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Hardcore Finger Counting

Ear­lier to­da­y, @el­no­mo­te­ta men­tio­ned in twi­tter that if you count wi­th your fin­gers you are in trou­ble, be­cau­se at least you ha­ve over­flo­ws.

That got me thi­nkin­g. Not about whe­ther the­re is an over­flo­w, sin­ce the­re is alwa­ys an over­flo­w, even if you count by elec­tron quan­tum sta­tes using the who­le uni­ver­se, be­cau­se in­fi­ni­ty, du­de, but about how hi­gh you can fin­ge­r-­coun­t.

Su­re, the naï­ve an­swer is ten, but tha­t's tri­vial to im­pro­ve. For exam­ple, he­re is a ve­ry sim­ple sys­tem to count to 99 but even that is ve­ry sim­plis­ti­c.

If you are a computer nerd, you may think you are clever by now saying \(2^{10}-1\) but really, how unimaginative is that? It's unimaginative enough that it has its own wikipedia page.

One thing I do (and I re­cog­ni­ze it as one of my most an­no­ying trai­ts) is to con­si­der unor­tho­dox an­swers to ques­tion­s. Be­cau­se often they wi­ll show that the one asking the ques­tion has on­ly a ve­ry va­gue idea of what he is askin­g, and ex­po­ses a ton of unex­press­ed as­sump­tion­s.

So, computer geek, \(2^{10}-1\), that is 1023. Congratulations, you have done much worse than the Venerable Bede, who in 710AD described in De Computo vel Loguela per Gestum Digitorum a system to express numbers up to 9999 using both hands.

So, le­t's thi­nk about the unex­press­ed as­sump­tions he­re.

Is a finger a bit?

He­ll no. A fin­ger is a fin­ge­r. Su­re, it can ex­press a bi­t, but it can al­so (in so­me ca­ses) ex­press mo­re. For exam­ple, I ha­ve 6 fin­gers I can bend in­de­pen­den­tly in mo­re than one pla­ce (thum­b, in­dex, pi­nk­y).

So, I could use those to have a ternary digit (if you pardon the pun), and count to \(3^6 2^4-1\) (or 11663)

Is finger-counting just about fingers?

If we consider it hand counting instead it's much better. For example, I could hold each hand palm-up or palm-down for 2 extra bits. That's \(3^6 2^6-1\) (or 46655)

Is finger-order relevant?

So, su­ppo­se I put my le­ft hand to the ri­ght of my ri­ght han­d. Sin­ce I can te­ll whi­ch hand is whi­ch, be­cau­se fin­gers are not all the sa­me, I can count that as an ex­tra bi­t, coun­ting to 93311.

How long can I take before I show you the number?

I could sa­y: "if a fin­ger­nail is lon­g, tha­t's a 3 (or a 4) de­pen­ding on whi­ch fin­ge­r". Su­re, it wi­ll then take me da­ys to ex­press a num­be­r, but I just rai­s­ed the num­ber I can count to, using my fin­ger­s, to a rea­lly lar­ge num­ber I wo­n't bo­ther cal­cu­la­ting (2985983)

Do I have to keep my fingers still?

Be­cau­se wi­th one fin­ger I could tap mor­se co­de for any num­ber gi­ven pa­tien­ce, a hard sur­fa­ce, a re­si­lient fin­ger and kno­w­le­dge of mor­se.

Can't I just keep on adding bits?

Of cour­se. I could bi­te on the ba­ck of my le­ft hand and lea­ve a ma­rk. I can use di­ffe­rent hand po­si­tions other than palm up/­do­wn and strai­gh­t/­cro­ss­e­d. I could ta­ttoo a num­ber on the pal­m. I could ex­press a URL to a si­te that con­tains a num­be­r. This is be­cau­se the amount of in­for­ma­tion on a per­so­n's hand is hu­ge.

So, su­re, you can count to ten, or 99, or 1023, or 2985983. The tra­deo­ff is, the hi­gher your sys­tem goes, the har­der it is to rea­d, and the mo­re pre­vious­ly agreed kno­w­le­dge you need be­tween the one ex­pres­sing the num­ber and the one rea­ding it.

Tha­t's why you sti­ll count wi­th your fin­gers just to 10. Be­cau­se it's ob­vious.

Chris Warrick / 2013-10-04 17:41:

The lazy bastard in me uses another system, the senary (or base 6) system, which just so happens to be described by the almighty Wikipedia[0], although it doesn’t get an entire article devoted to itself (just a section). Basically, one hand is devoted to counting sixes, while the other counts ones. So, for example:

00000 00001 1
00000 00010 2
00000 00100 3
00000 01000 4
00000 10000 5
00001 00000 6
00001 00001 7
and so on…


schettino72 / 2013-10-05 08:08:

Chinese people uses only one hand to count to 10. It is really used in practice, everyone knows that and it is quite convinient...

If you want to count over 10, fisrt you show the first digit than change the hand sign and show the second digit.

Lucio / 2013-10-05 09:48:

You can also use your thumb standalone (as proposed) and pointing to the other 4 fingers. Making it (7^2)(3^4)(2^4)==63504. (based on the Asian way of pointing to the finger bones)

I would say that morse code does not count, as the idea is that the hand plays the role of memory, not the case in morse code. :)

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