The distributive law of algebra is a(b+c) = ab + ac . You must not translate that into J as a*(b+c) -: a*b + a*c . How many mistakes do you see in that translation? Is J in fact suitable for math education?
On Tuesday, May 27, 2014, Joe Bogner <[email protected]> wrote: > Somewhat related, I've started reading The Princeton Companion to > Mathematics, an 1100 page reference that seems to cover the full spectrum > of mathematics at a significant depth. > > I was fascinated after 8 pages it introduces the grammar of mathematics. > > When I first started with J, I thought it was odd to have so much emphasis > on the parts of speech, > http://www.jsoftware.com/help/dictionary/dict2.htmand > http://www.jsoftware.com/help/dictionary/partsofspeech.htm , especially > looking at J as another general programming language. Learning it's math > roots more, it makes more sense. I don't remember (fairly long time ago) > any connection between English(?) and Math in my elementary, high school > and undergrad studies. I would guess 75% of the programmers I talk to would > struggle to recall what a gerund or conjunction is... I digress. > > > I don't know if this link will work everywhere, but Google Books has the > pages available for me at least: > > http://books.google.com/books/p/princeton?id=ZOfUsvemJDMC&lpg=PP1&pg=PA8#v=onepage&q&f=false > > Here is a an extract: > > "To illustrate the sort of clarity and simplicity that is > needed in mathematical discourse, let us consider the > famous mathematical sentence “Two plus two equals > four” as a sentence of English rather than of mathemat- > ics, and try to analyze it grammatically. On the face of it, > it contains three nouns (“two,” “two,” and “four”), a verb > (“equals”) and a conjunction (“plus”). However, looking > more carefully we may begin to notice some oddities. > For example, although the word “plus” resembles the > word “and,” the most obvious example of a conjunction, > it does not behave in quite the same way, as is shown > by the sentence “Mary and Peter love Paris.” The verb in > this sentence, “love,” is plural, whereas the verb in the > previous sentence, “equals,” was singular. So the word > “plus” seems to take two objects (which happen to be > numbers) and produce out of them a new, single object, > while “and” conjoins “Mary” and “Peter” in a looser way, > leaving them as distinct people. > Reflecting on the word “and” a bit more, one finds that > it has two very different uses. One, as above, is to link > two nouns, whereas the other is to join two whole sen- > tences together, as in “Mary likes Paris and Peter likes > New York.” If we want the basics of our language to be > absolutely clear, then it will be important to be aware > of this distinction. (When mathematicians are at their > most formal, they simply outlaw the noun-linking use > of “and”—a sentence such as “3 and 5 are prime num- > bers” is then paraphrased as “3 is a prime number and > 5 is a prime number.”) > > This is but one of many similar questions: anybody > who has tried to classify all words into the standard > eight parts of speech will know that the classification is > hopelessly inadequate. What, for example, is the role of > the word “six” in the sentence “This section has six sub- > sections”? Unlike “two” and “four” earlier, it is certainly > not a noun. Since it modifies the noun “subsection” it > would traditionally be classified as an adjective, but it > does not behave like most adjectives: the sentences “My > car is not very fast” and “Look at that tall building” are > perfectly grammatical, whereas the sentences “My car > is not very six” and “Look at that six building” are not > just nonsense but ungrammatical nonsense. So do we > classify adjectives further into numerical adjectives and > nonnumerical adjectives? Perhaps we do, but then our > troubles will be only just beginning. For example, what > about possessive adjectives such as “my” and “your”? In > general, the more one tries to refine the classification of > English words, the more one realizes how many different > grammatical roles there are. > " > > > > > On Tue, May 27, 2014 at 7:49 PM, Raul Miller > <[email protected]<javascript:;>> > wrote: > > > In fact... multiplication apparently looks something like this: > > > > unsum=: 3 :0 > > digits=. 10 #.inv y > > multipliers=. (*/\.(#digits)#10)%10 > > digits*multipliers > > ) > > > > areamodel=: |.@(*&.>/)&unsum > > > > x=: +/@,@;@areamodel > > > > unsum 123 > > 100 20 3 > > 123 areamodel 456 > > ┌─────┬────┬───┐ > > │1200 │150 │18 │ > > ├─────┼────┼───┤ > > │8000 │1000│120│ > > ├─────┼────┼───┤ > > │40000│5000│600│ > > └─────┴────┴───┘ > > 123 x 456 > > 56088 > > > > And I guess there's some kind of social issues behind the nature of this > > kind of standard. It seems a little odd, from my perspective (for > example: > > the boxes are somewhat indicative of the concept of area, but it's very > > definitely not-to-scale - but being to scale would be silly). But it's > > still kind of interesting. > > > > Thanks, > > > > -- > > Raul > > > > > > > > > > On Tue, May 27, 2014 at 7:31 PM, Raul Miller > > <[email protected]<javascript:;> > > > > wrote: > > > > > It looks to me like some significant part of the vocabulary of "common > > > core" math is very similar to that used in J. > > > > > > http://commoncore.org/maps/math/video-gallery/array-and-area-models > > > > > > Of course, there are some differences also - but perhaps J will be easy > > > for modern grade schoolers to pick up? > > > > > > Food for thought, > > > > > > -- > > > Raul > > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm -- Sent from Gmail Mobile ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
