Ian Stewart (mathematician) - Select Quotations

Select Quotations

• From What Does a Martian Look Like? The Science of Extraterrestrial Life:

"Science is the best defense against believing what we want to."

• From Catastrophe Theory and Its Applications:

"We may predict that ... as methods relevant to organized complexity develop in laboratory science, the social sciences will benefit in proportion. The new concepts — fusing with, changing, and adding to present understanding — may allow the definition and measurement of quantities more central to the health of the body politick than a 'standard of living' that includes useless packaging discarded, or a 'gross national product' that includes machines whose productivity is measured in megadeaths. ... If any mathematical methods can aid in the growth of such wisdom, then catastrophe theory will be part of them."

• From Does God Play Dice? The New Mathematics of Chaos on the concept of fungibility and how it applies to science:

"Lawyers have a concept known as 'fungibility'. Things are fungible if substituting one for another has no legal implications. For example, cans of baked beans with the same manufacturer and the same nominal weight are fungible: you have no legal complaint if the shop substitutes a different can when the assistant notices that the one you've just bought is dented. The fact that the new can contains 1,346 beans, whereas the old one contained 1,347, is legally irrelevant.

That's what `take as given' means, too. Explanations that climb the reductionist hierarchy are cascades of fungibilities. Such explanations are comprehensible, and thus convincing, only because each stage in the story relies only upon particular simple features of the previous stage. The complicated details a level or two down do not need to be carried upwards indefinitely. Such features are intellectual resting-points in the chain of logic. Examples include the observation that atoms can be assembled into many complex structures, making molecules possible, and the complicated but elegant geometry of the DNA double helix that permits the `encoding' of complex `instructions' for making organisms. The story can then continue with the computational abilities of DNA coding, onward and upward to goats, without getting enmeshed in the quantum wave functions of amino acids.

What we tend to forget, when told a story with this structure, is that it could have had many different beginnings. Anything that lets us start from the molecular level would have done just as well. A totally different subatomic theory would be an equally valid starting-point for the story, provided it led to the same general feature of a replicable molecule. Subatomic particle theory is fungible when viewed from the level of goats. It has to be, or else we would never be able to keep a goat without first doing a Ph.D. in subatomic physics."