this post was submitted on 30 Sep 2023
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So what do we do when we get to base 10? Do we use A, B, C, etc? No: Numbers larger than about 3.6 million are simply illegal.

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[–] [email protected] 54 points 2 years ago (1 children)

Finally, a system that uses more information to express less information.

[–] [email protected] 20 points 2 years ago (1 children)

According to this article, the factoradical system gets efficient for numbers larger than 20!, but i guess this here is a shining example of ~~less is~~ more is less

[–] [email protected] 1 points 1 year ago

It begins to improve related to regular base-10 after, well, 10!, but it takes a while to recover for lower base numbers before that.

[–] [email protected] 44 points 2 years ago (1 children)
[–] [email protected] 25 points 2 years ago (2 children)

I fell like this one really needs the explainxkcd and I still don’t get it 🤣

[–] [email protected] 19 points 2 years ago

The idea is, each number is expressed as a sum of n factorials, with n being the number of digits in the number post-conversion. You start with the highest factorial that you can subtract out of the original number and work your way down.

1 becomes 1, because 1 = 1!, so the new number says "1x(1)".

2 becomes 10, because 2 = 2!. The new number says "1x(2x1) + 0x(1)".

3 becomes 11, because it's 2 + 1. The new number says "1x(2x1) + 1x(1)".

21 becomes 311: 4! is 24, so that's too big, so we use 3!, which is 6. 3x6 = 18, so our number begins as 3XX.
That leaves 3 left over, which we know is 11. The new number says "3x(3x2x1) + 1x(2x1) + 1x(1)".

[–] [email protected] 10 points 2 years ago

I appreciated them correcting Randall's bad alt-text math - he was off by a power of ten!

[–] [email protected] 21 points 2 years ago

Good grief, it's far too early in the morning for this sort of thing. My brain hurts now.

[–] [email protected] 15 points 2 years ago

This is cursed, haha

[–] [email protected] 10 points 2 years ago (3 children)

What's the point of such a system ?

[–] [email protected] 6 points 2 years ago

Hum... Have you checked what site it's on?

[–] [email protected] 5 points 2 years ago

Idk trolling

[–] [email protected] 4 points 2 years ago
[–] [email protected] 7 points 2 years ago

0 = 0

1 = 1

2 = 10

3 = 11

4 = 20

5 = 21

6 = 100

101, 110, 111, 120, 121,

200, 201, 210, 211, 220, 221, 300, 301...

Amidoinitrite

[–] [email protected] 7 points 2 years ago* (last edited 2 years ago) (1 children)

This is actually a pretty cool idea.

[–] [email protected] 1 points 2 years ago (1 children)

Not really. The reality is that the only real metric for the utility of a notation is the speed of computation. A constant positional notation system is the most efficient, then you just optimise for a base whose multiplication table can be memorised (27 is a good one). Many people are under the impression that highly composite bases are better, but the reality is that it only optimises for euclidean division which is far out weighed by multiplication and addition (and can be easily computed using them).

[–] [email protected] 1 points 2 years ago

Well I didn't say practical or efficient, it's just a cool idea :)