
Post by Anonymous User on Jun 10, 2015 21:02:31 GMT 8
If you ever feel like writing something, you don't have to worry about signing up. You can just post right away.



Post by fcg710647 on Aug 16, 2015 22:37:18 GMT 8
It looks like a number of people are viewing the queues... why are none writing stuff?!? hahahaha maybe they don't care if the numbers of facebook friends or instagram photos they have are written as 320(doz.) and 221(doz.) as opposed to 456 or 313 lol If they have a party with six people and bake a great brownie, they might as well cut it into twelve or eighteen parts instead of eight or ten lol



Post by Buffoonery on Sept 12, 2015 21:08:43 GMT 8
I'd be more interested in using it adding fractions, something that is hard to do in decimal without using vulgar fractions. what's (1/3 + 1/4 + 1/8)? To most people that scares them, first you gotta get the lowest common denominator, then you gotta add them. But why not just say, hey, what's (0.4 + 0.3 + 0.16)? Oh, 0.7 + 0.16 = 0.86, done. Or in octadecimal, that'd be (0.6 + 0.49 + 0.249) = 0.cd9. Since there's no recurring decimals, no one's brain is in peril. No one would dare do this in decimal by hand. (0.333... + 0.25 + 0.125) = "Please god help me." If you wanted a good set of fractions to be added for octadecimal, that'd be (1/3 + 1/6 + 1/9) or (0.6 + 0.3 + 0.2) = 0.b . so basically you'd excel in multiples of 3, but still have the advantage of most 2's. hahaha, if only eh?



Post by fcg710647 on Sept 17, 2015 15:46:37 GMT 8
0.125 + 0.25 = 0.375, 0.375 + 0.333 = 0.378 + 0.330 = 0.708, then add the remaining 3s and you get 0.7083333333... it's more of a conceptual issue, it brings up limits, real numbers, geometric series, etc. etc. instead of just reducing fractions such as 0.25 = 25 / 100 = 1/4. I would agree in that I remember an elementary school question asking me to show how 3/4 was larger than 2/3, and that 0.75 versus 0.66666... wouldn't count (even though 0.75 is very clearly larger, LOL), but any recurring or terminating decimal IS a fraction, it just couldn't appeal to the teachers to handle recurring ones. Anyway, as I mentioned in the alphadecimal (hexatrigesimal) board, if you require the base number to contain both 3 and 4 as factors, I choose thirtysix.



Post by Buffoonery on Sept 17, 2015 18:14:00 GMT 8
Yeah 36 seems like one of the bases I'm interested in. The only drawback is the huge number of letters you'd have to use to represent them.
Whenever I'm looking at these bases, I like to imagine a tradesman using them, because I work with 16ths and multiples of 12, it would be nice to see them cleaned up. Using decimals like "10.3" instead of the vulgar fractions "12 1/4" would be extra handy when trying to remember a string of numbers you just measured. I always say to myself things like, "124 and 3/8 inches, that's 10ft plus 3 and 3/8 inches." Why do we punish ourselves like this? If you see 124 and 3/8ths, then moving the decimal over to 12.4 would give you the feet (in dozenal).
It'd just be nice to see a more efficient method that looks like metric, but doesn't run into as many recurring decimals. Using base 12 would hit 2 birds with 1 stone.



Post by fcg710647 on Sept 17, 2015 21:33:11 GMT 8
You use a lot of Imperial length measurements? Not to mention sixteen ounces in a pound, that might be it, a jumbled up system xD Sixteenths can't terminate in only one digit unless the base is a multiple of sixteen, and the necessary factor of 3 raises this to 48 already. Can 36 still settle it? Multiples of twelve: U, E, 10, 1U, 1E, 20, 2U, 2E, 30, 3U, 3E, 40, 4U, 4E, 50, ... 50(Ad.) is already 180 in decimal (fifteen feet if 180 inches) So using 36, x0 inches is 3*x feet (I don't have x in my symbols haha) J is sixteen... nonreducing sixteenths: 1/J = 0.29 3/J = 0.29 + 0.4y = 1/J + 1/8 = 0.6e 5/J = 0.29 + 0.9 = 1/J + 1/4 = 0.r9 7/J = 0.6e + 0.9 = 0.Ae 9/J = 0.29 + 0.y = 0.P9 r/J = 0.6e + 0.y = 0.Ee H/J = 0.r9 + 0.y = 0.m9 A/J = 0.Ae + 0.y = 0.ne
Not shabby. What about 144 inches? Looks weird in decimal, but it's 40 in base 36. Oh, 4 * 3 = U(twelve) feet.



Post by fcg710647 on Oct 8, 2015 19:07:59 GMT 8
On the subject of imperial units, there are 2^5 * 3 * 5 * 11 (decimal) feet in a mile....
How many miles are in a foot? Decimal: 0.0001893939393939393939..... Dozenal: 0.0003E163E163E163E163E16.... Octodecimal: 0.0011AAUHH798A0NU1N63... Quadrivigesimal: 0.002CP1Nb93F62CP1N.... Trigesimal: 0.0053U85HG2bvJtD85HG2b.... Alphadecimal: 0.008d3nH?d3nH?d3nH?d3.... Sievenal: 0.00C1C5CaJ1]64EyHFUb9wYm....
Well, that sucked. Decimal had the shortest recurring period, followed by doz. and Ad. This ratio would not terminate in any base less than three hundred and thirty, or 2*3*5*11. Lol.



Post by fcg710647 on Oct 16, 2015 17:38:38 GMT 8
On the other hand, some units can stay.
Feet in an inch:
Decimal: 0.083333333.... Dozenal: 0.1 Octodecimal: 0.19 Alphadecimal: 0.3 Sievenal: 0.3a // Nice, only decimal is a little busted.
Yards in an inch?
Decimal: 0.027777777777.... Dozenal: 0.04 Octodecimal: 0.09 Alphadecimal: 0.1 Sievenal: 0.17 // Similar results.



Post by fcg710647 on Oct 27, 2015 18:43:44 GMT 8
Am I overwhelming you a bit with all this information?
36 should be nice for your choice of fractions to add, namely 1/3 + 1/4 + 1/8 = 0.U + 0.9 + 0.4y = 0.a + 0.4y = 0.Ty



Post by Buffoonery on Nov 25, 2015 16:06:28 GMT 8
I took a long break from studying bases. Lately, I've been studying the languages German, French, Spanish, and most interestingly, "Lojban". I am not abandoning the study of bases, it just felt better to mix it up a bit. Though with work lately, it's hard to fit in the time I want to learn. From what I've concluded so far, base 12 seems to be the most interesting and useful base to me.
In Lojban, the numbers can go up to 16 independent digits: [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] no, pa, re, ci, vo, mu, xa, ze, bi, so [ A] [ B] [ C] [ D] [ E] [ F] dau, fei, gai, jau, rei, vai
Now I know most languages reach up to 12 independent digits, but in Lojban, you can express the difference between decimal and dozenal numbers easily. For example: Dozenal Ɛ = li fei Decimal 11 = li papa {li} means "the number / evaluated expression; convert number / operand / evaluated math expression..." Dozenal Ɛ4 = li feivo
So as an example sentence, I would say in Lojban: mi jgari feivo najnimre pare ju'ai I carry Ɛ4 oranges (base 12).



Post by fcg710647 on Dec 2, 2015 16:36:58 GMT 8
Oh so "li" is for more abstract purposes. I notice that "fei" and "papa" are analogous to "elv" or "eleven" versus "one one."



Post by Buffoonery on Dec 4, 2015 1:22:52 GMT 8
Yes, but, 100 = {panono} and 1,0,0 = {.i pa .i no .i no} {.i} is used to separate from the previous utterance.
saying "elv hundred and forty six" is the same as saying {feivoxa} where as, "elv four six" is said as, {.i fei .i vo .i xa}
so in a 12 digit countdown, it's like this: {.i pano .i fei .i dau .i so .i bi .i ze .i xa .i mu .i vo .i ci .i re .i pa} = "twelve, eleven, ten, nine, eight, seven, six, five, four, three, two, one."
but before you state that, you need to make sure the listener understands you are in dozenal by saying, {pare ju'ai} (base 12)
{li}, {lo}, {la}, etc. are used before to clarify what the selbri is. (Selbri is the central part of the sentence). mi cmene la James "my [name] is James"
***[The following is a bit confusing, you don't have to read this]***
la = "the one(s) called..." lo = "the one(s) which is/does..." or "those which are..." li = "the number/evaluated expression..." le = "the one(s) described as..."
So, you could think of it as being a very specific version of "the" that tells us what to expect next. It can even give the heads up that something is a verb or a noun, like this: {mi gleki lo nu do klama ti}
{mi gleki} = "I am happy" {lo nu} = "of the state of" {do klama ti} = "you are coming here"
"I am happy that you are coming here"
So if I said, {mi gleki klama ta} that would say, {I am} [happily] [going] [there]



Post by Buffoonery on Dec 4, 2015 1:39:46 GMT 8
To summarize, English: "604" as in a phone number is, "six oh four" "604" as in hundreds is, "six hundred four"
Lojban: "604" as in a phone number is, {.i xa .i no .i vo} "604" as in a phone number is, {li xanovo} "604" as in a phone number is, {me'o xanovo} "604" as in hundreds is, {xanovo}
{me'o} might be a better term to use, it means, "unevaluated mathematical expression" {li} means "evaluated mathematical expression"
{mi jgari vovo najnimre} I carry 44 oranges.
{mi jgari me'o vovo najnimre} I carry number 44 oranges. (as in, the numbers have something to do with the numbers 44, perhaps they have an engraving on them)



Post by fcg710647 on Dec 4, 2015 19:31:21 GMT 8
That's unusual, ".i" replaces "comma." Anyway, I believe your continued preference for dozenal stems from a shallow analysis. Dozenal is cool when you have only halves, thirds, quarters, sixths, and maybe eigths or twelfths. If you think of labeling a number line, though, you notice that those common fractions would generate a very incomplete illustration. You would need to move to 0.71, 0.72, ... and maybe 0.701, 0.702, and so on. Most importantly, the common fractions can't dwarf the presence of a massive number of other fractions. No matter what base you use, *most* fractions will recur.
That being said, really the only thing to do about repeating fractions is to shorten their patterns (on average). It's fine that you prefer to terminate the common fractions in only one significant place, but this means any multiple of twelve base can be used, provided that you can handle the symbol set. Honestly, I've looked into dozenal quite a bit and it's pretty boring besides dealing with the common fractions. I much prefer having 24 more symbols (relative to dozenal) to reach alphadecimal, because it is *square*. Other than symmetry, what's the big whoop about a square base?
Nonsquare bases, such as decimal and dozenal, can have very long recurring periods, especially with what are called cyclic numbers. A cyclic number is of the form ((base)^(prime  1)  1) / prime. In dozenal, the primes 5 and 7 are both capable of this, hence the recurring 0.24972497249724.... for 1/5 and 0.186X35186X35... for 1/7; the cyclic numbers are 2497 and 186X35. For eleven and thirteen, dozenal is not nearly as ugly because these primes are adjacent to twelve. 1/E = 0.11111111... and 1/11 = 0.0E0E0E0E0E0... and these are analogous to 1/9 = 0.1111111... and 1/11 = 0.0909090909... in decimal, because 9 and eleven are adjacent to ten.
In dozenal, the next prime, seventeen, is indeed cyclic (the prime is 15 in dozenal). 1/15 = 0.08579214E36429X708579214E36429X708.... Again, MOST fractions look like 0.X35186X35... or some other recurring thing, the common ones are a minority. Because alphadecimal is square (two senary digits for one alphadecimal digit), any repeating pattern in base six which has an even length gets cut in half when written in alphadecimal (this does not mean lost data, it means it is compressed). Furthermore, since 36 is even and any prime larger than 2 is odd, the possible maximum period of 1/(prime) for such primes, which is prime1, is even. Any cyclic number in base six gets cut in half in alphadecimal  alphadecimal has NO cyclic numbers.
Example: one thirteenth. Senary: 1/21 = 0.02434053121502434053121502434053121.... (twelvedigit cycle) Alphadecimal: 1/H = 0.2eEn8r2eEn8r2eEn8r.... (sixdigit period)
Here's the big repercussion, a configurable program that tests the recurring period lengths in given bases and finds the average period length. For this run, a base received a noticeable bonus if it terminated a fraction instead of recurring it. This helped out trigesimal (base thirty) a little bit, but not nearly enough to match the dominance from perfect power bases. Hexadecimal, a square *of* a square, can cut recurring periods from binary in half once or twice (if they are even or divisible by 4, respectively), so it has the lowest average, but it fails to terminate thirds and sixths and alphadecimal is thus superior overall.
Both decimal and dozenal have almost twice the average period lengths of hex and alphadecimal and their averages are very close to each other. Base 42 (duoquadragesimal) did a little better than dec. and doz. Centimal, another square base (one hundred) did very well but is much too large. Dicentahexadecimal is also way too large (the cube of six, cuts periods in senary that are divisible by three but can't shorten by two).
ScriptLog: Average number of repeat digits for select bases  reciprocals of some numbers within the range 32 to 985 ScriptLog: _.,._.,._.,._.,._.,._.,._.,._.,._ ScriptLog: Decimal: 93.077370 ScriptLog: Dozenal: 91.867142 ScriptLog: Hexadecimal: 48.807419 ScriptLog: Octodecimal: 91.803543 ScriptLog: Unvigesimal: 92.004944 ScriptLog: Trigesimal: 71.827446 ScriptLog: Duotrigesimal: 89.880806 ScriptLog: Alphadecimal: 50.570053 // A close second, only defeated by a fourth power. ScriptLog: Duoquadragesimal: 81.590164 ScriptLog: Dicentahexadecimal: 64.051788 ScriptLog: Centimal: 53.485477 ScriptLog: Prime: 110.042465 ScriptLog: ScriptLog: The victor is thus Hexadecimal.
Alphadecimal also allows one to repeatedly divide by 2, 3, or 6 and be able to fit two such divisions in each digit. The following numbers would get very ugly in decimal; they would terminate in dozenal but need twice as many digits.
Powers of 5/6 using alphadecimal.
0.d 0.T // 25/36 in decimal 0.Pd 0.NH // 625/1296 in decimal 0.CJd 0.U21 // In dozenal, this one is 0.402854 0.t1Ed 0.8HCT // 390625/1679616 in decimal .....



Post by Buffoonery on Dec 9, 2015 2:53:05 GMT 8
In Lojban, {.i} is similar to a comma in that it’s used as a sentence link, continuing sentences on the same topic. {.i} when followed by an attitudinal can change the meaning of a sentence completely. (The first sentence spoken does not require {.i} since there is nothing to link to) Here are some examples: .ui la djan klama [Yay!] John is coming! .uu la djan klama [Alas!] John is coming. .a'o la djan klama [Hopefully] John is coming. .ue la djan klama [Wow!] John is coming. .ianai la djan klama [Nonsense!] John is coming. That last one {ianai} is 2 parts, {ia}, meaning "belief" and {nai}, meaning "negative". So put them together, it means, "disbelief," {ianai}. The attitudinal can be placed any between the beginning and end of a sentence marked by the {.i}. So as an example: .a'o la djan klama .i a'o mi tugni .i ue mi viska ri [Hopefully] John is coming. [Hopefully] Yeah, I hope so too. [Surprise] I see him!  The 2 bases, Dozenal and Alphadecimal are achieving two different goals in my opinion. For Dozenal, it’s: easy to work with easy to memorize multiplication / division minimal additional digits decently short terminating fractionals Whereas for Alphadecimal, it’s: square (which leads to the following point) has shorter recurring periods (0.9724 9724 dozenal = 0.S alphadecimal) allows for more divisions consecutively without as many ugly fractions I realize that recurring fractionals are a pain and that having a longer fraction termination cycle is a detriment. However, these are my main reasons for choosing dozenal: Society has already adopted 12 partially, it plays a major part in time, music, and measurement. 12 is everywhere, but people get frustrated when they have to memorize their times tables up to 12 instead of just 10. If they had a cleaner multiplication table, maybe they would have an easier time. A lot of people are afraid of math, if they see a 6 they round it down, if they see a 4, they round it up. People take the path of least resistance, and I don’t blame them. But if we see a multiplication table and think, “wait, those patterns are simple, I can do this.” That’s exactly what I want, I want people to stop saying, “I hate math,” and to start saying, “that’s easy.” So when you can tell them by voice that, “4 of those makes 10,” and “3 of those makes 10,” it really takes a load off the mind. If it was logical to use a smaller base like 6 or 8, that would be great. Unfortunately, they have little use. Since as we take a look, 8 doesn’t work well with threes, and 6 is good with both twos and threes, but the combinations of fractions you can make are small. Say for example, if you want to cut in quarters, you already have a recurring decimal (0.222). So the next step is to move forward from our base 10, which this looks good when we reach 12, the only real drawback is the 2 additional symbols. If we keep going, the rewards are less and less with base 14. Then we reach b16 which is a square base, it’s useful for any math relating to 2 but terrible with 3s. The next base is 18, which looks good until you realize that how many additional digits you’ll have to remember to use. So by the time we reach base 36, we are having to learn 26 additional digits. I cannot imagine a construction worker or plumber using base 36 over base 12. My reasoning for this is that in many cases, I like to see the mirror of my number, like: 1 and 9 2 and 8 3 and 7 4 and 6 But if we had 36 digits, that would look like: 1 and Z 2 and Y 3 and X 4 and W 5 and V 6 and U 7 and T 8 and S 9 and R A and Q B and P C and O D and N E and M F and L G and K H and J … That’s a lot on the mind for anyone to remember. I’m trying to imagine the multiplication table for that, it would be enormous. Compared to dozenal and we only have 1 more pair to remember: 1 and Ɛ 2 and ᕍ 3 and 9 4 and 8 5 and 7 Then with that sacrifice we have an cleaner multiplication table with much easier to remember patterns. I think it's well worth it. prntscr.com/9c4elkvs prntscr.com/9c4ega

