science

Natura non facit saltus

Natura non facit saltus is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Natura non facit saltus rather than just read about it. In short: Natura non facit saltus (Latin for "nature does not make jumps") has been an important principle of natural philosophy. It appears as an axiom in the works of Gottfried Leibniz (New Essays, IV, 16: "la nature ne fait jamais des sauts", "nature never makes jumps"), one of the inventors of the infinitesimal calculus (see Law of Continuity).

Key takeaways

Natura non facit saltus belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Natura non facit saltus to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Natura non facit saltus from memory before moving on to harder problems.

Reference excerpt

Natura non facit saltus (Latin for "nature does not make jumps") has been an important principle of natural philosophy. It appears as an axiom in the works of Gottfried Leibniz (New Essays, IV, 16: "la nature ne fait jamais des sauts", "nature never makes jumps"), one of the inventors of the infinitesimal calculus (see Law of Continuity). It is also an essential element of Charles Darwin's treatment of natural selection in his Origin of Species. The Latin translation comes from Linnaeus' Philosophia Botanica.

Overview The principle expresses the idea that natural things and properties change gradually, rather than suddenly. In a mathematical context, this allows one to assume that the solutions of the governing equations are continuous, and also does not preclude their being differentiable (differentiability implies continuity). Modern day quantum mechanics is sometimes seen as violating the principle, with its idea of discrete transitions between energy states. Erwin Schrödinger in his objections to quantum jumps supported the principle, and initially developed his wave mechanics in order to remove these jumps. In the biological context, the principle was used by Charles Darwin and others to defend the evolutionary postulate that all species develop from earlier species through gradual and minute changes rather than through the sudden emergence of new forms. In botany in particular, Antoine-Laurent de Jussieu was a major proponent of this view as well. Modern evolutionary biology has terminology suggesting both continuous change, such as genetic drift, and discontinuous variation, such as mutation. However, as the basic structure of DNA is discrete, nature is now widely understood to make jumps at the biological level, if only on a very small scale.

Variant forms The principle is also variously referred to as:

Natura in operationibus suis non facit saltum (transl.: "Nature in its operations doesn't make a (any) jump") — 1613 appearance of a similar expression. Natura non faciat saltus, nec ab extremo ad extremum transeat nisi per medium (transl.: "Nature may not make jumps, nor may it pass from extreme to extreme except by way of a mean.") — John Ray (1682). Natura non saltum facit (literally, "Nature does not make a jump") is a variant form, sometimes attributed to Gottfried Leibniz. Natura non facit saltum is also the epigraph of Alfred Marshall's 1890 Principles of Economics. He most likely borrowed the phrase from Darwin's The Origin of Species. An admirer of Herbert Spencer, Marshall intended the epigraph both to proclaim his adherence to evolutionary thought and to justify his use of differential calculus as an analytical tool—a use seen in all the seminal thinkers of neoclassical economics. The spelling variation (saltus vs. saltum) displays a mere numerical difference: the Latin noun saltus, meaning "leap", belongs to the 4th declension, so its singular accusative is saltum (leap), while the plural is saltus (leaps). Die Natur macht keine Sprünge — German translation of the phrase.

See also In biology Anagenesis Cladogenesis Phyletic gradualism Punctuated equilibrium Punctuated gradualism Quantum evolution Saltation (biology) Stephen Jay Gould Continuous variation Continuum mechanics Mathematical concepts of "not making jumps": Continuous function Differentiable function Discontinuity Discrete mathematics vs mathematical analysis Smooth function Digital physics Weyl's tile argument

References

Worked examples

Example 1 — a first encounter with Natura non facit saltus

Start with the simplest possible case. Write down what Natura non facit saltus claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Natura non facit saltus before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Natura non facit saltus ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Natura non facit saltus

In research: Natura non facit saltus appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Natura non facit saltus in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Natura non facit saltus is common in secondary-school and first-year university syllabi. It links to neighbouring topics Latin philosophical phrases, Natural philosophy, so understanding it makes those chapters shorter.
In everyday life: Look for Natura non facit saltus outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Natura non facit saltus in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Natura non facit saltus means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Natura non facit saltus out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Natura non facit saltus in simple terms?

Why does Natura non facit saltus matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Natura non facit saltus?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Natura non facit saltus.