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Discussion of "kancu"
Comment #1:
Issues

Curtis W Franks (Sun Jan 1 08:25:23 2017)

I think that there really are two words here.
The first is "cardinality", which we already have. It is simple "x1 is the number of elements in/cardinality of set x2". This uses on kancu2 and kancu3 (antirespectively). This requires no counter (person doing the counting) and is independent of the method used to count.
The second word is something along the lines of "enumerate", "tabulate", "tally", or "count up". This is a task performed by someone (a counter) and depends on the method. I personally think that it would be fine to straightup delete kancu3 for this purpose, but perhaps we should just retool it (I am not sure how, though). Instead of trying to figure out the cardinality of a set (kancu2), it would just be producing a running tally of objects/divisions/units (kancu2'). In this way, it is not actually tied to the grand total, only what has thus far been counted. This word would be useful for estimation of the size of an army, counting coins or money values from a purse (counting by units), or counting down in units of time (kancu2' would just be something like "loi snidu"). In this word a new terbri could be introduced which designates the first value from which the counting starts; in counting down time, this would commonly be something like "ten [seconds]". (Aside: counting down would involve li ni'u (pa) in the units terbri.) Notice that the counter is not actually counting how many seconds are remaining; they are starting with that knowledge and then enumerating them in reverse order as they pass (within approximation  the counted seconds are not perfect, nor is the original tminusten mark).


Comment #2:
Re: Issues

Curtis W Franks (Sun Jan 1 08:27:07 2017)

krtisfranks wrote: > I think that there really are two words here. > > The first is "cardinality", which we already have. It is simple "x1 is the > number of elements in/cardinality of set x2". This uses on kancu2 and > kancu3 (antirespectively). This requires no counter (person doing the > counting) and is independent of the method used to count. > > The second word is something along the lines of "enumerate", "tabulate", > "tally", or "count up". This is a task performed by someone (a counter) and > depends on the method. I personally think that it would be fine to > straightup delete kancu3 for this purpose, but perhaps we should just > retool it (I am not sure how, though). Instead of trying to figure out the > cardinality of a set (kancu2), it would just be producing a running tally
> of objects/divisions/units (kancu2'). In this way, it is not actually tied > to the grand total, only what has thus far been counted. This word would be > useful for estimation of the size of an army, counting coins or money > values from a purse (counting by units), or counting down in units of time > (kancu2' would just be something like "loi snidu"). In this word a new > terbri could be introduced which designates the first value from which the > counting starts; in counting down time, this would commonly be something > like "ten [seconds]". (Aside: counting down would involve li ni'u (pa) in
> the units terbri.) Notice that the counter is not actually counting how > many seconds are remaining; they are starting with that knowledge and then > enumerating them in reverse order as they pass (within approximation  the > counted seconds are not perfect, nor is the original tminusten mark).
I run into this problem frequently and it basically makes the word, as presently defined, useless. It cannot be used for either of these meanings because it has the other meaning inappropriately but unavoidably wrapped up in it.



Comment #3:
Re: Issues

gleki (Sun Jan 1 09:33:57 2017)

krtisfranks wrote: > I think that there really are two words here. > > The first is "cardinality", which we already have. It is simple "x1 is the > number of elements in/cardinality of set x2". This uses on kancu2 and > kancu3 (antirespectively). This requires no counter (person doing the > counting) and is independent of the method used to count. > > The second word is something along the lines of "enumerate", "tabulate", > "tally", or "count up". This is a task performed by someone (a counter) and > depends on the method. I personally think that it would be fine to > straightup delete kancu3 for this purpose, but perhaps we should just > retool it (I am not sure how, though). Instead of trying to figure out the > cardinality of a set (kancu2), it would just be producing a running tally
> of objects/divisions/units (kancu2'). In this way, it is not actually tied > to the grand total, only what has thus far been counted. This word would be > useful for estimation of the size of an army, counting coins or money > values from a purse (counting by units), or counting down in units of time > (kancu2' would just be something like "loi snidu"). In this word a new > terbri could be introduced which designates the first value from which the > counting starts; in counting down time, this would commonly be something > like "ten [seconds]". (Aside: counting down would involve li ni'u (pa) in
> the units terbri.) Notice that the counter is not actually counting how > many seconds are remaining; they are starting with that knowledge and then > enumerating them in reverse order as they pass (within approximation  the > counted seconds are not perfect, nor is the original tminusten mark).
Previous discussion: https://groups.google.com/d/topic/lojbanbeginners/sWzqifBPUTU/discussion



Comment #4:
Re: Issues

Curtis W Franks (Mon Jan 2 18:24:45 2017)

krtisfranks wrote: > I think that there really are two words here. > > The first is "cardinality", which we already have. It is simple "x1 is the > number of elements in/cardinality of set x2". This uses on kancu2 and > kancu3 (antirespectively). This requires no counter (person doing the > counting) and is independent of the method used to count. > > The second word is something along the lines of "enumerate", "tabulate", > "tally", or "count up". This is a task performed by someone (a counter) and > depends on the method. I personally think that it would be fine to > straightup delete kancu3 for this purpose, but perhaps we should just > retool it (I am not sure how, though). Instead of trying to figure out the > cardinality of a set (kancu2), it would just be producing a running tally
> of objects/divisions/units (kancu2'). In this way, it is not actually tied > to the grand total, only what has thus far been counted.
Maybe this is a good option:
The cardinality of a set is equal to the cardinality of another set, by definition, iff there exists a bijection between the sets. A set A is called "countable" iff there exists a (possibly improper) subset of the set of natural numbers B such that there exists a bijection between A and B. If a set A is finite (therefore also countable), then its cardinality is the nonnegative integer n such that there is a bijection between A and ci'ai'u(n); A is countable and infinite iff its cardinality is alephnull.
The first word which I described would, for countable A, produce the n so described (or, iff appropriate, alephnull), regardless of which bijection is used in order to relate A to the other set.
Note that, if there were a counter, then the wrong n may be produced by a human method of counting (attempting but failing to produce a correct bijection). This does not change the cardinality of the set, it just means that the claim is false. For example, one can count by threes and come to the conclusion that there were six Beatles, but that would not make them correct. (In the current definition of kancu, they cannot possibly be incorrect because their method of counting allows for them to come to whichever conclusion they like.)
I offer a third possibility in replacing kancu now. This possibility does not have a counter terbri (so it is like the word for cardinality in this way) but it also does not have a terbri for the number at which the counting would arrive (so it is like the second word which I described in my first comment in this thread, which emphasizes the ongoing process of tallying). This word merely describes /which/ bijection or injection, in particular (of all of the possibilities), is being used/has been selected in order to attempt to enumerate (some subset of) the set, where the function maps from the set being counted to a subset of the natural numbers united with the singleton of 0. In fact, in order to allow for joke counting, repetition, or unforeseen uses, the function need not even be injective nor mapping to N; it just needs to exist/be welldefined and map to the set of extended real numbers (not even positive finite ones). Note that, in partovular, ci'ai'u is not necessarily involved and that ordering the range of the function is not necessary.



Comment #5:
Re: Issues

Curtis W Franks (Tue Jan 3 00:33:39 2017)

krtisfranks wrote: > The second word is something along the lines of "enumerate", "tabulate", > "tally", or "count up". This is a task performed by someone (a counter) and > depends on the method.
Maybe the best way to describe this meaning is the idea that the counter lists numbers sequentially (in order) (with a temporal or spatial delay between each entry in the ordered list).
Changing the structure of the word somewhat, this would just require the input of an ordered list, a description of what constitutes the start (if counting eggs, which is the first one? if counting down seconds, what marks when the countdown begins?), and what must happen in order to proceed from one item in the list to the next one (pointing at a different egg, one second passing, etc.). There would be no terbri for counting units/steps (current kancu4), as this would just be derived information from the list (and the counting unit would fluctuate/be variable as desired by the counter).
Aside: That last point is important too. kancu is broken because it cannot handle the counter adjusting the counting unit. Even if it could handle the meaning "count( )down", and I do not think that it can, the unit between numbers must be the same. That means that the events in that one scene from /Harry Potter and the Prisoner of Azkaban/ movie from 2004, which involves Dre Head counting down by varied units, cannot be described by kancu under my current interpretation (that kancu4 must be a constant).




