6 ms·
My maths teachers at school, like probably everyone else's, loved to tell us that we wouldn't be able to carry calculators around with us all the time when we'r
by efaref 11y ago
My maths teachers at school, like probably everyone else's, loved to tell us that we wouldn't be able to carry calculators around with us all the time when we're adults.
The joke's on them. I carry a supercomputer with wireless access to the collective knowledge of humanity in my pocket.
More seriously, if we assume we only have limited time and capacity to learn things, these tools surely free us from learning mundane "tricks" and allow us to further explore more interesting subjects. Sure, an understanding of arithmetic is important, so that we can verify our tools are working. But once that's obtained, let's move on.
- jarcane 11y agoYeah, except you look like a prick taking out your smartphone just to do some basic arithmetic. It's weird to me that a class of people who like to puff about how intelligent they are are so proud of refusing to function at an incredibly basic human skill.
- babuskov 11y agoShowing your intelligence at full usually requires that you are not distracted. That is hard to come by these days. I can calculate 16x180 in my head, but I would still pull out my smartphone to do it if the result is in any way important. Not because I'm lazy, but I know that the device won't make some silly mistake while doing it.
- Cyph0n 11y agoThat's a trivial calculation to do, so I think it would be hard to make a mistake. I think you could have provided a better example. Edit: To the poster below, you only need the multiplication tables and basic addition. I don't see the big deal. 18 * 10 = 180 10 * 6 = 60 8 * 6 = 48 = 288
- mobiuscog 11y agoI think you overestimate the capabililties of most people.
- jjoonathan 11y ago16x180 ... = 288 I think he overestimates the capabilities of himself. He also misidentified the tricky part of the problem as multiplication and addition. Holding intermediate place values is far more likely to cause issues, as we can see from his mistake. If we allow for simple mistakes, everyone here can do that multiplication in their head without issue. But that was babuskov's exact point. Calculators help with silly mistakes of this sort and they're present nearly everywhere.
- Cyph0n 11y agoI was calculating 18 * 16. For some reason I did not refer back to OP. The approach is similar however. I agree: holding values is quite difficult in many cases, but the whole discussion is about this example specifically. You only need to remember 3 values in this case, which should be easy for most people. And no I do not overestimate myself. I usually suffer from imposter syndrome.
- hueving 11y ago12x12 is the max for most memorized multiplication tables (at least in the US). 16x18 is going to require some actual mental work that is prone to errors.
- kqr 11y agoFor computer people, 16×18 is easily split into 16×20 - 16×2, which in turn is 320 - 32. If you don't know instinctively that 16×2 is 32 it might be a bit harder though.
- Cyph0n 11y agoSee my edit. The basic tables are all you need.
- Someone 11y ago16x18 = 17x17 - 1 = 289 - 1 = 288 Te squares up to 20x20 everybody should know by head. The only problem is that answer. Seeing 288 (2x12^2) immediately made me spend time double-checking the factors in the multiplicands.
- Joof 11y ago
- xbmcuser 11y agoThats not the answer he wrote 16x180=2880
- henry_vonfire 11y agoIt's funny how he ended up proving that @babuskov was right.
- Cyph0n 11y agoAh the extra zero makes it so very complicated. I was calculating 18 * 16 and didn't check OP.
- xbmcuser 11y agoThats not the answer he wrote 16x180=2880
- eachro 11y agoThat's still a bit slower than it needs to be. The real trick to doing something like is seeing that we have 10(18x16) = 10(17^2 - 1) = 10(289-1) Having the first 30 squares committed to memory has been pretty useful for me.
- bumbledraven 11y agoRight. And just to be explicit, we're using the fact that (x+1)(x-1) = x² -1. So to add in that step, it would be: 18 x 16 = (17+1)(17-1) = 10(17²-1)
- pdpi 11y agoMy preferred way of doing this is by subtracting instead of adding: 16*200=3200 16*20=320 16*180=3200-320=2880
- timthorn 11y ago> Showing your intelligence at full usually requires that you are not distracted. That is hard to come by these days. The irony that the loss of ability to concentrate is partly a result of smartphones is not lost on me.
- choosername 11y agoit's not "smartphones, it's the lack of adaption as evident from the disparity between generations. The speed of information, the signaltheoretic energy is just steadily increasing and small signals get lost in the noise ...
- DanBC 11y agoYou accept you might make a silly mistake while doing the calculation in your head. How do you know you won't make a silly mistake when you do the calculation using a machine? If you do both, or at least estimate the result, you can check the results. I don't think you'd make a silly mistake when using a calculator, but I think other people might. I think (although I have nothing to support me) that most people cannot use percentages in any meaningful way. If you say "I have a tv that currently costs $300, and I'm going to give you a 10% discount. What will it cost after the discount?" then they can show you the buttons they'd push to get that result. But if you ask them a slightly different version "I have a washing machine that currently costs $800. I've already given you a 10% discount. How much did it cost before the discount?" then I think you'll find a bunch of people who don't know what buttons to push. (Or worse don't know that they don't know and who'll get a close but incorrect answer.) So, that's not the kind of mental math trick talked about in the article, but calculators are tools and tools are most useful to people who know how to use them and most calculators and calculator apps don't make it easy for people who don't know math.
- meagain20000 11y agoWhat you are describing is high school math. Really simple high school math. Maybe even junior high school math. I would consider a trick something like, multiply large number by really large number in your head. That is a waste of time.
- Nadya 11y ago"Simple high school math" which is sometimes taught in a single hour of a single day and forgotten about by tomorrow because it isn't on the test and we really need to cover the quadratic formula before the mid-term. Something that I saw on HN not too long ago that really benefited me was something I should have been taught in school. I probably was - but as I mentioned. It was taught in a rush and I had forgotten it, if it was even taught at all. What is 36% of 25? I'll be honest. I find that's a pretty tricky one to do in my head. I can estimate it to 8 by taking 33% of 24 (close enough, right?). So I'd estimate it to be a bit over 8. Honest guess. Well the trick I learned on HN is to reverse it. Since % is really multiplication, the commutative property applies. Take 25% of 36 instead and bam! The answer is a flat 9. No estimating needed. Now the "I'm an idiot" part comes from the fact I always did percentage as multiplication of a decimal. I should have intuitively put 2 and 2 together and figured out the commutative property applies. I hadn't. :) Given the popularity and support the tip received - I'm going to guess I'm a good example of the average person. The average person was taught percentages in a way that they can convert to decimals but don't think about the math in decimal form. So they miss out on something that is obvious once someone stops and points it out. So to cut my rambling short: simple math is rarely simple for the average person. The average person, from my experience, is worse at math than they would probably like to admit. (And I'm also an average person.)
- kqr 11y agoThis is probably where I get bonus nerd points, but even before smartphones, it wasn't a huge hassle to carry a small slide rule. It still isn't.
- gherkin0 11y agoMine told me the same thing, and I listened. It turns out you can't think about numbers with a calculator.
- Joof 11y agoTurns out you don't need many numbers to think about math.