megane-kun

Calm and contented

For nothing happened today.

I am satisfied

Yeah, I alluded to that in an earlier response here (people who grew up with analog clocks do not really think of multiplication when reading off the clock), but I definitely didn’t explicitly say that. Also, the connection between multiplication and reading off the minute hand was briefly mentioned when we were taught multiplication (specifically, the times table for five) presumably as a means to reinforce multiplication (by connecting them with what we supposedly previously learned).

I suppose my point is if I am to teach how to read an analog clock to an adult who didn’t grow up with them, I’ll mention multiplication as a means to explain what’s happening. Even with analog clocks with no marks at all, there’s an assumption that we’re supposed to remember where the marks are—but since we’ve made an association between the shapes and the time, we can safely skip that step.

We’re just talking past each other.

If that’s your idea of a good time, then have at it.

I haven’t seen a “37” in an analog clock.

There’s a 7, there’s 8, and there are four spaces (which may or may not be marked) in between them.

Now, to the main topic:

But out of curiosity, do you really go “long pointer at 8, 8x5=40” internally when reading the clock?

No. But that’s because due to experience and exposure to analog clocks all my life—which, again, is not something that should be assumed nowadays. When I was taught how to read analog clocks (preschool or very early in primary school, IIRC—so, yes, before I was taught multiplication), I was told to “count by fives”. Hence: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and 00.

Now, when we were taught the multiplication table for 5 (maybe it’s just my teacher) we revisited how to read off minutes from the clock (digital displays are still rare back then).

Reading off the minutes from where the minute hand is pointed. If the minute hand is pointed at 8, you’d have to multiply 8 by 5 to get 40.

Sorry, I added it in the edit.

Actually, even in that case, reading off the minutes hand off an analog clock doesn’t involve the times table for 12, so your original claim holds.

I think a lot of the backlash against rote memorization is the rote part. Without understanding what you’re memorizing—treating the times table as a list of sequences (times table for 2, and then 4, and then 5, etc), the mental load memorizing it becomes unbearably high.

In my case, I was lucky enough to have been made to understand what’s going on (4 groups of 8 items = 40) before being asked to memorize the times table. The visualization also helped me memorize, as well as some tricks (what’s 6×7? 6×6 = 36, right? add 6 to arrive at 42) that as I memorize more and more of the table, become less and less necessary.

Analog clocks.

If the hour hand is pointing just past 1, and the minutes hand is very near 8, what time is the clock showing?

Now, ofc, it’s becoming somewhat of a lost art, with the increasing prevalence of digital clock displays, so, yeah. Personally, I just developed an intuition for it, having grown up in a time when digital clock displays are rare, and analog clocks are commonplace.

EDIT/PS:

Actually, even in that case, reading off the minutes hand off an analog clock doesn’t involve the times table for 12, so your original claim holds.

Yeah, even if’d think of it as a flat 20% tax on top (as an estimate), it’d still be a bit too much for my mental maths.

Let’s see… If I’ve got 30 USD running total, then I estimate a 20% total tax… No, let’s do it as 25%. That’d be around 37.50 USD with the tax estimate. Doing it as 20%, it should be around 36 USD.

Doing the calculation with 17.5% via a calculator, it is 35.25USD. Doing it with 20% seems to be close enough, 25% a bit too much. But that depends on what’s the total tax percentage–or if it even works that way. It’s something I’m too unamerican to understand.

Oh, I grew up during the time where calculators were actually forbidden even in Trigonometry exams (we were provided the necessary values along with the exam questions, or a table of sines/cosines/tangents). So yeah, it reinforced my knowledge of arithmetic (by basically forcing me to use it again and again).

And indeed, as I’ve mentioned in a top-level response to the thread, I’ve basically have my times tables (up to 10–because that’s what I was taught) memorized. I can recall it within a couple of seconds.

However, mental arithmetic usually just gets used when I estimate stuff. Mostly with groceries, but sometimes for estimating travel times. For example, if I left at 14:00, reached the midway point at around 15:15, I’d estimate I’d arrive at around 16:30, add a bit of leeway and say I’d arrive around 17:00.

You have six minutes to make 9 moves, how many seconds per move? And don’t take too long because the calculation eats into your time.

360 seconds in 6 minutes. Make 9 moves → 40 seconds per move. I actually took a few seconds realizing that 6 minutes = 360 seconds tho (went with 5 minutes = 300 seconds, 6 minutes = 300 seconds + 60 seconds).

And that’s probably one of the few remaining uses of mental arithmetic I have nowadays. I also got to practice rounding up numbers for estimating whether or not I’ve got enough money for groceries. It’s easier to keep up with a running total in my head if they’re nice (rounded-up) numbers instead of being surprised at the total cost at the end.

I was only taught up to 10×10 in primary school, and learned mostly by rote (and also, “skip counting”). I’ve also heard of some techniques like matching fingers to do one-digit multiplication, but I never really learned how to do that. By that point, I’ve mostly memorized the multiplication table up to 10.

For 11, it’s absurdly easy once I got the technique, just double the number (up until 9). 11×10 is just appending a zero, and 11×11 I just memorized.

For 12, I actually didn’t bother that much? 12×N = 10×N + 2×N. Thus, 12×11 = 110 + 24 = 134 and 12×12 = 120 + 24 = 144 (which I got memorized for some reason).

I still have some trouble with the 6, 7, and sometimes 8 multiplication tables, but I can usually recall it with a bit of effort. Not much, but not without some awkward pause.

Now, for how I got to memorize it. The process was hard at first. I had to recite the multiplication tables as a drill almost everyday. We also had long quizzes (hundred items) of one-digit multiplication and two-digit division (by the fourth grade), so there’s an incentive to memorize the tables if only to be able to get through those quizzes with minimal pain. There’s also a social stigma for being the last person to get done with those quizzes (or worse, running out of time), so there’s that pressure too.

Heros and anti-heros are united in that they genuinely want to do good. They just differ in the means (or what they’d allow to use as means) to their ends. For example, a hero will vehemently refuse to blow up a street market while an anti-hero might consider it if they deem it to be sufficiently helpful to their end.

I’d rather look at it as a sliding scale with “will never do anything bad” on one end, and “a villain who has good intentions” on the other. And even those two ends are subject to the questions “What do you mean by ‘’bad?” and “What do you mean by ‘good intentions’?” Thus, I think while heros and anti-heros across stories and genres have commonalities, one story’s anti-hero might as well be a hero in another story and that the best way to judge a character being a hero or an anti-hero is in the light of the story they’re in.

Which one? If all of them, I’m very screwed.

If it’s only one of them, I might still be fine. I often have more than one account in each “domain” to maintain some semblance of compartmentalism. If I can’t do that, I usually don’t post much, if at all.

“Instantiation” would be my guess.