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Comment by modo_ | Hacker News Reader

Cool! I've noticed a similar way of counting that's still quite common today in China. They point with their thumb to each segment of their four fingers to count up to 12 on one hand. The other hand tracks the number of 12 counts, which lets you keep track all the way up to 144 with both hands.

Not quite on the level of the Romans, but still a solid improvement over how I've done it my whole life!

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And the Babylonians, whose base-60 system's legacy lives on in our timekeeping, used the finger segments on one hand and entire fingers on the 2nd hand to count to 60.

Yeah, I use that one when I need to hand-count somewhat large quantities. The Roman system is better (larger numbers), but I can't independently bend my pinky, ring or middle fingers, so it's unusable sadly.

forgive my question, I am probably missing context and I am curious: why are you hand counting large quantities?

I mean, why do you keep it on your fingers rather than just counting out loudly, or possibly just keeping on the fingers numbers up to ten repeatedly for "double checking"?

I know there are clicker tally counters which can be useful for e.g. counting cattle or people on a plane, but counting up to 60 seems feasible in your mind.

Not parent, but back when I was young and couldn’t afford a sports watch, I kept track of distance while running by counting steps. I would count up a hundred step pairs in my head, and increment a counter on my fingers on each hundred. (I also used a simple system of my own devising to allow counting up to 99 on my fingers.)

I one little sentence, you answered a lifelong question. Why 60?

Thank you!

60 has nice properties, in that it is evenly divisible by 2,3,4,5,6,10,12,15,20,30. Helpful as a base since you can divide it into smaller units easily (monetary, measurement, etc).

Funny i just started reading(half way through, its a hard book to read) Micheal Hudson book "...And forgive them their debts" talks about bronze age economics etc and debt forgiveness and how their number base was usually taken for interests calculations.

The Babylonian Base-60 also obviously survives in a lot of circle measurements: degrees, minutes:seconds. While the metric system has mostly moved on to radians, metric proponents (and esp. the French Revolution) failed to find a base-10 time system that people could agree on that matches the convenience of Base-60 minutes:seconds.

Which arguably suggests we didn't settle on base 10 because we have 10 finger as seems to be often told. We settled on base 10 likely because of politics (in the broader sense of the word)

I imagine there's a natural gravitational pull toward base 10 from having fingers, and throughout prehistory and early civilization occasionally systems deviated to suit certain purposes (like sibling comment about even divisibility of 60) but usually came back to using 10. We've always needed to count, been smart enough to count, and had 10 fingers readily accessible to count, so I wouldn't count that theory out :)

I think the biggest strength of base 10 is not hand-counting (the OP and the Babylonian/Chinese base-12 method are both superior in that regard), but ease of performing pen-and-paper operations. You can literally teach a 6-year-old to multiply huge numbers effortlessly.

Couldnt you do the same using two additional digits? Say binary and hexedicmal arithmetic are as easy as decimal if you substract the bias of being used to decimal.

If you use any other base for writing numbers down, it's just as easy to perform pen-and-paper operations. The only problem with larger bases is that the multiplication tables increase quadratically. Whereas a base-10 multiplication table has 100 entries, a base-16 table already has 256 entries.

>a base-10 multiplication table has 100 entries

Not quite! You can safely ignore identities (0, 1, and 10 itself) so you only have 8 numbers in your table. And multiplication is commutative so you only need 8+7+6... (= (8+1)(8/2) as per Gauss) = 36 entries.

Base 16 would have (14+1)(14/2) = 105 entries. So proportional to base-10, actually slightly harder than you said.

The classic - detailed correction followed by "but yea you're totally right anyway" lmao

A fine demonstration how "basically correct in two sentences" is better than "technically correct in five sentences" in most situations.

This video convinced me that base 6 would be even better for simple pen-and-paper math, as well as just about everything else: https://youtu.be/qID2B4MK7Y0

It was a long time ago, so not likely anybody wrote it down. But wasn't it from India? Counting-sticks in boxes, when you got to nine (maybe all that would fit in the box?) you put one stick in the next box and 'cleared' the lower-significant box. Apparently zero is a drawing of an empty box...

And if you add the under part of each finger you get 16 x 16, which is pretty handy for software engineers because it overlaps the increments used in the binary system (16, 32, 64, 128, 256)

I've read that societies that used such a system for counting used base 12 (instead of base 10), and had names for one digit representations of numbers 10 and 11.

Such as system allows for quarters and thirds to be whole numbers, and is much more powerful once you get used to it.

Many of our numbers come from merges between the two base systems (12 hour days, 12 inch foot, etc.)

To clarify, I was taught that the reason we use base 10 is that we have ten fingers. In societies that used a twelve jont counting from a young age, they use base 12. I suspect that the reason that most people find subtraction harder than addition is that they have been doing addition from a younger age.

One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve... they're unique names. Then comes thirten, fourten.

Ten, eleven and twelve are unique names and probably have their entymology derived from a base-12 numbering system once primarily used in Anglo-speaking countries.

“Twelve” is suspiciously similar to “two” however, which makes me wonder about its origin.

It's simple enough to Google "etymology eleven" to see that it is a base 10 word.

Modern proponents of a dozenal system seem to prefer the words "el" and "doz" for eleven and twelve. I would totally be in for changing, but realistically it'll never happen.

Numberphile on the dozenal system: https://youtu.be/U6xJfP7-HCc

This reminded me of the system of musical notation using finger segments. http://www.openculture.com/2014/03/watch-the-guidonian-hand-...

A bit complicated. I am learning Tabla, and my teacher counts to 16 on one hand; 3 finger segments plus the bit below the finger, for a total of 4 per finger. Starts from top of index finger and ends at bottom of pinky finger.

In this way, each bar is one finger.

Thinking about my fingers while hitting something with my fingers might be a bit much for my brain! But actually it seems quite intuitive to layout a beat pattern that way. Thanks for prompting me to search what Tabla is, there is some great artists out there.

Actually, you don't do those things at the same time. The finger thing is mostly for clarifying the beat patterns before you start playing. On the Tabla, or actually in Northern Indian music, you do things like play a 27 beat bar and a 16 beat bar at the same time, and pseudo merging back on the 80th beat (16x4 and 27x3-1).

For a 5th position per finger you can add your fingernail. Count to 400 with both hands. Also has the nice property of 100 per finger on the second hand.

I and some friends in college sometimes used binary finger counting: it's a simple 10-bit finger up/down that counts up to 1023 on two hands.

It's also kind of obvious communication style if you are doing a lot of assembly programming or logic gates programming, so we certainly didn't invent the idea.

It got to the point that "132 to you" was a verbal shortcut/joke for a particular rude gesture that naturally results from counting to 132 this way.

I've used this before for counting. The way I've done it is based on what fingers are touching the desk, or my leg. Reason being, it's kind of awkward holding up/down some finger combinations in the air enough where it's distinct (eg only ring finger up).

So for me it doesn't work too well for communicating numbers, but counting works fine.

Yes, some finger combinations are interesting dexterity challenges (varying among individuals, too), which is why the hysteresis/expectation setting of what's up or down can be important when using it for communication (outside of 132 of course, which is usually pretty obvious). I vaguely recall having at least one drunken conversation with an electrical engineer about what the "voltage equivalent" was for various finger positions might be and what your finger logic gate would need to accept to properly determine finger binary state.

I grew up counting the segments on each hand, twice. But the 2 segments of the thumb are also included (you use the index to point at the thumb).

Total comes up to a much-shorter 14x2 = 28 though.

Sum types versus product types.

You’re doing

     data Number = Left Segment | Right Segment

but

     data Number = BothHands Segment Segment

is possible.

I just love how this illustrates the names sum and product types.

    permutations(sum of Segment) == permutations(Segment) + permutations(Segment)

vs.

    permutations(product of Segment) == permutations(Segment) * permutations(Segment)

(Edit: permutations is the wrong term, it should be cardinality or a non-mathematical concept like some colloquial concept of “variations” )

I don't think "permutations" is the right word. You probably want "cardinality".

You are right, I was thinking more from a programmers practical perspective and started with the word «varations» and changed it to «permutations» without thinking it through.

Thanks for the correction!

This is the same way I learned growing up in India as well.

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