[Edu-sig] mathematics and language

[Christian Mascher]

Hi all,

thanks for your reactions. Just wanted to clarify a bit, although most 
of you seemed to have understood me quite well.

>> Sorry, I don't know J (Kirby does), but this is exactly the reason I prefer
>> Python. Readability counts (for me).

Of course this was a bit offensive, telling someone who is really in 
love with something (in this case J) that you're not that interested. 
Gives rise to some hard feeling.

Every teacher experiences this. I work as a teacher - I know how it 
feels, when students don't share your own enthusiasm. And they never 
semm to have good reasons ;-), just "feelings".

Every teacher knows these questions: Oh, why do we have to learn this? I 
will never need this. What will we do next? When will we start with 
something different? Real students tend to ask these questions, 
communicating: "This is hard stuff, I have other things on my mind I 
consider more important...".

And now sometimes I find myself in a similar position; although I 
consider myself a person who is constantly learning new things. But my 
time is limited and I can choose my interests now.

When I studied physics in university (got a diploma in physics, 5 years 
of study) I had chosen a subject with lots of maths (mostly together 
with the mathematicians), I really liked it. I like maths. But that 
level is esoteric for most other peaople and more scary: most of it is 
far away and esoteric stuff for me now, too.

Last week because I needed some space in my workplace I stacked away 
lots of university textbooks. In over ten years as a high-school teacher 
I never needed most of them, especially the highly mathematical texts. 
It was kind of sad, but I said farewell to them as I realized I would 
probably never in my life use them anymore. (I kept Feynman lectures 
though.)

> This turns out not to be the case. The complete syntax table for J
> consists of 12 lines. You are talking glibly about a topic on which
> you have no information.

Thats how it is. I can't be an knowledgable in everything. So many 
things I can just talk about as an outsider.

In the past years I have taught myself Python, Java and Smalltalk in my 
free time together with OO-thinking, Linux,... . I have also looked into 
Scheme/Lisp a bit. Smalltalk was the most interesting experience, the 
famous "syntax table on a postcard". But while Python is a tool I 
actually use, Smalltalk was considerably harder to get to grips with. In 
school we use Java (with BlueJ) in the upper classes. For my personal 
bio I decided to switch interests away from programming for a while.


> And without a lesson? Do you believe that Python syntax is intuitive,
> and can be guessed without a manual or lessons? In i., the i stands
> for index. It is easy to learn, and reasonably mnemonic.

No, nothing is intuitive when you start from scratch. I can understand 
people who don't (want to?) learn Python, although I would always say it 
is useful and looks easy for me. But I had to invest there too.
> 
> 
>>> % x is reciprocal of x, so o. % 180 is pi/180
>> Don't think that is very useful.
> 

I meant: if I have a division operator then I don't have to learn about 
another special symbol for the reciprocal.

> These objections are trivial and uninformed. You aren't a
> mathematician, you don't like math and math notation, so there is
> nothing more to say, except please stand out of the way of people who
> can benefit from it and want it.

I don't stand in your way. Go ahead.

But I like math, believe it or not ;-).

>> Lost you there...
I put this in in remembrance of the late Arthur Siegel. Hope he doesn't 
mind... But he could have posted this.

> LOL. Math notation is what mathematicians use, not schoolchildren.
> They are constantly inventing more of it. What you call math notation
> is known to mathematicians as "arithmetic".
> 
> There is no standard math notation.

Every mathematician (person who creates maths) is free to invent the 
symbols he finds useful.

Still: I often think of mathematics as a language, at least as hard to 
learn as latin. You can use it to think (communicate with yourself) or 
to express your ideas in the most clear way for others to follow the 
reasoning.

Over the years some symbols have proven to be more useful than others 
(think of d/dx Leibniz versus Newton). Some symbols are just handy 
because they are more or less universally agreed upon (like the 
indo-arabic numerals, function names sin(), mathematical constants e, 
pi, ...). For starting to learn maths I have to teach pupils the most 
common vocabulary, and the correct way to express yourself. For 
instance: An expression carries no meaning if it doesn't contain a =, <, 
 > or !=. High-schoolers tend to forget that and write only one side of 
an equation
	-p/2 +- sqrt((p/2)**2-q)
when they actually want to solve a quadratic equation. I have to correct 
this, because it is like a sentence without a verb.

Mathematics as a language is more than just the vocabulary. 
Mathematicians have agreed about what counts as a proof (on levels of 
rigorousness) for instance.


All the best to you, sorry for the long post,

-- Christian