I got a new stove that has a countdown digital timer. When I BBQ I set it to an hour. If it says 46, I don’t subtract 46 from 60 and get 14. I visualize an analog clock hand say “oh, about 15 minutes”.
Google didn’t get me anything but I’m not sure how to word it.
Visualization seems to be a right word for it, I think. (Not necessarily the only right word.)
No answer on the word, but I recall a survey, back last century, where it was shown that when people look at a clock or a watch, that are far more likely to want to know ‘how long since’ or ‘how long to’ than to know that it is fourteen minutes past three. This is why digital watches virtually died out in favour of analoge, where estimating is much easier.
I do this, too, but don’t think there’s a name beyond “visualization.” When I see a digital clock, I convert the time to an analog clock face in my mind so I have an idea of how much “pie wedge” of time I have to go whatever.
I don’t do this when looking at a digital clock, but for calculating fractional hours in my head I go back to the clock face. The background of people might be interesting here, from about the age of 10 digital clocks were around (those old flap card versions for many years) along with the common analog clocks. My younger brother could barely read an analogue clock as a child because the digitals were readily available all his life. And at work we have 24 hour analogue clocks up showing the times at our international offices and they just annoy me.
So I wonder where on the analog/digital clock spectrum people fall, I’m in the middle somewhere, but I know there are people who strongly favor one or the other, possibly like the OP.
I was quite shocked to read on a Wikipedia talk page recently a comment from someone who said that he was an adult computer programmer, but never learned to read an analog clock. He wanted a Wikipedia article about clocks to have a more detailed explanation about how to read one. He claimed he recently needed to know the time and only had access to an analog clock, but couldn’t figure it out. Are there really a lot of people today who have no idea how to read an analog clock?
–Mark
The analog clock system is not inherently obvious, but most people learn it as a child. They still have to be taught it, and there probably is exactly zero information on the internet about how to read an analog clock because its value is so incredibly low compared to porn, cat pictures, etc. The number of people who don’t learn how to read analog clocks as children is vanishingly small, but for such a person I don’t doubt it might be hard to find information about it.
There’s a fictional story in a Ramona Quimby book about the protagonist not learning the terminology correctly, and being 10 minutes late to school one day when her mother wasn’t available at the time she had to leave and just told her “quarter past”. The story went that was she knew a quarter was 25 cents, and that you multiplied the hour by 5 to get what minute it was when the minute hand pointed at that hour number. I remember the essence of this story quite well despite only having read it once in close to 30 years ago, because it spoke to how odd the system we use to keep time is compared to how we keep track of other things. Has such a thing ever happened in real like? I have no idea, but hopefully that gives you a sense of why someone might find it strange to learn on their own if they were never taught.
Ah, times when there was no problem letting your 6-year-old walk by themselves 15 minutes to school in the morning…
Now that I think about it I actually do that too. It seems more subtle, or subconscience. I didn’t see a digital clock until I was probably 15.
Actually, there are exactly several sites about how to read an analog clock. Here’s one. For the most part, I think, they are designed as on-line lessons for younger readers. There are youtube lessons too. Just google for how to read an analogue clock.
Visualization can be a valuable technique for learning various mathematical principles too. It can be as simple as picturing a rectangular array of blocks to represent multiplication, or slices of volumes of revolution to explain the integration formulas for the volumes. Look in any math textbook at just about any level (well, any level from first grade through college sophomore anyway) and you’ll see illustrations.
My fourth grade teacher used an illustration to show us why multiplication is commutative. My seventh grade teacher used an illustration to demonstrate the distributive principle. He used another illustration to demonstrate the Pythagorean formula for right triangles. A slight elaboration of the illustration for the distributive rule will illustrate that
(a + b)(c + d) = ac + ad + bc + bd
far more clearly than the atrociously pure rote memory FOIL rule.
More complicated example: Perhaps you know that numbers of the form 2[sup]n[/sup] - 1 (that is, one less than a power of 2) are called Mersenne Numbers, and they are of some mathematical interest, and some of them are prime. But such a number can only be prime if the exponent n is prime (and even then, not always). A friend once asked me to prove this. It’s not too difficult with a bit of algebra. But I didn’t know that at the time. Instead, I concocted a visualization in my head that proved it, all in about 30 seconds.
Interesting. Can u share that visualization?
(Re: 30-second mental proof, with visualization, that 2[sup]n[/sup] - 1 can be prime only if n is prime.
Wanna play along? Open the spoilers step by step, and see how quickly you can see where I’m going with this!
By contraposition, the statement “2[sup]n[/sup] - 1 is prime only if n is prime” (which is to be proved) is equivalent to:
[spoiler]If n is composite then 2[sup]n[/sup] - 1 is composite. We will prove this.
If n is composite, then it can be represented as . . .[/spoiler]
. . . the product jk of two integers j and k (each > 1), and 2[sup]n[/sup] - 1 can be written as 2[sup]jk[/sup] - 1. Now, visualize that number written in base 2 . . .
2[sup]n[/sup] - 1 or 2[sup]jk[/sup] - 1, written in base 2, is just a string of n (or jk) 1’s. Example: 2[sup]24[/sup] - 1 is 111111111111111111111111. If n (or jk) is composite . . .
. . . then those jk 1’s can be grouped into j groups of k digits, or k groups of j digits. Example: 2[sup]24[/sup] - 1 can be written as
111111 111111 111111 111111 – or as: 1111 1111 1111 1111 1111 1111.
Do you see the proof yet?
Take 111111 111111 111111 111111 for example. This is clearly divisible by 111111, and thus is composite.
And similarly, writing 2[sup]jk[/sup] - 1 as j groups of k digits, it is clearly divisible by one group of k digits, or 2[sup]k[/sup] - 1. Or, writing it as k groups of j digits, divisible by one group of j digits,
or 2[sup]j[/sup] - 1.
Whoa. Mind blown.