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Since the theme is one of precise language...

"I'm thinking, which side should statisticians put themselves? We identify as mathematicians but we also regard numbers as uncertain measurements."

Are you claiming that numbers are measurements, rather than mathematical objects? I don't think that's true. A measurement can be uncertain (e.g. 9 units long, with some error in both the estimate of the count of units and the magnitude of a unit), but I suspect you're not at all uncertain about the meaning of '9' in '9 units'.

Even from the short extract here, Seife's point seems pretty clear: mathematicians may deal with 'number' (correctly) as an abstract concept, but most people only come across numbers in the context of counting or measurement, and so frequently conflate the concepts. Since measurements have error, numbers also - colloquially, at least - have error.

"'Two plus two is always four. It was always so, long before our species walked the earth, and it will be so long after the end of civilization.' This is just wrong. Arithmetic is a human invention."

Arithmetic is a human invention, that's true. But it's an invention that seems to reflect (under some circumstances; negative numbers can, obviously, be a problem) the way the universe works. Even if humans hadn't existed, it seems wilfully perverse to assert that if exactly two fish came together with exactly two fish, there would be some number other than four fish as a result (fishy pregnancy notwithstanding). Siefe's not wrong here.

"Besides, 2+2=4 only works in base 10 so it's not even always true today."

It works in bases five and up, if we retain the common symbols for each number. If we swap symbols about it holds in all bases. If we interpret 'two' and 'four' to mean the quantities 'two' and 'four', rather than the symbols '2' and '4', then 10 + 10 = 100 is a perfectly valid expression of the persistent concept that 'two plus two is four' that Siefe states. Assuming that we're happy to retain the usual meaning of 'plus' as an operation in this context, of course ;)

Mitchell: Whether statistics/probability is math was actually quite controversial. Statisticians, especially of the Bayesian variety, treat every number as uncertain. So yes, when you say 9 units, we think it's 9 on average, and we impose a probability distribution around the number 9.

Please read my general review of the Seife book. I already noted that his book contains few glaring errors, unlike many other books in this genre.

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