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 Systematic Dozenal Nomenclature, Intro/FAQ/wiki/spec/discussion...
Kodegadulo
Posted: Oct 21 2015, 01:15 AM


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Okay, here's a quick little Java program to show the algorithm for "basifying" SDN, including power-prefix forms in bases ending in zero:

CODE

public class SDNBasifier {

   private static String getDigitRoot(char value) {
       switch (value) {
           case '0': return "nil";
           case '1': return "un";
           case '2': return "bi";
           case '3': return "tri";
           case '4': return "quad";
           case '5': return "pent";
           case '6': return "hex";
           case '7': return "sept";
           case '8': return "oct";
           case '9': return "enn";
           case 'a':
           case 'A':
           case 'x':
           case 'X': return "dec";
           case 'b':
           case 'B':
           case 'e':
           case 'E': return "lev";
           default: throw new IllegalArgumentException();      
       }
   }
   
   private static String getMultiplierGlue(char value) {
       switch (value) {
           case '0':
           case '1': return "i";
           case '2':
           case '3': return "na";
           case '4': return "ra";
           case '9': return "ea";
           default: return "a";
       }
   }
   
   private static String getDigitString(String value) {
       StringBuilder builder = new StringBuilder();
       for (char val : value.toCharArray()) {
           builder.append(getDigitRoot(val));
       }
       return builder.toString();
   }
   
   private static String basify(long value) {
       String multiplier = Long.toString(value, 12);
       int zeroes = 0;
       while (multiplier.length() > 1 && multiplier.endsWith("0")) {
           multiplier = multiplier.substring(0,  multiplier.length()-1);
           zeroes++;
       }
       String power = "";
       if (zeroes > 0) {
           power = Integer.toString(zeroes,12);
           power = getDigitString(power) + "qua";
       }
       char last = multiplier.charAt(multiplier.length()-1);
       multiplier = getDigitString(multiplier) + getMultiplierGlue(last);
       if (!power.isEmpty()) {
           if (multiplier.equals("uni")) {
               multiplier = "";
           } else {
               switch (power.charAt(0)) {
                   case 'u':
                   case 'o':
                   case 'e':
                       multiplier += "n";
               }
           }
       }
       String basified = multiplier + power + "al";
       basified = basified.replaceAll("nnn", "nn");
       basified = basified.replaceAll("aa", "a");
       return basified;
   }
   
   public static void main(String... args) {
       for (long value = 0; value <= 3456L; value++) {
           String dozenal = Long.toString(value, 12);
           dozenal = dozenal.replaceAll("a", "X").replaceAll("b", "E");
           System.out.printf("%4s : %s\n", dozenal, basify(value));
       }
   }
}


This program prints out the SDN names for the first 2000z bases. I've attached the output as a file.


Attached File ( Number of downloads: 23 )
Attached File  basifier.txt (73.51 kb)
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icarus
Posted: Oct 21 2015, 02:49 AM


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Algorithm was written according to this post. Fix it tomorrow. (Sent form my dumbPhone)
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Kodegadulo
Posted: Oct 21 2015, 08:42 AM


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QUOTE (icarus @ Oct 21 2015, 02:49 AM)
Algorithm was written according to this post.

Well, sure, but that was a while back, and this stuff has been evolving. I guess I should go back and edit that post or point to something more recent.

Don't get me wrong, inserting an -im- syllable or substituting an -ary ending instead of -al are still acceptable variations, on the philosophy that SDN wants to be inclusive about existing forms. But it seems lately like people are open to using forms that come out of an even more regular algorithm. I just showed the simplest, most regular algorithm that will produce something that's still "correct".

But the optional variations would still build off the multiplier glue. At least, I think so:

deca + al = decal
deca + ary = decary ?
deca + imal = decimal

bina + al = binal
bina + ary = binary
bina + imal = binimal ?

trina + al = trinal
trina + ary = trinary
trina + imal = trinimal ?

uni + al = unial
uni + ary = unary (hmm, irregular exception? Or is that the rule?)
uni + imal = unimal ?

nili + al = nilial
nili + ary = niliary (hmm, nilary? nillary?)
nili + imal = nilimal

qaudra + al = quadral
quadra + ary = quadrary ?
quadra + imal = quadrimal ?

It seems like the first variation in each case is something people can live with, least common denominator. Other variations might feel more "natural", but which one does in each case looks like a source of irregular exceptions .

Then there's the whole question of when to cut over to -qual. Is binilial, trinilial, etc good enough, or should we go to binanunqual, trinanunqual? The latter are bulkier and actually seem more awkward, so maybe it's better to save the cutover for -biqual, -triqual, etc.

Also I've been rethinking the need for that euphonic n before unqual. Forms like binaunqual, decaunqual, etc might be okay. If people read the au as two syllables or just one long aw, either way works.

Eliding the a into the u for binunqual, trinunqual was an early idea that I regret now. It's too easy to mix this up with biunqual, triunqual.
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icarus
Posted: Oct 21 2015, 11:16 AM


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Oh dear. DumbPhone ate the I'll, as in I'll fix it tomorrow! I'm sorry. I sound horribly angry but I am not at all. Sorry kode.

No I am sure the system evolved and this is the first time we took a fully systemic look at the numbers.

Same thing happened with the Lamadrid system. I think the coding exercise is useful because we suss out issues with created systems and help define / refine them. We don't necessarily care about obscure grand base names but as they are systemic, hiccups pop up and thus the algorithm is a method for ensuring euphony and order throughout. What's keen about SDN is that it can go much beyond the thousands (limit of "plain English"). At the OEIS, we say that by coding we help define a sequence. So in the same vein coding should help not just this but much of what I conceptualized. Indeed, when I wrote the digit mapping script it partially validated the concepts behind it. (The neutral digits/numbers proofs are what validate it, along with already-available proofs about other kinds of digits).

Your suggestion is cogent and I'll use it. I tried to use StringReplace as a sort of shortcut but yes, we'll need two cycles at least for bases that are = 0 (mod 12). The zero extraction is a brilliant idea (but then, you're Kodegadulo, just living up to your name).

See why I call it dumbPhone? I'm mortified about that missing word and don't know how it happened. I had in iPhone since it first came out. You'd think I would be acquainted with its idiosyncrasies. When I first got this particular phone I asked Siri when my wife's birthday was (hint, it was that very day). Siri snarked "I don't *know* your wife." My wife scoffed but listen to what Siri did next. So I have a contact list older than a couple members of this forum. I fixed the problem and then asked Siri the same question. "Which wife?" She quipped. Oh boy. At least it was good for a laugh but I don't use Siri (wife says, "that woman") except if I want pizza in a strange town. My wife is in my contact list 3 times (3 addresses). That Woman saw 3 entries and ought to have said "Which address".

(Sent from my dumbPhone)
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Kodegadulo
Posted: Oct 21 2015, 05:55 PM


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QUOTE (icarus @ Oct 21 2015, 11:16 AM)
DumbPhone ... Siri ...

Artificial intelligences...aren't. smile.gif
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icarus
Posted: Oct 21 2015, 06:26 PM


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smile.gif Working on it! This time using your list and program. Starting from scratch.

Yes, Mathematica is proprietary but it's a good toolbox.
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Kodegadulo
Posted: Oct 21 2015, 07:01 PM


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QUOTE (icarus @ Oct 21 2015, 05:18 PM)
Some statistics given the Lamadrid base names for bases between 2 and 5040 inclusive. I extended the program to cover base 5040, the algorithm range is {2, 5999} inclusive.

Word length and population.
...
Smallest words pertain to bases {1, 8} at 5 letters ("unary", "octal"), longest to bases {4454, 4455, 4457} at 42 letters ("quadramillequadringentotetraquinquagesimal", "quadramillequadringentopentaquinquagesimal", "quadramillequadringentoheptaquinquagesimal"). There are no Lamadrid base names with 8 letters in them.

Mean word size is 27.3444 letters for the span {2, 5040} inclusive. The mode in that range is 30 letters long. Mean word size is 13.7583 between {2, 120} inclusive and 8.8 between {2, 20} inclusive.

I ran some similar stats on SDN over a comparable, though larger range:
Range: 0 .. 3EEE[z] (6911[d])

Length
[d]
Count
[d]
First Last
56uniallevial
6 7nilialbiqual
7 14quadraltriqual
8 44untrinallevleval
9 68unquadralbibileval
10 201triquadrallevbileval
11 493binanunqualbibibileval
12 896trinanunqualtribibileval
13 1443quadranunqualtrilevbileval
14 1648untrinanunqualtrilevlevleval
15 1172unquadranunqualtrilevlevenneal
16 565triquadranunqualtrilevlevquadral
17 235quadquadranunqualtrilevlevanunqual
18 92unnilquadranunqualtrilevenneanunqual
19 25unquadquadranunqualtrilevquadranunqual
20 3triquadquadranunqualtriseptquadranunqual


Average word length: 13.5932[d]
Mode: 14[d]

Interesting... smile.gif
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icarus
Posted: Oct 21 2015, 07:36 PM


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SDN is pretty succinct.

Lamadrid was produced mainly to generate "plain English"-like extrapolations to the current dominant base name lexicon. We retained "-ary" below decimal, "octal", "decimal", ("duodecimal"), "hexadecimal", "vigesimal", "sexagesimal", "-imal" for bases larger than 9. I recently allowed "-ary" for bases that are a power of ten plus {1, ..., 9} to avoid further complication. I think it does a grand job and really like it for the purpose of furnishing "canonical" "plain English" like names for bases.

SDN does a different job. It provides a more or less plenary and ultra-extensible system to furnish base names, using dozenal rather than antique decimal for the base-of-name. Because it largely avoids power delimiting and usually simply catenates numeral tags, it's really pretty short.

A similar thing could be done for "plain English" but it wouldn't be Lamadrid, and it wouldn't be "plain English" like. It would resemble a decimal SDN name system. (I am not proposing this. If I want "neutrality" then I need to use "plain English"-like systems).

----- off topic:

While writing code I get this new set of calendar months based on the number names:

levember, nilember, unember, (January, February, March) here we go with the -ary again!
biember, triember, quadrember, (April, May, June)
pentember, hexember, september, (July, August, September)
octember, ennember, december (October, November, December)

I was born 1 Pentember 1182. Very odd. Somewhat restores the "natural order" of months, if we start with Unember and run to Nilember as the last month, taking "nil" to mean 0 (mod 12). Otherwise it might be unquember, *very* close to unember. For me, tell you the truth, unquember might as well be unember. I am a summer boy and can't stand winter.
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Kodegadulo
Posted: Oct 21 2015, 07:55 PM


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Sounds cool, although I'd put the multiplier glue on 2, 3 to make it binember, trinember. Nilember could also be zenember (with a nod toward argam).

Note that you get unique single-letter abbreviations for the months this way. Or you could make them two letters, first and last, so it would always be an r at the end, e.g. today's date would be 11EE-Or-19[z].
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Kodegadulo
Posted: Oct 21 2015, 08:25 PM


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QUOTE (icarus @ Oct 21 2015, 07:36 PM)
A similar thing could be done for "plain English" but it wouldn't be Lamadrid, and it wouldn't be "plain English" like. It would resemble a decimal SDN name system. (I am not proposing this. If I want "neutrality" then I need to use "plain English"-like systems).

Take a look at Systematic Decimal Nomenclature. It's just like SDN, except that it's limited to roots nil through enn, and every prefix sports an extra des syllable to mark it as decimal, e.g. desunnili = undesqua = ten. Sorry, but I am dozenally biased (and defiantly so tongue.gif ), so the decimal version gets the burden of an extra marker.

I abbreviate it SXN (after Roman numeral X for ten) because unfortunately the dozenal version SDN snagged the D already. Historical accident. (Well, what did I know back then?) We probably should have abbreviated the latter SZN and given SDN to the decimal version (and we'd want to reserve SXN for a potential Systematic Hexadecimal Nomenclature), but it seems too late for that now.

Oh well, perhaps we could finesse it as a general "Systematic Nomenclature" (SN) system, with Dozenal [z], Decimal [d], Hexadecimal[x], and even Decal-Unqual [d•z] and Unqual-Decal [z•d] extensions.

Systematic Nomenclature: Dozenal (SN[z])
Systematic Nomenclature: Decimal (SN[d])
Systematic Nomenclature: Hexadecimal (SN[x])
Systematic Nomenclature: Decal-Unqual (SN[d•z])
Systematic Nomenclature: Unqual-Decal (SN[z•d])
... and whatever else...
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Kodegadulo
Posted: Oct 21 2015, 08:37 PM


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QUOTE (Kodegadulo @ Oct 21 2015, 07:55 PM)
Nilember could also be zenember (with a nod toward argam).

Heh, given the association of months with astrological signs, maybe it should be Zodember instead. smile.gif

Never thought of zodial as particularly romantic, but St. Valentine's day would be the zody-second of Zodember. smile.gif
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icarus
Posted: Oct 21 2015, 09:41 PM


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Latest code. It doesn't quite match your stats so some tweaking to be made.

CODE

sdnbase[n_] :=
Block[{basename = {"nil", "un", "bi", "tri", "quad", "pent", "hex",
    "sept", "oct", "enn", "dec", "lev", "not supported"},
  b = IntegerDigits[n, 12], z, a, g, w},
 z = Length@ TakeWhile[Reverse@ b, # == 0 &];
 g[x_] :=
  Which[n >= 1,
   StringReplace[#, {"aa" -> "a", "nnn" -> "nn"}] &@
    StringJoin[basename[[# + 1]] & /@ b,
     Which[Last@ b == 0, "", Last@ b == 1, "i", Last@ b == 2, "na",
      Last@ b == 3, "na", Last@ b == 4, "ra", Last@ b == 9, "ea", True,
      "a"]]];
 Which[z == 0, w = g@ b,
  z > 0, b = Take[b, Length@ b - z];
  w = StringJoin[If[b == {1}, "", g@ Most@ b], basename[[z + 1]],
    "qua"],
  True, basename[[13]]
  ]; StringReplace[#, {"aa" -> "a", "iunq" -> "inunq",
     "aunq" -> "anunq", "nnn" -> "nn"}] &@ StringJoin[w, "al"]]


Stats:

CODE

5     6
6     6
7    14
8    44
9    68
10  201
11  492
12  896
13 1436
14 1643
15 1179
16  570
17  235
18   92
19   26
20    3
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Kodegadulo
Posted: Oct 21 2015, 10:22 PM


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Hmm there's a bug in my Java code: I put the euphonic n in front if a power prefix that starts with a vowel whenever there was any multiplier prefix, but it's only needed when the multiplier ends in -a. If the multiplier ends in -i (e.g. uni-) it can just glide into the next vowel (e.g., ununi + unqua + al = ununiunqual). I'll fix this and post a new version.

Icarus what it means for you is you can just drop the "iunq" -> "inunq" replacement. That's how I spotted my mistake: you faithfully replicated it. My bad. smile.gif
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Oschkar
Posted: Oct 22 2015, 01:04 AM


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Also, isn't the euphonic syllable in "binanunqual" and "trinanunqual" redundant? Wouldn't the -n- after the multiplier prefix be enough to keep it from being confused with the two dozen first and three dozen first power of twelve?
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Kodegadulo
Posted: Oct 22 2015, 01:14 AM


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QUOTE (Oschkar @ Oct 22 2015, 01:04 AM)
Also, isn't the euphonic syllable in "binanunqual" and "trinanunqual" redundant? Wouldn't the -n- after the multiplier prefix be enough to keep it from being confused with the two dozen first and three dozen first power of twelve?

You're talking about eliding the -a in the multiplier on 2,3, as in "bin-unqual, trin-unqual". Like I said, it was an early idea I had that I regret now, because it is just too close to "biunqual, triunqual".

I could go with "binaunqual, trinaunqual, ..., decaunqual, levaunqual", i.e. leave off the euphonic -n- between, with either a three or four syllable pronunciation being acceptable.
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Kodegadulo
Posted: Oct 22 2015, 01:27 AM


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Here's a new version of the Java code to generate SDN base names:
CODE

import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.SortedMap;
import java.util.TreeMap;

public class SDNBasifier
{
   private static String getDigitRoot(char value) {
       switch (value) {
           case '0': return "nil";
           case '1': return "un";
           case '2': return "bi";
           case '3': return "tri";
           case '4': return "quad";
           case '5': return "pent";
           case '6': return "hex";
           case '7': return "sept";
           case '8': return "oct";
           case '9': return "enn";
           case 'a':
           case 'A':
           case 'x':
           case 'X': return "dec";
           case 'b':
           case 'B':
           case 'e':
           case 'E': return "lev";
           default: throw new IllegalArgumentException();
           
       }
   }
   
   private static String getMultiplierGlue(char value) {
       switch (value) {
           case '0':
           case '1': return "i";
           case '2':
           case '3': return "na";
           case '4': return "ra";
           case '9': return "ea";
           default: return "a";
       }
   }
   
   private static String getDigitString(String value) {
       StringBuilder builder = new StringBuilder();
       for (char val : value.toCharArray()) {
           builder.append(getDigitRoot(val));
       }
       return builder.toString();
   }
   
   private static String basify(long value)
   {
       String multiplier = Long.toString(value, 12);
       int zeroes = 0;
       while (multiplier.length() > 1 && multiplier.endsWith("0")) {
           multiplier = multiplier.substring(0,  multiplier.length()-1);
           zeroes++;
       }
       String power = "";
       if (zeroes > 0) {
           power = Integer.toString(zeroes,12);
           power = getDigitString(power) + "qua";
       }
       char last = multiplier.charAt(multiplier.length()-1);
       multiplier = getDigitString(multiplier) + getMultiplierGlue(last);
       if (!power.isEmpty()) {
           if (multiplier.equals("uni")) {
               multiplier = "";
           } else if (multiplier.endsWith("a")){
               switch (power.charAt(0)) {
                   case 'u':
                   case 'o':
                   case 'e':
                       multiplier += "n";
               }
           }
       }
       String basified = multiplier + power + "al";
       basified = basified.replaceAll("nnn", "nn");
       basified = basified.replaceAll("aa", "a");
       return basified;
   }
   
   public static void main(String... args)
   {
       System.out.printf("Value\tSDN\n");
       SortedMap<Integer, List<String>> wordLists = new TreeMap<>();
       for (long value = 0; value <= 3456L*2-1; value++) {
           String dozenal = Long.toString(value, 12);
           dozenal = dozenal.replaceAll("a", "X").replaceAll("b", "E");
           String basified = basify(value);
           int length = basified.length();
           List<String> wordList = wordLists.get(length);
           if (wordList == null) {
               wordList = new ArrayList<>();
               wordLists.put(length, wordList);
           }
           wordList.add(basified);
           System.out.printf("%s\t%s\n", dozenal, basified);
       }
       System.out.printf("\nLength\tCount\tFirst\tLast\n");
       for (Map.Entry<Integer, List<String>> entry : wordLists.entrySet()) {
           int length = entry.getKey();
           List<String> wordList = entry.getValue();
           int count = wordList.size();
           String first = wordList.get(0);
           String last = wordList.get(count-1);
           System.out.printf("%d\t%d\t%s\t%s\n", length, count, first, last);
       }
   }
}


And here are the resulting stats:

Length
[d]
Count
[d]
FirstLast
56unialleval
67nilialbiqual
714quadraltriqual
844untrinallevleval
968unquadralbibileval
10201triquadrallevbileval
11495binanunqualbibibileval
12900trinanunqualtribibileval
131444quadranunqualtrilevbileval
141657untrinanunqualtrilevlevleval
151169unquadranunqualtrilevlevenneal
16555triquadranunqualtrilevlevquadral
17232quadquadranunqualtrilevlevanunqual
1892unnilquadranunqualtrilevenneanunqual
1925unquadquadranunqualtrilevquadranunqual
203triquadquadranunqualtriseptquadranunqual


Average word length = 13.58358663d
Mode = 14d

With a range of 0 .. 3EEEz the program output was too large to attach. I reduced the range to 0 .. 1EEEz and attached that.

Attached File ( Number of downloads: 26 )
Attached File  basifier.txt (65.4 kb)
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icarus
Posted: Oct 22 2015, 10:59 PM


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Ho, that really worked! (I took out "iunq", etc.)

The only stat wrong between us is that I have 6 six-letter words and you have seven. That's pretty amazing if you ask me!

Here are my six-letter SDN base names:

{trinal, pental, septal, enneal, unqual, biqual}.

Oh, you have "nilial".

No daylight between us!!

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icarus
Posted: Oct 23 2015, 12:48 PM


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(Kode, we should change the base name post to jive with these algorithms, since it is linked to from hella posts in the Tour des Bases.)
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icarus
Posted: Nov 11 2016, 05:14 PM


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Kode,

I am preparing to launch a website with SDN base name use (see Tour des Bases thread).

1. Do I have permission to use SDN there, given that the SDN base names is all I will employ, possibly with Treisaran's suggested "encoding" for base 6-on-10, etc., also the algorithm we produced together above?
2. Do you have a preferred page (not on the forum) wherein you've written out the naming method?

Thank you.
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Kodegadulo
Posted: Nov 12 2016, 07:06 PM


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QUOTE (icarus @ Nov 11 2016, 05:14 PM)
Kode,

I am preparing to launch a website with SDN base name use (see Tour des Bases thread).

1. Do I have permission to use SDN there, given that the SDN base names is all I will employ, possibly with Treisaran's suggested "encoding" for base 6-on-10, etc., also the algorithm we produced together above?
2. Do you have a preferred page (not on the forum) wherein you've written out the naming method?

Thank you.

No need to ask for permission. I certainly don't "own" SDN. It's had several contributors other than me, and it's free for anyone to use to whatever extent they find it useful. Indeed, if you're asking about its application to base names, I think the scheme Treisaran came up with was a masterful idea as is. I don't have a better webpage for it anywhere else so I would just suggest following Treisaran's post about that.
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Kodegadulo
Posted: Feb 2 2018, 07:08 PM


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Here's a post from the Teliosadik thread:

QUOTE (Kodegadulo @ Jan 28 2018, 07:31 PM)
Note that Werneburg prescribes a highly-convoluted recursively-nested scheme for achieving large powers.  For instance, to express a power like "dozen to the eleven-gross ten-dozen ninth power", 10Ɛᘔ9z, we must first peel off one power of dozen to make the rest a power of gross:

10Ɛᘔ9z = 10·10Ɛᘔ8z = 10·1005Ɛ4z

But then we must factor out each of the digits in the exponent, in reverse order:

10Ɛᘔ9z = 10·1004·100Ɛ0·100500z

in order to then render each factor as a word:

10Ɛᘔ9z = taun vierarde möroide fünfiaden

This is on the path towards the Byzantine complexity of Knuth's recursive "dozen-gross-myriad-myllion-byllion-..." system (though of course Knuth's was the most extreme possible expression of that idea).

Frankly, I find SDN's strategy (also described here) much more straightforward:

10Ɛᘔ9z = levdecennqua

and therefore easier to construct, easier to read, and easier to scale up even higher... even if that entails a different approach to solving the "apposition problem" than Werneburg chose.
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Kodegadulo
Posted: Feb 2 2018, 07:42 PM


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QUOTE (Kodegadulo @ Feb 2 2018, 07:08 PM)
Here's a post from the Teliosadik thread:

QUOTE (Kodegadulo @ Jan 28 2018, 07:31 PM)
Note that Werneburg prescribes a highly-convoluted recursively-nested scheme for achieving large powers.  For instance, to express a power like "dozen to the eleven-gross ten-dozen ninth power", 10Ɛᘔ9z, we must first peel off one power of dozen to make the rest a power of gross:

10Ɛᘔ9z = 10·10Ɛᘔ8z = 10·1005Ɛ4z

But then we must factor out each of the digits in the exponent, in reverse order:

10Ɛᘔ9z = 10·1004·100Ɛ0·100500z

in order to then render each factor as a word:

10Ɛᘔ9z = taun vierarde möroide fünfiaden

This is on the path towards the Byzantine complexity of Knuth's recursive "dozen-gross-myriad-myllion-byllion-..." system (though of course Knuth's was the most extreme possible expression of that idea).

Frankly, I find SDN's strategy (also described here) much more straightforward:

10Ɛᘔ9z = levdecennqua

and therefore easier to construct, easier to read, and easier to scale up even higher... even if that entails a different approach to solving the "apposition problem" than Werneburg chose.

As I alluded in a thread which was unexpectedly deleted, Pendlbury's prefixes, which inspired SDN, are equally as straightforward in expressing any dozenal power:

10Ɛᘔ9z = lefdexneena

Pendlebury is to be credited with the notion of using a simple set of composable (and reasonably intelligible) syllables to directly express the digits of a dozenal exponent, distinct from the words normally used for mantissa digits in English. He also kept the composition rules to blindingly simple agglutination, without any complicating morphological declension. SDN largely follows his lead, though it does offer some incremental improvements and extensions on the idea.

Any such direct scheme (so long as it is equally intelligible) would be an improvement over a recursively-nested scheme like Werneburg's or Knuth's -- in my opinion.
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