## Le Tour Des Bases

Obsessive poster
Obsessive poster
Joined: Sep 10 2011, 11:27 PM
icarus wrote: Kode et al.;

I am hoping to automatically generate a ruler in base b. Now the odd thing about a ruler in any base is that we have to do some ground work assumption about the basis of the b-lengthel. I am okay with dividing the day fully "base"-imally, getting a second-like unit, and then basing the lengthel on the acceleration of earth-gravity. I'd like the lengthel to be close to a foot / 30 cm long. It is not prescriptive, but merely to demonstrate a concept. I don't think the ridiculously large bases would get a lengthel (I hope I am not abusing this word), just the human scale bases.

I like Double sharp's suggestion that bases "in the hundreds" would instead of having auxiliaries, show which bases they could be an auxiliary for, based on the assumptions I'd programmed in the code, i.e., a goal maximum prime, a solid range of small primes brought about by sacrificing large prime factors of bases with gaps among distinct primes.

By the same token, defining a unit of length even for sake of argument would need to describe its fundamentals. The division of time would be presumed to be fully basimal or according to base b auxiliary a. Then we would use acceleration g to arrive at a unit of length ℓ. Maybe we let it lie and not try to cut it to a foot-like length, but if I fail to make it a sensible length, then it could be seen as trying to thumb the scale. Therefore it should be a useful length.
Do you have any suggestions?
Well, Quantitels are all about coherent physics metrologies, but your proposal for generating rulers doesn't need to be tied to that at all.  All that  "�lengthel" means is "the coherent fundamental unit of length in coherent physics metrology �".  Not every metrology necessarily has to be a "coherent physics metrology", i.e., a system of units that assumes every type of quantity gets one and only one fundamental unit that's coherent (in a 1:1 relationship) with the coherent unit of every other quantity.  For instance, I don't think that Do-Metric was necessarily designed to be a coherent physics metrology.

However, I think your proposal does need to assume that it's dealing with metrologies that are "base-b-metric". That is, whatever fundamental length L they pick, by whatever criteria, and whatever base b they pick, you can generate units U = bn×L of any integer order of magnitude n you wish. It doesn't even matter whether L itself is anywhere near the size of a foot or inch or centimeter or decimeter or millimeter or what have you. As long as at least one of its orders-of-magnitude U lands within the desired size range for your ruler, you should be good to go.

That said, if you do want to tie this specifically to coherent metrologies, and even more specifically to day-and-gravity-based metrologies, see the Day-Gravity-Water System spreadsheet, along with the thread about it. It's got the particulars for several such metrologies, in various bases, that Double sharp, Oschkar and I have worked up. (Although some examples in there, like  = Système International itself, don't actually count as DGW systems, technically.) Should be straightforward to work out from the spreadsheet what formulas your ruler-generator would need to use. (Just please make sure you create your own copy of the spreadsheet in Google Drive and tinker with that, so any changes I might make to the original doc will not mess up whatever you do with your copy.)
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

Dozens Demigod
Double sharp
Dozens Demigod
Joined: Sep 19 2015, 11:02 AM
There's also the Day-Gravity-Water spreadsheet for large bases (which, due to the lack of associations for large numbers, mostly uses names taken directly from the asteroids for large-base day-gravity-water metrologies). In both of these, you can play around with the Adhoc metrology.

Dozens Demigod
icarus
Dozens Demigod
Joined: Apr 11 2006, 12:29 PM
Thank you for this input!

I think there will be a couple approaches.

The first is going to be a "chips fall where they may" approach. "What happens if we divide a circle into b parts?" and we get what we get. Sure, I could divide a foot/meter into b inches/divisions and might do that for the "chips fall where they may" approach. It should be evident that dividing a circle into b parts is not always keen and makes other bases preferable, just as a digit map in base b might indicate the base is "out of tune". We can mitigate that with the auxiliary base a approach. A circle divided into a parts would be keener, for instance, even given base b. Many of the approaches to lengthels would then follow, and need not be illustrated since the very basis length is pure conjecture. They've already seen a ruler divided into b versus a parts, etc. The second approach is, "Suppose we had a length-time basis, what might a lengthel look like?" This lengthel would be a day-gravity-water basis; I think that basis as a uniform what-if is stable and industrially reproducible for all bases. The second constraint is merely for visualization purposes. I would like to make a footlike lengthel and indeed would choose some power or friendly multiple as such so that we have a common frame. I would make a 30 cm, 1 foot "ruler" that kids could print out with "base b lengthel" on it. But we could also say that, for instance, were we to choose a more self-evident lengthel, it could be equivalent to 7.5572 feet or 29.54 m etc. We could also make visuals for that, but they wouldn't be rulers they could use.

I won't get into mass or density etc. at all, just length, division of a circle, and time, merely to illustrate the concept of a rudimentary (NOT prescriptive) base b system of measure. I think kids (our readers tend to be young males especially brilliant but not universally so) would love to visualize, say, a tetradecimal world where "37" is the new "25" and the day is clumsily broken into fourteen parts or "deseen" (two dozen) via auxiliary, just like ours, with "sixta" minutes each. (I have an old ismarragam nomenclature that is about as developed as "plain English" uncial nomenclature, which is handy for simple number words in many small bases. We have the argam name for a digit, then add -een for numbers b < k < 2b, then -ta to the multiple of b, etc. so tetradecimal twenty is "sixeen", not to be prescriptive, but as a spring-point for imagination). Then consider lengths in whatever falls. I could have a stock of common things, like a workshift of eight hours, the foot or the meter, the average height of a man, the size of a brick, the marathon length, etc. as things to make them ponder, and then their imagination might take off from there. We don't want to do all the work of imagining such things for the kids, but give them just enough to tantalize, and then let their own minds do the rest. Of course, folks completely disinterested in any of this aren't an audience in the first place. I also am not interested in producing a competing version of what you've done, nor am I interested in reinventing a whole bunch of well-thought-out ideas merely for it to be "all mine".

I am eager to incorporate the work you all have done and will link and credit. Would like to align the work at my site with your work. Thus, the same process to use would be to ensure I have the right nomenclature, etc. and credit. (I am crediting people's names, not avatars; I know your names). There will be a single-point page for all credits such that it is a one-stop shop for such, in case your pages migrate.

Since the idea would be to have a uniform, reproducible algorithm similar to the SDN and LaMadrid base name conventions, I need to do this upfront while coding it. I like the graphic of the ruler recently put up and will model mine similarly, however I have a tick routine that I use that will apply to base b lengthels which makes division into d parts proportional to d. Thus for uncial we have .6 = 1/2, .4, .8 = 1/3, .3, .9 = 1/4, etc. If it is ok, I would like to use the terms lengthel and timel appropriately. I am not sure we need bother with saying "base b lengthel" because of course, on a page of base b concepts, the "lengthels" are base b.

What is the value of the assumptions you'd used to get to the uncial lengthel? (meaning g). I have a lot of reading to brush up on, maybe it's in there. From there I think using the basis timel, things follow. Then in any base, we can divide the day strictly into basimal parts and then, from these parts, construe a lengthel from any of the powers to get one close to the foot/30 cm range, and if necessary use a clement divisor d to cut it down if such a lengthel is yet too large. (I am tolerant of lengthels about an inch long, so I am aiming for 1-16 inches thereabout, but if we want a printable 1:1 PDF, then even the footlong is too long for most printers.) I guess that is the starting point; the basis of your approach.