listed, please visit www.pearsongloableditions.com/McKeen. CourseSmart eTextbooks Online CourseSmart* is an exciting new choice for students looking to save money. As an alter- native to purchasing the print textbook, students can purchase an electronic version of the same content and save up to 50 percent off the suggested list price of the print text. With a CourseSmart etextbook, students can search the text, make notes online, print out reading assignments that incorporate lecture notes, and bookmark important pas- sages for later review. www.coursesmart.co.uk. * This product may not be available in all markets. For more details, please visit www.coursesmart.co.uk or contact your local Pearson representative. The Genesis of This Book Since 1990 we have been meeting quarterly with a group of senior IT managers from a number of leading-edge organizations (e.g., Eli Lilly, BMO, Honda, HP, CIBC, IBM, Sears, Bell Canada, MacDonalds, and Sun Life) to identify and discuss critical IT manage- ment issues. This focus group represents a wide variety of industry sectors (e.g., retail, manufacturing, pharmaceutical, banking, telecommunications, insurance, media, food processing, government, and automotive). Originally, it was established to meet the com- panies’ needs for well-balanced, thoughtful, yet practical information on emerging IT management topics, about which little or no research was available. However, we soon recognized the value of this premise for our own research in the rapidly evolving field of IT management. As a result, it quickly became a full-scale research program in which we were able to use the focus group as an “early warning system” to document new IT management issues, develop case studies around them, and explore more collaborative approaches to identifying trends, challenges, and effective practices in each topic area.3 3 This now includes best practice case studies, field research in organizations, multidisciplinary qualitative and quantitative research projects, and participation in numerous CIO research consortia. A01_MCKE0260_03_GE_FM.indd 19 26/11/14 9:32 PM
- 25. 20 Preface As we shared our materials with our business students, we realized that this issues-based approach resonated strongly with them, and we began to incorporate more of our research into the classroom. This book is the result of our many years’ work with senior IT manag- ers, in organizations, and with students in the classroom. Each issue in this book has been selected collaboratively by the focus group after debate and discussion. As facilitators, our job has been to keep the group’s focus on IT management issues, not technology per se. In preparation for each meeting, focus group members researched the topic within their own organization, often involving a number of members of their senior IT management team as well as subject matter experts in the process. To guide them, we provided a series of questions about the issue, although members are always free to explore it as they see fit. This approach provided both struc- ture for the ensuing discussion and flexibility for those members whose organizations are approaching the issue in a different fashion. The focus group then met in a full-day session, where the members discussed all aspects of the issue. Many also shared corporate documents with the group. We facilitated the discussion, in particular pushing the group to achieve a common understanding of the dimensions of the issue and seeking examples, best practices, and guidelines for deal- ing with the challenges involved. Following each session, we wrote a report based on the discussion, incorporating relevant academic and practitioner materials where these were available. (Because some topics are “bleeding edge,” there is often little traditional IT research available on them.) Each report has three parts: 1. A description of the issue and the challenges it presents for both business and IT managers 2. Models and concepts derived from the literature to position the issue within a con- textual framework 3. Near-term strategies (i.e., those that can be implemented immediately) that have proven successful within organizations for dealing with the specific issue Each chapter in this book focuses on one of these critical IT issues. We have learned over the years that the issues themselves vary little across industries and organizations, even in enterprises with unique IT strategies. However, each organization tackles the same issue somewhat differently. It is this diversity that provides the richness of insight in these chapters. Our collaborative research approach is based on our belief that when dealing with complex and leading-edge issues, “everyone has part of the solution.” Every focus group, therefore, provides us an opportunity to explore a topic from a variety of perspectives and to integrate different experiences (both successful and oth- erwise) so that collectively, a thorough understanding of each issue can be developed and strategies for how it can be managed most successfully can be identified. A01_MCKE0260_03_GE_FM.indd 20 26/11/14 9:32 PM
- 26. About the Authors James D. McKeen is Professor Emeritus at the Queen’s School of Business. He has been working in the IT field for many years as a practitioner, researcher, and consultant. In 2011, he was named the “IT Educator of the Year” by ComputerWorld Canada. Jim has taught at universities in the United Kingdom, France, Germany, and the United States. His research is widely published in a number of leading journals and he is the coau- thor (with Heather Smith) of five books on IT management. Their most recent book—IT Strategy: Issues and Practices (2nd ed.)—was the best-selling business book in Canada (Globe and Mail, April 2012). Heather A. Smith has been named the most-published researcher on IT management issues in two successive studies (2006, 2009). A senior research associate with Queen’s University School of Business, she is the author of five books, the most recent being IT Strategy: Issues and Practices (Pearson Prentice Hall, 2012). She is also a senior research associate with the American Society for Information Management’s Advanced Practices Council. Aformer senior IT manager, she is codirector of the IT Management Forum and the CIO Brief, which facilitate interorganizational learning among senior IT executives. In addition, she consults and collaborates with organizations worldwide. 21 A01_MCKE0260_03_GE_FM.indd 21 26/11/14 9:32 PM
- 27. Acknowledgments The work contained in this book is based on numerous meetings with many senior IT managers. We would like to acknowledge our indebtedness to the following individuals who willingly shared their insights based on their experiences “earned the hard way”: Michael Balenzano, Sergei Beliaev, Matthias Benfey, Nastaran Bisheban, Peter Borden, Eduardo Cadena, Dale Castle, Marc Collins, Diane Cope, Dan Di Salvo, Ken Dschankilic, Michael East, Nada Farah, Mark Gillard, Gary Goldsmith, Ian Graham, Keiko Gutierrez, Maureen Hall, Bruce Harding, Theresa Harrington, Tom Hopson, Heather Hutchison, Jim Irich, Zeeshan Khan, Joanne Lafreniere, Konstantine Liris, Lisa MacKay, Mark O’Gorman, Amin Panjwani, Troy Pariag, Brian Patton, Marius Podaru, Helen Restivo, Pat Sadler, A. F. Salam, Ashish Saxena, Joanne Scher, Stewart Scott, Andy Secord, Marie Shafi, Helen Shih, Trudy Sykes, Bruce Thompson, Raju Uppalapati, Len Van Greuning, Laurie Schatzberg, Ted Vincent, and Bond Wetherbe. We would also like to recognize the contribution of Queen’s School of Business to this work. The school has facilitated and supported our vision of better integrat- ing academic research and practice and has helped make our collaborative approach to the study of IT management and strategy an effective model for interorganizational learning. James D. McKeen Kingston, Ontario Heather A. Smith School of Business June 2014 22 A01_MCKE0260_03_GE_FM.indd 22 26/11/14 9:32 PM
- 28. S ec t ion I Delivering Value with IT Chapter 1 The IT Value Proposition Chapter 2 Delivering Business Value through IT Strategy Chapter 3 Making IT Count Chapter 4 Effective Business–IT Relationships Chapter 5 Business–IT Communication Chapter 6 Effective IT Leadership Mini Cases ■ Delivering Business Value with IT at Hefty Hardware ■ Investing in TUFS ■ IT Planning at ModMeters M01_MCKE0260_03_GE_C01.indd 23 12/3/14 8:33 PM
- 29. 24 C h a p t e r 1 The IT Value Proposition1 1 This chapter is based on the authors’ previously published article, Smith, H. A., and J. D. McKeen. “Developing and Delivering on the IT Value Proposition.” Communications of the Association for Information Systems 11 (April 2003): 438–50. Reproduced by permission of the Association for Information Systems. I t’s déjà vu all over again. For at least twenty years, business leaders have been trying to figure out exactly how and where IT can be of value in their organizations. And IT managers have been trying to learn how to deliver this value. When IT was used mainly as a productivity improvement tool in small areas of a business, this was a relatively straightforward process. Value was measured by reduced head counts— usually in clerical areas—and/or the ability to process more transactions per person. However, as systems grew in scope and complexity, unfortunately so did the risks. Very few companies escaped this period without making at least a few disastrous invest- ments in systems that didn’t work or didn’t deliver the bottom-line benefits executives thought they would. Naturally, fingers were pointed at IT. With the advent of the strategic use of IT in business, it became even more difficult to isolate and deliver on the IT value proposition. It was often hard to tell if an invest- ment had paid off. Who could say how many competitors had been deterred or how many customers had been attracted by a particular IT initiative? Many companies can tell horror stories of how they have been left with a substantial investment in new forms of technology with little to show for it. Although over the years there have been many improvements in where and how IT investments are made and good controls have been established to limit time and cost overruns, we are still not able to accurately articulate and deliver on a value proposition for IT when it comes to anything other than simple productivity improvements or cost savings. Problems in delivering IT value can lie with how a value proposition is conceived or in what is done to actually implement an idea—that is, selecting the right project and doing the project right (Cooper et al. 2000; McKeen and Smith 2003; Peslak 2012). In addition, although most firms attempt to calculate the expected payback of an IT invest- ment before making it, few actually follow up to ensure that value has been achieved or to question what needs to be done to make sure that value will be delivered. M01_MCKE0260_03_GE_C01.indd 24 12/3/14 8:33 PM
- 30. Random documents with unrelated content Scribd suggests to you:
- 31. demonstration: which is not limited to the idea of extension, figure, number, and their modes.—Locke, John. An Essay concerning Human Understanding, Bk. 4, chap. 2, sect. 9. 1442. Now I shall remark again what I have already touched upon more than once, that it is a common opinion that only mathematical sciences are capable of a demonstrative certainty; but as the agreement and disagreement which may be known intuitively is not a privilege belonging only to the ideas of numbers and figures, it is perhaps for want of application on our part that mathematics alone have attained to demonstrations.—Leibnitz. New Essay concerning Human Understanding, Bk. 4, chap. 2, sect. 9 [Langley].
- 32. CHAPTER XV MATHEMATICS AND SCIENCE 1501. How comes it about that the knowledge of other sciences, which depend upon this [mathematics], is painfully sought, and that no one puts himself to the trouble of studying this science itself? I should certainly be surprised, if I did not know that everybody regarded it as being very easy, and if I had not long ago observed that the human mind, neglecting what it believes to be easy, is always in haste to run after what is novel and advanced.—Descartes. Rules for the Direction of the Mind; Philosophy of Descartes [Torrey], (New York, 1892), p. 72. 1502. All quantitative determinations are in the hands of mathematics, and it at once follows from this that all speculation which is heedless of mathematics, which does not enter into partnership with it, which does not seek its aid in distinguishing between the manifold modifications that must of necessity arise by a change of quantitative determinations, is either an empty play of thoughts, or at most a fruitless effort. In the field of speculation many things grow which do not start from mathematics nor give it any care, and I am far from asserting that all that thus grow are useless weeds, among them may be many noble plants, but without mathematics none will develop to complete maturity.—Herbart, J. F. Werke (Kehrbach), (Langensalza, 1890), Bd. 5, p. 106.
- 33. 1503. There are few things which we know, which are not capable of being reduc’d to a Mathematical Reasoning, and when they cannot, it’s a sign our knowledge of them is very small and confus’d; and where a mathematical reasoning can be had, it’s as great folly to make use of any other, as to grope for a thing in the dark, when you have a candle standing by you.—Arbuthnot. Quoted in Todhunter’s History of the Theory of Probability (Cambridge and London, 1865), p. 51. 1504. Mathematical Analysis is ... the true rational basis of the whole system of our positive knowledge.—Comte, A. Positive Philosophy [Martineau], Bk. 1, chap. 1. 1505. It is only through Mathematics that we can thoroughly understand what true science is. Here alone we can find in the highest degree simplicity and severity of scientific law, and such abstraction as the human mind can attain. Any scientific education setting forth from any other point, is faulty in its basis.—Comte, A. Positive Philosophy [Martineau], Bk. 1, chap. 1. 1506. In the present state of our knowledge we must regard Mathematics less as a constituent part of natural philosophy than as having been, since the time of Descartes and Newton, the true basis of the whole of natural philosophy; though it is, exactly speaking, both the one and the other. To us it is of less use for the knowledge of which it consists, substantial and valuable as that knowledge is, than as being the most powerful instrument that the human mind can employ in the investigation of the laws of natural phenomena.— Comte, A. Positive Philosophy [Martineau], Introduction, chap. 2.
- 34. 1507. The concept of mathematics is the concept of science in general.—Novalis. Schriften (Berlin, 1901), Teil 2, p. 222. 1508. I contend, that each natural science is real science only in so far as it is mathematical.... It may be that a pure philosophy of nature in general (that is, a philosophy which concerns itself only with the general concepts of nature) is possible without mathematics, but a pure science of nature dealing with definite objects (physics or psychology), is possible only by means of mathematics, and since each natural science contains only as much real science as it contains a priori knowledge, each natural science becomes real science only to the extent that it permits the application of mathematics.—Kant, E. Metaphysische Anfangsgründe der Naturwissenschaft, Vorrede. 1509. The theory most prevalent among teachers is that mathematics affords the best training for the reasoning powers;... The modern, and to my mind true, theory is that mathematics is the abstract form of the natural sciences; and that it is valuable as a training of the reasoning powers, not because it is abstract, but because it is a representation of actual things.—Safford, T. H. Mathematical Teaching etc. (Boston, 1886), p. 9. 1510. It seems to me that no one science can so well serve to co- ordinate and, as it were, bind together all of the sciences as the queen of them all, mathematics.—Davis, E. W. Proceedings Nebraska Academy of Sciences for 1896 (Lincoln, 1897), p. 282.
- 35. 1511. And as for Mixed Mathematics, I may only make this prediction, that there cannot fail to be more kinds of them, as nature grows further disclosed.—Bacon, Francis. Advancement of Learning, Bk. 2; De Augmentis, Bk. 3. 1512. Besides the exercise in keen comprehension and the certain discovery of truth, mathematics has another formative function, that of equipping the mind for the survey of a scientific system.— Grassmann, H. Stücke aus dem Lehrbuche der Arithmetik; Werke (Leipzig, 1904), Bd. 2, p. 298. 1513. Mathematicks may help the naturalists, both to frame hypotheses, and to judge of those that are proposed to them, especially such as relate to mathematical subjects in conjunction with others.—Boyle, Robert. Works (London, 1772), Vol. 3, p. 429. 1514. The more progress physical sciences make, the more they tend to enter the domain of mathematics, which is a kind of centre to which they all converge. We may even judge of the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation.—Quetelet. Quoted in E. Mailly’s Eulogy on Quetelet; Smithsonian Report, 1874, p. 173. 1515. The mathematical formula is the point through which all the light gained by science passes in order to be of use to practice; it is also the point in which all knowledge gained by practice, experiment, and observation must be concentrated before it can be scientifically grasped. The more distant and marked the point, the more
- 36. concentrated will be the light coming from it, the more unmistakable the insight conveyed. All scientific thought, from the simple gravitation formula of Newton, through the more complicated formulae of physics and chemistry, the vaguer so called laws of organic and animated nature, down to the uncertain statements of psychology and the data of our social and historical knowledge, alike partakes of this characteristic, that it is an attempt to gather up the scattered rays of light, the different parts of knowledge, in a focus, from whence it can be again spread out and analyzed, according to the abstract processes of the thinking mind. But only when this can be done with a mathematical precision and accuracy is the image sharp and well-defined, and the deductions clear and unmistakable. As we descend from the mechanical, through the physical, chemical, and biological, to the mental, moral, and social sciences, the process of focalization becomes less and less perfect,—the sharp point, the focus, is replaced by a larger or smaller circle, the contours of the image become less and less distinct, and with the possible light which we gain there is mingled much darkness, the sources of many mistakes and errors. But the tendency of all scientific thought is toward clearer and clearer definition; it lies in the direction of a more and more extended use of mathematical measurements, of mathematical formulae.—Merz, J. T. History of European Thought in the 19th Century (Edinburgh and London, 1904), Vol. 1, p. 333. 1516. From the very outset of his investigations the physicist has to rely constantly on the aid of the mathematician, for even in the simplest cases, the direct results of his measuring operations are entirely without meaning until they have been submitted to more or less of mathematical discussion. And when in this way some interpretation of the experimental results has been arrived at, and it has been proved that two or more physical quantities stand in a definite relation to each other, the mathematician is very often able to infer, from the existence of this relation, that the quantities in
- 37. question also fulfill some other relation, that was previously unsuspected. Thus when Coulomb, combining the functions of experimentalist and mathematician, had discovered the law of the force exerted between two particles of electricity, it became a purely mathematical problem, not requiring any further experiment, to ascertain how electricity is distributed upon a charged conductor and this problem has been solved by mathematicians in several cases.— Foster, G. C. Presidential Address British Association for the Advancement of Science, Section A (1877); Nature, Vol. 16, p. 312-313. 1517. Without consummate mathematical skill, on the part of some investigators at any rate, all the higher physical problems would be sealed to us; and without competent skill on the part of the ordinary student no idea can be formed of the nature and cogency of the evidence on which the solutions rest. Mathematics are not merely a gate through which we may approach if we please, but they are the only mode of approach to large and important districts of thought.— Venn, John. Symbolic Logic (London and New York, 1894), Introduction, p. xix. 1518. Much of the skill of the true mathematical physicist and of the mathematical astronomer consists in the power of adapting methods and results carried out on an exact mathematical basis to obtain approximations sufficient for the purposes of physical measurements. It might perhaps be thought that a scheme of Mathematics on a frankly approximative basis would be sufficient for all the practical purposes of application in Physics, Engineering Science, and Astronomy, and no doubt it would be possible to develop, to some extent at least, a species of Mathematics on these lines. Such a system would, however, involve an intolerable awkwardness and prolixity in the statements of results, especially in
- 38. view of the fact that the degree of approximation necessary for various purposes is very different, and thus that unassigned grades of approximation would have to be provided for. Moreover, the mathematician working on these lines would be cut off from the chief sources of inspiration, the ideals of exactitude and logical rigour, as well as from one of his most indispensable guides to discovery, symmetry, and permanence of mathematical form. The history of the actual movements of mathematical thought through the centuries shows that these ideals are the very life-blood of the science, and warrants the conclusion that a constant striving toward their attainment is an absolutely essential condition of vigorous growth. These ideals have their roots in irresistible impulses and deep-seated needs of the human mind, manifested in its efforts to introduce intelligibility in certain great domains of the world of thought.—Hobson, E. W. Presidential Address British Association for the Advancement of Science, Section A (1910); Nature, Vol. 84, pp. 285-286. 1519. The immense part which those laws [laws of number and extension] take in giving a deductive character to the other departments of physical science, is well known; and is not surprising, when we consider that all causes operate according to mathematical laws. The effect is always dependent upon, or in mathematical language, is a function of, the quantity of the agent; and generally of its position also. We cannot, therefore, reason respecting causation, without introducing considerations of quantity and extension at every step; and if the nature of the phenomena admits of our obtaining numerical data of sufficient accuracy, the laws of quantity become the grand instruments for calculating forward to an effect, or backward to a cause.—Mill, J. S. System of Logic, Bk. 3, chap. 24, sect. 9.
- 39. 1520. The ordinary mathematical treatment of any applied science substitutes exact axioms for the approximate results of experience, and deduces from these axioms the rigid mathematical conclusions. In applying this method it must not be forgotten that the mathematical developments transcending the limits of exactness of the science are of no practical value. It follows that a large portion of abstract mathematics remains without finding any practical application, the amount of mathematics that can be usefully employed in any science being in proportion to the degree of accuracy attained in the science. Thus, while the astronomer can put to use a wide range of mathematical theory, the chemist is only just beginning to apply the first derivative, i.e. the rate of change at which certain processes are going on; for second derivatives he does not seem to have found any use as yet.—Klein, F. Lectures on Mathematics (New York, 1911), p. 47. 1521. The bond of union among the physical sciences is the mathematical spirit and the mathematical method which pervades them.... Our knowledge of nature, as it advances, continuously resolves differences of quality into differences of quantity. All exact reasoning—indeed all reasoning—about quantity is mathematical reasoning; and thus as our knowledge increases, that portion of it which becomes mathematical increases at a still more rapid rate.— Smith, H. J. S. Presidential Address British Association for the Advancement of Science, Section A (1873); Nature, Vol. 8, p. 449. 1522. Another way of convincing ourselves how largely this process [of assimilation of mathematics by physics] has gone on would be to try to conceive the effect of some intellectual catastrophe, supposing such a thing possible, whereby all knowledge of mathematics should be swept away from men’s minds. Would it not be that the departure
- 40. of mathematics would be the destruction of physics? Objective physical phenomena would, indeed, remain as they are now, but physical science would cease to exist. We should no doubt see the same colours on looking into a spectroscope or polariscope, vibrating strings would produce the same sounds, electrical machines would give sparks, and galvanometer needles would be deflected; but all these things would have lost their meaning; they would be but as the dry bones—the disjecta membra—of what is now a living and growing science. To follow this conception further, and to try to image to ourselves in some detail what would be the kind of knowledge of physics which would remain possible, supposing all mathematical ideas to be blotted out, would be extremely interesting, but it would lead us directly into a dim and entangled region where the subjective seems to be always passing itself off for the objective, and where I at least could not attempt to lead the way, gladly as I would follow any one who could show where a firm footing is to be found. But without venturing to do more than to look from a safe distance over this puzzling ground, we may see clearly enough that mathematics is the connective tissue of physics, binding what would else be merely a list of detached observations into an organized body of science.—Foster, G. C. Presidential Address British Association for the Advancement of Science, Section A (1877); Nature, Vol. 16, p. 313. 1523. In Plato’s time mathematics was purely a play of the free intellect; the mathematic-mystical reveries of a Pythagoras foreshadowed a far-reaching significance, but such a significance (except in the case of music) was as yet entirely a matter of fancy; yet even in that time mathematics was the prerequisite to all other studies! But today, when mathematics furnishes the only language by means of which we may formulate the most comprehensive laws of nature, laws which the ancients scarcely dreamed of, when moreover mathematics is the only means by which these laws may be understood,—how few learn today anything of the real essence of
- 41. our mathematics!... In the schools of today mathematics serves only as a disciplinary study, a mental gymnastic; that it includes the highest ideal value for the comprehension of the universe, one dares scarcely to think of in view of our present day instruction.—Lindeman, F. Lehren und Lernen in der Mathematik (München, 1904), p. 14. 1524. All applications of mathematics consist in extending the empirical knowledge which we possess of a limited number or region of accessible phenomena into the region of the unknown and inaccessible; and much of the progress of pure analysis consists in inventing definite conceptions, marked by symbols, of complicated operations; in ascertaining their properties as independent objects of research; and in extending their meaning beyond the limits they were originally invented for,—thus opening out new and larger regions of thought.—Merz, J. T. History of European Thought in the 19th Century (Edinburgh and London, 1903), Vol. 1, p. 698. 1525. All the effects of nature are only mathematical results of a small number of immutable laws.—Laplace. A Philosophical Essay on Probabilities [Truscott and Emory] (New York, 1902), p. 177; Oeuvres, t. 7, p. 139. 1526. What logarithms are to mathematics that mathematics are to the other sciences.—Novalis. Schriften (Berlin, 1901), Teil 2, p. 222. 1527. Any intelligent man may now, by resolutely applying himself for a few years to mathematics, learn more than the great Newton
- 42. knew after half a century of study and meditation.—Macaulay. Milton; Critical and Miscellaneous Essays (New York, 1879), Vol. 1, p. 13. 1528. In questions of science the authority of a thousand is not worth the humble reasoning of a single individual.—Galileo. Quoted in Arago’s Eulogy on Laplace; Smithsonian Report, 1874, p. 164. 1529. Behind the artisan is the chemist, behind the chemist a physicist, behind the physicist a mathematician.—White, W. F. Scrap-book of Elementary Mathematics (Chicago, 1908), p. 217. 1530. The advance in our knowledge of physics is largely due to the application to it of mathematics, and every year it becomes more difficult for an experimenter to make any mark in the subject unless he is also a mathematician.—Ball, W. W. R. History of Mathematics (London, 1901), p. 503. 1531. In very many cases the most obvious and direct experimental method of investigating a given problem is extremely difficult, or for some reason or other untrustworthy. In such cases the mathematician can often point out some other problem more accessible to experimental treatment, the solution of which involves the solution of the former one. For example, if we try to deduce from direct experiments the law according to which one pole of a magnet attracts or repels a pole of another magnet, the observed action is so much complicated with the effects of the mutual induction of the magnets and of the forces due to the second pole of each magnet, that it is next to impossible to obtain results of any great accuracy. Gauss, however, showed how the law which applied
- 43. in the case mentioned can be deduced from the deflections undergone by a small suspended magnetic needle when it is acted upon by a small fixed magnet placed successively in two determinate positions relatively to the needle; and being an experimentalist as well as a mathematician, he showed likewise how these deflections can be measured very easily and with great precision.—Foster, G. C. Presidential Address British Association for the Advancement of Science, Section A (1877); Nature, Vol. 16, p. 313. 1532. Give me to learn each secret cause; Let Number’s, Figure’s, Motion’s laws Reveal’d before me stand; These to great Nature’s scenes apply, And round the globe, and through the sky, Disclose her working hand. —Akenside, M. Hymn to Science. 1533. Now there are several scores, upon which skill in mathematicks may be useful to the experimental philosopher. For there are some general advantages, which mathematicks may bring to the minds of men, to whatever study they apply themselves, and consequently to the student of natural philosophy; namely, that these disciplines are wont to make men accurate, and very attentive to the employment that they are about, keeping their thoughts from wandering, and inuring them to patience in going through with tedious and intricate demonstrations; besides, that they much improve reason, by accustoming the mind to deduce successive consequences, and judge of them without easily acquiescing in anything but demonstration.—Boyle, Robert. Works (London, 1772), Vol. 3, p. 426.
- 44. 1534. It is not easy to anatomize the constitution and the operations of a mind [like Newton’s] which makes such an advance in knowledge. Yet we may observe that there must exist in it, in an eminent degree, the elements which compose the mathematical talent. It must possess distinctness of intuition, tenacity and facility in tracing logical connection, fertility of invention, and a strong tendency to generalization.—Whewell, W. History of the Inductive Sciences (New York, 1894), Vol. 1, p. 416. 1535. The domain of physics is no proper field for mathematical pastimes. The best security would be in giving a geometrical training to physicists, who need not then have recourse to mathematicians, whose tendency is to despise experimental science. By this method will that union between the abstract and the concrete be effected which will perfect the uses of mathematical, while extending the positive value of physical science. Meantime, the use of analysis in physics is clear enough. Without it we should have no precision, and no co-ordination; and what account could we give of our study of heat, weight, light, etc.? We should have merely series of unconnected facts, in which we could foresee nothing but by constant recourse to experiment; whereas, they now have a character of rationality which fits them for purposes of prevision.— Comte, A. Positive Philosophy [Martineau], Bk. 3, chap. 1. 1536. It must ever be remembered that the true positive spirit first came forth from the pure sources of mathematical science; and it is only the mind that has imbibed it there, and which has been face to face with the lucid truths of geometry and mechanics, that can bring into full action its natural positivity, and apply it in bringing the most complex studies into the reality of demonstration. No other discipline can fitly prepare the intellectual organ.—Comte, A.
- 45. Positive Philosophy [Martineau], Bk. 3, chap. 1. 1537. During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true. Even in those sciences which are not yet under the dominion of mathematics, and perhaps never will be, a working copy of the mathematical process has been made. This is not known to the followers of those sciences who are not themselves mathematicians, and who very often exalt their horns against the mathematics in consequence. They might as well be squaring the circle, for any sense they show in this particular.—De Morgan, A. A Budget of Paradoxes (London, 1872), p. 2. 1538. Among the mere talkers so far as mathematics are concerned, are to be ranked three out of four of those who apply mathematics to physics, who, wanting a tool only, are very impatient of everything which is not of direct aid to the actual methods which are in their hands.—De Morgan, A. Graves’ Life of Sir William Rowan Hamilton (New York, 1882-1889), Vol. 3, p. 348. 1539. Something has been said about the use of mathematics in physical science, the mathematics being regarded as a weapon forged by others, and the study of the weapon being completely set aside. I can only say that there is danger of obtaining untrustworthy results in physical science, if only the results of mathematics are used; for the person so using the weapon can remain unacquainted
- 46. with the conditions under which it can be rightly applied.... The results are often correct, sometimes are incorrect; the consequence of the latter class of cases is to throw doubt upon all the applications of such a worker until a result has been otherwise tested. Moreover, such a practice in the use of mathematics leads a worker to a mere repetition in the use of familiar weapons; he is unable to adapt them with any confidence when some new set of conditions arise with a demand for a new method: for want of adequate instruction in the forging of the weapon, he may find himself, sooner or later in the progress of his subject, without any weapon worth having.—Forsyth, A. R. Perry’s Teaching of Mathematics (London, 1902), p. 36. 1540. If in the range of human endeavor after sound knowledge there is one subject that needs to be practical, it surely is Medicine. Yet in the field of Medicine it has been found that branches such as biology and pathology must be studied for themselves and be developed by themselves with the single aim of increasing knowledge; and it is then that they can be best applied to the conduct of living processes. So also in the pursuit of mathematics, the path of practical utility is too narrow and irregular, not always leading far. The witness of history shows that, in the field of natural philosophy, mathematics will furnish the more effective assistance if, in its systematic development, its course can freely pass beyond the ever-shifting domain of use and application.—Forsyth, A. R. Presidential Address British Association for the Advancement of Science, Section A; Nature, Vol. 56 (1897), p. 377. 1541. If the Greeks had not cultivated Conic Sections, Kepler could not have superseded Ptolemy; if the Greeks had cultivated Dynamics, Kepler might have anticipated Newton.—Whewell, W.
- 47. History of the Inductive Science (New York, 1894), Vol. 1, p. 311. 1542. If we may use the great names of Kepler and Newton to signify stages in the progress of human discovery, it is not too much to say that without the treatises of the Greek geometers on the conic sections there could have been no Kepler, without Kepler no Newton, and without Newton no science in the modern sense of the term, or at least no such conception of nature as now lies at the basis of all our science, of nature as subject in the smallest as well as in its greatest phenomena, to exact quantitative relations, and to definite numerical laws.—Smith, H. J. S. Presidential Address British Association for the Advancement of Science, Section A; Nature, Vol. 8 (1873), p. 450. 1543. The silent work of the great Regiomontanus in his chamber at Nuremberg computed the Ephemerides which made possible the discovery of America by Columbus.—Rudio, F. Quoted in Max Simon’s Geschichte der Mathematik im Altertum (Berlin, 1909), Einleitung, p. xi. 1544. The calculation of the eclipses of Jupiter’s satellites, many a man might have been disposed, originally, to regard as a most unprofitable study. But the utility of it to navigation (in the determination of longitudes) is now well known.—Whately, R. Annotations to Bacon’s Essays (Boston, 1783), p. 492. 1545. Who could have imagined, when Galvani observed the twitching of the frog muscles as he brought various metals in contact with them, that eighty years later Europe would be overspun
- 48. with wires which transmit messages from Madrid to St. Petersburg with the rapidity of lightning, by means of the same principle whose first manifestations this anatomist then observed!... He who seeks for immediate practical use in the pursuit of science, may be reasonably sure, that he will seek in vain. Complete knowledge and complete understanding of the action of forces of nature and of the mind, is the only thing that science can aim at. The individual investigator must find his reward in the joy of new discoveries, as new victories of thought over resisting matter, in the esthetic beauty which a well-ordered domain of knowledge affords, where all parts are intellectually related, where one thing evolves from another, and all show the marks of the mind’s supremacy; he must find his reward in the consciousness of having contributed to the growing capital of knowledge on which depends the supremacy of man over the forces hostile to the spirit.—Helmholtz, H. Vorträge und Reden (Braunschweig, 1884), Bd. 1, p. 142. 1546. When the time comes that knowledge will not be sought for its own sake, and men will not press forward simply in a desire of achievement, without hope of gain, to extend the limits of human knowledge and information, then, indeed, will the race enter upon its decadence.—Hughes, C. E. Quoted in D. E. Smith’s Teaching of Geometry (Boston, 1911), p. 9. 1547. [In the Opus Majus of Roger Bacon] there is a chapter, in which it is proved by reason, that all sciences require mathematics. And the arguments which are used to establish this doctrine, show a most just appreciation of the office of mathematics in science. They are such as follows: That other sciences use examples taken from mathematics as the most evident:—That mathematical knowledge is, as it were, innate to us, on which point he refers to the well-known dialogue of Plato, as quoted by Cicero:—That this science, being the
- 49. easiest, offers the best introduction to the more difficult:—That in mathematics, things as known to us are identical with things as known to nature:—That we can here entirely avoid doubt and error, and obtain certainty and truth:—That mathematics is prior to other sciences in nature, because it takes cognizance of quantity, which is apprehended by intuition (intuitu intellectus). “Moreover,” he adds, “there have been found famous men, as Robert, bishop of Lincoln, and Brother Adam Marshman (de Marisco), and many others, who by the power of mathematics have been able to explain the causes of things; as may be seen in the writings of these men, for instance, concerning the Rainbow and Comets, and the generation of heat, and climates, and the celestial bodies”—Whewell, W. History of the Inductive Sciences (New York, 1894), Vol. 1, p. 519. Bacon, Roger: Opus Majus, Part 4, Distinctia Prima, cap. 3. 1548. The analysis which is based upon the conception of function discloses to the astronomer and physicist not merely the formulae for the computation of whatever desired distances, times, velocities, physical constants; it moreover gives him insight into the laws of the processes of motion, teaches him to predict future occurrences from past experiences and supplies him with means to a scientific knowledge of nature, i.e. it enables him to trace back whole groups of various, sometimes extremely heterogeneous, phenomena to a minimum of simple fundamental laws.—Pringsheim, A. Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 13, p. 366. 1549. “As is known, scientific physics dates its existence from the discovery of the differential calculus. Only when it was learned how to follow continuously the course of natural events, attempts, to construct by means of abstract conceptions the connection between
- 50. phenomena, met with success. To do this two things are necessary: First, simple fundamental concepts with which to construct; second, some method by which to deduce, from the simple fundamental laws of the construction which relate to instants of time and points in space, laws for finite intervals and distances, which alone are accessible to observation (can be compared with experience).” [Riemann.] The first of the two problems here indicated by Riemann consists in setting up the differential equation, based upon physical facts and hypotheses. The second is the integration of this differential equation and its application to each separate concrete case, this is the task of mathematics.—Weber, Heinrich. Die partiellen Differentialgleichungen der mathematischen Physik (Braunschweig, 1882), Bd. 1, Vorrede. 1550. Mathematics is the most powerful instrument which we possess for this purpose [to trace into their farthest results those general laws which an inductive philosophy has supplied]: in many sciences a profound knowledge of mathematics is indispensable for a successful investigation. In the most delicate researches into the theories of light, heat, and sound it is the only instrument; they have properties which no other language can express; and their argumentative processes are beyond the reach of other symbols.— Price, B. Treatise on Infinitesimal Calculus (Oxford, 1858), Vol. 3, p. 5. 1551. Notwithstanding the eminent difficulties of the mathematical theory of sonorous vibrations, we owe to it such progress as has yet been made in acoustics. The formation of the differential equations proper to the phenomena is, independent of their integration, a very important acquisition, on account of the approximations which mathematical analysis allows between questions, otherwise
- 51. heterogeneous, which lead to similar equations. This fundamental property, whose value we have so often to recognize, applies remarkably in the present case; and especially since the creation of mathematical thermology, whose principal equations are strongly analogous to those of vibratory motion.—This means of investigation is all the more valuable on account of the difficulties in the way of direct inquiry into the phenomena of sound. We may decide the necessity of the atmospheric medium for the transmission of sonorous vibrations; and we may conceive of the possibility of determining by experiment the duration of the propagation, in the air, and then through other media; but the general laws of the vibrations of sonorous bodies escape immediate observation. We should know almost nothing of the whole case if the mathematical theory did not come in to connect the different phenomena of sound, enabling us to substitute for direct observation an equivalent examination of more favorable cases subjected to the same law. For instance, when the analysis of the problem of vibrating chords has shown us that, other things being equal, the number of oscillations is in inverse proportion to the length of the chord, we see that the most rapid vibrations of a very short chord may be counted, since the law enables us to direct our attention to very slow vibrations. The same substitution is at our command in many cases in which it is less direct.—Comte, A. Positive Philosophy [Martineau], Bk. 3, chap. 4. 1552. Problems relative to the uniform propagation, or to the varied movements of heat in the interior of solids, are reduced ... to problems of pure analysis, and the progress of this part of physics will depend in consequence upon the advance which may be made in the art of analysis. The differential equations ... contain the chief results of the theory; they express, in the most general and concise manner, the necessary relations of numerical analysis to a very extensive class of phenomena; and they connect forever with
- 52. mathematical science one of the most important branches of natural philosophy.—Fourier, J. Theory of Heat [Freeman], (Cambridge, 1878), Chap. 3, p. 131. 1553. The effects of heat are subject to constant laws which cannot be discovered without the aid of mathematical analysis. The object of the theory is to demonstrate these laws; it reduces all physical researches on the propagation of heat, to problems of the integral calculus, whose elements are given by experiment. No subject has more extensive relations with the progress of industry and the natural sciences; for the action of heat is always present, it influences the processes of the arts, and occurs in all the phenomena of the universe.—Fourier, J. Theory of Heat [Freeman], (Cambridge, 1878), Chap. 1, p. 12. 1554. Dealing with any and every amount of static electricity, the mathematical mind has balanced and adjusted them with wonderful advantage, and has foretold results which the experimentalist can do no more than verify.... So in respect of the force of gravitation, it has calculated the results of the power in such a wonderful manner as to trace the known planets through their courses and perturbations, and in so doing has discovered a planet before unknown.—Faraday. Some Thoughts on the Conservation of Force. 1555. Certain branches of natural philosophy (such as physical astronomy and optics), ... are, in a great measure, inaccessible to those who have not received a regular mathematical education....— Stewart, Dugald. Philosophy of the Human Mind, Part 3, chap. 1, sect. 3.
- 53. 1556. So intimate is the union between mathematics and physics that probably by far the larger part of the accessions to our mathematical knowledge have been obtained by the efforts of mathematicians to solve the problems set to them by experiment, and to create “for each successive class of phenomena, a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature.” Sometimes, indeed, the mathematician has been before the physicist, and it has happened that when some great and new question has occurred to the experimentalist or the observer, he has found in the armoury of the mathematician the weapons which he has needed ready made to his hand. But, much oftener, the questions proposed by the physicist have transcended the utmost powers of the mathematics of the time, and a fresh mathematical creation has been needed to supply the logical instrument requisite to interpret the new enigma.—Smith, H. J. S. Presidential Address British Association for the Advancement of Science, Section A; Nature, Vol. 8 (1873), p. 450. 1557. Of all the great subjects which belong to the province of his section, take that which at first sight is the least within the domain of mathematics—I mean meteorology. Yet the part which mathematics plays in meteorology increases every year, and seems destined to increase. Not only is the theory of the simplest instruments essentially mathematical, but the discussions of the observations—upon which, be it remembered, depend the hopes which are already entertained with increasing confidence, of reducing the most variable and complex of all known phenomena to exact laws—is a problem which not only belongs wholly to mathematics, but which taxes to the utmost the resources of the mathematics which we now possess.—Smith, H. J. S. Presidential Address British Association for the Advancement of Science, Section A; Nature, Vol. 8 (1873), p. 449.
- 54. 1558. You know that if you make a dot on a piece of paper, and then hold a piece of Iceland spar over it, you will see not one dot but two. A mineralogist, by measuring the angles of a crystal, can tell you whether or no it possesses this property without looking through it. He requires no scientific thought to do that. But Sir William Roman Hamilton ... knowing these facts and also the explanation of them which Fresnel had given, thought about the subject, and he predicted that by looking through certain crystals in a particular direction we should see not two dots but a continuous circle. Mr. Lloyd made the experiment, and saw the circle, a result which had never been even suspected. This has always been considered one of the most signal instances of scientific thought in the domain of physics.—Clifford, W. K. Lectures and Essays (New York, 1901), Vol. 1, p. 144. 1559. The discovery of this planet [Neptune] is justly reckoned as the greatest triumph of mathematical astronomy. Uranus failed to move precisely in the path which the computers predicted for it, and was misguided by some unknown influence to an extent which a keen eye might almost see without telescopic aid.... These minute discrepancies constituted the data which were found sufficient for calculating the position of a hitherto unknown planet, and bringing it to light. Leverrier wrote to Galle, in substance: “Direct your telescope to a point on the ecliptic in the constellation of Aquarius, in longitude 326°, and you will find within a degree of that place a new planet, looking like a star of about the ninth magnitude, and having a perceptible disc.” The planet was found at Berlin on the night of Sept. 26, 1846, in exact accordance with this prediction, within half an hour after the astronomers began looking for it, and only about 52′ distant from the precise point that Leverrier had indicated.—Young, C. A. General Astronomy (Boston, 1891), Art. 653.
- 55. 1560. I am convinced that the future progress of chemistry as an exact science depends very much indeed upon the alliance with mathematics.—Frankland, A. American Journal of Mathematics, Vol. 1, p. 349. 1561. It is almost impossible to follow the later developments of physical or general chemistry without a working knowledge of higher mathematics.—Mellor, J. W. Higher Mathematics (New York, 1902), Preface. 1562. ... Mount where science guides; Go measure earth, weigh air, and state the tides; Instruct the planets in what orb to run, Correct old time, and regulate the sun. —Thomson, W. On the Figure of the Earth, Title page. 1563. Admission to its sanctuary [referring to astronomy] and to the privileges and feelings of a votary, is only to be gained by one means,—sound and sufficient knowledge of mathematics, the great instrument of all exact inquiry, without which no man can ever make such advances in this or any other of the higher departments of science as can entitle him to form an independent opinion on any subject of discussion within their range.—Herschel, J. Outlines of Astronomy, Introduction, sect. 7. 1564. The long series of connected truths which compose the science of astronomy, have been evolved from the appearances and observations by calculation, and a process of reasoning entirely
- 56. geometrical. It was not without reason that Plato called geometry and arithmetic the wings of astronomy; for it is only by means of these two sciences that we can give a rational account of any of the appearances, or connect any fact with theory, or even render a single observation available to the most common astronomical purpose. It is by geometry that we are enabled to reason our way up through the apparent motions to the real orbits of the planets, and to assign their positions, magnitudes and eccentricities. And it is by application of geometry—a sublime geometry, indeed, invented for the purpose—to the general laws of mechanics, that we demonstrate the law of gravitation, trace it through its remotest effects on the different planets, and, comparing these effects with what we observe, determine the densities and weights of the minutest bodies belonging to the system. The whole science of astronomy is in fact a tissue of geometrical reasoning, applied to the data of observation; and it is from this circumstance that it derives its peculiar character of precision and certainty. To disconnect it from geometry, therefore, and to substitute familiar illustrations and vague description for close and logical reasoning, is to deprive it of its principal advantages, and to reduce it to the condition of an ordinary province of natural history. Edinburgh Review, Vol. 58 (1833-1834), p. 168. 1565. But geometry is not only the instrument of astronomical investigation, and the bond by which the truths are enchained together,—it is also the instrument of explanation, affording, by the peculiar brevity and perspicuity of its technical processes, not only aid to the learner, but also such facilities to the teacher as he will find it very difficult to supply, if he voluntarily undertakes to forego its assistance. Few undertakings, indeed, are attended with greater difficulty than that of attempting to exhibit the connecting links of a chain of mathematical reasoning, when we lay aside the technical symbols and notation which relieve the memory, and speak at once to the eyes and the understanding:....
- 57. Edinburgh Review, Vol. 58 (1833-1834), p. 169. 1566. With an ordinary acquaintance of trigonometry, and the simplest elements of algebra, one may take up any well-written treatise on plane astronomy, and work his way through it, from beginning to end, with perfect ease; and he will acquire, in the course of his progress, from the mere examples put before him, an infinitely more correct and precise idea of astronomical methods and theories, than he could obtain in a lifetime from the most eloquent general descriptions that ever were written. At the same time he will be strengthening himself for farther advances, and accustoming his mind to habits of close comparison and rigid demonstration, which are of infinitely more importance than the acquisition of stores of undigested facts. Edinburgh Review, Vol. 58 (1833-1834), p. 170. 1567. While the telescope serves as a means of penetrating space, and of bringing its remotest regions nearer us, mathematics, by inductive reasoning, have led us onwards to the remotest regions of heaven, and brought a portion of them within the range of our possibilities; nay, in our own times—so propitious to the extension of knowledge—the application of all the elements yielded by the present conditions of astronomy has even revealed to the intellectual eyes a heavenly body, and assigned to it its place, orbit, mass, before a single telescope has been directed towards it.—Humboldt, A. Cosmos [Otte], Vol. 2, part 2, sect. 3. 1568. Mighty are numbers, joined with art resistless.—Euripides. Hecuba, Line 884.
- 58. 1569. No single instrument of youthful education has such mighty power, both as regards domestic economy and politics, and in the arts, as the study of arithmetic. Above all, arithmetic stirs up him who is by nature sleepy and dull, and makes him quick to learn, retentive, shrewd, and aided by art divine he makes progress quite beyond his natural powers.—Plato. Laws [Jowett,] Bk. 5, p. 747. 1570. For all the higher arts of construction some acquaintance with mathematics is indispensable. The village carpenter, who, lacking rational instruction, lays out his work by empirical rules learned in his apprenticeship, equally with the builder of a Britannia Bridge, makes hourly reference to the laws of quantitative relations. The surveyor on whose survey the land is purchased; the architect in designing a mansion to be built on it; the builder in preparing his estimates; his foreman in laying out the foundations; the masons in cutting the stones; and the various artisans who put up the fittings; are all guided by geometrical truths. Railway-making is regulated from beginning to end by mathematics: alike in the preparation of plans and sections; in staking out the lines; in the mensuration of cuttings and embankments; in the designing, estimating, and building of bridges, culverts, viaducts, tunnels, stations. And similarly with the harbors, docks, piers, and various engineering and architectural works that fringe the coasts and overspread the face of the country, as well as the mines that run underneath it. Out of geometry, too, as applied to astronomy, the art of navigation has grown; and so, by this science, has been made possible that enormous foreign commerce which supports a large part of our population, and supplies us with many necessaries and most of our luxuries. And nowadays even the farmer, for the correct laying out of his drains, has recourse to the level—that is, to geometrical principles.—Spencer, Herbert. Education, chap. 1.
- 59. 1571. [Arithmetic] is another of the great master-keys of life. With it the astronomer opens the depths of the heavens; the engineer, the gates of the mountains; the navigator, the pathways of the deep. The skillful arrangement, the rapid handling of figures, is a perfect magician’s wand. The mighty commerce of the United States, foreign and domestic, passes through the books kept by some thousands of diligent and faithful clerks. Eight hundred bookkeepers, in the Bank of England, strike the monetary balance of half the civilized world. Their skill and accuracy in applying the common rules of arithmetic are as important as the enterprise and capital of the merchant, or the industry and courage of the navigator. I look upon a well-kept ledger with something of the pleasure with which I gaze on a picture or a statue. It is a beautiful work of art.—Everett, Edward. Orations and Speeches (Boston, 1870), Vol. 3, p. 47. 1572. [Mathematics] is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to Human Affairs. In which last Respect, we may be said to receive from the Mathematics, the principal Delights of Life, Securities of Health, Increase of Fortune, and Conveniences of Labour: That we dwell elegantly and commodiously, build decent Houses for ourselves, erect stately Temples to God, and leave wonderful Monuments to Posterity: That we are protected by those Rampires from the Incursions of the Enemy; rightly use Arms, skillfully range an Army, and manage War by Art, and not by the Madness of wild Beasts: That we have safe Traffick through the deceitful Billows, pass in a direct Road through the tractless Ways of the Sea, and come to the designed Ports by the uncertain Impulse of the Winds: That we rightly cast up our Accounts, do Business expeditiously, dispose, tabulate, and calculate scattered Ranks of Numbers, and easily compute them, though expressive of huge Heaps of Sand, nay immense Hills of Atoms: That we make pacifick Separations of the Bounds of Lands, examine the Moments of Weights in an equal Balance, and distribute every one his own by a
- 60. just Measure: That with a light Touch we thrust forward vast Bodies which way we will, and stop a huge Resistance with a very small Force: That we accurately delineate the Face of this Earthly Orb, and subject the Oeconomy of the Universe to our Sight: That we aptly digest the flowing Series of Time, distinguish what is acted by due Intervals, rightly account and discern the various Returns of the Seasons, the stated Periods of Years and Months, the alternate Increments of Days and Nights, the doubtful Limits of Light and Shadow, and the exact Differences of Hours and Minutes: That we derive the subtle Virtue of the Solar Rays to our Uses, infinitely extend the Sphere of Sight, enlarge the near Appearances of Things, bring to Hand Things remote, discover Things hidden, search Nature out of her Concealments, and unfold her dark Mysteries: That we delight our Eyes with beautiful Images, cunningly imitate the Devices and portray the Works of Nature; imitate did I say? nay excel, while we form to ourselves Things not in being, exhibit Things absent, and represent Things past: That we recreate our Minds and delight our Ears with melodious Sounds, attemperate the inconstant Undulations of the Air to musical Tunes, add a pleasant Voice to a sapless Log and draw a sweet Eloquence from a rigid Metal; celebrate our Maker with an harmonious Praise, and not unaptly imitate the blessed Choirs of Heaven: That we approach and examine the inaccessible Seats of the Clouds, the distant Tracts of Land, unfrequented Paths of the Sea; lofty Tops of the Mountains, low Bottoms of the Valleys, and deep Gulphs of the Ocean: That in Heart we advance to the Saints themselves above, yea draw them to us, scale the etherial Towers, freely range through the celestial Fields, measure the Magnitudes, and determine the Interstices of the Stars, prescribe inviolable Laws to the Heavens themselves, and confine the wandering Circuits of the Stars within fixed Bounds: Lastly, that we comprehend the vast Fabrick of the Universe, admire and contemplate the wonderful Beauty of the Divine Workmanship, and to learn the incredible Force and Sagacity of our own Minds, by certain Experiments, and to acknowledge the Blessings of Heaven with pious Affection.—Barrow, Isaac.
- 61. Mathematical Lectures (London, 1734), pp. 27-30. 1573. Analytical and graphical treatment of statistics is employed by the economist, the philanthropist, the business expert, the actuary, and even the physician, with the most surprisingly valuable results; while symbolic language involving mathematical methods has become a part of wellnigh every large business. The handling of pig- iron does not seem to offer any opportunity for mathematical application. Yet graphical and analytical treatment of the data from long-continued experiments with this material at Bethlehem, Pennsylvania, resulted in the discovery of the law that fatigue varied in proportion to a certain relation between the load and the periods of rest. Practical application of this law increased the amount handled by each man from twelve and a half to forty-seven tons per day. Such study would have been impossible without preliminary acquaintance with the simple invariable elements of mathematics.— Karpinsky, L. High School Education (New York, 1912), chap. 6, p. 134. 1574. They [computation and arithmetic] belong then, it seems, to the branches of learning which we are now investigating;—for a military man must necessarily learn them with a view to the marshalling of his troops, and so must a philosopher with the view of understanding real being, after having emerged from the unstable condition of becoming, or else he can never become an apt reasoner. That is the fact he replied. But the guardian of ours happens to be both a military man and a philosopher. Unquestionably so.
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