Tuesday, May 24, 2016

FAQ 8 How does toki pona deal with large quantities?



Short answer: use 'mute'.  You can expand to 'mute mute' or 'mute suli'  but you don't need to. except maybe for comparisons.

Much longer answer:
Basic toki pona has two numbers, 'wan' and 'tu', from English.  Early on, it has two more, 'tuli' and 'po', also from English.  These were dropped very early, presumably as unneeded. It is not clear why the Daoist advice, "stop off at One," was not heeded, giving just 'ala'. 'wan' and 'mute' for quantities.  But 'tu' remains and anything larger than that is strictly 'mute'.

But, against one sort of toki pona philosophy, people would notice and be concerned with details: four is more than three and five more than either, not differences to be lost in 'mute'.  So toki pona came to allow strings of numbers which together made new numbers.  In particular, 'tu's could be strung out, with a 'wan' at the end for odd numbers, to designate the sum of the string: 'tu wan' 3, 'tu tu' 4, 'tu tu wan' 5, and so on.  In print, this technique can eventually represent any number, of course, but practically, and especially in spoken language, the intelligible limit, under the best circumstances, is 14 (max 5+/- 2 'tu's), not enough for a toki poner to give their age, even.

As a result, in this already suspect idiom, larger units were adopted.  The first, from very early, was 'luka' (relevantly "hand") for 5.  This usage is totally standard, tough officially deprecated occasionally.  In the construction of new numbers, the 'luka's come before the 'tu's, with the lone 'wan' still at the end, if at all (but no longer uniformly marking odd numbers). This extends the reasonable numbers to 35, though 33 and 34, don't quite make the limit.   This covers most toki poner's ages now, probably, but leaves little room for growth or geezers.

Aside from its historical allusions, the choice of 'luka' was wise, since 'luka', as "foreleg, hand"  would never in the normal run of conversation appear in a place where numbers do. Thus, no ambiguities were added in effect.  But the proposed solution to the limits of the 'luka' system, adding 'mute' 20 and 'ale' 100, immediately adds ambiguities -- and ones context often cannot readily break, since both these words are already quantity expressions, going exactly where numbers might also go.  But, in fact, they generally occur as numbers in strings of numbers, where "all" and "many" would not go, so the effect is actually rather minor.  These additions bring reasonable numbers up to 140 and then 700, now with several gaps in each case.  The order is still from largest to smallest: 'ale mute luka tu wan'.  This is as far as official or even generally agreed expressions go.

So, here speculation begins -- and has been going on since 'luka's earliest days.  One can, of course, keep proposing new words for ever larger quantities ('pipi' for 1,000, 'kala' for '10,000 or 1,000,000, say).  But the results are always unsatisfying and, in particular, clunky, according to the speculators.  The problem is generally conceded (by those involved) to be that additive increases make for too long expressions in general.  The internal structure of number strings needs to be opened up.

The first obvious suggestion is to bring multiplication in.  It gets bigger numbers faster and yet is still familiar enough to not require a lot of calculation at each step. Just how to bring multiplication in has led to several ingenious schemes.  One can, for example, take numbers out of their canonical order to mark a product: so 'luka tu' is 7 (canonical, additive), but 'tu luka' is 10.  Or one can move the additive features over to 'en' and use standard modification for multiplication: 'luka en tu' is 7, but 'luka tu'  is 10, "two 5s".  Or one can add an explicit multiplier ('mute' suggested, so back to the 'luka' system, apparently) 'luka tu' is still 7 but 'luka mute tu' is 10.    All of these require some further rules about grouping ('pi', for starters) and various details.  Each of them presents some problems with the transition from the current language -- or even the old 'luka' system.  And, according to some speculators and many contented current users, the results is always a tangled mass of pluses and times (and minuses, even), that is hard to comprehend at a glance (so moving away from an optimal seven item number).

No one (I think) has suggested using exponentiation directly in number string structures.  But the more practical side of that, place notation, is the other obvious way to open number string structue.  Each number in the string is to be taken as a multiplier of a different power of the base of the system and the resulting number is the sum of these products: wyz in base b is  (w x b^2)+ (y x b) + z.  For toki pona, the obvious base is 3, since it has three numbers (counting 0).  So, 'tu tu' is 8, 'tu wan ala' is 21, and so on.  Of course, there is no longer a use for 'luka' ('wan tu').  And reasonable numbers even include this year.  To be sure, learning a new number system is a bit of a pain, but not nearly as bad as it seems in prospect, though decoding the year is a task (2016 is 2201221).

But, so the argument goes, so long as we accept the notion of place notation, why not use the familiar -- virtually universal -- one, decimal?  We could allow 'luka' and use base 6 (Happy 13200!) but that has all the relearning problems of base 3 and no real advantages.  The problem now is to find new words for the missing digits, assuming we would keep 'wan' and 'tu' and 'ala' -- or a whole new set, if not.  Starting from 'luka' as exemplar, the suggestions have focused on body parts, from 'sewi' to anpa' or some subset, or on living types, from 'jan' to 'pipi' or 'kasi' or, on another tack, the first word of each of the nine consonants.  And so on.  Or just a bunch of new words, from wherever, just for numbers.  This last is clearly not toki ponish, which tries to keep the wordlist small.  One cute intermediate suggestion was based on abacus numbers -- how many beads up to the bar and whether or ot one is also down to the bar -- so adding in 'si' ('tuli' is ungainly) and 'po' and then, with the drop,
luka, luwan, lutu, lusi lupo'.  A lesser change than a whole new set.  And, of course, 'luka' can be reanalysed as 'bar and 0' giving a new word for 0 and getting rid of the 'ala'/'ale' muddle.

But none of these are going to get acceptance on their own terms; even 'luka' and certainly 'ali' and 'mute' are still provisional.   So why this drive to get a number system that includes large numbers?  Because large numbers are important in our ordinary lives.  Or so it seems.  But we don't spend much of our lives (most of us) counting things or doing arithmetic.  I do arithmetic maybe twice a week (balance a checkbook, figure out what pan to use), but I use big numbers constantly: PINs, credit cards, telephone numbers, IP addresses, ZIP codes, order numbers, and so on.  But the joke is that none of these are numbers in a strict sense; they are neither cardinal nor ordinal, they don't add or multiply in any meaningful way.  They are, in fact, names, which just happen to be built of digits rather than letters (letters would actually be more efficient, but somehow harder to use). Some of them have an inner structure, not unlike given names, others are just distinctive strings, with no internal structure beyond the order of the digits. Even the few numbers of this class that are numbers in some usual sense, dates, for example, fall easily over into the class of more structured indices.

So, if this is a major driving force in the look for a better number system, we are looking in the wrong place.  We don't need to expand upon 'wan', 'tu', and whatever others we allow nor upon the combination rules.  We need to introduce some system into the realm of Unofficial Words (i.e., proper names).  We need some (quasi) official names for digits (and for letters as well, I would insist).  Then all these problems disappear: mi jo e ilo toki [new name] e ilo sona [another new name] e lipu mani [yet another, longer name].  Where to go for these names (other than the toki pona numbers, of course) will no doubt keep the discussion flowing for a while, but some consensus is surely possible here, where it was not with numbers, so near the core of toki pona.

And, once we have a way to deal with dates and debit cards, someone will figure out a wa y to apply this idiom to counting sheep.




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