Nature makes no leaps...

Reacting to Jerry Coyne's guest blog on The Loom, Brian Switek at Laelaps discusses, among other things, the objection to Darwin's theories that Huxley put forward, both in personal correspondence and in print:

The only objections that have occurred to me are 1st that you have loaded yourself with an unnecessary difficulty in adopting 'Natura non facit saltum' so unreservedly. I believe she does make small jumps--and 2nd. it is not clear to me why if external physical conditions are of so little moment as you suppose variation should occur at all--

Darwin indeed used that phrase, which he got from Linnaeus, several times in the Origin, particularly this, from Chapter 6 (p 194 in the first edition):

Although in many cases it is most difficult to conjecture by what transitions an organ could have arrived at its present state; yet, considering that the proportion of living and known forms to the extinct and unknown is very small, I have been astonished how rarely an organ can be named, towards which no transitional grade is known to lead. The truth of this remark is indeed shown by that old canon in natural history of "Natura non facit saltum." We meet with this admission in the writings of almost every experienced naturalist; or, as Milne Edwards has well expressed it, nature is prodigal in variety, but niggard in innovation. Why, on the theory of Creation, should this be so? Why should all the parts and organs of many independent beings, each supposed to have been separately created for its proper place in nature, be so invariably linked together by graduated steps? Why should not Nature have taken a leap from structure to structure? On the theory of natural selection, we can clearly understand why she should not; for natural selection can act only by taking advantage of slight successive variations; she can never take a leap, but must advance by the shortest and slowest steps.

This phrase, then, marks a major rupture in the thinking of biologists before and since Darwin. But, as so often, it doesn't mean what you think it means...

The phrase has a history. You can find it in John Ray, who wrote, in the Methodus plantarum of 1682:

… I would not have my readers expect something perfect or complete; something which would divide all plants so exactly as to include in positions anomalous or peculiar; something which would so define each genus by its own characteristics that no species be left, so to speak, homeless or be found common to many genera. Nature does not permit anything of the sort. Nature, as the saying goes, makes no jumps and passes from extreme to extreme only through a mean. She always produces species intermediate between higher and lower types, species of doubtful classification linking one type with another and having something common with both – as for example the so-called zoophytes between plants and animals.

Notice that Ray does not mean things happen gradually, but that they exist in gradations. This is not, either in Ray or in Linnaeus, a temporal process. So, what is it, and why?

The saying itself goes back a long way. I haven't been able to find the origin, but it can be found in Aquinas' teacher, Albertus Magnus: “nature does not make [animal] kinds separate without making something intermediate between them, for nature does not pass from extreme to extreme nisi per medium” (quoted in Lovejoy 1936: 79). The idea can be traced back to the views of Plotinus and Porphyry, and probably also to the Gnostic idea of emanation. Ray also used similar phrases: Natura nihil facit frustra (nature makes nothing in vain) and Natura non abundant in superfluis, nec deficit in necessarius (Nature abounds not in what is superfluous, neither is [it] deficient in necessaries) – in the Wisdom of God (quoted in Cain 1999: 233). This saying is also found in a similar form in Leibniz’s New Essays: “In nature everything happens by degrees, and nothing by jumps”, (Leibniz 1996 Bk IV, ch xvi, p473).

The Great Chain view consisted of a number of related theses held in varying ways by its adherents. One of these, named by Lovejoy (1936: 52) the principle of plenitude, has it that the world is as full of all the things it could be, or, as Lovejoy himself stated it, “… the universe is a plenum formarum in which the range of conceivable diversity of kinds of living things is exhaustively exemplified, but also any other deductions from the assumption that no genuine potentiality of being can remain unfulfilled, that the extent and abundance of the creation must be as great as the possibility of existence and commensurate with the productive capacity of a ‘perfect’ and inexhaustible Source, and that the world is better, the more things it contains”. In short, everything that can be, is, and the world is made to be everything it can be. This is where Leibniz’s doctrine of the lex completio came from, that Voltaire so wickedly caricatured in his Candide as the teachings of Dr Pangloss. It is found in Plato’s writings, but not in Aristotle: who famously wrote in the Metaphysics (II, 1003a 2, and XI, 1071b 13), “it is not necessary that everything that is possible should exist in actuality”, and “it is possible for that which has a potency not to realize it” (quoted by Lovejoy 1936: 55). However, the second plank of the great chain is the law of continuity (Leibniz calls it the lex continui) – that all qualities must be continuous, not discrete. While Aristotle did not make all things linear, arranged in a single ascending series, he did require that there be no sudden “jumps”, from which the medieval claim came. Aristotle’s version did not itself insist that one would classify a single living being in one and only one series, nor that an organism that is graded as superior in one respect must be superior in all (Lovejoy 1936: 56f) but that became the general impression later.

Linnaeus employed the Great Chain of Being in a rather unusual way. Most “chainists” of the period accepted the Principle of Plenitude (the lex completio), which stated that God would create everything that could be created, since he would not make an incomplete creation (Lovejoy 1936; Glass 1959). This usually meant that species graded into each other is a series of varieties. Linnaeus instead represented species using the metaphor of countries adjoining each other (in the Philosophia botanica §77). In his early writing, all the territory is pretty much filled – as he said, nature does not make jumps – but the countries are discrete and distinct from one another. In the later work, this strict fixism of the first edition of the Systema Naturae has been modified. All hybrids did was fill in a rare empty bit of territory in God’s time and plan. The borders were set by the genera, and all genera arose from a single species created by God. At the end of the 1750s, says Hagberg (1952: 199), Linnaeus was in a state of perplexity with respect to species. In 1755, he published Metamorphosis plantarum, dealing primarily with the development of plants, but also with monstrosities and varieties. Such later hybrids he called the “children of time” in an anonymous entry in a competition at St Petersburg in 1759 (Hagberg 1952: 201f), and also in the Species plantarum (1753, 2nd edition 1762-63), where he speculated that a species of Achillea (yarrow, or staunchweed), alpina, might have formed from another, ptarmica, “[an] locus potuerat ex praecedenti formasse hanc?” (“Could this have been formed from the preceeding one by the environment?”). As time went on, he removed the statement that there were no new species from his 1766 edition of the Systema Naturae, and crossed out the statement natura non facit saltum from his own copy of his Philosophia Botanica.

In an interesting and suggestive book, Peter F. Stevens (1994) has argued that the territorial metaphor became less and less occupied as discontinuities between taxa were identified. First Tournefort, then Jussieu, used the metaphor. Like Linnaeus, Jussieu held that plants have affinities like a regions on geographical map. The natural method

… links all kinds of plants by an unbroken bond, and proceeds step by step from simple to composite, from the smallest to the largest in a continuous series, as a chain whose links represent so many species or groups of species, or like a geographical map on which species, like districts, are distributed by territories and provinces and kingdoms. [355]

However, as Stevens observes, the geography was becoming sparser in the regions occupied (Stevens 1994: 74ff). Where for Linnaeus, the entire territory was filled, more or less, for de Jussieu, there were large unoccupied regions, and for Mirbel and de Candolle fils the groupings become discrete and separate.

Charles Bonnet was the last explicit static Great Chainist. He wrote:

If there are no cleavages in nature, it is evident that our classifications are not hers. Those which we form are purely nominal, and we should regard them as means relative to our needs and to the limitations of our knowledge. Intelligences higher than ours perhaps recognize between two individuals which we place in the same species more varieties than we discover between two individuals of widely separated genera. Thus these intelligences see in the scale of our world as many steps as there are individuals. [Contemplation de la Nature, 2nd edn, 1769, I, p28, (quoted in Lovejoy 1936: p231)]

At about the same time, Buffon held that there were no actual discontinuities anywhere, and that "species" were simply arbitrary points at which we identified sufficient phenomenal difference between individual organisms to call them different species. Lamarck, however, a student and friend of Buffon's, temporalised this so that now there were no gaps in the sequence of transforming organisms. He, too, denied species a real existence.

So what did Darwin do? Was he a Great Chainist? Not at all. Elsewhere in the Origin he notes

To sum up, I believe that species come to be tolerably well-defined objects, and do not at any one period present an inextricable chaos of varying and intermediate links: firstly, because new varieties are very slowly formed, for variation is a very slow process, and natural selection can do nothing until favourable variations chance to occur, and until a place in the natural polity of the country can be better filled by some modification of some one or more of its inhabitants. And such new places will depend on slow changes of climate, or on the occasional immigration of new inhabitants, and, probably, in a still more important degree, on some of the old inhabitants becoming slowly modified, with the new forms thus produced and the old ones acting and reacting on each other. So that, in any one region and at any one time, we ought only to see a few species presenting slight modifications of structure in some degree permanent; and this assuredly we do see. [p177f]

So, Darwin's answer to the problem of the lex completio is that extinction and modification leaves us with tolerably well-defined species, and that gradations of structure occur slowly. This is exactly what is at issue in the Hopeful Monster debates. Stephen Jay Gould tended to stress discontinuities in his Punctuated Equilibrium Theory, but even he did not expect that there would be a leap from one fully formed type to another, and just as Coyne states, the Hopeful Monster is still just a vain hope in biology.


Cain, Arthur J. 1999. John Ray on the species. Archives of Natural History 26 (2): 223-238.

Darwin, Charles. 1859. On the origin of species by means of natural selection, or The preservation of favoured races in the struggle for life. London: John Murray.

Glass, Bentley. 1959. The germination of the idea of biological species. In Forerunners of Darwin, 1745-1859, edited by B. Glass, O. Temkin and W. L. Straus Jr. Baltimore: Johns Hopkins Press: 30-48.

Hagberg, Knut. 1952. Carl Linnaeus. Translated by A. Blair. London: Jonathan Cape.

Leibniz, Gottfried Wilhelm. 1996. New Essays on Human Understanding. Translated by P. Remnant and J. Bennett. Cambridge UK: Cambridge University Press. Original edition, 1765.

Lovejoy, Arthur O. 1936. The great chain of being: a study of the history of an idea. Cambridge, Mass.: Harvard University Press.

Ray, John. 1682. Methodus plantarum nova brevitatis & perspicuitatis causa synoptice in tabulis exhibita; cum notis generum tum fummorum tum subalternorum characteristics, observationibus nonnullis de feminibus plantarum & indice copioso, Early English Books, 1641-1700/1044:07: Londini: Impensis Henrici Faithorne & Joannis Kersey ...

Stevens, Peter F. 1994. The development of biological systematics: Antoine-Laurent de Jussieu, nature, and the natural system. New York: Columbia University Press.


More like this

principle of plenitude, has it that the world is as full of all the things it could be, or, as Lovejoy himself stated it, ". the universe is a plenum formarum in which the range of conceivable diversity of kinds of living things is exhaustively exemplified, but also any other deductions from the assumption that no genuine potentiality of being can remain unfulfilled, that the extent and abundance of the creation must be as great as the possibility of existence and commensurate with the productive capacity of a `perfect' and inexhaustible Source,

Hmmm. When I was younger I used to wonder why there was no single species with the strength of an elephant, the speed of a cheetah, the intelligence of a human, and the reproductive capacity of a mosquito. Such a creature may be asking too much of the ether :) (...and may also be an argument against a supreme being.)

"You can't always get what you want. But if you try sometime, you just might find, you get what you need."

Thanks for writing this, John! It's quite impressive, and obviously you have more of an understanding of the intellectual background than I do.

One small remark: Nature *makes* in fact leaps, so the "lex completio" is wrong.

Examples in physics and engineering are phase transitions and nonlinear forced oscillators where drastic changes can occur with very small differences. In the 70s the modeling of the mathematical circumstances in the topological space, the "catastrophe theory", was born.

Biology is another matter...

Notice that Ray does not mean things happen gradually, but that they exist in gradations. This is not, either in Ray or in Linnaeus, a temporal process.

This had never occured to me. Thank you for pointing it out.

TSK: I know that and you know that, but in the 16th century and after, it was still open to discussion.