[NTG-context] Kaktovik numerals

[NTG-context] Kaktovik numerals

[Henning Hraban Ramm via ntg-context]

I just came across this thread about the base-20 system of the Inuit 
people and the numerals invented for it in the 1990s:
https://mathstodon.xyz/@johncarlosbaez/110215432175491555

This makes simple calculations just beautiful.

Hraban
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Re: [NTG-context] Kaktovik numerals

[Arthur Rosendahl via ntg-context]

On Tue, Apr 18, 2023 at 10:57:14AM +0200, Henning Hraban Ramm via ntg-context wrote:
> I just came across this thread about the base-20 system of the Inuit people
> and the numerals invented for it in the 1990s:
> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
> 
> This makes simple calculations just beautiful.

  It is beautiful :-)  Thanks for the pointer!

	Best,

		Arthur
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Re: [NTG-context] Kaktovik numerals

[Hans Hagen via ntg-context]

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On 4/18/2023 10:57 AM, Henning Hraban Ramm via ntg-context wrote:
> I just came across this thread about the base-20 system of the Inuit 
> people and the numerals invented for it in the 1990s:
> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
> 
> This makes simple calculations just beautiful.
interesting ... quick hack attached

Hans

-----------------------------------------------------------------
                                           Hans Hagen | PRAGMA ADE
               Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
        tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
-----------------------------------------------------------------

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%D \module
%D   [       file=meta-imp-kaktovik,
%D        version=2023.04.18,
%D          title=\METAPOST\ Graphics,
%D       subtitle=Kaktovik Numbers,
%D         author=Hans Hagen,
%D           date=\currentdate,
%D      copyright={PRAGMA ADE \& \CONTEXT\ Development Team}]
%C
%C This module is part of the \CONTEXT\ macro||package and is
%C therefore copyrighted by \PRAGMA. See mreadme.pdf for
%C details.

%D Just a quick hack for Hraban (after a post on the mailing list).

\startMPcalculation{simplefun}

    path kaktovik_glyphs[] ;

    def InitializeKaktovik =

        save p, d, u ;

        pair p[] ; numeric d ; d := .1 ; numeric u ; u := .15 ;

      % d := getparameterdefault "mpsfont" "d" .10 ;
      % u := getparameterdefault "mpsfont" "u" .15 ;

        p[0] := (0,1) ;
        p[1] := (1,0) ;
        p[2] := (2,1 -  d) ;
        p[3] := (3,0) ;
        p[4] := (4,1 - 2d) ;

        p[5] := (4,1 +  u) ;
        p[6] := (0,1 + 2u) ;
        p[7] := (4,1 + 4u) ;

        kaktovik_glyphs[0] := (1,1)  { right } .. { left } (2,1/2) { left } .. { right } (3,1);

        for i= 1 upto 4 :
            kaktovik_glyphs[i] := p[0] for j=1 upto i : -- p[j] endfor ;
        endfor ;

        kaktovik_glyphs[ 5] := p[5] -- p[0] ;                for i= 6 upto  9 : kaktovik_glyphs[i] := p[5] -- kaktovik_glyphs[i-5] ; endfor ;
        kaktovik_glyphs[10] := p[6] -- kaktovik_glyphs[ 5] ; for i=11 upto 14 : kaktovik_glyphs[i] := p[6] -- kaktovik_glyphs[i-5] ; endfor ;
        kaktovik_glyphs[15] := p[7] -- kaktovik_glyphs[10] ; for i=16 upto 19 : kaktovik_glyphs[i] := p[7] -- kaktovik_glyphs[i-5] ; endfor ;

    enddef ;

    vardef Kaktovik(expr i) =
        draw image (
            draw kaktovik_glyphs[i]
                xscaled (10/20 -1/20)
                yscaled (25/20 -2/20)
                withpen (pencircle xscaled 1/20 yscaled 5/20) rotated -(2*20)
              % withpen (pencircle xscaled 1/40 yscaled 5/40) rotated -(2*20)
              % withpen (pencircle xscaled 2.5/40 yscaled 5/40) rotated -(2*20)
            ;
        ) shifted (2/20,2/20)
    enddef ;

    lmt_registerglyphs [
        name     = "kaktovik",
        units    = 2,
        usecolor = true,
        width    = 2,
        height   = 2,
        depth    = 0,
        preamble = "InitializeKaktovik"
    ] ;

    for i=0 upto 19 :
        lmt_registerglyph [
            category = "kaktovik",
            unicode  = 119488 + i, % "0x1D2C0"
            code     = "Kaktovik(" & decimal i & ")"
        ] ;
    endfor ;

\stopMPcalculation

\startluacode
    interfaces.implement {
        name      = "kaktoviknumerals",
        arguments = "integer",
        actions   = function(n)
            local digits = { }
            local count  = 1
            while true do
                digits[count] = utf.char(0x1D2C0 + (n % 20))
                n = n // 20
                if n == 0 then
                    break;
                end
                count = count + 1
            end
            context("%t",digits)
        end
    }
\stopluacode

\unprotect

\permanent\def\kaktoviknumerals#1{\clf_kaktoviknumerals\numexpr#1\relax}

\defineconversion [kaktoviknumerals] [\kaktoviknumerals]
\defineconversion [K]                [\kaktoviknumerals]

\definefontfeature
  [kaktovik]
  [metapost=kaktovik]

\protect

\continueifinputfile{meta-imp-kaktovik.mkxl}

\definefontfeature
  [default]
  [default]
  [metapost=kaktovik]
% [metapost={category=kaktovik,u=.25,d=.20,x=}]

\setupbodyfont[dejavu]

% \nopdfcompression

\startTEXpage[offset=1ts,width=3es]

    \start
    \showglyphs
        KAKTOVIK
        \dostepwiserecurse{0}{19}{1}{\kaktoviknumerals{#1}\space }
    \stop

    kaktovik \start
        \red\glyphxscale 700
        \dostepwiserecurse{0}{19}{1}{\kaktoviknumerals{#1}\space }
    \stop

    \startitemize[packed,K][color=orange,stopper=]
        \startitem first  \stopitem
        \startitem second \stopitem
        \startitem third  \stopitem
    \stopitemize

    KAKTOVIK \start
        \red  \kaktoviknumerals{2023} --
        \green\kaktoviknumerals{4}    --
        \blue \kaktoviknumerals{18}
    \stop

    KAKTOVIK
\stopTEXpage



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Re: [NTG-context] Kaktovik numerals

[Willi Egger via ntg-context]

Hi!

dit is really interesting, I just spent two hours reading different sources. And yes, the SIL GentiumKatovik made the wikipedia show everything nicely!

Thanks Hraban

Willi

> On 18 Apr 2023, at 10:57, Henning Hraban Ramm via ntg-context <ntg-context@ntg.nl> wrote:
> 
> I just came across this thread about the base-20 system of the Inuit people and the numerals invented for it in the 1990s:
> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
> 
> This makes simple calculations just beautiful.
> 
> Hraban
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
> 
> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : https://contextgarden.net
> ___________________________________________________________________________________

___________________________________________________________________________________
If your question is of interest to others as well, please add an entry to the Wiki!

maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
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wiki     : https://contextgarden.net
___________________________________________________________________________________

Re: [NTG-context] Kaktovik numerals

[Willi Egger via ntg-context]

Hans, genial. Once you told to me “hoe krijg je het voor elkaar…”. Now I tell you, how do you get this done… the mail has not even had the time to “cool” down and you post this. I am astonished.

Kind regards

Willi

> On 18 Apr 2023, at 15:01, Hans Hagen via ntg-context <ntg-context@ntg.nl> wrote:
> 
> On 4/18/2023 10:57 AM, Henning Hraban Ramm via ntg-context wrote:
>> I just came across this thread about the base-20 system of the Inuit people and the numerals invented for it in the 1990s:
>> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
>> This makes simple calculations just beautiful.
> interesting ... quick hack attached
> 
> Hans
> 
> -----------------------------------------------------------------
>                                          Hans Hagen | PRAGMA ADE
>              Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
>       tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
> -----------------------------------------------------------------
> <meta-imp-kaktovik.pdf><meta-imp-kaktovik.mkxl>___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
> 
> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : https://contextgarden.net
> ___________________________________________________________________________________

___________________________________________________________________________________
If your question is of interest to others as well, please add an entry to the Wiki!

maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
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___________________________________________________________________________________

Re: [NTG-context] Kaktovik numerals

[Rudolf Bahr via ntg-context]

Am Tue, Apr 18, 2023 at 10:57:14AM +0200 schrieb Henning Hraban Ramm via ntg-context:
> I just came across this thread about the base-20 system of the Inuit people
> and the numerals invented for it in the 1990s:
> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
> 
> This makes simple calculations just beautiful.
> 
> Hraban
> ___________________________________________________________________________________


Very nice, Hraban, thank you for posting it!

Rudolf

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Re: [NTG-context] Kaktovik numerals

[Otared Kavian via ntg-context]

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Great indeed ! And the quick answer by Hans impressive, as usual…
What a great community !

Best regards: Otared

> On 18 Apr 2023, at 10:57, Henning Hraban Ramm via ntg-context <ntg-context@ntg.nl> wrote:
> 
> I just came across this thread about the base-20 system of the Inuit people and the numerals invented for it in the 1990s:
> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
> 
> This makes simple calculations just beautiful.
> 
> Hraban
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
> 
> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : https://contextgarden.net
> ___________________________________________________________________________________

Otared Kavian
e-mail: otared@gmail.com
Phone: +33 6 88 26 70 95





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___________________________________________________________________________________
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wiki     : https://contextgarden.net
___________________________________________________________________________________

Re: [NTG-context] Kaktovik numerals

[Henning Hraban Ramm via ntg-context]

Am 18.04.23 um 15:01 schrieb Hans Hagen via ntg-context:
> On 4/18/2023 10:57 AM, Henning Hraban Ramm via ntg-context wrote:
>> I just came across this thread about the base-20 system of the Inuit 
>> people and the numerals invented for it in the 1990s:
>> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
>>
>> This makes simple calculations just beautiful.
> interesting ... quick hack attached

Thank you very much!
I want to use this for paginations ;))

(Sorry for somewhat erratical response behavior – I’m quite busy 
preparing for the book fair in Leipzig…)

Hraban

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Re: [NTG-context] Kaktovik numerals

[Willi Egger via ntg-context]

Hi everybody,

because I am not a mathematician, I looked on the internet for more explanations for the Katovik numerals. I found on YouTube films, worthwhile to enjoy:

https://www.youtube.com/watch?v=fIZB4bRwxqI&ab_channel=Dave%27sMathVideos

https://www.youtube.com/watch?v=ObRFHiU_r9I&ab_channel=TheFerret

Willi

> On 18 Apr 2023, at 10:57, Henning Hraban Ramm via ntg-context <ntg-context@ntg.nl> wrote:
> 
> I just came across this thread about the base-20 system of the Inuit people and the numerals invented for it in the 1990s:
> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
> 
> This makes simple calculations just beautiful.
> 
> Hraban
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
> 
> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : https://contextgarden.net
> ___________________________________________________________________________________

___________________________________________________________________________________
If your question is of interest to others as well, please add an entry to the Wiki!

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___________________________________________________________________________________

Re: [NTG-context] Kaktovik numerals

[Willi Egger via ntg-context]

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Hi all,

after playing around and watching YouTube the attached  composition is made…

Willi

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% ConTeXT file
% filename: kaktovik-numerals-intro.tex
% W. Egger
% 19-04-2023

\input meta-imp-kaktovik.mkxl

\definefontfeature
  [default]
  [default]
  [metapost=kaktovik]

\setupbodyfont[dejavu]

\setuppagenumbering[location=footer]

\setuplayout
 [header=0pt]


\starttext
\starttitle[title=Kaktovik-numerals]

\startsubject[title=Intro]
On 18-04-2023 Haraban Ramm posted on the mailing-list about the Kaktovik numerals.
\blank
https://mathstodon.xyz/@johncarlosbaez/110215432175491555
\blank

The Inuit have a counting system based on the base 20. Back in 1994 in the local school at Kaktovik in Alaska students developed a counting system for the local language on the base 20. There is a subunit in the form of 5.

The counting system with base 20 is known in different cultures. e.g. The Mayans (Mexico) used a system with dots and horizontal bars.

Even in modern languages there are traces of the base 20 counting system. e.g. French express 80 as \quote{quatre-vingt} and 90 as \quote{quatre-vingt-dix}...

\stopsubject

\startsubject[title=Hans Hagen's implementation]

A couple of hours after Hraban's post, Hans came already up with an implementation of the Kaktovik-numeral-shapes in \METAFUN.

\blank

meta-imp-kaktovik.mkxl
\stopsubject

\startsubject[title=Further information on the Kaktovik-numerals-system]

https://www.youtube.com/watch?v=EyS6FfczH0Q&ab_channel=Artifexian

https://www.youtube.com/watch?v=fIZB4bRwxqI&ab_channel=Dave%27sMathVideos

https://www.youtube.com/watch?v=ObRFHiU_r9I&ab_channel=TheFerret

\stopsubject

\startsubject[title=The key to writing numbers in Kaktovik system]

In order to understand how numbers are composed hereunder is the way in the decimal and in the Kaktovik system.



\bTABLE
  \bTR
	  \bTD[nx=4,align=center] Decimal \eTD
		\bTD \strut \eTD
		\bTD[nx=4,align=center] Kaktovik \eTD
	\eTR
	\bTR
	  \bTD $10^3$ \eTD
		\bTD $10^2$ \eTD
		\bTD $10^1$ \eTD
		\bTD $10^0$ \eTD
		\bTD \strut \eTD
	  \bTD $20^3$ \eTD
		\bTD $20^2$ \eTD
		\bTD $20^1$ \eTD
		\bTD $20^0$ \eTD
  \eTR
	\bTR
	  \bTD 1 \eTD
		\bTD 0 \eTD
		\bTD 0 \eTD
		\bTD 0 \eTD
		\bTD \strut \eTD
	  \bTD 8 \eTD
		\bTD 0 \eTD
		\bTD 0 \eTD
		\bTD 0 \eTD	
  \eTR
\eTABLE

The following table shows the relation between the vertical bars (1 to 4) and the horizontal bars tuplets of 5

\blank

\bTABLE
  \setupTABLE[r][each][frame=off,align=flushright]
	\setupTABLE[r][even][style=\tfxx]
	\setupTABLE[r][odd][style=\tfd]
	\setupTABLE[c][1][frame=on]
	\setupTABLE[r][1][frame=on]
	\bTR
	 \bTD[frame=off] \kaktoviknumerals{0}\eTD
	 \bTD \kaktoviknumerals{1}\eTD
	 \bTD \kaktoviknumerals{2}\eTD
	 \bTD \kaktoviknumerals{3}\eTD
	 \bTD \kaktoviknumerals{4}\eTD
	\eTR
	\bTR
	 \bTD 0\eTD
	 \bTD 1\eTD
	 \bTD 2\eTD
	 \bTD 3\eTD
	 \bTD 4\eTD
	\eTR
	\bTR
	 \bTD \kaktoviknumerals{5}\eTD
	 \bTD \kaktoviknumerals{6}\eTD
	 \bTD \kaktoviknumerals{7}\eTD
	 \bTD \kaktoviknumerals{8}\eTD
	 \bTD \kaktoviknumerals{9}\eTD
	\eTR
	\bTR
	 \bTD 5\eTD
	 \bTD 6\eTD
	 \bTD 7\eTD
	 \bTD 8\eTD
	 \bTD 9\eTD
	\eTR
	\bTR
	 \bTD \kaktoviknumerals{10}\eTD
	 \bTD \kaktoviknumerals{11}\eTD
	 \bTD \kaktoviknumerals{12}\eTD
	 \bTD \kaktoviknumerals{13}\eTD
	 \bTD \kaktoviknumerals{14}\eTD
	\eTR
	\bTR
	 \bTD 10\eTD
	 \bTD 11\eTD
	 \bTD 12\eTD
	 \bTD 13\eTD
	 \bTD 14\eTD
	\eTR
	\bTR
	 \bTD \kaktoviknumerals{15}\eTD
	 \bTD \kaktoviknumerals{16}\eTD
	 \bTD \kaktoviknumerals{17}\eTD
	 \bTD \kaktoviknumerals{18}\eTD
	 \bTD \kaktoviknumerals{19}\eTD
	\eTR
	\bTR
	 \bTD 15\eTD
	 \bTD 16\eTD
	 \bTD 17\eTD
	 \bTD 18\eTD
	 \bTD 19\eTD
	\eTR	
\eTABLE

\stopsubject

\startsubject[title=Examples]

\starttabulate[|r|Mr|r|]
 \NC 20   \NC 1 \times 20^1 + 0 \times 20^0\NC \kaktoviknumerals{1}\kaktoviknumerals{0} \NC\NR
 \NC 30   \NC 1 \times 20^1 + 10 \times 20^0\NC \kaktoviknumerals{1}\kaktoviknumerals{10} \NC\NR
 \NC 40   \NC 2 \times 20^1  + 0 \times 20^0 \NC \kaktoviknumerals{2}\kaktoviknumerals{0} \NC\NR
 \NC 100  \NC 5 \times 20^1 + 0 \times 20^0\NC \kaktoviknumerals{5}\kaktoviknumerals{0} \NC\NR
 \NC 1000 \NC 2 \times 20^2 + 10 \times 20^1 + 0 \times 20^0 
 \NC \kaktoviknumerals{2}\kaktoviknumerals{10}\kaktoviknumerals{0}\NC\NR
 \NC 2023 \NC 5 \times 20^2 + 0 \times 20^1 + 3 \times 20^0  
 \NC \kaktoviknumerals{5}
 \kaktoviknumerals{0}\kaktoviknumerals{1}\kaktoviknumerals{3}\NC\NR
\stoptabulate

\blank
So the date of today would be:
\blank
19 - 4 - 2023
\blank
\kaktoviknumerals{19} -- \kaktoviknumerals{4} --
\kaktoviknumerals{5}\kaktoviknumerals{0}\kaktoviknumerals{1}\kaktoviknumerals{3}

\blank

Frappant is the possibility to solve arithmetic visually with these Kaktovik-numerals. The approach is to look how patterns fit in the left and right part of the equation.


\starttabulate[|Ml|l|][EQ={$\rightarrow$}]
  \NC \rm Decimal \NC Kaktovik \NC\NR
  \NC 2 + 2 = 4 
	\EQ
\kaktoviknumerals{2} $+$ \kaktoviknumerals{2} $=$ \kaktoviknumerals{4}
	\NC\NR
	\NC 17 - 7 = 10 
	\EQ
	\kaktoviknumerals{17} $-$ \kaktoviknumerals{7} $=$ \kaktoviknumerals{10}
	\NC\NR
	\NC 1503 / 3 
	\EQ
	\kaktoviknumerals{3}\kaktoviknumerals{15}\kaktoviknumerals{3} $/$ \kaktoviknumerals{3} $=$ \kaktoviknumerals{1}\kaktoviknumerals{5}\kaktoviknumerals{1}
	\NC\NR
	\NC 364 / 3
	\EQ
	\kaktoviknumerals{18}\kaktoviknumerals{4} $/$ \kaktoviknumerals{3} $=$ \kaktoviknumerals{6}\kaktoviknumerals{1} remainder \kaktoviknumerals{1}
\stoptabulate

\stopsubject
\stoptitle
\stoptext

[-- Attachment #4: Type: text/plain, Size: 878 bytes --]



> On 18 Apr 2023, at 10:57, Henning Hraban Ramm via ntg-context <ntg-context@ntg.nl> wrote:
> 
> I just came across this thread about the base-20 system of the Inuit people and the numerals invented for it in the 1990s:
> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
> 
> This makes simple calculations just beautiful.
> 
> Hraban
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
> 
> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : https://contextgarden.net
> ___________________________________________________________________________________


[-- Attachment #5: Type: text/plain, Size: 496 bytes --]

___________________________________________________________________________________
If your question is of interest to others as well, please add an entry to the Wiki!

maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
archive  : https://bitbucket.org/phg/context-mirror/commits/
wiki     : https://contextgarden.net
___________________________________________________________________________________

Re: [NTG-context] Kaktovik numerals

[Gavin via ntg-context]

Hi Willi,

What fun! I think I found a couple math items to correct.

1) The second line of the tables at the top of page 2 should be:
    1000' 100, 10, 1; 8000, 400, 20, 1

2) For the year conversion: 2023 = 5x20^2 + 1x20 + 3. (Your 0 should be my 1). This will give a three digit Kaktovik numeral. You have 4 digit Kaktovik numerals for 2023, with both a 0 and a 1.

Gavin


> On Apr 19, 2023, at 12:36 PM, Willi Egger via ntg-context <ntg-context@ntg.nl> wrote:
> 
> Hi all,
> 
> after playing around and watching YouTube the attached  composition is made…
> 
> Willi
> <kaktovik-numerals-info.pdf><kaktovik-numerals-info.tex>
> 
>> On 18 Apr 2023, at 10:57, Henning Hraban Ramm via ntg-context <ntg-context@ntg.nl> wrote:
>> 
>> I just came across this thread about the base-20 system of the Inuit people and the numerals invented for it in the 1990s:
>> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
>> 
>> This makes simple calculations just beautiful.
>> 
>> Hraban
>> ___________________________________________________________________________________
>> If your question is of interest to others as well, please add an entry to the Wiki!
>> 
>> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
>> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
>> archive  : https://bitbucket.org/phg/context-mirror/commits/
>> wiki     : https://contextgarden.net
>> ___________________________________________________________________________________
> 
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
> 
> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : https://contextgarden.net
> ___________________________________________________________________________________

___________________________________________________________________________________
If your question is of interest to others as well, please add an entry to the Wiki!

maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
archive  : https://bitbucket.org/phg/context-mirror/commits/
wiki     : https://contextgarden.net
___________________________________________________________________________________

Re: [NTG-context] Kaktovik numerals

[Willi Egger via ntg-context]

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Hello Gavin,

thank you so much for your input. — Indeed you are right. Please find attached the corrected version.


[-- Attachment #2: kaktovik-numerals-info.pdf --]
[-- Type: application/pdf, Size: 28423 bytes --]

[-- Attachment #3: kaktovik-numerals-info.tex --]
[-- Type: application/octet-stream, Size: 5436 bytes --]

% ConTeXT file
% filename: kaktovik-numerals-intro.tex
% W. Egger
% 19-04-2023

\input meta-imp-kaktovik.mkxl

\definefontfeature
  [default]
  [default]
  [metapost=kaktovik]

\setupbodyfont[dejavu]

\setuppagenumbering[location=footer]

\setuplayout
 [header=0pt]


\starttext
\starttitle[title=Kaktovik-numerals]

\startsubject[title=Intro]
On 18-04-2023 Haraban Ramm posted on the mailing-list about the Kaktovik numerals.
\blank
https://mathstodon.xyz/@johncarlosbaez/110215432175491555
\blank

The Inuit have a counting system based on the base 20. Back in 1994 in the local school at Kaktovik in Alaska students developed a counting system for the local language on the base 20. There is a subunit in the form of 5.

The counting system with base 20 is known in different cultures. e.g. The Mayans (Mexico) used a system with dots and horizontal bars.

Even in modern languages there are traces of the base 20 counting system. e.g. French express 80 as \quote{quatre-vingt} and 90 as \quote{quatre-vingt-dix}...

\stopsubject

\startsubject[title=Hans Hagen's implementation]

A couple of hours after Hraban's post, Hans came already up with an implementation of the Kaktovik-numeral-shapes in \METAFUN.

\blank

meta-imp-kaktovik.mkxl
\stopsubject

\startsubject[title=Further information on the Kaktovik-numerals-system]

https://www.youtube.com/watch?v=EyS6FfczH0Q&ab_channel=Artifexian

https://www.youtube.com/watch?v=fIZB4bRwxqI&ab_channel=Dave%27sMathVideos

https://www.youtube.com/watch?v=ObRFHiU_r9I&ab_channel=TheFerret

\stopsubject

\startsubject[title=The key to writing numbers in Kaktovik system]

In order to understand how numbers are composed hereunder is the way in the decimal and in the Kaktovik system.



\bTABLE
  \bTR
	  \bTD[nx=4,align=center] Decimal \eTD
		\bTD \strut \eTD
		\bTD[nx=4,align=center] Kaktovik \eTD
	\eTR
	\bTR
	  \bTD $10^3$ \eTD
		\bTD $10^2$ \eTD
		\bTD $10^1$ \eTD
		\bTD $10^0$ \eTD
		\bTD \strut \eTD
	  \bTD $20^3$ \eTD
		\bTD $20^2$ \eTD
		\bTD $20^1$ \eTD
		\bTD $20^0$ \eTD
  \eTR
	\bTR
	  \bTD 1000 \eTD
		\bTD 100 \eTD
		\bTD 10 \eTD
		\bTD 1 \eTD
		\bTD \strut \eTD
	  \bTD 8000 \eTD
		\bTD 400 \eTD
		\bTD 20 \eTD
		\bTD 1 \eTD	
  \eTR
\eTABLE

The following table shows the relation between the vertical bars (1 to 4) and the horizontal bars tuplets of 5

\blank

\bTABLE
  \setupTABLE[r][each][frame=off,align=flushright]
	\setupTABLE[r][even][style=\tfxx]
	\setupTABLE[r][odd][style=\tfd]
	\setupTABLE[c][1][frame=on]
	\setupTABLE[r][1][frame=on]
	\bTR
	 \bTD[frame=off] \kaktoviknumerals{0}\eTD
	 \bTD \kaktoviknumerals{1}\eTD
	 \bTD \kaktoviknumerals{2}\eTD
	 \bTD \kaktoviknumerals{3}\eTD
	 \bTD \kaktoviknumerals{4}\eTD
	\eTR
	\bTR
	 \bTD 0\eTD
	 \bTD 1\eTD
	 \bTD 2\eTD
	 \bTD 3\eTD
	 \bTD 4\eTD
	\eTR
	\bTR
	 \bTD \kaktoviknumerals{5}\eTD
	 \bTD \kaktoviknumerals{6}\eTD
	 \bTD \kaktoviknumerals{7}\eTD
	 \bTD \kaktoviknumerals{8}\eTD
	 \bTD \kaktoviknumerals{9}\eTD
	\eTR
	\bTR
	 \bTD 5\eTD
	 \bTD 6\eTD
	 \bTD 7\eTD
	 \bTD 8\eTD
	 \bTD 9\eTD
	\eTR
	\bTR
	 \bTD \kaktoviknumerals{10}\eTD
	 \bTD \kaktoviknumerals{11}\eTD
	 \bTD \kaktoviknumerals{12}\eTD
	 \bTD \kaktoviknumerals{13}\eTD
	 \bTD \kaktoviknumerals{14}\eTD
	\eTR
	\bTR
	 \bTD 10\eTD
	 \bTD 11\eTD
	 \bTD 12\eTD
	 \bTD 13\eTD
	 \bTD 14\eTD
	\eTR
	\bTR
	 \bTD \kaktoviknumerals{15}\eTD
	 \bTD \kaktoviknumerals{16}\eTD
	 \bTD \kaktoviknumerals{17}\eTD
	 \bTD \kaktoviknumerals{18}\eTD
	 \bTD \kaktoviknumerals{19}\eTD
	\eTR
	\bTR
	 \bTD 15\eTD
	 \bTD 16\eTD
	 \bTD 17\eTD
	 \bTD 18\eTD
	 \bTD 19\eTD
	\eTR	
\eTABLE

\stopsubject

\startsubject[title=Examples]

\starttabulate[|r|Mr|r|]
 \NC 20   \NC 1 \times 20^1 + 0 \times 20^0\NC \kaktoviknumerals{1}\kaktoviknumerals{0} \NC\NR
 \NC 30   \NC 1 \times 20^1 + 10 \times 20^0\NC \kaktoviknumerals{1}\kaktoviknumerals{10} \NC\NR
 \NC 40   \NC 2 \times 20^1  + 0 \times 20^0 \NC \kaktoviknumerals{2}\kaktoviknumerals{0} \NC\NR
 \NC 100  \NC 5 \times 20^1 + 0 \times 20^0\NC \kaktoviknumerals{5}\kaktoviknumerals{0} \NC\NR
 \NC 1000 \NC 2 \times 20^2 + 10 \times 20^1 + 0 \times 20^0 
 \NC \kaktoviknumerals{2}\kaktoviknumerals{10}\kaktoviknumerals{0}\NC\NR
 \NC 2023 \NC 5 \times 20^2 + 1 \times 20^1 + 3 \times 20^0  
 \NC \kaktoviknumerals{5}
\kaktoviknumerals{1}\kaktoviknumerals{3}\NC\NR
\stoptabulate

\blank
So the date of today would be:
\blank
19 - 4 - 2023
\blank
\kaktoviknumerals{19} -- \kaktoviknumerals{4} --
\kaktoviknumerals{5}\kaktoviknumerals{1}\kaktoviknumerals{3}

\blank

Frappant is the possibility to solve arithmetic visually with these Kaktovik-numerals. The approach is to look how patterns fit in the left and right part of the equation.

\blank

The presented examples are from: 

https://www.youtube.com/watch?v=ObRFHiU_r9I&ab_channel=TheFerret

\starttabulate[|Ml|l|][EQ={$\rightarrow$}]
  \NC \rm Decimal \NC Kaktovik \NC\NR
  \NC 2 + 2 = 4 
	\EQ
\kaktoviknumerals{2} $+$ \kaktoviknumerals{2} $=$ \kaktoviknumerals{4}
	\NC\NR
	\NC 17 - 7 = 10 
	\EQ
	\kaktoviknumerals{17} $-$ \kaktoviknumerals{7} $=$ \kaktoviknumerals{10}
	\NC\NR
	\NC 1503 / 3 
	\EQ
	\kaktoviknumerals{3}\kaktoviknumerals{15}\kaktoviknumerals{3} $/$ \kaktoviknumerals{3} $=$ \kaktoviknumerals{1}\kaktoviknumerals{5}\kaktoviknumerals{1}
	\NC\NR
	\NC 364 / 3
	\EQ
	\kaktoviknumerals{18}\kaktoviknumerals{4} $/$ \kaktoviknumerals{3} $=$ \kaktoviknumerals{6}\kaktoviknumerals{1} remainder \kaktoviknumerals{1}
\stoptabulate

\stopsubject
\stoptitle
\stoptext

[-- Attachment #4: Type: text/plain, Size: 2746 bytes --]


Willi

> On 19 Apr 2023, at 20:58, Gavin via ntg-context <ntg-context@ntg.nl> wrote:
> 
> Hi Willi,
> 
> What fun! I think I found a couple math items to correct.
> 
> 1) The second line of the tables at the top of page 2 should be:
>    1000' 100, 10, 1; 8000, 400, 20, 1
> 
> 2) For the year conversion: 2023 = 5x20^2 + 1x20 + 3. (Your 0 should be my 1). This will give a three digit Kaktovik numeral. You have 4 digit Kaktovik numerals for 2023, with both a 0 and a 1.
> 
> Gavin
> 
> 
>> On Apr 19, 2023, at 12:36 PM, Willi Egger via ntg-context <ntg-context@ntg.nl> wrote:
>> 
>> Hi all,
>> 
>> after playing around and watching YouTube the attached  composition is made…
>> 
>> Willi
>> <kaktovik-numerals-info.pdf><kaktovik-numerals-info.tex>
>> 
>>> On 18 Apr 2023, at 10:57, Henning Hraban Ramm via ntg-context <ntg-context@ntg.nl> wrote:
>>> 
>>> I just came across this thread about the base-20 system of the Inuit people and the numerals invented for it in the 1990s:
>>> https://mathstodon.xyz/@johncarlosbaez/110215432175491555
>>> 
>>> This makes simple calculations just beautiful.
>>> 
>>> Hraban
>>> ___________________________________________________________________________________
>>> If your question is of interest to others as well, please add an entry to the Wiki!
>>> 
>>> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
>>> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
>>> archive  : https://bitbucket.org/phg/context-mirror/commits/
>>> wiki     : https://contextgarden.net
>>> ___________________________________________________________________________________
>> 
>> ___________________________________________________________________________________
>> If your question is of interest to others as well, please add an entry to the Wiki!
>> 
>> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
>> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
>> archive  : https://bitbucket.org/phg/context-mirror/commits/
>> wiki     : https://contextgarden.net
>> ___________________________________________________________________________________
> 
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
> 
> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : https://contextgarden.net
> ___________________________________________________________________________________


[-- Attachment #5: Type: text/plain, Size: 496 bytes --]

___________________________________________________________________________________
If your question is of interest to others as well, please add an entry to the Wiki!

maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
archive  : https://bitbucket.org/phg/context-mirror/commits/
wiki     : https://contextgarden.net
___________________________________________________________________________________

Re: [NTG-context] Kaktovik numerals

[Hans Hagen via ntg-context]

[-- Attachment #1: Type: text/plain, Size: 1391 bytes --]

On 4/19/2023 10:45 PM, Willi Egger via ntg-context wrote:
> Hello Gavin,
> 
> thank you so much for your input. — Indeed you are right. Please find attached the corrected version.
> 
> 
> 
> Willi
> 
>> On 19 Apr 2023, at 20:58, Gavin via ntg-context <ntg-context@ntg.nl> wrote:
>>
>> Hi Willi,
>>
>> What fun! I think I found a couple math items to correct.
>>
>> 1) The second line of the tables at the top of page 2 should be:
>>     1000' 100, 10, 1; 8000, 400, 20, 1
>>
>> 2) For the year conversion: 2023 = 5x20^2 + 1x20 + 3. (Your 0 should be my 1). This will give a three digit Kaktovik numeral. You have 4 digit Kaktovik numerals for 2023, with both a 0 and a 1.
je kunt direct dat nummer converteren maar blijkbaar gaf ik de verkeerde 
volgorde uit:

\useMPlibrary[kaktovik] % de officiele manier

\definefontfeature
   [default]
   [default]
   [metapost=kaktovik]

\setupbodyfont[dejavu]

\starttext
  2023 \kaktoviknumerals{5}\kaktoviknumerals{1}\kaktoviknumerals{3}

\kaktoviknumerals{2023} % deze split dus voor je, order fixed

\stoptext


-----------------------------------------------------------------
                                           Hans Hagen | PRAGMA ADE
               Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
        tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
-----------------------------------------------------------------

[-- Attachment #2: meta-imp-kaktovik.mkxl --]
[-- Type: text/plain, Size: 4363 bytes --]

%D \module
%D   [       file=meta-imp-kaktovik,
%D        version=2023.04.18,
%D          title=\METAPOST\ Graphics,
%D       subtitle=Kaktovik Numbers,
%D         author=Hans Hagen,
%D           date=\currentdate,
%D      copyright={PRAGMA ADE \& \CONTEXT\ Development Team}]
%C
%C This module is part of the \CONTEXT\ macro||package and is
%C therefore copyrighted by \PRAGMA. See mreadme.pdf for
%C details.

%D Just a quick hack for Hraban (after a post on the mailing list).

\startMPcalculation{simplefun}

    path kaktovik_glyphs[] ;

    def InitializeKaktovik =

        save p, d, u ;

        pair p[] ; numeric d ; d := .1 ; numeric u ; u := .15 ;

      % d := getparameterdefault "mpsfont" "d" .10 ;
      % u := getparameterdefault "mpsfont" "u" .15 ;

        p[0] := (0,1) ;
        p[1] := (1,0) ;
        p[2] := (2,1 -  d) ;
        p[3] := (3,0) ;
        p[4] := (4,1 - 2d) ;

        p[5] := (4,1 +  u) ;
        p[6] := (0,1 + 2u) ;
        p[7] := (4,1 + 4u) ;

        kaktovik_glyphs[0] := (1,1)  { right } .. { left } (2,1/2) { left } .. { right } (3,1);

        for i= 1 upto 4 :
            kaktovik_glyphs[i] := p[0] for j=1 upto i : -- p[j] endfor ;
        endfor ;

        kaktovik_glyphs[ 5] := p[5] -- p[0] ;                for i= 6 upto  9 : kaktovik_glyphs[i] := p[5] -- kaktovik_glyphs[i-5] ; endfor ;
        kaktovik_glyphs[10] := p[6] -- kaktovik_glyphs[ 5] ; for i=11 upto 14 : kaktovik_glyphs[i] := p[6] -- kaktovik_glyphs[i-5] ; endfor ;
        kaktovik_glyphs[15] := p[7] -- kaktovik_glyphs[10] ; for i=16 upto 19 : kaktovik_glyphs[i] := p[7] -- kaktovik_glyphs[i-5] ; endfor ;

    enddef ;

    vardef Kaktovik(expr i) =
        draw image (
            draw kaktovik_glyphs[i]
                xscaled (10/20 -1/20)
                yscaled (25/20 -2/20)
                withpen (pencircle xscaled 1/20 yscaled 5/20) rotated -(2*20)
              % withpen (pencircle xscaled 1/40 yscaled 5/40) rotated -(2*20)
              % withpen (pencircle xscaled 2.5/40 yscaled 5/40) rotated -(2*20)
            ;
        ) shifted (2/20,2/20)
    enddef ;

    lmt_registerglyphs [
        name     = "kaktovik",
        units    = 2,
        usecolor = true,
        width    = 2,
        height   = 2,
        depth    = 0,
        preamble = "InitializeKaktovik"
    ] ;

    for i=0 upto 19 :
        lmt_registerglyph [
            category = "kaktovik",
            unicode  = 119488 + i, % "0x1D2C0"
            code     = "Kaktovik(" & decimal i & ")"
        ] ;
    endfor ;

\stopMPcalculation

\startluacode
    interfaces.implement {
        name      = "kaktoviknumerals",
        arguments = "integer",
        actions   = function(n)
            local digits = { }
            local count  = 1
            while true do
                digits[count] = utf.char(0x1D2C0 + (n % 20))
                n = n // 20
                if n == 0 then
                    break;
                end
                count = count + 1
            end
            table.reverse(digits)
            context("%t",digits)
        end
    }
\stopluacode

\unprotect

\permanent\def\kaktoviknumerals#1{\clf_kaktoviknumerals\numexpr#1\relax}

\defineconversion [kaktoviknumerals] [\kaktoviknumerals]
\defineconversion [K]                [\kaktoviknumerals]

\definefontfeature
  [kaktovik]
  [metapost=kaktovik]

\protect

\continueifinputfile{meta-imp-kaktovik.mkxl}

\definefontfeature
  [default]
  [default]
  [metapost=kaktovik]
% [metapost={category=kaktovik,u=.25,d=.20,x=}]

\setupbodyfont[dejavu]

% \nopdfcompression

\startTEXpage[offset=1ts,width=3es]

    \start
    \showglyphs
        KAKTOVIK
        \dostepwiserecurse{0}{19}{1}{\kaktoviknumerals{#1}\space }
    \stop

    kaktovik \start
        \red\glyphxscale 700
        \dostepwiserecurse{0}{19}{1}{\kaktoviknumerals{#1}\space }
    \stop

    \startitemize[packed,K][color=orange,stopper=]
        \startitem first  \stopitem
        \startitem second \stopitem
        \startitem third  \stopitem
    \stopitemize

    KAKTOVIK \start
        \red  \kaktoviknumerals{2023} --
        \green\kaktoviknumerals{4}    --
        \blue \kaktoviknumerals{18}
    \stop

    KAKTOVIK
\stopTEXpage



[-- Attachment #3: Type: text/plain, Size: 496 bytes --]

___________________________________________________________________________________
If your question is of interest to others as well, please add an entry to the Wiki!

maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
archive  : https://bitbucket.org/phg/context-mirror/commits/
wiki     : https://contextgarden.net
___________________________________________________________________________________

Re: [NTG-context] Kaktovik numerals

[Willi Egger via ntg-context]

Hans thank you very much for this update. Indeed now automatic conversion comes out correctly.

Willi

> On 19 Apr 2023, at 23:41, Hans Hagen via ntg-context <ntg-context@ntg.nl> wrote:
> 
> On 4/19/2023 10:45 PM, Willi Egger via ntg-context wrote:
>> Hello Gavin,
>> thank you so much for your input. — Indeed you are right. Please find attached the corrected version.
>> Willi
>>> On 19 Apr 2023, at 20:58, Gavin via ntg-context <ntg-context@ntg.nl> wrote:
>>> 
>>> Hi Willi,
>>> 
>>> What fun! I think I found a couple math items to correct.
>>> 
>>> 1) The second line of the tables at the top of page 2 should be:
>>>    1000' 100, 10, 1; 8000, 400, 20, 1
>>> 
>>> 2) For the year conversion: 2023 = 5x20^2 + 1x20 + 3. (Your 0 should be my 1). This will give a three digit Kaktovik numeral. You have 4 digit Kaktovik numerals for 2023, with both a 0 and a 1.
> je kunt direct dat nummer converteren maar blijkbaar gaf ik de verkeerde volgorde uit:
> 
> \useMPlibrary[kaktovik] % de officiele manier
> 
> \definefontfeature
>  [default]
>  [default]
>  [metapost=kaktovik]
> 
> \setupbodyfont[dejavu]
> 
> \starttext
> 2023 \kaktoviknumerals{5}\kaktoviknumerals{1}\kaktoviknumerals{3}
> 
> \kaktoviknumerals{2023} % deze split dus voor je, order fixed
> 
> \stoptext
> 
> 
> -----------------------------------------------------------------
>                                          Hans Hagen | PRAGMA ADE
>              Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
>       tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
> -----------------------------------------------------------------
> <meta-imp-kaktovik.mkxl>___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
> 
> maillist : ntg-context@ntg.nl / https://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : https://www.pragma-ade.nl / http://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : https://contextgarden.net
> ___________________________________________________________________________________

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