The one I came up with used both hands. Each finger on one hand has 9 points - three on the left side, three on the middle surface, and three on the right - which were the values 1-9. The fingers of the other hand indicate the point, by touching the point. If the value is 0 then there's no touch.
I find using the thumb for the first digit much better, since it's the one switching each time when counting up or down. I use this for counting down reps on one hand and sets on the other during exercise.
18 is conspicuously missing, is anyone (everyone?) incapable of extending both their thumb and their ring finger? Or extending their ring finger alone, without using their thumb to hold down the middle finger?
On my right hand, I can move my ring finger as independently as any other, but on my left hand, I cannot extend it fully by itself. I can extend it if I simultaneously extend the adjacent pinky, but not alone.
The muscle which extends the ring finger (at the MP joint at the base of the finger) also extends the middle finger.
It’s basically impossible (for me at least) to simultaneously flex the middle finger at that joint while extending the ring finger, unless I relax the relevant muscles and use some other force (e.g. my other hand) to hold my middle finger down or my ring finger up.
More generally, there are lots of shared muscles between the last three fingers and especially between middle and ring fingers, so moving them with some degree of independence takes training and isn’t ever perfect. The index finger and thumb are much more independent and flexible.
You can flex the middle joint on the middle finger while mostly extending the ring finger, to sort of make a passable #18 by the scheme in the wiki article. Overall though that binary counting method isn’t all that well aligned with comfortable finger motions. A better one could probably be developed, but it might be a bit more complex.
If you lock your fist, you can extend your ring finger, then your thumb -- leaving the other three fingers "hanging" in your fist. Will probably be a little painful, and won't be pretty -- but it's (sort-of) possible.
Ah, misspent youth!... I remember having completions with my friends, at 17, to see who could cycle through all 1024 states the fastest. AFAIK, I'm still the record holder at just over six minutes. I'm 33 now, with no sign of arthritis ;)
Just as there is a pattern to "regular" binary coding, there is a pattern to the Gray code -- albeit, perhaps, a more complex one. I'd imagine that after practicing counting from 0 to, say, 15, you'll be able to count further up on your own.
It helps me visually understand and debug bitwise operations. I suppose you could also compare inputs and outputs by printing the resulting integer as binary text, but I've always just used my hands.
It can also be nifty for ASCII conversions, as letters A-Z and a-z are the numbers 0-26, but with different prefixes (010 and 011 accordingly). This means you can read people's binary tattoos.
Oooooh, I love "guess what the interviewer is thinking instead of answering his question."
For example the natural response might be, "Well, I personally can count to ten" and, after you pressed about alternative schemes: "On a more theoretical level you could of course enumerate way more states than ten using your fingers. Just think of American sign language, which has 26 letters only one of which includes motion (the Z).[1] And that's on a single hand, so just counting the letters in ASL only - and no other gestures, you can count to at least 676. Add a few more static hand shapes - there are lots of shapes in ASL- maybe try to learn a hundred per hand, which is good because you can encode two digits in each hand, I could confidently count to 10,000 using just my fingers. It would probably take no more than a few days to learn."
Would I pass your interview? Probably not, because it wasn't what you were thinking of. Even though I just showed you that I could count to ten times higher than the number you were thinking of.
And I wouldn't even mention what I was REALLY thinking which is "Hmmmm, I wonder where the limit is. A human hand has about 26 degrees of freedom, so two hands have about 52, if we encode a degree using just 2 bits - one of four levels of flexion - we're at 52 * 2 = 104 bits. So something like 10^31 = what is that 'ten nonillion'. I probably shouldn't say nonillion. No, I definitely shouldn't say nonillion. Probably even a million is pushing it, I shouldn't say that. But I bet it's possible - a million is just twenty bits, that's just 10 bits per hand, or two bits per finger and it's obvious that a finger has way more than 4 positions it can take - looking at my own hand my first knuckles are independent of the crook of the finger, it doesn't take much effort at all to control them independently.... I bet I can count to a million."
Maybe you wouldn't get the job not because you gave a different answer, but because you assumed the worst about the interviewer; that he was a fool who didn't know how to run an interview.
That's a shame, because if I were to ask that question in an interview (and I would be unlikely to merely because of the fact that too many people dislike those kinds of questions), that last discussion would be precisely what I would be hoping to hear.
In fisrt (2?) novels of The Baroque Cycle there is a section explaining this system and character who uses it as a trader. Wall street floor traders use(d) their own system for quickly flashing round numbers in ranges higher than ten http://1.bp.blogspot.com/-xRJQ7X06g_I/TgyPveGUbqI/AAAAAAAAAl...
I taught my wife to count this way. She is a teacher and 31 is about as big as a class gets at her school, so she can count her kids as they come in and still carry her books or her laptop etc. Its quite a simple pattern once you get then hang of it. She can just advance the count without thinking and then look at her hand and work out what she is up to.
I'd suggest inverting the numbers so that your thumb is 1, your index finger 2, you middle 4, etc. That way your more dexterous fingers do the fast movements of 1's, and 2s and 4s while your slower ring and pinky count up in 8 and 16s.
It really can be rather handy.
I find the most useful times is when you think of your hands as two five bit registers... when you need to count two things at once.
I've used this for years to count measures when playing with an orchestra. I have to continually support my instrument with one hand, so I use the other hand to count.
Do you think the numbers given as example are just randomly choosen?
7 (ok sign)
8 (pointing finger)
11 (should have been 13?)
12 (peace sign)
25 (satan/metal hand sign)
I learned this as a kid -- I think from a program in Cursor Magazine (distributed on cassette tape!) for the Commodore Pet. You can only count to 99, but it's a little more practical for base 10 calculation:
There is binary code, and of course you can represent it with fingers. Nobody does this, though. That is to say, there is no cultural practice of "finger binary". Finger binary is not a "thing" that's "out there". Whoever wrote this Wikipedia page just made it up. The Wikipedia must document the existence of real things that are out there, and can be properly referenced.
Should there be a Jelly Bean Binary wikipedia page, just because you can use jelly beans of two colors to represent binary? How about Othello Binary? Using the two-colored chips from the disc-flipping game for counting in binary?
> That is to say, there is no cultural practice of "finger binary".
... That you know of. When did you memorize the exhaustive list of all cultural practices?
> Finger binary is not a "thing" that's "out there".
... In your social circle. If someone mentions a programming language you've never heard of, do you immediately decry them as having "made it up"?
I was taught finger binary several years ago as a way of counting the WPM of speeches. The method I use puts the LSB on the index finger, and involves tapping a table rather than forming a fist, in order to count more quickly. I have since taught several others. This certainly qualifies it as a cultural practice that's "out there."
While you can count very high using this method, it's quite difficult to make some of the numbers. I've found the optimal tradeoff to be base-6; using one hand to keep track of the first position and the other the second position.
54 comments
[ 2.8 ms ] story [ 116 ms ] threadThis could encode the values 0-99,999.
On my right hand, I can move my ring finger as independently as any other, but on my left hand, I cannot extend it fully by itself. I can extend it if I simultaneously extend the adjacent pinky, but not alone.
It’s basically impossible (for me at least) to simultaneously flex the middle finger at that joint while extending the ring finger, unless I relax the relevant muscles and use some other force (e.g. my other hand) to hold my middle finger down or my ring finger up.
More generally, there are lots of shared muscles between the last three fingers and especially between middle and ring fingers, so moving them with some degree of independence takes training and isn’t ever perfect. The index finger and thumb are much more independent and flexible.
You can flex the middle joint on the middle finger while mostly extending the ring finger, to sort of make a passable #18 by the scheme in the wiki article. Overall though that binary counting method isn’t all that well aligned with comfortable finger motions. A better one could probably be developed, but it might be a bit more complex.
http://www.madsci.org/posts/archives/2005-05/1117326759.An.r...
https://news.ycombinator.com/item?id=10131057
And actual submission: https://news.ycombinator.com/item?id=10128815
I can count binary. I don't know which bit/finger to flip to count in gray code.
http://www.amazon.com/dp/B000BXFN4E
(notice that extended fingers indicate 0, not 1)
It can also be nifty for ASCII conversions, as letters A-Z and a-z are the numbers 0-26, but with different prefixes (010 and 011 accordingly). This means you can read people's binary tattoos.
For example the natural response might be, "Well, I personally can count to ten" and, after you pressed about alternative schemes: "On a more theoretical level you could of course enumerate way more states than ten using your fingers. Just think of American sign language, which has 26 letters only one of which includes motion (the Z).[1] And that's on a single hand, so just counting the letters in ASL only - and no other gestures, you can count to at least 676. Add a few more static hand shapes - there are lots of shapes in ASL- maybe try to learn a hundred per hand, which is good because you can encode two digits in each hand, I could confidently count to 10,000 using just my fingers. It would probably take no more than a few days to learn."
Would I pass your interview? Probably not, because it wasn't what you were thinking of. Even though I just showed you that I could count to ten times higher than the number you were thinking of.
And I wouldn't even mention what I was REALLY thinking which is "Hmmmm, I wonder where the limit is. A human hand has about 26 degrees of freedom, so two hands have about 52, if we encode a degree using just 2 bits - one of four levels of flexion - we're at 52 * 2 = 104 bits. So something like 10^31 = what is that 'ten nonillion'. I probably shouldn't say nonillion. No, I definitely shouldn't say nonillion. Probably even a million is pushing it, I shouldn't say that. But I bet it's possible - a million is just twenty bits, that's just 10 bits per hand, or two bits per finger and it's obvious that a finger has way more than 4 positions it can take - looking at my own hand my first knuckles are independent of the crook of the finger, it doesn't take much effort at all to control them independently.... I bet I can count to a million."
[1] http://www.lifeprint.com/asl101/pages-layout/handshapes.htm
"No, I wasn't flipping you off with both hands, I was trying to tell you the number 132 in binary."
I'd suggest inverting the numbers so that your thumb is 1, your index finger 2, you middle 4, etc. That way your more dexterous fingers do the fast movements of 1's, and 2s and 4s while your slower ring and pinky count up in 8 and 16s.
It really can be rather handy.
I find the most useful times is when you think of your hands as two five bit registers... when you need to count two things at once.
They missed 4 (the finger) 17 (phone sign)
Coincidence? I don't think so... Aliens, maybe.
https://en.wikipedia.org/wiki/Chisanbop
Should there be a Jelly Bean Binary wikipedia page, just because you can use jelly beans of two colors to represent binary? How about Othello Binary? Using the two-colored chips from the disc-flipping game for counting in binary?
... That you know of. When did you memorize the exhaustive list of all cultural practices?
> Finger binary is not a "thing" that's "out there".
... In your social circle. If someone mentions a programming language you've never heard of, do you immediately decry them as having "made it up"?
I was taught finger binary several years ago as a way of counting the WPM of speeches. The method I use puts the LSB on the index finger, and involves tapping a table rather than forming a fist, in order to count more quickly. I have since taught several others. This certainly qualifies it as a cultural practice that's "out there."
Finger hex is much simpler, though you can't count as high (2^5):
* Your thumb is the pointer
* Your other 4 fingers have 4 joints each
You can figure it out from there. That's 2^4 on each hand. You also could do the alphabet, with a few code joints[1] left over.
[1] Sorry, couldn't resist