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by throwupper247 3792 days ago
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

2 comments

> 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.