Ken Umbach (researchguy) wrote,
Ken Umbach

A calculating commenatary

Someone I'll call "Jim" here (not his given name), posted this on Facebook:

"Come on, Mythbusters. Two plus two times three is most certainly NOT twelve. Letter forthcoming. . . . The scene in question was in relation to testing whether men or women were better at multitasking. (Women by far.) They asked one of the ladies this question, she replied with 12, and they gave her credit for a right answer."

Jim's argument is that 2 + 2 x 3 = 8 because the order of operations in a mathematical expression requires doing multiplication before addition (assuming nothing is enclosed in parentheses to change the order of operations). That is, by default, the expression is the same as 2 + (2 x 3).

True enough, the lady's answer (12) would have been incorrect IF she had been presented with the equation on paper or on a screen. Someone "doing the math" would have multiplied 2 by 3, and then added 2 to the resulting quantity.

But she was NOT given the problem on paper or on a screen. She heard it spoken aloud: "What is two plus two times three?"

I have not heard the episode in question, and so have to speculate here that the question was read as written above, without inflection or pauses. If so, the speaker GAVE her the order of operations (add and then multiply) rather than interpreting the mathematical expression to get the proper mathematical order of operations ("What is two times three [pause] plus two?" or, conceivably, "What is two [pause] plus quantity two times three?"). So the woman was fully justified in interpreting the question as, "What is two plus two, quantity, times three?"

If you enter the following into your calculator, the answer will be 12: 2 + 2 * 3 = . (There may be specialized calculators that will give a different result or that require the operations to be entered in a different order. Reverse Polish Notation comes to mind. See -- but that is wandering afield.)

This, in essence, is how most people, I believe, would perform the calculation: Two plus two (quantity [that is, the mental = key)], times three.

If you enter =2+2*3 into a cell in Excel and press the return key, you get the result 8, as Excel knows to do the operations in proper mathematical order.

I just tested this with two intelligent women, both of whom have taken mathematics in school and have much experience with numbers, but neither of whom is a mathematician or scientist. I recited the question aloud without pauses or inflection. Both answered 12, using just the reasoning I outlined above.

So, my advice to Jim: relax. No letter to Mythbusters required. The correct answer WAS 12. However, had the woman answered 8, that, too, could reasonably have been scored as a correct answer, as she might have pictured the expression as if on paper or a screen and done the order of operations accordingly.
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