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Full text of "Greek science and modern science, a comparison & a contrast; inaugural lecture delivered at University college, London, on 12 May, 1920"

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A Comparison & a Contrast 



ON 12 MAY, 1920 




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A Comparison & a Contrast 



ON 12 MAY, 1920 











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ALTHOUGH the philosophical historian has flourished 
in England as perhaps nowhere else in the world, the 
approach to Science through History has yet been much 
neglected in this country. The subject was well opened, 
it is true, by the great Master of Trinity to whom the 
Cambridge scientific school owes so much, and he was 
ably seconded by one of the most brilliant and original 
men who have adorned this College. But it is nigh 
three generations since Whewell and De Morgan 
wrote the masterpieces that have carried their names 
to our day, and no historian of Science has since 
appeared among us to rival Tannery and Schiaparelli 
in philosophic grasp, or Boncompagni, Cantor and 
Duhem in learning. In the kindred department of the 
History of Medicine our record has, if anything, been 
even worse. With the single exception of Francis 
Adams, who belonged to the same generation as 
Whewell and De Morgan, we have had no medical 
historian whose achievements have been of the front 
rank, no one to place by the side of Sprengel, Haeser, and 
Pagel in Germany ; of De Renzi in Italy ; and of Darem- 
berg, Malgaigne, and Nicaise in France. Left without 
academic recognition, the History of Science and the 
History of Medicine have indeed earned in this country 
a reputation for triviality and inconsequence by their 

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frequent alliance either with a superficial type of bio- 
graphy which seems interested in every item of a 
scientific man's life save his mental processes, or with 
an antiquarianism, rightly termed curious, which con- 
cerns itself with the quaint and exceptional rather than 
with the actual development of scientific thought. 

It is appropriate and it is natural that the College 
where Augustus de Morgan spent the whole of his 
active life, and on which he lavished all his great powers 
of heart and head, should be the first institution in 
England to make any serious endeavour to remedy this 
defect. Under the stimulus and on the initiative of my 
friend and colleague Dr. Wolf, a beginning has been 
made towards a systematic course of lectures in the 
History of Science and of Scientific Ideas. May I say, 
in all humility, that I look forward to carrying on some 
fraction of De Morgan's work and to aiding Dr. Wulf 
and his collaborators in placing before students an 
outline sketch of the long and intricate story which 
begins with the confused ideas of the relation of cause 
and effect inherent in the mind of every savage, and 
culminates in the great store of natural knowledge that 
has become the peculiar heritage of our age. 

A new need for the historical treatment of this 
material has arisen. We must frankly recognize that 
the whole scheme of ''education is undergoing rapid 
transformation. We need not discuss these changes, 
but it is sufficiently obvious that the staple education of 
the near future will be increasingly vocational. It seems 
certain that the discipline of Science must largely replace 
the training in the older Humanities. It is a function 
of education, perhaps its main function, to provide each 
generation with a working theory of how it came to be 
what it is. Such a Working theory was, in fact, success- 


fully provided by the old Humanities from the period 
of the Revival of Learning until a generation or two 
ago. The basic doctrine of these older Humanities was 
that outside the domain of religion all we have and all we 
are come to us from the civilizations of Greece and Rome. 
But it is a theory of life which has become untenable in 
the form held by our grandfathers; the revelations 
of archaeology, the discoveries of anthropology and 
recent developments of psychology are all against it. 
The Classics, indeed, still are and always will be pursued 
with ardour and admiration, yet they can never be 
regarded in quite the old way. These literatures are now 
studied, and can only be studied, scientifically and analyti- 
cally as part of our heritage from the past ; they are for 
us the best explored and best known, the sanest and 
most complete, the most worth}'- and in many ways the 
most lovable type, that antiquity has to offer. But they 
can no longer take the place of antiquity itself, still less 
do/ttiey cover the wide range of human aspiration. 
!/ The Classics in the old sense as the staple of education 
were thus perhaps inevitably doomed. But Science, as 
such I use the word for the moment in its restricted 
meaning though it may displace the Humanities, cannot 
replace them, for it cannot provide juts with jny clear 
record of how we have developed mentally. For this we 
must turn to History, but History not in the narrow 
sense in which that word has so often been used as 
equivalent to Political History, nor even Sociological 
History. It is the history of mankind as a whole that 
we need, the history of civilization, the history of man's 
thoughts, of man's knowledge, of man's self. 

For those whose education is mainly grounded in 
Science, and especially for those who are to follow 
Science as a career, the History of Science is thus in 



itself surely an appropriate study. But there is, I think, 
another and more immediately practical ground on 
which we may plead for the introduction of History into 
the scientific curriculum. We are well accustomed to 
recognize that the store of acquired scientific knowledge 
is a general treasury from which all men draw, by which 
alone it has been possible for our material state to rise 
above that of the savage. Yet we seldom remind our- 
selves that the guardianship of this treasury, the heri- 
tage of all men, has always been in the hands of a very 
small band, and this has been so in all its wanderings. 
From the lands of the ancient East it passed to Greece, 
then having dwelt awhile among the Saracens it came to 
Italy, and it has at last reached the West. In all these 
countries and at all these periods the organic apparatus 
by which new knowledge has been created has been the 
work of a mere handful. 

Surely the contemplation of the conditions under 
which these men worked and lived, the examination of 
their training and mental history, of their environment and 
manner of development, must be of value even in the 
practical everyday sense to those who would follow in 
their footsteps. And the other skie of the picture is 
also not without its application. The study of those 
social and economic and philosophical conditions that 
fail to produce effective scientific fruit, or that yield 
only bizarre and deformed products, has also its lesson. 
Some idea of the Science of these retrograde periods 
must also be included in any course on the History 
of Science, and should form an integral part of any 
scientific education worthy of the name. The scientific 
student would thus be grounded in the elements of 
what we may call the Embryology, the Physiology and 
the Pathology of his special study. 


But there is yet another aspect of the History of 
Science. Our scientific system of its nature claims an 
independence of all race, nationality, or creed. It is of 
all studies the most truly international. The scientific 
man may, better than most", claim with St. Paul that 
he is a citizen of no mean city, that he is the true 
citizen of the world. Nevertheless, in all countries and 
at all periods there has been a certain local and temporal 
stamp in the Science that has been produced. These 
differences, however, concern the processes and methods 
of Science rather than its results or aims. Now among 
the processes and methods of Modern Science there are, 
as it seems to me, certain new factors of an order that 
the world has not before seen ; and though he must be 
sanguine indeed who believes that, of our nature and 
because we are who we are, the guardianship of the 
scientific treasury will always remain with us, yet these 
new factors give us some hope of a permanence in our 
scientific results of a character never before attained. 
It is the facts on which the hope of such permanence 
may be based that I propose to discuss to-day. 

To bring these points in our scientific system into 
adequate relief we need some basis of comparison. 
I propose to use for this purpose the best defined scien- 
tific system of antiquity that is presented to the historian's 
vipw, I mean the scientific system of the Greeks. 

Greek Science may be said to take its origin among 
the Ionian colonies in the seventh century B.C. Whence 
did it derive ? We may probably distinguish three roots : 
W the Mesopotamian. (2) the Egyptian, and (3) the 
Minoan ; and our knowledge of these three sources is in 
the order named. From Mesopotamia the Ionian Greek 
derived his basic mathematical conceptions, together 
with much of his astronomical and cosmological system. 

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Above all, he inherited from the valley of the Euphrates 
a whole mass of effective observations upon which, in 
the first instance, his scientific system was built. From 
Egypt he inherited chiefly mechanical devices ; some 
knowledge of drugs and certain elements in his method 
of reckoning time. Nor can we, despite the absence of 
direct evidence, afford to neglect the uniformity with 
which Greek tradition attributes the special development 
of geometry to the Egyptians. The Minoan inheritance, 
in the absence of a key to the script, is an entirely un- 
certain quantity, but it is very tempting to connect the 
serpent so frequently present in Minoan relics with the 
well-known chthonic and Aesculapian symbol. Even 
the very earliest Greek medical writings, some of which 
can be referred back to the seventh century B.C., pre- 
suppose long generations of research and of the careful 
record of observations. Now what we know of the 
Greeks of this period and of their state of civilization 
does not yield a picture of conditions under which such 
observations could easily be made and recorded. It 
seems more likely that this element also was an inheri- 
tance, and since we cannot suppose that any system 
of scientific medicine was derived from such neigh- 
bours of the Greeks as the Babylonians or Egyptians, 
we are thrown back on the Minoan civilization as a 

/ Whatever its sources may have been, however, Greek 
Science began its course along with or rather as an 
essential part of Greek philosophy in the Ionian cities 
of Asia Minor in the seventh century B.C. In the great 
social systems of the East there had long been accumu- 
lating great masses of observation, and upon them rough 
generalizations had been erected. These generalizations 
on which the Greeks so largely drew, appear to have 


been an evolutionary product of what may be called the 
v/social consciousness rather than the definite fruit of 
individual minds. From all the civilizations of the 
ancient East, save from Greece alone, scarcely the name 
of a discoverer or an inventor has come down to us. . Jt 
is characteristic Q.Lthi&. pre-Greek maimaHhatJtJs_a 
social, not an individual product. 

Into this great anonymous Oriental heritage the 
philosophers of the Ionian cities were fortunate enough 
to enter. /They come often under grave suspicion of 
concealing their debt to antiquity, and it is unfortunate 
that the more reliable accounts of the origin of Greek 
Science, such as the History of Mathematics by 
Eudemus, the pupil of Aristotle, are lost to us. But 
once the Greeks had inherited this scientific system 
they impressed it with their own individuality in their 
own self-centred way. Their self-centred character has 
often been remarked, and had indeed been observed by 
the Greeks themselves. Thej^hpjug^ 
as a people ; and the Science that they inherited from 
antiquityTJrom being anonymous became, in their hands, 
eponymous, a character which it has ever since retained. 
Science from their time to ours has always been the 
fruit of individual minds and not a product of the 
social consciousness. 

But there is another point in which the Science of the 
Greeks divides them from the ancient East and unites 
them with us. ^lt is their conviction of Order, their faith 
that Order reigns in Nature. This is their great and 
most vital contribution to scientific thought. Now it is 
very interesting to observe that this trust in the reign 
of law was with them a fcith nr inhiiHnn and in no sense 
the result of observation. The actual basis of observed 
fact on which the Ionian philosophy was founded was 


of the flimsiest. Further, the Greeks, it would be easy 
to show, were on the whole a credulous people. Yet 
their earliest scientific works of which we have sub- 
stantial remains are as free from that scepticism con- 
cerning the essential order of the Universe that we 
call superstition, as full of the idea of natural and 
discoverable law as any modern treatise on Physiology 
or Physics. Greek scientific works often blunder in 
observation or err in inference, they all too frequently 
accept facts at second hand or without verification, and it 
is their besetting sin that they constantly make sweeping 
generalizations on inadequate evidence. Rut their fjrm 
faith in order is that which marks off their view of^the 
Universe from that of all other ancient and from all 
primitive peoples. It is a truly marvellous thing to 
contemplate how sincerely and how fervently, how 
constantly and under what a variety of character the 
Greeks expressed their vision of a wholly reasonable 
world, their Theuna^ which, according to the greatest of 
them all, literally makes man like God. 

Theirs is a view that has justified itself in the cen- 
turies that have since passed. The Greek's knowledge 
of Nature was a very little thing placed by the side of 
the vast hoard that the centuries have brought to us. 
Yet the more we investigate our world and probe its 
mysteries, the further do we trace that order on which 
the Greek based his faith. It is not, of course, that the 
mystery becomes less, but it becomes more circum- 
ferential. As we make our clearing in this infinite forest, 
the space around us widens, the trees recede, and if 
the forest gets no smaller at least there smite less upon 
our ears those wild and uncouth forest notes, those 

enchantments drear 
Where more is meant than meets the ear. 


Pt is this sense of the reign of law together with the 
personal character of scientific investigation that the 
Greeks have handed down to us. It is these things 
that unite us with them and separate our Science from 
that of the ancient East. 

So far we have considered the resemblance of our 
Science to that of the Greeks. We may now turn to 
the elements which separate us from them. In con- 
sidering these elements we must, for the moment, 
expressly exclude mathematical Science which, as we 
shall see, needs to be considered apart. 

When the philosophers of Ionian Greece had at last 
entered on the heritage of antiquity, they began at once 
to engage on that continuous and active process of 
cosmic speculation that became the ancestor of the 
characteristic Greek Philosophy and through it of Greek 
Science. vNo people were ever more free from theo- 
logical and social prejudices, and Greek thought de- 
veloped without any of those trammels from which the 
modern system has but very slowly disengaged itself. 

As time went on knowledge accumulated, and separate 
sciences were gradually differentiated from the philo- 
sophy from which they had sprung. The earliest 
departments to be thus separated were naturally those 
in which the idea of number could be invoked. Mathe- 
matics thus_ became the first science in point of time, 
and by the extent to which mathematical principles can 
be applied we must still often test the stage that any 
science has reached. In the course of centuries the 
sciences became separated more and more from the 
parent stock of philosophy, but it is peculiar to Greek 
scientific thought that it never loses its relationship 
dependence on its parent. Whether we look to the 
earliest traces of the scientific spirit in the seventh 


century B.C., when Pythagoras was working out his 
first formulated conceptions of the relation of number to 
form, or whether we look to the last vitally original* 
works of Greek Science in the second century C.E., when 
Galen was giving to the world those ideas on anatomy 
y'and physiology which were to control medical thought 
for a millennium and a half, from end to end Greek 
Science betrays its relationship to Greek Philosophy. 
It is thus in Jkeeping with the rest of the storyjthat both 
Pythagoras and Galen were in intimate relation with 
philosophical sects. 

No such ancestry can be ascribed to Modern Science, 
and herein we differ from the Greeks. The exponents 
of our modern scientific system have seldom sought to 
follow the Greek metaphysician in his attempts to pass 
the flaming ramparts of the world. Until lately it was 
the custom to regard the period of the Revival of 
Learning as identical with that of the Revival of Science, 
but the facts will not accommodate themselves to this 
view, and it may easily be shown that the roots of the 
scientific revival extend much further back in time than 
the Renaissance. But the history of the childhood of 
Modern Science has not been adequately written, nor 
are the facts yet in our hands for such work. Before it 
is possible much more research into sources is needed. 
It is some reflection on the humanistic education that 
has prevailed for four hundred years that while the 
records of ancient philosophy have been explored from 
end to end, we still await the material for any com- 
prehensive statement of the developmental stages in the 
characteristic mode of thought of our own age. While 
scholars ransack the monasteries of the East or the dust- 
heaps of Egypt for such remains of Greek literature as 
may yet be recovered from the fragments of parchment 


0f papyrus, the works of our first scientific thinker, 
v Roger Bacon, lie here at hand, unedited, forgotten, 

Yet despite this neglect, certain facts concerning the 
beginnings of Modern Science have been ascertained 
and are sure and firm. Firstly, Modern Science did not \ 
arise. offspring of Philosophy, nor until it had 
gained some strength of its own did it form any alliance 
therewith. Formal Philosophy, unknown apart from 
Theology in the Middle Ages, played a subordinate 
part in the Revival of Letters, nor were the earlier 
Renaissance philosophers at all in line with scientific 
discovery. Secondly, the Revival of Science was not-jk 
directly related to_ the revived knowledge of Greek. 
The Greek scholars of the Renaissance showed no 
more sympathy with scientific investigation than was 
exhibited by their colleagues the philosophers, and the 
early frupianistir,.. period was, on the whole, backward 
andjsven retQgrp-^iygj_n its scientific conceptions. 

Greek Science, we have seen, was from its birth in- 

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extncablyjnterwoyen wjthj^hjlosoph y. Modern Science 

^ has in fact passed through its earlier stages of develop- 

( ment without this relationship and in a very different 

1 environment from that of Greek Science. Limited on 

every side, forbidden the field of free speculation, cut 

off from the departments held to be the peculiar domain 

of the mediaeval ecclesiastic, lawyer or statesman, 

Science in its early stages applied itself almost ex- / 

clusively to the solution of so-called practical problems.*' 

The mariner availed himself of the compass without 

holding any theory of terrestrial magnetism. He boldly 

put to sea with charts to aid him that had been prepared 

by mapmakers as innocent as he was himself of the 

Ptolemaic or of any other system of spherical projection. 


Free _speculatJQirwa^as yet an ^impossibility for the age, 
and the rulers of the age were in union agai fist 1C But 
minds closed to argument may be open to evidence. 
7* Prince and Prelate were ready enough to curtail the 
activities of one who held unsettling views on the ideal 
nature of the State or the theoretical form of the World. 
./Yet these potentates were perfectly willing, nay were 
eager, to experiment on their enemies with the newly 
discovered combination of carbon, sulphur, and nitre 
known as gunpowder, or to aid their failing vision by 
the contrivance of a spectacle lens in order to draw up 
an appropriately minatory denunciation of the critics of 
the old order. 

Nothing could be less like the Greek environment. 
Nothing could be more detestable and hampering from 
the point of view of Modern Science. Yet the question 
may be seriously raised whether this mediaeval limitation 
of liberty has not been of some value to Science. That it 
has done much harm, more harm than good, we are all 
of us of course quite satisfied, but the point I want to 
raise with you is that there are in fact certain elements 
in our Science which we do, in part at least, owe to this 

The trouble about Greek Science excepting always 

1 its mathematical work is the intolerable amount of 

.A reckless speculation of a philosophical or semi-philo- 

( sophical character that it contains, or rather that contains 

j it. The Greek was always seeking to introduce general 

1 laws rather than actual instances, and the greatest of the 

I schoolmen, ^Albertus, Magmis r taking his parable from 

] them and becoming more Greek than the Greeks, 

\ gravely assures us that scientia concerns herself only 

^with universals, not particulars. Science, as we know 

it to-day, could never flourish under such a theory. 


The scientia of Albertus was in fact not the Science that 
we know but the Queen of Sciences, Theology, whose 
aim and end was foreknown and whose advocates had 
only to busy themselves with the formal proof and 
demonstration thereof. But the mediaeval limitation of 

the region of speculation, which has extended for some 
purposes right into our own time, by keeping the man 
of Science to his own task and deflecting him from 
Philosophy has perhaps had its share in building up an 
effective apparatus for research. 

Growing out of this and on the bad side, however, 
has been the corresponding tendency to scientific 

Specialization, by which workers in one department lose 
touch with workers in another. It is, I believe, this 
tendency to lose contact with each other and with 

^general ideas, and not any innate and essential wicked- 
*0 ness in non-scientific humanity, that has prevented 
Science from obtaining her rightful share in the govern- 
ment of the State and the education of youth. I do 
not here refer to what may be called natural specializa- 
tion, the specialization inherent in the human mind, 
which does in fact turn men toward mathematical methods 
or biological observation or physical experimentation. 

\ Specialization of this kind was as pronounced with 

\ the Greeks as it is with us. It was and is necessary 

/ a sign of health and growth. But with us there is another 

type of specialism derived, as it seems to me, from 

the mediaeval divorce of Philosophy from Experience 

which has been fostered by those institutions, the 

Universities, that took their characteristic form in the 

Middle Ages. This specialism is based not on the type 

of knowledge, nor even on the means of acquiring it, but 

rather on the area of knowledge to be studied. 

As education is becoming more largely scientific, both 



these restraints will perhaps be removed. Scientific 
education will ally itself with Philosophy and take 
interest in wider generalization.^ Further, as Science 
becomes the basis of education, the Science taught will 
itself need to be more general in character, and will of 
its nature link together the specialists in the various 
departments. In the return of Science to its old alle- 
giance to Philosophy, and in the greater generalization 
of Science teaching we are likely to retrace our steps 
toward the Greeks. Let us hope that it will not be 
to enter again on the path of fruitless and baseless 
speculation which proved their bane. 

But there is another characteristic of Ancient Science 
on which we may profitably dwell. If we examine any 
Greek work of Science, other than mathematical, we 
<>shall perceive certain very striking differences in 
f ) technical treatment as compared with a modern work. 
These differences have often been obscured by the 
panegyrics of those who are more interested in demon- 
strating the brilliance of the Greek results than in 
analysing the Greek method. Yet many have felt it 
difficult to understand, why, with all their brilliance, 
the Greeks did not carry their physical investigations 
further than they did. These difficulties are in part at 
least explained when we examine closely the Greek 
method of recording results. 

Now, omitting always the mathematical works, Greek 
scientific treatises may be divided into two classes which 
show a perpetual tendency to overlap. First there are 
works like Aristotle's De Generatione et Corruptione or 
his Meteorica which seek to set out a general theory of 
the Universe. These are not profoundly based on 
observation and are mainly made up of ratiocination. 
If written to-day they would be placed by a modern 


librarian under some such heading as ' Philosophy 
\ of Science ' or ' Scientific Theory ' rather than in the 
\ class of Science proper. These works serve to empha- 
( size once again the close relation of Greek Science 
with Philosophy and to demonstrate the tempera- 
I mental distaste of the Greek mind for the separation of tf 
\a part of the Universe to be considered in and by 

But there is a second group of Greek scientific writ- 
ings, consisting mainly of biological works, which exhibit 
another aspect. This group is best illustrated by such 
works as Aristotle's History of Animals or his Genera- 
tion of Animals. These works contain a host of valuable 
observations that is still not exhausted. From time to 
time recent observations made by naturalists are found 
on due investigation to have been anticipated by the 
Greek philosopher. 

But why should such constant re-investigation be 
necessary? Why cannot we take one of these great 
biological works of Aristotle as a whole and either verify/' 
or reject his conclusions ? Why should these justifica- 
tions of his powers as a naturalist turn up only from 
time to time? Many competent scholars and men of 
Science have examined and commented on the Aristo- 
telian writings. Why have none of them thoroughly 
re- investigated the field of Aristotle's Biology once and 
for all, and then drawn up for us a clear statement of 
where he can and where he cannot be safely trusted ? 

The^.a&swer~to these qupsti n n g li**s in the nature of 
the Greek scientific method, and that answer contains, 
to my mind, the second main distinction between Ancient 
Science and Modern Science and the ultimate explana- 
tion of the failure and bankruptcy of the ancient system. 

It is sometimes said that Greek Science failed because 


it was without instrumental aids and thus could not reach 
the degree of precision attained by Modern Science. 
>But this answer does but beg the question and gives 
* a. very partial view of the difference between the 
two systems. The whole question is why had they no 
instruments of precision ? Instruments of precision, like 
the observations made with their aid, are themselves 
a product of the scientific method, and the point in 
discussion is why that scientific method failed in one 
case and succeeded in the other. We shall, therefore, 
perhaps get a clearer answer if we apply the scientific 
method itself to the subject of our discussion and turn 
from discourse concerning the nature and history of 
Ancient and of Modern Science to actual observations 
upon the systems. Let us therefore consider examples 
of the two methods concretely. 

Now recent Science has developed a characteristic 
mode of expression in the so-called Journal, a periodi- 
cal issue of memoirs on special and very narrow 
problems. Such articles or memoirs have a character- 
istic and almost constant structure which we may briefly 
examine : The author of the memoir having stated his 
problem reviews the efforts made by others to solve it. 
He points out their errors or he decides to accept their 
work and to base his own upon it. Perhaps he distrusts 
their experimentsor would like to reinterpret their results. 
Having surveyed their labours he proceeds to detail his 
own experiments and observations. Finally, he gives 
us his deductions from these. 

But he is not able to tell us of all his experiments 
and observations. If he did, scientific literature would 
be even more bulky than it already is and Science would 
quickly perish, suffocated under the dead weight of its 
own verbosity. Our author, in fact, omits a great many 


of his mental processes. ^vHe tells us nothing of how 
he embarked on many different lines of work and 
abandoned them as unprofitable or too difficult. He 
tells us nothing of the months or years spent in merely 
repeating the experience of others. He says not a word 
of how he acquired and improved his experimental skill 
and technical experience. He tells merely of the final 
line of work that has yielded him results. But he does 
not tell us all even of that. When he had after many 
trials at last discerned an apparently profitable and 
feasible direction for his investigations, he reached after 
a time those conclusions which his final line of work 
has verified and rendered more exact. It is this final 
process of verification that he mainly describes in his 
article, and it is the details of this that occupy the bulk, 
perhaps nineteen-twentieths or more, of all that he has 
to say. Then having described these verificatory ex- 
periments, he summarizes his conclusions in a short 
paragraph of a few lines. 

Now, how do the scientific works of antiquity compare 
with_material such as this? The corpus of ancient 
science is of course less in quantity and often frag- 
mentary in character, but it is not that which makes 
comparison difficult. The difficulty arises from the 
habit of the Gre^k writers of setting down only 
conclusions. vTheir methods of work, even the verifi- 
catory observations and experiments, they have almost 
completely hidden from us, and those methods were 
almost as completely hidden from their more immediate 
successors. It is as though we had a collection of the 
last few lines of a series of scientific articles. To grasp 

scientific method from a 


scientific article is difficult enough, since not all the 
mental processes involved are represented. In the case 


y of Greek Science the difficulty is far greater, for here 
v we have only the conclusions with hardly any or with 
none of the processes. 

In almost all I have said as to the contrast between 
Greek and Modern Science, Mathematics have been 
excluded, and for this there is a special reason. The 
defective Greek scientific method of recording only 
results is practicably inapplicable to Mathematics. 
Mathematical results without mathematical processes 
would be a meaningless inanity. Ancient Mathematics, 
like everything else that has come down to us from 
antiquity, have of course suffered from the accidents of 
time, but the obscuring power of time is a mere light 
veil compared to that heavy impenetrable curtain that 
the Greeks have themselves drawn over their biological 

Thus it comes about that we can form a clear and 
consecutive picture of the nature and progress of Greek 
Mathematics. But a corollary to the completeness of 
this mathematical record is a peculiar phenomenon in 
the History of Mathematics shared by no other Science. 

/ft is that for Mathematics there are no Middle Ages. 

This does not mean that there was no period when 
the mathematical knowledge of Europe was backward 
xfr arrested or that progress was not at times slow. It 
is of course true that those disturbances, political and 
economic, religious and philosophical, that followed the 
break \up of the Roman Empire and destroyed the 
intellectual life of antiquity, destroyed equally mathema- 
tical progress and mathematical thought. But the 
reason wliy we can say that there were no Middle_Ages 
for Mathematics is this, that when and where civiliza- 
tion became settled and when and where the Greek 
record became accessible, then and there it was possible 


for the wprk to be taken up just where the Greeks had 
left it. w hus Hindu and Arabic mathematical work is 
vital and real and valuable and has not those stigmata 
of degeneration to which the historian of Science is so 
well accustomed in the Biology and Medicine of Indian 
or Arabian origin. So the story of Mathematics can 
be told as one continuous progress from early Greek 
times to our own day. It is true that the scene 
changes from continent to continent. It is true that 
progress is sometimes so slow as to be almost inappreci- 
able. But the progress is there and is continuous, and 
the historian of Mathematics is able to tell his story as 
a continuous development of human thought. 

It is of course another question altogether as to 
whether his task as historian is then complete. It is 
another question whether he should not rather aim at 
an account of the mathematical powers, aspirations, and 
achievements of the human mind as a whole throughout 
the ages. But the point is that it is possible for him to 
tell his story as one continuous progress. This is 
a privilege denied to the historian of Medicine or of 
Biology. Why ? v/lBecause at many stages the basis of 
progress, the knowledge of method of investigation, has 
been concealed and sometimes wantonly concealed. 

O negfthe causes why Chemistry was so long arrested 
was the_desire of the alchemist to conceal his knowledge. 
His motives were selfish, personal enrichment or glori- 
fication by the discovery of the quintessence or of the 
philosopher's stone. His methods were secret and there- 
fore his manuscripts are among the most obscure and 
difficult with which the historian of Science ever has 
to deal. But the alchemist omitsjiisj>rocesses by choice, 
the Greek on principle, on the principle that it is the 
general conclusions that matter and that the processes 


are but means to them. The historian of Science knows 
better. It is precisely the processes that he seeks. He 
/knows that the conclusions are but a temporal and 
local accident. 

It has been said that the measure of advance of 
a Science is the degree to which its conclusions are 
susceptible of expression in mathematical form. But 
there is another and perhaps a deeper and more con- 
stant sense in which all Sciences must borrow from 
mathematical method. It is in the record of processes. 
Of nothing is it more true than of Science that the dead 
govern the living. By the amount to which our pro- 
cesses are clearly and succinctly recorded, by so much 
do we ensure the permanence of our work, by so much 
can we guarantee that our successors can begin where 
we leave off. 

This truth can even be applied to the History of 
/Science which is itself, as I would plead to you, an 
independent Science. By the degree to which we give 
our references and document our material, by the care 
with which we edit our manuscripts and index our 
investigations, by that degree will posterity be grateful 
to us. 

It is, therefore, I submit to you, the distinctive hope 
and glory of the Science of our age and I would 
here use the word Science in its widest sense that it 
will place in the hands of the inheritors of our civiliza- 
tion and our thought, whoever they may be, an instru- 
ment that will enable them to carry on our work, without 
halt or pause, from the point at which we leave it. 




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