History: fy. fancu lo'i ni terzu'e lo'i ni selsnada .ije li ma'o fy.boi du'e du li mo'a

Source of version: 1 (current)

((ckinytadji)) How can we express "Too many goals means too few accomplishments" in a quantitative form? * The fact that all of us are having such trouble with a quantity relationship shows the sorry state of development of the quantitative potentials of Lojban. This is a shame, because of all languages, Lojban offers the greatest power of clean handling of functional relationships. What we are doing here is relying on a natlang idiom of using a single extreme point to define a function. Here, we are saying "Given the axes of terzu'e and selsnada, there exists a point with very positive tezu'e and very negative selsnada". That natlang idiom was undoubtedly developed in the mists of mathematical ignorance, millenia before the discovery of Calculus. Lojban lets us precisely define the actual function: '''li ni'u cu parbi le'i terzu'e le'i selsnada''' This is Lojban's real strength. --((xod)) ** Let me try: ''lo roroi jdika ca'a fancu le'i terzukmei le'i selsadmei''Literally: "An always-decreasing thing is an actual function from the set of how-many-goals to the set of how-many-successes." How's that? (It doesn't mean quite the same thing as the original was meant to.) *** Pretty good! Except le fancu is the function's name, and the expression is the velfancu. And I'll throw in a ni because it feels right. So, I would try ''fancu le'i terzukmei le'i selsadmei le ni ce'u roroi jdika'' --((xod)) ***"Always" is of course metaphorical here, right? There is no time involved.As for -''mei'', I have used it to distinguish ''pa valsi'', one word, from the concept of ''pa vlamei'', one wordage, one mass of words. Here it seems to be used as a number, i.e. ''lo terzukmei'' as the number of goals, but that is not what ''mei'' means ordinarily. ''lo remei'' is a pair, not the number 2. *** '''Experimental suggestion:''' Let roi and all tense refer to whatever reference frame is given for the bridi or context. Default = time. In this case, to make "roroi" fit our discussion, we could use ''ma'iki le terzukmei ku fa'u le selsadmei'' -- ((xod)) ** So the idea proposed is that zero goals will give the highest number of accomplishments, and as you increase the number of goals, the number of accomplishments decreases. The proposed function is something like:A(G) = M - K*Gwhere A = number of accomplishments, M = maximum number of accomplishments, G = number of goals, K = some constant. ** It seems to me that "too many goals means too few accomplishments" suggests that for a reasonable number of goals, the number of accomplishments would grow proportionately with that of goals, but if you exceed that reasonable number (too many) then the number of accomplishments starts to lag behind (too few). *** Agreed, but I couldn't think of a short way to say it with ''fancu''. ''.i ko stidi'' *** .iecai this formula is better. selsnada(terzu'e) increases linearly going rightward from the origin, until it hits the maximum, where it decreases (one assumes asymptotically?) back down to zero as the terzu'e goes to positive infinity. '''We really need an elegant, concise way to describe this behavior'''. --((xod)) *****''le se klani be lei selsnada cu kansa le se klani be lei terzu'e le ka banro kei ze'a le nu le remoi na dukse iku'ibabo le pamoi co'a je ca'o jdika''"The number of accomplishments accompanies the number of goals in growth while the latter is not excessive. But afterwards, the former starts and continues to decrease." --((xorxes)) ** I'll try again: ''da poi fancu le'i terzukmei le'i selsadmei zo'u li na'u me da du'e du li mo'a'' *** Question: Is there a better construction to turn ''da'' syntactically into an operator? ''li na'u me da'' seems clumsy. Hmm, maybe it works if we use a name ''fy.'' instead of ''da''. **** ma'o da = The function "da" **** Thanks! ''fy. fancu lo'i terzukmei lo'i selsadmei .ije li ma'o fy.boi du'e du li mo'a'' **** Now, how does this work? f(t, s) du'e = mo'a? I don't quite understand. **** There exists a function f from terzukmei to selsadmei such that f(too many) = too few. *** How would you feel about le terzuklai? **** But we're talking about numbers, ''se klani'', not about space-time objects, ''klani'', aren't we? ''li du'e se klani gi'enai klani'' --((xorxes)) **** We need a concise way to refer to the count of a referent. Since -lai is a lujvo, its meaning can be stretched to be exactly what we are busting our heads trying to come up with here. "le se klani be lei broda" is way too chewy. ***** I feel uncomfortable using ''-lai'' as a rafsi for ''se klani'', but if you like it go ahead and try it. --((xorxes)) ****However it remains true that a set is never "big" nor "small"; its cardinality is. So I think it can be argued that the Book offers usage that paves the way for context to enable the replacement of a set-reference with a cardinality-reference. No examples of ambiguity have yet been offered to contradict this usage, and usage of sets in general is historically underexplored, so new usages may arise and should not be suppressed apriori. *****Let a thousand flowers bloom, even if they make no sense to me. I can live with it. *** ''le'i ni terzu'e'' should be "the set of quantities of terzu'e". No? **** Above, Jorge writes that ''"le ni ce'u me le'i broda" is... the extent to which something is a set, a totally different thing from the cardinality of the set. '' What would that make "le'i ni terzu'e"? **** ''le gencku cu cusku di'e'' - ''ni'' means "x1 is the amount of (the bridi) on scale x2." A quantity is a measured amount; if necessary for precision, we can specify that using ''ni'' x2. In other words, ''ni'' has a meaning vague between "the degree to which ..." and "the number of ..." (and other kinds of amounts), but you can specify if you need to. ***** I'm not sure exactly how, though. ''le'i ni terzu'e kei be ma'' *** One more problem: This only says that such a function exists--which isn't saying much! For precision, we should add that this function describes the real world. **** I think if you assert a relationship between two real (da'inai) entities, you're asserting that the entities obey the relationship. ***** In the context of ((LojbanAphorisms)), sure, everyone will assume that. But not in the context of ((cmaci))! ''But in the context of cmaci, x and y are da'i. In a discussion about da'inai selsnada and da'inai terzu'e, the le xusra of a le fancu is trying to discuss reality.'' .ienaisai A function is a mathematical object in its own right, and to assert that one exists (whether or not it relates actual da'inai values) is to say exactly nothing about the real world. Otherwise all theories would be true! ''Do you assert a relationship between smoking and lung cancer? Do you assert a relationship between underwear color and lung cancer?'' '''''| if you're a chaotician, yes ;-) |''''' ***** We should think twice before relying on such natural language assumptions in Lojban. It depends on how exact we want to be. ''If we want to purge all inherited natlang ghosts, let's rely solely on da'i and da'inai to specify hypotheticality. But I should think, in a discussion about toast and jelly, that if someone claims there is a relationship between the two, that they feel there actually "is" such a relationship, even it's being assumed only for the sake of argument (ru'a). If the level of assertion isn't even this strong, I can't imagine what it would mean to bother stating anything. --((xod))'' ---- ''Meta: I now agree with Jorge, that lo'i broda should not have the default meaning of le brodylai --xod''