
Seximal: A better way to count [video] - aleyan
https://www.youtube.com/watch?v=qID2B4MK7Y0
======
gnicholas
In college, I noticed that my roommate counted things in chunks of three. I
had only ever counted items either individually or in chunks of two, but for
most physical items I count, there are fewer than 50 of them, and counting by
3s up to that number is about as easy as counting even numbers. I was
surprised to see that visually identifying three of an item was not harder
than going by twos. Of course, it's also faster to count by 3 than by 2.

I'd be interested to know if others count by 1, 2, 3, or something else.
(Another trick I learned working retail is to count out X coins, stack them
vertically, and then make more stacks of the same height. Much faster than
counting them all out individually!)

~~~
kjeetgill
I've always counted in 5s, or really more like a 3+2 or 2+2+1. The garden
party for me is keeping the number in my head so knowing the last digit is
always 0 or 5 makes it easy. Then you just add the remainder at the end.

That's roughly how you count change too.

Ex: if I were to count 21 items my mental count would be 2,3 [5] 3,2 [10]
2,2,1 [15] 2,3 [20] and 1. [21]

Hope that makes sense!

~~~
gnicholas
Very interesting — I'd like to try this. Do you have any sense of whether this
is as reliable as counting by one, two or three? That is, if you were counting
out something really important, would you do it this way? Was there much of a
learning curve?

~~~
kjeetgill
I think its advantage is reliability. I don't know if it does much for speed.

You can't make off by 1 or 2 errors because then you'd end up with a count
like 23 or 27. You're counting by 5... the last digit needs to be 0 or 5! And
you're not going to make an off by 10 error.

You can visually pick out 2s and 3s to make your 5 before you add them in.

~~~
jolmg
In my experience, you can make off by 1 or 2 errors when you accidently
include 1 or 2 items in different groups of 5 at the same time. You end up
with 25 when you should have ended up with 23. It may also happen that you
don't include 1 or 2 items in the groups, because you thought you'd already
included them, while visually scanning the area. When that happens, you end up
with 25 when you should have ended with 27.

------
cjensen
Base-12 is nice because, like Seximal it is divisible by both the first and
second prime number (2 and 3). But it is also divisible by the first prime (2)
twice, and doesn't immediately overflow into extra digits.

So 10 in base 12 can be exactly divided by 2, 3, 4, 6, 8, and 9.

Compare this to base 10 where 10 can only be exactly divided by 2, 4, 5, and
8.

~~~
airstrike
How exactly can 10 be divided by 4 and 8?

~~~
thomastjeffery
In decimal:

10 / 4 = 2.5

2.5 can be represented exactly in decimal. As opposed to:

10 / 3 = 3.33333333333...

which cannot.

In duodecimal (10=dozen, A=ten): 10 / 3 = 4 A / 3 = 3.4

~~~
gowld
you need an extra blank line, or indent 3 spaces, to preserve linebreaks:

10 / 3 = 4

A / 3 = 3.4

    
    
         10 / 3 = 4
         A / 3 = 3.4

~~~
thomastjeffery
Unfortunately, it is too late to edit; but thanks!

------
resource0x
Only tangentially related, but it's fascinating how number 12 emerges in music
naturally. And the fact that 12 has many divisors is a _big_ coincidence
without which Western music as we know it would be impossible. I have a short
write-up on this:
[https://github.com/resource0x/concert0x/blob/master/doodle-s...](https://github.com/resource0x/concert0x/blob/master/doodle-
script.md#chromatic-scale)

~~~
contravariant
To the best of my knowledge the divisibility of 12 is rarely used in music.
Most chords consist use several different intervals.

The popularity of pentatonic music also suggests divisibility isn't
unmissable.

~~~
resource0x
It's very important in jazz. Diminished scale is all over. Augmented scale,
too (e.g T. Monk's tunes). Tritone substitution is the basis of
reharmonization (due to 12=6*2). Jazz uses everything (including pentatonic),
that's why it's so rich.

~~~
hessenwolf
So rich, and sounds like a racket.

------
mdellabitta
I was taught basic counting, addition, and subtraction using a finger-abacus
system called Chisanbop:
[https://en.wikipedia.org/wiki/Chisanbop](https://en.wikipedia.org/wiki/Chisanbop)

Now I'm plagued by off-by-one errors in my mental math, particularly when it
comes to intervals. If you ask me how many days there are between now and
Christmas, I will be uncertain about the answer unless I individually count
them all off on my fingers.

~~~
darkerside
Yeah, that's not an uncommon malady. That's why off-by-one errors are one of
the two most common errors in computer programming, along with naming things
and cache invalidation.

~~~
chalence
Thanks for the chuckle.

------
Aardwolf
I think hexadecimal is better, it has the advantage of super easy conversion
from/to binary, the most fundamental number system.

We just need a good naming scheme for counting in hex :)

~~~
FroshKiller
It's been posted before: [http://www.bzarg.com/p/how-to-pronounce-
hexadecimal/](http://www.bzarg.com/p/how-to-pronounce-hexadecimal/)

------
Asooka
Human brains seem to be suited to verbally counting in base ten however. I
mean, languages as unconnected as Japanese, Chinese, Russian, Finnish,
Hungarian, Italian, German, English, Navajo _all_ count in base ten. There are
of course outliers, but those tend to be very small isolated language
communities. I think the ease of communication in base ten for humans
outweighs any arithmetic improvements. You can always count things in groups
of 12 or 60 if you want to be able to easily divide the group, but keep the
numbers in base ten.

~~~
jagger11
Russian, German and English have the same language root (PIE), the same for
Finnish and Hungarian, so it's not an accident.

~~~
jwilk
> Russian, German and English have the same language root (PIE)

Same for Italian.

German and English are even more closely related: they are both West Germanic
languages.

~~~
yurishimo
I've heard this before and literally every time I hear it my mind is blown.

As a native English speaker, I cannot see any similar patterns between German
in English when I happen across random conversations on a site like Reddit in
German. But looking at romance languages, I can see more similarities.

Maybe it's because of my childhood environment in Texas, where most English
speakers learn some basic Spanish by interacting with other people.

I would love to see a passage of German that can be intuitively reasoned about
by an English speaker with no experience with German solely based on context
and perhaps root words.

In all honesty I'd probably get confused though. :(

~~~
DoreenMichele
Written German and spoken German are somewhat different, just like written and
spoken English are. You might find conversational German more legible.

There was an episode of Barney Miller where one of the cops was translating
for a German woman. At some point she says "Das ist mein bebe." Bebe is
pronounced very similar to baby and means the same thing.

I can't find a video of just the scene. It is Season 5, Episode 5 The Baby
Broker.

The Daily Motion has the episode, but it keeps glitching on me. I haven't been
able to get to the scene in question.

I also used to have German language resources that built on words that were
readily understood by English speakers.

------
tomtimtall
If you want to build a new counting system, Why not use new symbols for all
the numbers? I mean the practicality that 1-9 mean the samme when on their own
seem completely eclipsed by the fact that any number represented by more than
one symbol means something else. It’s like trying to “build a new better C”
where everything works “like you’d expect from C” as long as your program is
no more than 4 characters long.

------
cup-of-tea
Learning about positional number systems was definitely a challenge but one of
the best "mind opening" experiences of my life. I thoroughly recommend reading
chapter 4 of Knuth's _The Art of Computer Programming_ for the history of
counting systems and notation of numbers. I didn't realise how much of what I
thought I knew about counting was tied to decimal notation.

------
cecilpl2
This is hilarious :)

~~~
0xdeadbeefbabe
A studio audience would help me score higher on jokes received.

------
hessenwolf
I remember my maths teacher teaching that in 1995. He was pretty good at
explaining it, but not as good as this video.

We should really be seeing a great education dividend from the availability of
material these days.

------
russdill
There are a large number of seximalish systems. Degrees (360), hours, minutes,
seconds, am/pm hours, feet/inches, troy ounces, months in a year, etc.

------
yiyus
1 is not really a prime factor. But anyway, if you consider it a prime factor
for 12, you should consider it a prime factor of 10 too.

~~~
cup-of-tea
I think that was actually a joke. He surreptitiously only mentioned the prime
factors of ten (2 and 5) and then listed all the factors of twelve (1, 2, 3,
4, 6, 12). Ten, of course, has four factors: 1, 2, 5, 10 and twelve only has
two _prime_ factors as well: 2 and 3.

------
tehabe
How would metric measures work in such a system? Or time?

~~~
tomtimtall
The same as decimal metric measures. The reason metric measures play great
together is because of what you are counting (units), not the way you write
the count down on paper (the numbers representing decimal or decimal or even
just lines scratched in wood)

------
amelius
Related question: how do ducks count their offspring?

~~~
carapace
Holographic Reduced Representations

------
hessenwolf
Eighths are pretty nice in decimal..

------
compsciphd
same person posting the same video every so often

[https://news.ycombinator.com/item?id=17083858](https://news.ycombinator.com/item?id=17083858)

~~~
Nadya
Once is not "every so often" [0] and reposting something that you feel is
worthwhile but didn't gain traction is acceptable. This is mentioned in the
FAQ [1] as it's basically a "keep it reasonable" honor system. Sometimes when
you post something matters. For example, I've posted something and it got 1
upvote and fell off the front page - then was reposted 2 days later by someone
else and was on the front page for the day. I just had poor timing as there
were other far more popular stories going on at the time.

>Are reposts ok?

>If a story has had significant attention in the last year or so, we kill
reposts as duplicates. If not, a small number of reposts is ok.

On topic: I agree with Aardwolf, I prefer Hexadecimal but having a better
symbols for A-F would improve it.

[0]
[https://news.ycombinator.com/submitted?id=aleyan](https://news.ycombinator.com/submitted?id=aleyan)

[1]
[https://news.ycombinator.com/newsfaq.html](https://news.ycombinator.com/newsfaq.html)

~~~
compsciphd
so, you're right in a sense. I wanted a non video link to read about it, so
googled, and all I found up top was 2 hacker news links (apparently one of
them was the same as this, google indexed it pretty quickly) and the youtube
video (so didn't do me much good).

I assumed (incorrectly) that 2 links I saw via google would have made this 3
at least)

