I count difference between small numbers and enums on my fingers.
This includes e.g.
- the distance between months
- the distance between wall clocks
It's simpler for me to say "The number of months between March and September is... April, May, June, July, August, September, six." than "The number of months between March, 3, and September, 9, is 9-3 = 6," because I don't cache the numeric value of the months. Maybe I would if I were a Chinese speaker, where September's name is 九月 jiǔ yuè = nine month.
For wall clocks that wrap around midnight, it's simpler to count because it removes dealing with negative numbers.
I count the number of days in a month on my knuckles.
I check my knuckles if its 30/31 days in a given month. Start counting months on first knuckle while including the depth between knuckles as well. Height means 31, depth means 30.
I still do this as well. I never understood why the little poem was so popular. At that point it’s just coming down to rote memorization, as pretty much any month can be used in any order and it will still sound right.
The thing one does need to remember with the knuckle method is to count the end twice before going back the other way. July and August are both 31. I suppose this isn’t an issue if 2 fists are used, but I was taught to use one, so I could use my finger to track and feel the peaks and valleys.
This is because September used to be the seventh month. March was the new year and coinsided with spring planting, the spring equinox. At some point we switched from a solar calendar to a lunar one and that's when the new year month changed. Source for all this is the dead sea scrolls, see the book "Ancient Mysteries of the Essenes" for a deep dive on our calendar.
I thought the reason is because they added two months named July and August after emperors, which offset all the numbers by 2. (Sept, Oct, Nov, Dec - 7, 8, 9, 10)
That happened later, well after January and February had been added. I think the twelve month Roman calendar was from pre-history so we don't know when or why it was done. July and August were Quintilis and Sextilis, five and six.
All of the months with numerical prefixes are wrong by the same offset, though. So as long as you remember that as well, it can be useful. Particularly since they're the last ones and thus take the longest to count to.
Although in general I also count the difference in months on my fingers, this particular example from March to September just automatically pops a "six" because they are both ends of financial quarters. "Three months after Feb?" I need to count. "Three months after March? That's the next quarter, so June."
As a fun reminder of how different people are, the months to me are basically only their numeric value, and if someone starts taking about October I think to myself "October? Oh ya, the 10th month, got it."
I still do this as well, I distinctly remember a time in my life where that song didn’t make sense to me though for a weird reason.
The l,m,n,o,p part is often sung very quickly so to my 5(?) year old brain I never understood where this “elemenopy” business came in and what it had to do with the alphabet. One day it clicked but for a while there I was just along for the ride!
I can relate to this kind of confusion. When your brain expects useful information encoded in a detail, BUTT the author just did it for some trivial reason.
I do this too. I can also start at L if my intuition tells me the letter(s) I'm testing come after L. But that's it - I have to start at L or A. I don't know why L and not some other letter.
Supposedly “ampersand” comes from when the alphabet song/rhyme used to end in “and ‘per se’ and”. School kids mushed it together into “ampersand”, and over time it became the name for &.
The reason for L is probably because of the rhythm of the usual way the song goes. l, m, n... are rushed together because "elemenopee" is easy and fun to say quickly.
... a
b c d
e f g
h / i
j / k
l m n o p
q / r / s
t / u / v
w / x
y and z
I don't even need the song for the first couple lines these days!
Probably also for memorization. If the song were linear, letters would all cuddle together in the little children’s mind.
It’s quite funny that, as a French native, we are all taught exactly the same song! Same pace, same tone, same elemenopy, but later in life, somehow y’all just smash tough/thorough/through/trough letters together, and we go on with our hon/hen/heim.
I've been able to start at A, E, L, or T, and your explanation makes sense.
I usually know a letter is near one of those four, but not if it is before or after, so if I am looking for P for example, I'll start with T for a bit, realize I've gone too far, and start over at L in hopes of finding it.
It is delightful to be in a foreign country where English is not primary language but is taught and hear/see a little child rattling off the 'abcedefg' song.
I don’t count on my fingers, but that, I do. I can think through to some subset of the order to find a target letter but it’s usually faster to just run through the song quickly in my head, from the beginning, so that’s what I do.
I mean, it’s like 4s worst-case to find the letter anyway. I can “sing” it in my head fast. Not something I really need to work on making faster.
They can be a miniature sort-of-abacus. Keeping track of a number while you're scanning a lot of other things that occupy your mind. You can even sort of hold both the 10¹ digit and the 10⁰ digit on your hands if you're used to it, by semi-extending fingers or other methods, counting up to 100 and "physically" keeping the number in "memory".
Most of the time it's not necessary but if I'm particularly tired I use it sometimes.
The mini-abacus is how I use them as well. I was in a math competition where you were not allowed to use any scratch paper or make any stray marks on the test nor could you attempt to correct your mistakes with an eraser or trying to turn a 7 into a 9 or similar. There was nothing against counting on fingers, so there are time where I still calculate with my finger tips
What's the highest number you can count on your fingers?
When I need to do something repeatedly for a large number of times, I use my thumb to count the joints of my fingers, where the right hand is the "ones" and the left hand the "tens" column. In practice, I only go up to a hundred (ie. I use the first three fingers on each hand while counting - three on each finger, for 1-9), because decimal. But, the same system could get to 12x12 or 13x13.
A really neat alternative is to count on your fingers using binary. The right thumb is 0, the pointer 2, the middle finger 4, the ring finger 8, etc.
Amazingly, this gets you to over 1000 on your two hands, which is a really neat trick in the right setting. (Casually counting aloud off you fingers is great way to break the ice when you use binary - it is familiar but unexpected, dumb but smart.)
Even more than that, I use my fingers to multiply. When I was in grade school, I had a mental block about memorizing my multiplication tables. I just couldn't do it (and I still don't have most of them memorized, but much more now than then).
My teacher ended up teaching me a finger trick to let me quickly compute any multiplication from 6x6 to 10x10 and I use it to this day. This "one weird trick" was one of the most important things I learned when I was a young lad.
Once you visualise a calculator in your head there's no need to count on fingers. But I've recently learned that there are people incapable of visualizing anything at all, so there's that.
A very common technique used in Hindu/Buddhist Japa Meditation is to count the phalanges/creases in each finger including the tip thus making 4x5=20 count in one hand. For each 20 count of the right hand use 1 phalange/crease of the left hand and thus you can easily count upto 20x20=400 in a single complete cycle.
What I did find interesting is that I've used it more for Japanese especially when I'm
in Japan. I've been very slowly learning Japanese and of course counting in Japanese. So if I'm ordering food someplace I try to either count (yen) change or figure out the amount of an item I'm ordering.
I remember when I moved to the U.K. and asked at my new workplace for some memory sticks.
- How many do you need?
- Two. And I raised two fingers accordingly.
- Here, in the UK, you don't do that with your fingers.
That day I learnt something new about cultural differences.
I do. Whenever I'm holding my fingers up to indicate a number, I do it with my palms facing me. I'm in the US, though, where there is no special meaning for the two-fingers-raised hand gesture no matter which way your palms face.
Then deliberately struggling more isn't going to help you.
It's possible that you've reached the limit of your mental arithmetic ability (at least for now), but even professors of mathematics can struggle with mental arithmetic. Mental arithmetic is mostly important in school, and while shopping, but it's not really important for doing maths (especially not now we have calculators).
IIRC some cultures use a nifty method where the right hand is the ones column, the left hand is the tens column, and the thumb indicates five (sort of like an abacus).
Then each hand can represent 0 to 9, and together they go to 99.
No, I count with my toes on both sides: 1 is all left toes and 2 is all right toes, 3 left again and so on. With a small break after each even number. I guess one could call it a tic.
This reminds me of something from the early Internet.
There was a video (Flash?) of someone counting in binary on one hand, with acapella background music that sounded (to my untrained ear) like maybe some Nordic folk song.