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Finger binary

en.wikipedia.org

50 pointslobo_tuerto48 comments

I love to teach finger binary to kids but they always start giggling when I hit 4 and they never really ignore it :(

Ha! I find that I can tap my fingers on a surface easier than pulling fingers down in many of those combinations. Perhaps it would be less distracting if they saw you just lowering the middle finger onto a table?

My friend and I tried to use this method while scuba diving to communicate how much air we had left. It seems perfect- 1 quick flash of 5 fingers can display any number between 0 and 31, which in this system would be 0 to 3100 PSI.

(Scuba air in the US is measured in PSI and scuba tanks cap out at 4500 PSI, and since you never care about accurately communicating your air level unless its down past 50% or so, the upper limit of 3100 is sufficient)

Unfortunately, since thinking in binary doesn't come naturally to us, we would have to convert the binary into decimal in our head, which is difficult, error prone, and ultimately more work than just using one of the tried and true methods for communicating how much air you have left. We went back to the normal way after a few dives.

I think with practice though it could work.

What kind of tanks were you diving with at 4500psi? I worked for a scuba shop for a couple years and we never did even a hot fill past 3400 on an aluminum tank, never mind steel tanks.

You're right, I'm mistaken. 3400 PSI on our high pressure steel tanks. You can tell it's been a while since we dove a lot =P

You can also go pseudo-base-5, which will get you 99 and it's relatively easy to know where you are: right hand fingers are 1s, right hand thumb is 5, left hand fingers are 10s, left hand thumb is 50. Edit: Someone in another comment points out this is just Chisanbop: http://en.wikipedia.org/wiki/Chisanbop

ViHart did a video on this: https://www.youtube.com/watch?v=OCYZTg3jahU

When I first tried this, years ago, I found it too awkward. I eventually settled on using my thumbs for five, and my fingers for single digits (like a Japanese abacus).

This feels reasonably comfortable to me, is easy to use, and covers a sufficient range of numbers for my needs.

Sounds like Chisanbop/Fingermath:

https://en.wikipedia.org/wiki/Chisanbop

Yeah, pretty much identical, except there is no table involved. Thanks for the link.

There is another trick, which yields 12 digits per hand.

Using your thumb, tap each of the 3 joints of your fingers as you count, starting from the base. Go from your index finger to the pinky. If you need more, just wrap around and continue counting.

http://en.wikipedia.org/wiki/Sexagesimal

It explains why 12 and 60 are such important numbers for measuring time and angles, amongst other things.

This is how I taught my daughter binary when she was 6 years old. It stuck with her and is the one thing I taught her that I can point to as giving her confidence in math. When I was satisfied with her retainment, I bought her one of those, "There are 10 kind of people..." shirts. She still wears it.

She has yet to figure out why my wife and I laugh when she gets to 4.

In primary school my mom told me she learned different bases of numbers in math. She said her dad kept saying "who would ever need this!"

That is awesome. I feel that kids today are expected to be successful but not really learn; at least here the US. Though, in my daughter's school they are learning simple circuits in the 4th grade.

Coolest dad ever!

Thanks! She worked the code.org lessons and has been working through codeacademy lessons recently. She wants to build a game with me; so, it is way to have productive quality time together.

Clearly. And to mix fun with learning.

Brings new meaning to the word "digital". I'll be here all night.

I mean, that is the origin of the word "digital":

>1650s, "pertaining to fingers," from Latin digitalis, from digitus (see digit). Meaning "using numerical digits" is from 1938, especially of computers after c.1945; in reference to recording or broadcasting, from 1960.

Source: http://www.etymonline.com/index.php?term=digital

On my college freshman orientation sheet, I put down counting binary by finger as something "interesting" I knew. Afterwards , I felt silly but now that there is a dedicated Wikipedia page, I feel better.

Using whole fingers for binary is more useful on a table or when trying to remember numbers.

On the go, I find myself using the finger-bone counting method, where you use your thumb to point to each of your finger bones (3 per finger) allowing you to count 12 on a hand. This probably has a name since it's so easy. And 12 has lots of really nice factors when doing math on the go.

If you point at the joints plus the tip of each finger, you have 4 positions per finger (i.e., nibbles), which can be useful for working through power-of-2 stuff.

This has a reference to how I got taught which months have 31 days: knuckles (31) vs space between knuckles (30/28) days. As between July and August you have to skip hands, that's the only two months in succession with 31 days.

Cute:

  It is possible to use anatomical digits to represent numerical digits[...]

Also, 8 and 23 are really difficult for me (and the left hand equivalents).

This thing makes me so nostalgic. There was a "magic" which we kids used to play with others in primary.

We created a list of 15 random items, and asked one to pick anyone of it. After which we asked the volunteer to tell which of the four sublists has the item. When this was done, we proudly told him / her what was it and it literally left them clueless how we did it, until of course, the trick went viral and everyone was doing it with others.

I don't think I understand the trick. Could you explain it more? It sounds very interesting...

An idea I had -- perhaps it's been already thought by lots of people:

Use the binary system to give access to tons (well, at least 128 or 256) notes to a musical instrument design.

You just need like 8 buttons (compared to over a dozen for a flute or 88 for a piano), so you can make it quite compact.

I'm thinking of some digital controller like instrument, but if they could pull off an analog one, that would be interesting too.

I'm far from a musical expert, but I thought this was essentially how many instruments work: Each string/hole/whatever produces a different resonant frequency which is orthogonal from the others the instrument produces; therefore any combination of strings/holes/whatevers creates a sound that cannot be created by any other combination of strings/holes/whatevers.

Please, correct me if I'm wrong.

Edit (before someone nitpicks, I'll do it!): I'm aware interacting with instruments doesn't produce _only_ resonant frequencies; and that the off-resonance is what gives an instrument its characteristic sound, even when playing the same note as a different instrument.

That is exactly correct, for wind instruments at least: and in fact, some wind instruments have more than 10 holes or keys. But many combinations produce identical sounds, limiting the range of the instrument. The limiting factor on a wind instrument is the fact that it can only play a single note, (yes, with resonant frequencies, of course) and the length of the instrument, which determines the lowest note it can play.

Thanks for that. A little more to slow burn in my understanding of instruments before I eventually learn one!

The problem is the 88 keys don't just produce 88 notes. The combinations also produce unique sounds. Of course there aren't 88! factorial combinations in practice, but you couldn't get the necessary range from 8 keys.

You can also half-bend fingers and use base 3, getting up to 59048, even though some numbers are somewhat complex to "form"

Range of 1023 versus 10 for decimal. I like it.

The number 132 is pretty unfortunate. Showing it might cause miscommunication.

"Normal" counting is unary (base 1, amount of fingers shown = number represented). Decimal would mean 10 states for each finger.

It can be whatever you want it. 10 states for two hands. Or take 8 fingers and you get a byte.

If it were decimal you'd be able to show us 6552920451 using your ||||||||||

Hopefully nobody will be offended by 4.

Curiously, the example photos don't demonstrate the obvious values of 4, 128, or 132. http://en.wikipedia.org/wiki/Finger_(gesture)

Oh, someone already addressed this: https://news.ycombinator.com/item?id=6863804 ;)

No 22 either

Or 69!

Reminds me of a finger binary ASCII art generator for Python: https://gist.github.com/sublee/600592

My dad taught me how to count like this when I was a child. Only he taught me to use my thumb as the 16 place, which makes it easier to count quickly in my opinion.

Cool, I was looking for a system to implement Ender's Game's 5-fingers keyboard. ASCII to hex to binary to finger binary!

I think Doug Engelbart deserves credit for introducing the chord keyboard, which he demonstrated in "The Mother of All Demos", not a fictional book written by that homophobic anti-American bigoted foaming at the mouth lunatic Mormon cult member who sits on the board of directors of the National Organization for Marriage. https://en.wikipedia.org/wiki/Chorded_keyboard http://www.youtube.com/watch?v=JfIgzSoTMOs http://americablog.com/2009/04/mormon-leader-of-nom-appears-...

I own an original Enbelbart chord keyboard and mouse set. It was given to me by a friend who worked at SRI, who maintained Doug's PDP-10 that he used to give demos of his work. Some day I hope to hook them up to an Arduino, so I can use them on a more portable computer that a PDP-10!

I've been meaning to make a habit of counting this way, but it's quite rare that I count using my fingers at all.

I could cycle through all 1023 combinations in under six minutes when I was 17... Hmm... Misspent youth!

How come Wikipedia doesn't show how to do 4?

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