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]> 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]> > 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
