View source for Potential Issues with the 26 Sep. A.D. 1994 English Definition of "satci"

The 26 Sep. A.D. 1994 English Definition of "satci" is as follows: "<b>x<sub>1</sub> [measurement/match] is exact/precise to precision x<sub>2</sub> in property/quantity x<sub>3</sub> (ka/ni)</b>".

This article is an elaboration of concerns that I (lai .krtisfranks.) have over this definition. I welcome commentary or responses, since it very well could just be a lack of understanding on my part.

== Overview ==

The following is my current interpretation.

If the typing of satci<sub>1</sub> were not included or (obviously) if it were only "[measurement]", then I would say that "satci" is numeric and, moreover, is fundamentally about/dealing with measurement. But with the current typing, maybe other possibilities sometimes exist. In any case, I would hesitate to translate all cases of English "exact(ly)" to Lojban "satci".

For example, consider "I am annoyed by people referring to Hillary Clinton as '''exactly''' "Secretary Clinton" when she should be called "former Secretary Clinton". Here, the first name is not an incomplete quotation which leaves out the "former"; I am saying that they call her "Secretary Clinton" and nothing more is mentioned.". I am not sure that "exactly" should be "satci". Names do not get measured. I have no ruler or scale with which I can tell "Secretary Clinton" from "former Secretary Clinton"; neither can be measured, so neither can be measured to be more precise (technical sense) than the other. One is more correct than the other though. On the other hand, perhaps it could be considered a case of matching - I do not know, since I do not know what "match" means.

== satci<sub>1</sub> ==

I am not really sure what a 'match' is. Is it just the substring of digits which correspond and are equivalent in expressions of two numbers (a measurement/approximation and its ideal)? Maybe we can also include lists (matching term-/entry-wise). Anything else?

For example: "the match (between 22/7 and π) {{note | The order does not really matter (it is symmetric) but there might be implications that the second term is the goal or the exact/perfect/ideal/true result.} is precise to, including, and not exceeding/following the second digit after the radix point in standard decimal notation".

== satci<sub>2</sub> ==

Since "satci" deals with measurements, it actually does not even mean "exact" in a mathematical/ideal sense. I would call it "precision" unless satci2 is ''li ci'i'' or ~''li ci'ipici'i'' {{note | Meaning that it is to infinite precision/sigfigs in all integer and all non-integer fractional digits (respectively: digits before and after the radix point). I do not mean א<sub>.∞</sub> (aleph-sub-point-infinity), which is actually the only meaning allowed by the definition - uh-oh!}} or something, in which case it can be "exact", since it means that the precision is infinite. But how does this specification work? Consider a word (string) with an infinite number of digits, then a radix point (Lojban: ''pi''), and then infinitely many more digits. First, maybe the precision or matching needs to consecutive. So, matching every other digit is not infinitely precise. But is saying "infinitely precise" (Lojban: "satci li ci'i") enough to mean that every digit is correct? Or could it just be the case that every digit after (xor before) a certain digit is correct? Note that this is a problem even for semi-infinite words such as that of the standard decimal expansion of π (id est: "3.1415926..."); doubly-infinite ones just happen to be a more dramatic illustration. So, how does one say that every digit matches? I actually would not use "ci'i" but instead "ro". But this still does not allow us to specify that every digit before (but not after){{note | This is "exactly before"; notice the use of the word "exactly". How would you translate it?}} a certain one is correct?

If digits match to a certain point, then do not, and then do again (even just upon occasion, not constantly or regularly), then do the latter matches count for improving the matching? It does not really meaningfully improve the precision, but there are more matches. For example, "2.718'''3'''8'''2'''8" matches "2.718'''2'''8'''1'''8" except for the bolded digits; the former is precise to the first bolded digit in approximating the second, but it matches in further digits (which actually matters proportionately as well since the strings are finite).


I am also not sure how to count digits. Consider the approximation 22/7 for π. Then the digits match until but not including the second "1" in the decimal expansion of π (<math>\approx</math> 3.14'''1'''59) and the first "2" in the decimal expansion of 22/7 (<math>\approx</math> 3.14'''2'''85), as shown bolded in the parentheticals. Further matches in corresponding digits might (actually: should with probability 1) occur later, but they do not matter for this discussion nor for the precision of the approximation. Which digit is this? It is the third after the decimal point, the fourth "number" digit overall", and the fifth digit if we count every character. In Lojban "pi" is in PA, making it as much of a digit as any other; I suppose that it is also nice to know that the decimal points line up too. So, it should be the fifth digit. (But what if there is an infinite number of digits prior to the decimal point too? Then we would label it as 'd<sub>-3</sub>', meaning that it is the negative third digit. But what label does the decimal point receive? 'd<sub>0</sub> is the singles digit, 'd<sub>-1</sub>' is the tenths digit). Which precision is this? Is it to the fifth digit (in this sense) -  the first one which does not match? Or is it to the fourth digit (in this sense) - the last one which matched?

Now that I think about it, how is precision even specified.  Say that I want to say that some approximation or measurement is precise to the fourth digit. How would I say this (even just ignoring decimal points, which do not get a digit label in English nor in math except notationally)? Is satci<sub>2</sub> filled by ''li vo''? Or is it filled by ''li ny gei dau'' (where "ny" represents the correct power of ten for what we mean by "fourth digit")? How is the decimal point specified in the latter case? Or would one just take the ratio of the approximation/measurement divided by the ideal value, the result being the precision? So 22/7 approximates π with precision <math>\approx 1.00040249</math> {{note | And now we need to worry about the precision of the precision!}}.

== satci<sub>3</sub> ==

I just do not find the third terbri to be helpful or non-redundant in any way whatsoever. I am not even sure what it means.

I am not sure what satci<sub>3</sub> would be in the case of matching, still, but maybe it has a purpose.


My confusion with the definition: a measurement should only be of one thing (one dimension/property regarding some phenomenon or object or subpart thereof {{note | For example: objects have many line segments the lengths of which could be measured. A subpart of an object, in this context, is one such line segment. A table has a height, a distance between its legs, the side length of the longest side of its top, and the length of its diagonal; its subparts would be the line segments along which these measurements would ideally be made}}). It does have any aspect to it. Everything that one needs to know about a measurement is how it was conducted (methodology), what it actually measured (which dimension of which subpart of which phenomenon object), and what its result was. A measurement is precise (to some precision) in the property which it measured, which is inherent to it. I cannot say that something measures to be two meters (plus or minus .01 meters) in mass. People sometimes say "it is two meters in length" - but of course it is in length, that is the only dimension that meters can record/realize/represent. But maybe they mean "in its longest direction" rather than "in length"? Again, I say that this is wrapped up in the measured quantity - it is not a table that is measured, it is a dimension of a subpart of the table (its longest side length, or its vertical length (height), or its mass, etc.). So, what I am saying, is that if satci<sub>1</sub> is a measurement, then the phenomenon/object subpart and the dimension being measured are all described in the measurement which constitutes satci<sub>1</sub> and thus there is no need for satci<sub>3</sub> in the property ("ka") sense {{note | Nor, for the record, can satci<sub>1</sub> or satci<sub>2</sub> be filled by a phenomenon/object - the first must be filled by a measurement (a whole process, the result, etc.) and the second must be filled by a number which represents the amount of precision.}; if satci<sub>1</sub> is a measurement, then the numeric quantity of precision is the result of the measurement, so satci<sub>3</sub> is not needed in the quantity ("ni") sense.


 
If satci<sub>1</sub> is a match between the representations of two numbers, I would say that the first term is really a match between the <u>digits</u> of those two numbers' representation in the base. Thus, "digits" cannot non-redundantly be the sumti which would fill satci<sub>3</sub> (and if it did, would it be "ka"?).