The principles of science

by William Stanley Jevons

There are unequivocal indications, as I have said, that the material universe, as we at present see it, is progressing from some act of creation, or some discontinuity of existence of which the date may be approximately fixed by scientific inference. It is progressing towards a state in which the available energy of matter will be dissipated through infinite surrounding space, and all matter will become cold and lifeless. This constitutes, as it were, the historical period of physical science, that over which our scientific foresight may more or less extend. But in this, as in other cases, we have no right to interpret our experience negatively, so as to infer that because the present state of things began at a particular time, there was no previous existence. It may be that the present period of material existence is but one of an indefinite series of like periods. All that we can see, and feel, and infer, and reason about may be, as it were, but a part of one single pulsation in the existence of the universe.

After Sir W. Thomson had pointed out the preponderating tendency which now seems to exist towards the conversion of all energy into heat-energy, and its equal diffusion by radiation throughout space, the late Professor Rankine put forth a remarkable speculation.‍[613] He suggested that the ethereal, or, as I have called it, the adamantine medium in which all the stars exist, and all radiation takes place, may have bounds, beyond which only empty space exists. All heat undulations reaching this boundary will be totally reflected, according to the theory of undulations, and will be reconcentrated into foci situated in various parts of the medium. Whenever a cold and extinct star happens to pass through one of these foci, it will be instantly ignited and resolved by intense heat into its constituent elements. Discontinuity will occur in the history of that portion of matter, and the star will begin its history afresh with a renewed store of energy.

This is doubtless a mere speculation, practically incapable of verification by observation, and almost free from restrictions afforded by present knowledge. We might attribute various shapes to the adamantine medium, and the consequences would be various. But there is this value in such speculations, that they draw attention to the finiteness of our knowledge. We cannot deny the possible truth of such an hypothesis, nor can we place a limit to the scientific imagination in the framing of other like hypotheses. It is impossible, indeed, to follow out our scientific inferences without falling into speculation. If heat be radiated into outward space, it must either proceed ad infinitum, or it must be stopped somewhere. In the latter case we fall upon Rankine’s hypothesis. But if the material universe consist of a finite collection of heated matter situated in a finite portion of an infinite adamantine medium, then either this universe must have existed for a finite time, or else it must have cooled down during the infinity of past time indefinitely near to the absolute zero of temperature. I objected to Lucretius’ argument against the destructibility of matter, that we have no knowledge whatever of the laws according to which it would undergo destruction. But we do know the laws according to which the dissipation of heat appears to proceed, and the conclusion inevitably is that a finite heated material body placed in a perfectly cold infinitely extended medium would in an infinite time sink to zero of temperature. Now our own world is not yet cooled down near to zero, so that physical science seems to place us in the dilemma of admitting either the finiteness of past duration of the world, or else the finiteness of the portion of medium in which we exist. In either case we become involved in metaphysical and mechanical difficulties surpassing our mental powers.

The Divergent Scope for New Discovery.

In the writings of some recent philosophers, especially of Auguste Comte, and in some degree John Stuart Mill, there is an erroneous and hurtful tendency to represent our knowledge as assuming an approximately complete character. At least these and many other writers fail to impress upon their readers a truth which cannot be too constantly borne in mind, namely, that the utmost successes which our scientific method can accomplish will not enable us to comprehend more than an infinitesimal fraction of what there doubtless is to comprehend.‍[614] Professor Tyndall seems to me open to the same charge in a less degree. He remarks‍[615] that we can probably never bring natural phenomena completely under mathematical laws, because the approach of our sciences towards completeness may be asymptotic, so that however far we may go, there may still remain some facts not subject to scientific explanation. He thus likens the supply of novel phenomena to a convergent series, the earlier and larger terms of which have been successfully disposed of, so that comparatively minor groups of phenomena alone remain for future investigators to occupy themselves upon.

On the contrary, as it appears to me, the supply of new and unexplained facts is divergent in extent, so that the more we have explained, the more there is to explain. The further we advance in any generalisation, the more numerous and intricate are the exceptional cases still demanding further treatment. The experiments of Boyle, Mariotte, Dalton, Gay-Lussac, and others, upon the physical properties of gases, might seem to have exhausted that subject by showing that all gases obey the same laws as regards temperature, pressure, and volume. But in reality these laws are only approximately true, and the divergences afford a wide and quite unexhausted field for further generalisation. The recent discoveries of Professor Andrews have summed up some of these exceptional facts under a wider generalisation, but in reality they have opened to us vast new regions of interesting inquiry, and they leave wholly untouched the question why one gas behaves differently from another.

The science of crystallography is that perhaps in which the most precise and general laws have been detected, but it would be untrue to assert that it has lessened the area of future discovery. We can show that each one of the seven or eight hundred forms of calcite is derivable by geometrical modifications from an hexagonal prism; but who has attempted to explain the molecular forces producing these modifications, or the chemical conditions in which they arise? The law of isomorphism is an important generalisation, for it establishes a general resemblance between the forms of crystallisation of natural classes of elements. But if we examine a little more closely we find that these forms are only approximately alike, and the divergence peculiar to each substance is an unexplained exception.

By many similar illustrations it might readily be shown that in whatever direction we extend our investigations and successfully harmonise a few facts, the result is only to raise up a host of other unexplained facts. Can any scientific man venture to state that there is less opening now for new discoveries than there was three centuries ago? Is it not rather true that we have but to open a scientific book and read a page or two, and we shall come to some recorded phenomenon of which no explanation can yet be given? In every such fact there is a possible opening for new discoveries, and it can only be the fault of the investigator’s mind if he can look around him and find no scope for the exercise of his faculties.

Infinite Incompleteness of the Mathematical Sciences.

There is one privilege which a certain amount of knowledge should confer; it is that of becoming aware of the weakness of our powers compared with the tasks which they might undertake if stronger. To the poor savage who cannot count twenty the arithmetical accomplishments of the schoolboy are miraculously great. The schoolboy cannot comprehend the vastly greater powers of the student, who has acquired facility in algebraic processes. The student can but look with feelings of surprise and reverence at the powers of a Newton or a Laplace. But the question at once suggests itself, Do the powers of the highest human intellect bear a finite ratio to the things which are to be understood and calculated? How many further steps must we take in the rise of mental ability and the extension of mathematical methods before we begin to exhaust the knowable?