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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.

Lunchtime Nikola Feature: graphviz

Since we are in the process of adding a plug­in re­po for Niko­la, I want­ed to add a sim­ple plug­in there so that we can show how it work­s.

So here it is. You use this:

.. graphviz::

   digraph foo {
       "Idea" -> "tap tap tap" -> "Code";
   }

And you get (as­sum­ing graphviz is in­stalled, and this plug­in is in­stalled, etc.) this:

Read more…

Hola, estoy supuestamente cometiendo un delito. Policía!

Di­cen las malas lenguas que el go­b­ier­no pro­vin­cial de Tu­cumán ha pro­hibido el uso no ofi­cial de la pal­abra Policía. Si bi­en no en­cuen­tro en ningún la­do el de­cre­to o lo que fuere que sea que se supone que hicieron (con lo que de­bo asumir que no ex­is­te) acá es­tá mi pe­queño gra­no de are­na por las du­das:

Que con­ste que la policía tu­cumana en sí me la fu­ma en pi­pa y que el go­b­ier­no pro­vin­cial de Tu­cumán me la fu­ma en nar­guile, pero si va­mos a em­pezar a de­cir que no se pueden us­ar al­gu­nas pal­abras, la solu­ción es us­ar más pal­abras, y us­ar­las más segui­do.

Si me lle­gan a ini­ciar una causa (que no cre­o) les cuen­to.

Acá es­tá la "noti­ci­a"

Así que ya saben es­ti­ma­dos chichipíos tu­cuma­nens­es, yo (Rober­to Alsi­na) acabo de abrir una cuen­ta en una de las re­des so­ciales mas grandes, que no so­lo usa la pal­abra "policía" si no que usa "policía tu­cumana" y la es­toy us­an­do para man­dar fru­ta so­bre ust­edes. Denún­cien­me, por fa­vor, que quiero ser famoso.

Trivial Nikola Deployment Using Pancake.io and Backlift

So, you want to pub­lish a site and want to do it now? As in, re­al­ly right now? And for free? And you are a Niko­la us­er.

If you are a Dropbox user, open an account at Pancake.io Then set your OUTPUT_DIR to something like /home/yourname/Dropbox/Apps/Pancake.io and build. That's it. No deploy step.

Or open an account at Backlift and set OUTPUT_DIR to /home/yourname/Dropbox/Backlift/foo where foo is your site's name as configured in Backlift. Build. No deploy step.

Or open an ac­count on Drop­Pages.­com or KISSr or Site44.­com or just use a Drop­box pub­lic fold­er.

Each of these ser­vices has ad­van­tages and dis­ad­van­tages, from lame URLs to cost­ing mon­ey, but hey, for a quick thing they are cool. You can al­ways up­grade to the re­al thing lat­er.


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