For whatever reason, 6x7, 6x8, 7x7 and 7x8 are a persistent hole in my ability to memorize. Sure I can temporarily memorize them, but they shortly evaporate back into the void and I’ll have return to quickly having to calculate them out again.
I’ve also got this thing where I get mixed up between verbal “eleven” and “twelve”. They sound different, but at the same time somehow sound just similar enough that the boundary that should exist around them as symbols never properly formed. I have to pause and manually match the number to the sound, every time. What’s especially funny to me is I have no such problem distinguishing between onze and douze from French, which I only know a few words of and certainly never hear in real life.
I’d like to think the first problem I’d eventually fix if I was using those multiples constantly, but I’m not so sure because the second problem definitely doesn’t improve.
> but at the same time somehow sound just similar enough that the boundary that should exist around them as symbols never properly formed.
I definitely relate to that for some things. I have a distinct memory of struggling to memorize 6x7, 7x7 and 7x8 in elementary school. What I settled on was just artificially making the numbers "stick out" in my head... It's hard to explain, but for example for 7x7=49, the way I pronounce it in my head is really distinct, and I'm also very "passionate" (as a mnemonic, but also genuinely) about how it "makes no sense" that the numbers 7 and 7 could make 49. Similarly with 42, I have this idea of 6 and 7 combining in such a clunky way that they somehow produce 42, and this image of them forming a kind of gnarled-up branch to "reach" 42.
Anyway, just an interesting thing I've never put into words about this point -- I'm realizing that when I can't remember something, I kind of toss around a concept in my head until one of these nonsense mnemonics has a match. I'm also reminded of "memory palaces," where people assign concepts to a mental location even when there's not necessarily a correlation, and it drastically improves their recall. Maybe I should try this more -- now I'm wondering why I apply this to some things and not others.
Hitch hikers guide to the galaxy helped me learn 67 with 42, the answer to life the universe and everything.
And my dad had me trained to reply 49 when asked "what's 77?" early, to pull off as a party trick. Though I couldn't answer and followup questions hahah.
I don't really bother to keep them memorized 'uncompressed', I remember a jumble of them that stuck for one reason or another (eg 7x7=49 just sort of makes me feel 'satisfied' somehow) and just have built up an instinct to 'disassemble' the multiplication into the ones I remember more strongly. Eg for 7x8, while I did instantly think 56, I still automatically checked it as 7x7+7. This also helps with larger multiplications, since my first instinct is to simplify the problem to something that is trivially solvable and checkable.
Nowadays I don't often have to use these tricks, the vast majority of the time I'm already typing into something that can give me the result (a browser, or a terminal), or am in no rush and can just use my phone or watch. At most it makes for an occasionally nice trick to show in conversations.
Very similar story. Never managed to memorize multiplication table. Can do it, but it vanishes. By that I mean the "tricky" pairs but I don't know what is tricky about them. Been programming computers for close to 30 years, do lots of math but multiplication table is still tricky to me.
Been playing guitar for 20+ years, can't memorize the note names on some frets.
Studied music in college, I still need to count lines sometimes when reading sheet music, besides some reference points I can't seem to memorize the locations of notes on the staff.
Not like I have a general memorization problem. I am good with human languages, programming languages. Have very good working memory etc. But some things just stump me.
Interesting. I play three instruments, primary is piano. We were expected to memorized our pieces for recitals each year. I've yet to determine if I memorized every single note or by playing the entire piece one memorized via touch and position. I'm horrible at programming, to busy asking question behind the 'why' does it work that way.
I'm in the same boat. The multiplication tables for me in that zone are constructs from other principles. :) So, Fives and Nines are easy and I can derive the Sixes Sevens and Eights from those. It's definitely extra steps. I think I'm reasonably good at the sort of mental arithmetic described in another post, Those particular operations just remain as symbols until I absolutely need to define them more precisely. I don't have a problem with 11s and 12s, but 5s and Rs trip me up.
The way that our brains process symbols is fascinating. If anyone out there has any literature or reading on this, I'd be interested. Especially, as related to ADHD/Autism.
The Hitchhiker's Guide to the Galaxy (see start of chapter 32) lets me remember that "what do you get when you multiply six by seven?" was a proposed Ultimate Question for The Answer. I couldn't remember it until I started remembering it in that context.
I wonder if it would help to remember that etymologically "eleven" comes from "one left" (as in, I counted the first ten and there was still one more) and "twelve" comes from "two left".
As for the others, I think remembering these in several different ways is stickiest. For example, you might think of 7·7 = (5 + 2)² = 25 + 2·10 + 4 or perhaps 7·7 = (6 + 1)² = 36 + 2·6 + 1 or 7·7 = 7·(10 − 3) = 70 − 21. If you already know 7·7, then 6·8 = (7 − 1)(7 + 1) = 49 − 1. You can try computing 7·8 by repeatedly doubling: 7, 14, 28, 56. Etc.
The squares of primes become memorable if you've ever tried searching for primes in your head. That's because 7*7 is the smallest product of prime factors that are all larger than or equal to 7: in other words, you can check for the primality of numbers smaller than that by testing for division by 2, 3, or 5 only, because they must divide by one of those or be prime.
Because of this pointless mental exercise it also sticks in my mind that 11 squared is 121 and 13 squared is 169 (though the presence of 69 helps with that one).
I like the shove it to the nearest 10 approach. It makes a lot of calculations much simpler b/c they can be transformed to a simple multiplication by 10 and a addition or subtraction or two.
1. 6⋅7 = (6⋅10) - (6⋅3) = 60 - 18 = 42
2. 7⋅7 = (7⋅10) - (7⋅3) = 70 - 21 = 49
3. 13⋅19 = (13⋅20) - (13⋅1) = 260 - 13 = 247
4. 58⋅61 = (58⋅60) + (58⋅1) = 3480 + 58 = 3538
If we go up another order of magnitude, then the system starts really grinding to a halt though tbh :)
For whatever reason, 6x7, 6x8, 7x7 and 7x8 are a persistent hole in my ability to memorize. Sure I can temporarily memorize them, but they shortly evaporate back into the void and I’ll have return to quickly having to calculate them out again.
I’ve also got this thing where I get mixed up between verbal “eleven” and “twelve”. They sound different, but at the same time somehow sound just similar enough that the boundary that should exist around them as symbols never properly formed. I have to pause and manually match the number to the sound, every time. What’s especially funny to me is I have no such problem distinguishing between onze and douze from French, which I only know a few words of and certainly never hear in real life.
I’d like to think the first problem I’d eventually fix if I was using those multiples constantly, but I’m not so sure because the second problem definitely doesn’t improve.