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Comment by qb45 | Hacker News Reader

I think parent wondered how it's possible that she remembered 16+16=32.

Children raised on positional decimal arithmetic are "supposed" to figure that 10+10=20 or 20+20=40 and then add/subtract 5+5.

Of course it's easier to associate 15 with 16 than with 10 or 20, but the fact that she immediately knew 2·16 and was able to proceed further says something about either her experience with binary arithmetic or some tendency to spontaneously count in binary.

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I don't know, I always remembered things like 6+7 = 13 and if numbers I was adding were close to 6 and 7 I knew instantly how to proceed. Of course there's other tricks like, subtracting the 1 out of 6 to get 5 and then adding it to 7 making 8 then removing the 5 to get 10 with the other 5 and you are left with 10 and 3 which is easy, I guess.

At least for me it was just silly shortcuts that stuck with me like 6+7=13 or 7*7=49. Maybe why I'm little fixated to 7 is that 5 and below is easy, but with 6 and up things get little more "math-y", so with some quick shortcuts like these it's easy to adjust to 7. Or most likely I'm just full of shit, that is usually the case.

I think that's what you get with unsupervised learning.

Tricks only get you so far, you can't do 6+7 on fingers or 7·7 as (4+3)(4+3) (I had a huge problem with this one, too many numbers to track). So you fail. And when you fail, you memorize the problematic cases and go on with tricks based on those.

And yes, it's completely incomprehensible for people who learned the pencil-and-paper algorithms and think that those are the end of the world.

The real trick is nothing more than the distributive property.

  (2)(16) = (2)(15 + 1)

"Mathematical properties" are just hacks that become popular because they generalize. [0]

[0] http://slatestarcodex.com/2014/03/03/do-life-hacks-ever-reac...

In the decimal system it is just as easy to associate 5+5=10.

5xN is easier to remember than 16xN on account of 5 being the smaller number.

2^n is logarithmic whereas 5*n is linear. Arguably, logarithms are not too complicated, even if linear seems to be a degree easier, seeing that the decimal system is also logarithmic as that's a denser representation.

edit: how to enter an aterisk as the multiplication operator sign

> 5xN is easier to remember than 16xN on account of 5 being the smaller number.

By that logic, shouldn't it be easier to remember 7 * n than 10 * n, because 7 is the smaller number?

> 2^n is logarithmic

Also, as Jtsummers (https://news.ycombinator.com/item?id=10973381) points out, the function `n \mapsto 2^n` is exponential: its growth is significantly faster, not significantly slower, than exponential.

I didn't talk about growth, i was specifically thinking about a comment that called our number system logarithmic and it stands to reason, if you wan't to find x in 10^x=y, unless you do calculus in your head at the age of five, you may as well look at a grap of the exponential progression. now that's two incoherent arguments, but the latter should point out that it doesn't really matter which way, and the first alludes that there is something more basic to the logarithm, something easier to capture. If I look at the grid pattern in logarithmic plots, it's not a runaway progression but a nice repetition where the zeros in the end of the numbers at each 10^n interval behave like the unary number system, which is the basic positional system and arguably easier even then binary.

Please read 'linear' in place of the last word 'exponential' in my reply. Oops.

Re edit: Put a space between the * and the characters.

  5 * N

versus

5*N

Pairs of asterisks adjacent to non-space characters become markers indicating italicized text.

  5*N is easier to remember than 16*N

5N is easier to remember than 16N

Versus

  5 * N is easier to remember than 16 * N

5 * N is easier to remember than 16 * N

And I think the word you want is exponential, not logarithmic. Related to each other, since exponential expressions become linear on a logarithmic scale, but exponential describes the growth of 2^n better.

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