I’ve been asking myself this question… or putting together this statement, in quite a few ways lately.
Last weekend included יום כיפור (Yom Kippur) on Friday-Saturday, and this week, I have gotten back to research. Last week, things were not making sense with my research, as I was appearing to get two conditions for a single unknown variable, and these conditions were inconsistent. Clearly, I knew that SOMETHING was wrong.
So, since I always incubate my work over the weekend, I returned with a fresh mind (and a cleared conscience from Ritual Purification), and discovered why it was wrong: a subtle-but-pernicious typo in which I had lost a couple of critical superscripts! In algebraic manipulation, there are so many ways to be wrong.
I have found, however, that I have gotten much better at recognizing when something is wrong when doing mathy things. Part of being a successful researcher is realizing when you have made a mistake, even when it is not easy to find where the error is.
An underrated sense that I want to teach my calculus students is how to use common sense and approximations in order to see when numerical results are reasonable. For example, on the first quiz in MATH 234 this quarter, students had to integrate a function over a region such that the integrand was always negative. Therefore, because an integral is basically a sum, if you add nothing but negative numbers, your result better be negative!
When considering integration in multiple variables, geometric and symmetric arguments often make the work easier. It’s not just about evaluating integrals, but also about seeing when things simplify.
Shifting to another take on the title of the post, and making it short, I feel like the word “wrong” is onomatopoeic with two degrees of separation. Why is this? When I pronounce the word “wrong” in certain situations, I make it sound like a buzzer, or at least say it in a deeper tone of voice. And as I explained in the linked post above, “BUZZ” is onomatopoeic. And I often associate a buzzer with a wrong answer! Thus, a second-degree link of assertions.
Well, I’m off to the office to make more sense of the research! Have a great day, everyone!
Today is the two-hundred and eightieth day of M.M.X.I.V. That makes forty weeks.
Today is the eighty-fifth day of the Character Building Trial. That makes twelve weeks and one day.
Today is the seventh day of the third round of O.C.T.O.B.E.R. That makes one week.