... one wonders whether McEvoy is misremembering the actual question ("impossible to imagine that 2+2=5")
Actually, I've always thought that it was impossible to imagine a logical impossibility (e.g., 2+2=5). The statement is one of those facts in philosophy that has gone unexamined. Everyone thought it was true. Well, it's not. Please strike this from your logic and philosophy books.
In the work we currently do, there's quite a few numbers, and I've noticed that many people aren't good at numbers. The ones I deal with are bright people, and they know simple arithmatic, but when it gets to log numbers, percentages of large numbers, ratios, and so on, they can't do it without a calculator. It's not intuitive to them.
I noticed that many people simply don't know how to deal with large numbers. Anything over 30 or 40, and the results start to get soft. Often, they either guess (and they know it's a guess) or they definitely know the result. They state clearly to me that they know, and I just smile and say "try it on your calculator." This is a perfect example of "imaging an illogical impossibility". There's no difference in "2+2=5" and "3.07% of 4,324,227 = 11,342"; both are mathematically wrong.
I'm not a numbers person (I studied philosophy, not mathematics!) and this isn't some sort of autistic skill. My grandfather had a factory and my dad worked there as a kid and learned how to factor numbers in his head. Mathematics isn't as easy as it sounds. Biologists have found that crows and porpoises can calculate the square roots of numbers, but for humans, it's a learned skill. There used to be a lots of methods for doing this, before there were calculators. He taught me this when I was a kid, and for many years, it was a fairly useless skill, like knowing the rivers of Russia or whatever. But in the last ten years, it became useful and often, I've been teaching many of my co-workers how to factor numbers.
By the way, be careful with formulas and numbers in your textbooks. I've found errors, even in "well-known" formulas. Remarkably, nobody notices, and many people use those formulas.
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