Subject: RE: [hackers-il] Re: Re: Lightning Speed Math Teaching

From: Chen Shapira <[email-masked]>
Date: Wed, 3 Jan 2001 17:29:39 +0200

> But where would that desire come from? Don't underestimate the
> parents' influence on the kid's development. A kid who'd want to do
> that has developed in that direction from very early stages. What I'm
> saying is that kids should *not* develop in that direction as much as
> they shouldn't develop in the opposite direction -- refusing to learn
> altogether, and that's because I think that balance is the most
> important thing in any development, and generally in life too. A kid
> who grew up with such deviations, in *any* direction, will be an
> unbalanced person, and I happen to know what unbalanced people are
> like.

I don't think I follow you about what is a balanced person.
Each person has preferences by definition, infact I don't know one person
who likes all things equally (more or less).
If I understand you correctly this is your definition of balance? But why do
you consider this to be better than being unbalanced and strongly prefering
math (or history or music or dancing)? Why do you think that balanced
individuals are happier? perhaps a person who strongly concentrates on his
favorite thing in life is happier than someone who shifts around in life not
sure what he likes? Perhaps all this has absolutly nothing to do with
happiness?

---

From: Shlomi Fish <[email-masked]>
Date: Wed, 3 Jan 2001 22:39:23 +0200 (IST)

I'm not quoting anybody because I want to make a point clear. I meant that
in the same time-span and with the same corriculum (no extra hours, Chen),
a kid can be taught much more math than that is taught today. IMO, algebra
should be taught at very low grades. Instead of telling a child that if a
square plus 5 equals 6 than the square equals 6 minus 5, we should show
him that he can subtract 5 from both sides. Then we can teach him about 2
squares plus 9 that equal 3 squares plus 6. I once worked as an assembly
line worker in my father's factory, and my supervisor could not solve such
equations. Neither could one of the secretaries. 

I also believe all kids should be introduced to mathemtical and logical
puzzles. Give them the bugs in the square (see my homepage) question at
11th grade (or whenever they are taught about limeses, and converging
geometrical series - sorry for the spoiler). That's just an example -
there are plenty of problems that can be solved with high school grade
mathematics. 

Now, as for AlexSh: it's true knowledge is not everything, but math is not
all about knowledge. Math knowledge is later a valuable tool in analysing
and understanding Science and Engineering. For example, most of the modern
theory of Electrical Engineering is based on Fourier Transforms and the
Theory of Probability. Biologists can't move without Statistics.
Cryptographers depend on Number Theory and Group Theory. Almost every
engineer needs Linear Algebra, without which Matlab and similar tools
(Scilab, octave, perl-DL) cannot be fully understood.

Besides, the more knowledge a person has, the more is he equiped to deal,
analyse and integrate other knowledge. Or would you prefer persons to be
igorant. That's slightly what Chen said, so I won't go on.

From what I understood from OlegG's comment, the Russian way of teaching
, at least in the above average Russian school, is superior. But
naturally, adopting it or a similar method will require superior teachers.
And that will require better salaries. And the best solution for this, is
IMO, privatizing schools. That or raising the budget of education from the
Israeli budget.

One of my dreams is to establish a network of affordable private schools,
where among else the teachers will teach the students in such advanced
methods. Then, the parents can fight for getting a tax reduction. But
right now, I have Linear Circuits on my mind.

Chen was right in the fact that I do feel that I could have studied all
the math I know today in much less time than the teachers taught me. For
that matter, some of the university courses seem to me like they could fit
in much less than 4 monthes. But I don't trust myself, much less the
textbooks enough to not attend lectures and tutorials. And I think
Homework is very important for fully integrating new knowledge.

I studied a couple of things from books and from the Net or online
documentation, but I'm not sure if such methodology can as easily be
applied to Electrical Engineering.

As for studies of other subjects, I have not studied them in University so
I cannot testify for the Elementary/Junior High/High school level. It
seems to me we beat too much around the Bush in History, trying to analyze
the smallest details of relatively insignificant documents, instead of
trying to grasp the greater picture. I liked Bible studies better than
Literature because there was an end to our analyses which was
understanding the text better. 

Physics was OK, and pretty much covered introducory physics in the
university, although the lack of math knowledge made a difference. What
else? I only studied CS for one year, but I guess it was OK for people who
were not programmers. Of course, the only real way to study about
computers nowadays is to install Linux, start downloading stuff, and learn
using the Internet. I still do that.

What else? I believe the level of English studies is OK, more or less. In
University it's much higher, but one cannot build a building without first
laying the foundation. (I did not study the "Technical English" course in
the Technion, because my Bagruth and Psychometric tests were high enough.
And I know English much better now that I did when I took either of them)
Maybe Gaal Yahas who is an English/Philosophy major can fill in this gap.

I also studied French for three years and Arabic for six, but I don't know
them well enough to judge how well they were taught. Arabic was very
tailored to the needs of the Arm of Intelligence, but that may change
soon.

A final note in regard to MosheZ comment: Academic math is indeed not
based too much on High School math, but it still assumes such knowledge
that 3.2 - 1.7 = 1.5. The case is more clear for people who study for
engineering courses. So it is important, and those years are not entirely
wasted.

Regards,

	Shlomi Fish

----------------------------------------------------------------------
Shlomi Fish        [email-masked] 
Home Page:         http://t2.technion.ac.il/~shlomif/
Home E-mail:       [email-masked]

The prefix "God Said" has the extraordinary logical property of 
converting any statement that follows it into a true one.

---

From: Alex Shnitman <[email-masked]>
Date: Thu, 4 Jan 2001 01:39:54 +0200

Hi, Chen!

On Wed, Jan 03, 2001 at 05:29:39PM +0200, you wrote the following:

> math (or history or music or dancing)?

Evidently I didn't manage to get my point across.

Of course each person has preferences. That's an obvious fact, and
that's how it should be. I was talking about kids with unhealthy
obsessions. I know people who became so much engrossed in computers
during school that they didn't see the light of day. They're not
interested in any other subject from early on, and they think it's
fine. It can happen with any subject.

I'll try to summarize myself on the subject again. Apart from all the
other roles of the school, its educational role is to give the pupil
an overview of all the subjects, so that he can later (and actually
during the last grades too via "megamot") choose whatever he's
interested in and learn it further. I do not think that the program of
*any* subject in school needs to be significantly advanced; certainly
not high mathematics which are of no use to the lion's share of the
population. If the level of the education is to raise, it should raise
equally in all the subjects.

And in case anyone wonders, I'm not against raising the level of the
education; I'm against adding more hours to the school program, or
otherwise significantly increasing the pressure on the pupils. Nadav
has made some good points about maths studies in school. I can't
comment on them in detail because my school time was so hectic that I
didn't have time to pay attention to maths. (Not related to the school
itself, but just too many other things happened at the same time.) If
the program is indeed as silly as Nadav describes it, it surely needs
reworking. But I don't think that it necessarily entails increasing
the amount of the material. Maybe if you optimize the program, you'll
have to, but I certainly don't think that it should be a goal of the
optimization. (Same can be true for any other subject as well.)

-- 
Alex Shnitman                            | http://www.debian.org
[email-masked], [email-masked]   +-----------------------  
http://alexsh.hectic.net    UIN 188956    PGP key on web page
       E1 F2 7B 6C A0 31 80 28  63 B8 02 BA 65 C7 8B BA

I couldn't repair your brakes, so I made your horn louder.

---

From: Alex Shnitman <[email-masked]>
Date: Thu, 4 Jan 2001 01:51:24 +0200

Hi, Shlomi!

> (Scilab, octave, perl-DL) cannot be fully understood.

Math is indeed essential for engineering, but I for example would be
full of joy just as much if my kid became a good photographer. Or a
cinema reviewer in a newspaper. Or any other interesting profession --
you get my drift. I don't regard engineering as the holy grail. That's
why I think that maths should not get more attention than any other
subject in school.

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From: Oleg Goldshmidt <[email-masked]>
Date: 04 Jan 2001 10:00:11 +0200

Shlomi Fish <[email-masked]> writes:

> From what I understood from OlegG's comment, the Russian way of
> teaching, at least in the above average Russian school,

A special school.

> is superior. 

My guess is it is superior is some ways, inferior in others, compared
to a good Israeli school. I tried to describe an example of how it
could work, not how it should work.

> But naturally, adopting it or a similar method will require superior
> teachers.  And that will require better salaries. And the best
> solution for this, is IMO, privatizing schools. That or raising the
> budget of education from the Israeli budget.

The way it worked in the former Soviet Union, there were elite schools
in a few large cities with close relations to universities and
research institutions, with obvious benefits to curriculum, outside
lecturers, lab equipment, etc. The interest of the universities and
research institutes was in grooming good students and future
researchers from the school bench. The students had no obligations
though.

You thing the technion or TAU would be interested?

Yes, good teachers should be paid well, on a differentiated scale.

> in much less than 4 monthes. 

Just to give another example from personal experience.

There was a course in "Methods of Mathematical Physics" (read: PDEs)
in my second year of university, at least a semester long. Given that
everybody had had a year-long Linear Algebra course (with spectral
analysis, eigenvalues and eigenvectors, and such) in the first year, I
had a distinct feeling that the course could be taugh in 4-5
lectures. After all, the vast majority of methods taught was spectral
analysis in Hilbert spaces. I suspect though, that the Russian system
did not emphasize inter-subject relations sufficiently, and many
students got a sum of knowledge, and did not make the connection
themselves. The lecturer didn't, either.

It might not be that easy to self-educate oneself. A
well-thought-through curriculum is important.  I recall students who
came to study electronics and neglected lectures on hydrodynamics in
the second year as irrelevant. In the fourth year that had to find
time to attend those lectures with the second-year students, because
by that time they realized how related it was.

-- 
Oleg Goldshmidt | Comgates Ltd. | [email-masked] 
"... We work by wit, and not by witchcraft;
 And wit depends on dilatory time." [Shakespeare]

---

From: Shlomi Fish <[email-masked]>
Date: Thu, 4 Jan 2001 10:19:54 +0200 (IST)

> why I think that maths should not get more attention than any other

OK. Imagine a world without professional photographers or cinema
reviewers. Now: imagine a world without exact scientists and engineers. I
think engineers are more crucial to 21st century life than the two
professions you mentioned, and I expect this trend to grow. Not that I
have anything against photographers, etc.

Plus, I think even the most mundane photographer should have the knowledge
and skill to be able to become an engineer or an exact scientist. We're
better off with %50 of the populace as engineers or scientists in
potentia than %10.

BTW, there was an article in Yedioth Ahronoth that said that Israel has
the highest percentage of qualified engineers in the world. Something like
130 per 100,000 people, whereas the US which is second has 70. I don't
know if engineers include people who have a B.Sc. in Computer Science, (or
in what the Technion calls Software Engineering), but it's still an
impressive figure. And here's another fact: we need more, and most other
countries in the world, need more engineers.

You could become a good photographer by having very little knowledge, but
no engineer can do without proper knowledge of arithmetics, algebra,
calculus, linear algebra, analytic geometry and trigonometry. Would you
rather children and teenagers _not_ learn all those, so they later cannot
become engineers? Or would you rather, that in the same hours per week as
now, they learn much more math, so they will later can become scientists
and engineer much more easily and quickly. (I hope to see the day when it
will take 2 years to get a diploma in Electrical Engineering).

As somebody who studies EE in the Technion, I can tell you that some of
the courses given by the EE faculty, are purely mathematical. Not to
mention that we take a lot of courses by the Faculty of Mathematics.
Electrical Engineering is more dependant on math than many other
Engineering fields (except naturally Software Engineering), but every
engineer needs to know a minimal amount of Math.

Regards,

	Shlomi Fish
 
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---

From: "Nadav Har'El" <[email-masked]>
Date: Thu, 4 Jan 2001 12:14:28 +0200

> (Scilab, octave, perl-DL) cannot be fully understood.

This is true. The need for math education is also strong in some (but not
all) "humanistic" subjects: statistics and probability theory are essential
tools in many "madaei-hachevra" subjects, and it is important not to know
only the "formulas", but also to have an intuitive feel of the concepts of
statistics and probability, so you don't make obvious blunders in polls or
experiments. Since each subject requires a different area of math, it is
important that a "general" education contains the fundamentals of math
(arithmetic, but also the concept of proof, algebra, calculus, etc.) that
is used by all areas of math. There's no need to study "algebraic topology"
in school, for example, unless one chooses to, because indeed most people
will not need that knowledge, and it doesn't give you an important new
thought-tool.

> igorant. That's slightly what Chen said, so I won't go on.

As they say, "Ignorance is Bliss"...

If you believe that for a moment, consider what was happening in the dark
ages and middle ages. Millions of people were dying from disease caused by
bad hygiene because they didn't know better. Having half of your children
dying from now-curable disease was the norm. Millions of people were killed
because of their differing beliefs (when you only "know" a few "facts", and
didn't get them in a way of "proving" but rather "preaching", you tend to
fight violently to keep your few "facts" true).
Unfortunately, the history of the previous century also showed how even
"enlightened" (use here as the opposite of ignorant) nations can commit
horrid atrocities, so education isn't the magic bullet here....

A quick calculation shows that in the last millennium, about 500 million (!!)
people were killed by their fellow humans because of their different beliefs
or wishes, in wars, massacres, genocides, and other atrocities. Got to
make you think what the phrase "happy millennium" should mean...

But I digress...

> Homework is very important for fully integrating new knowledge.

If you'd have finished highschool-level math by the 9th grade, then it
doesn't mean you'd learn college-level math in grades 10-12: it means you
could choose whether to continue with college-level math, or stop studying
math altogether, and spend the next 3 years concentration on subjects you
prefer, be they history, philosophy, or Tanach.

> What else? I believe the level of English studies is OK, more or less. In

I think that English study is OK, but not more than that. Is this _really_
the best we can do in 9 years (!) of studying English? I doubt it. Again, I'm
not assuming that everyone is an "English genius" here - even below-average
people will learn good English if you stick them in the U.S. for two years
(especially kids), so I'm sure there's a way to teach them in Israel too.

> them well enough to judge how well they were taught.

Doesn't that tell you something?? You study a language for 3, or even 6, years,
and then "don't know them well enough to judge"? The same thing happened to
me with French. I studied it for 3 years, got a "10" grade all the time (I
really liked it), but if you stick me in Paris, I could hardly speak or
understand anything someone says to me. Somehow I get the feeling that I
should have gotten a better knowledge of French after 3 years...

> Arabic was very

Yes, this is incredibly unfortunate. I didn't study Arabic (except one year
of spoken Arabic in 6th grade) because I was under the impression that only
people who went to modiin needed it (actually, I wasn't given a choice - my
class studied French instead of Arabic - but I didn't object). They should
have emphasized talking to our neighbors (not only other countries - also
our neighbors in Chalisa, Daliat-El-Carmel, Sachnin, etc.), and the fact
that Hebrew and Arabic are similar (so learning Arabic can help understand
the structure of Hebrew).

> engineering courses. So it is important, and those years are not entirely

Unfortunately, the math taught to Engineers many times continues with the
tradition of school arithmetic: learning to do an integral is important,
but placing so much emphasis on doing dozens of integrals and getting
proficient at doing them is annoying. I still remember a physics test
(physics 2m, I think) where more than half of the time of the test was spent
on actually calculating the integral. This was a complete waste of time.

The math taught to math students rarely involves "calculations" per se, and
rather deals with concepts, understanding, and proving.

-- 
Nadav Har'El                        |       Thursday, Jan 4 2001, 9 Tevet 5761
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |Long periods of drought are always
http://nadav.harel.org.il           |followed by rain.

---

From: "Nadav Har'El" <[email-masked]>
Date: Thu, 4 Jan 2001 12:30:37 +0200

> will take 2 years to get a diploma in Electrical Engineering).

I don't think what I (and other people) previously said about the pace of
learning in schools can be extended to BA studies (at least Math, in the
Technion, I don't know about EE). I did a 3-year BA, and it was quite hard,
and _very_ intensive. Sometimes I worked very hard, until 3am each night,
and felt like I was going to buckle under the load. Of course, I could have
made less of an effort but then I wouldn't have learned as much, or gotten
the grades I got. Anyway, after finishing these 3 years, I felt like I'd
learned so much, yet still have so much to learn! There's _no way_ I could
have learned the same material in 2 years, and I even believe that I didn't
learn enough in my BA, and that I should have continued for another year
(I made up for this in my MSc, when I took a lot of extra courses).

I know people that, for example, studied "math & physics" in 3 years. Such
people (and I hope I'm not offending anybody here) are under the impression
that they learned everything in math and in physics in 3 years, which means
you can learn each subject in 2 years. But this is false. Only when these
people go to do an MSc they suddenly realise about all the very fundumental and
important subjects they didn't learn! They suddenly realise that they never
learned topology, probability theory, measure theory, and a lot of other
very important things.

-- 
Nadav Har'El                        |       Thursday, Jan 4 2001, 9 Tevet 5761
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |Birthdays are good for you - the more
http://nadav.harel.org.il           |you have the longer you live.

---

From: Alex Shnitman <[email-masked]>
Date: Thu, 4 Jan 2001 13:02:04 +0200

Hi, Shlomi!

> have anything against photographers, etc.

From the above, and most of the rest of the mail, I see that you
regard the importance of engineering very highly. I personally don't
want to live in a world without the advanced humanities that we have
now just as much as I don't want to live in a world without the
engineers. (Yes, I absolutely mean it.) So we're in a disagreement
about this point, but I suppose there's not much use to argue about
it.

> calculus, linear algebra, analytic geometry and trigonometry.

I'm sorry, but I disagree most strongly, and I think you're totally
wrong of this, even objectively and not just from my point of view. I
don't think you realize what it takes to excel in humanities.

> Would you rather children and teenagers _not_ learn all those, so
> they later cannot become engineers?

Yes, otherwise they'll all become engineers and I'll commit suicide. ;-)

Good advice is something a man gives when he is too old to set a bad example.
	-- La Rouchefoucauld

---

From: Alex Shnitman <[email-masked]>
Date: Thu, 4 Jan 2001 13:07:47 +0200

Hi, Nadav!

On Thu, Jan 04, 2001 at 12:14:28PM +0200, you wrote the following:

> [...]

OK, so I wake up in the morning and find out that I've been a preacher
for ignorance and going back to the dark ages, and also responsible
for the killing of 500 million people for good measure. Now that's a
good way to start a day. ;-)

> prefer, be they history, philosophy, or Tanach.

Now, this actually sounds acceptable.

Ambition is a poor excuse for not having enough sense to be lazy.

---

From: "Nadav Har'El" <[email-masked]>
Date: Thu, 4 Jan 2001 14:22:49 +0200

> good way to start a day. ;-)

Obviously, I didn't claim that you were pro-ignorance! Not being ignorant
doesn't have to do only with engineering. There's a lot of knowledge in
philosophy, psychology, medicine, and even (surprise!) politics. A person
with a good basic education plus a good understanding in photography
(to use your example) is not ignorant. It is only a person surrounded by truths
(about the physical world, medicine, philosophy, and even photography)
but chooses to ignore them will become ignorant (it's not a coincidence
that "ignorant" and "ignore" are similar).

Sorry if it sounded like I claimed you were an "Ignorance is Bliss" supporter.
I certainly didn't mean to.

> Now, this actually sounds acceptable.

Good :) That was my main point - forget all my rants about the lousy
millennium - sometimes I just get carried away ;)

-- 
Nadav Har'El                        |       Thursday, Jan 4 2001, 9 Tevet 5761
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |I have an open mind - it's just closed
http://nadav.harel.org.il           |for repairs.

---

From: Moshe Zadka <[email-masked]>
Date: 4 Jan 2001 13:10:28 -0000

On Thu, 4 Jan 2001, "Nadav Har'El" <[email-masked]> wrote:

> Yes, this is incredibly unfortunate.

Well, the Intellegience corps is the only place with sufficient numbers
of Arabic experts in Israel to write books and dictionaries. In case
you didn't know, all the material you study Arabic from is declassified
Military Intel. stuff.

> rather deals with concepts, understanding, and proving.

Yes, when I talked about math, I of course refrred to what is being
studied in the Math department. There, I didn't know that 1.3-1.2 = 1.1 until
I was taught what the decimal system is (don't laugh: in Infi, this was given
as an alternate construction of the reals. An incredibly yucky one, but
such is life). If you come to math knowing nothing but natural numbers
and the operations (and you need to know them only to the point where
multiplication is just adding lots of times), you can come out a good
mathematician in the end. 

Here's how I'd imagine a good math curriculum for school would look like

Age 6: Natural numbers. Unary representation, decimal representation,
the operations. Some practice, too.
Age 7: Set theory 101. Sets, powers, equivalence classes, etc.
Age 8: Construction of the real numbers: whole numbers, rationals
cuts. Basic completeness theorems.
Age 9: Logic. Propositional logic, then predicate logic.
Age 10: Fields and vector spaces. Beginnings of inner-product spaces,
complex numbers.
Age 11: Algebraic structures: groups, rings, modules.
Age 12: Non-standard analysis, and building the whole of infi from it.
Age 13: Complex functions
Age 14: Multi-dimensional infi: integrating forms, cohomologies.
Age 15: ODE, PDE.

Last 3 years, student can specialize in whatever he wants. Note: 
there is no need for more then the now-adays hours for that: I think
there already is a factor of at least 2 compared to the hours in the
university.

---

From: "Nadav Har'El" <[email-masked]>
Date: Thu, 4 Jan 2001 15:47:17 +0200

Hmm.. Moshe - after all the preaching about buggy mail-clients on linux-il,
you end up sending your post twice to the mailing-list (because you used
both to: and cc: with the same address) :) Hasandlar Holech Yachef :)

> you didn't know, all the material you study Arabic from is declassified

This is just like saying that the NSA is the largest employer of mathematicians
in the U.S. (it's true, or at least was true). It doesn't mean that the U.S.
schools focus on cryptography, or that a person is discouraged from taking
math if he doesn't show an inclination for working in a secret organization.

So kids should be encouraged to learn arabic for the purpose of chatting with
their neighbors, not (only) for spying on them.

> Age 14: Multi-dimensional infi: integrating forms, cohomologies.

Are you serious? I don't think that more than 10% of the kids will be able to
undertake such a curriculum... Also, what about geometry, and simple algebra
(polynoms, equations, word problems, etc.)? Are you sure that children can
fully comprehend infinitessimal calculus at the age of 12 (with all the "for
all epsilon there exists a delta....")? You and I could proabably have (though
I waited till I was 15 ;)), but most kids won't :(

-- 
Nadav Har'El                        |       Thursday, Jan 4 2001, 9 Tevet 5761
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |Preserve wildlife -- pickle a squirrel
http://nadav.harel.org.il           |today!

---

From: Shlomi Fish <[email-masked]>
Date: Thu, 4 Jan 2001 20:22:09 +0200 (IST)

> about this point, but I suppose there's not much use to argue about

I did not say that I want to live in a world without advanced humanities.
Like Hazal said: "Without bread there is no Torah; Without Torah there is
no bread." However, I think a good grasp of mathematics can very much aid
in correctly understanding and analyzing Humanity studies. In Math, one is
dependant on Logic, Creativity and Imagination as tools required for
solving problems and knowing what to investigate at one point. Those
skills are later very beneficial for other areas.

IMO, you don't get this kind of grasp of those subjects from studying
humanities per-se. Looking back, I am quite unimpressed by the pragmatism
of many of my teachers in High School, and many of them have B.A.s. If we
wish to have proper intellectuals (i.e: persons who can reach logical,
ethical, creative and integrated solutions given a certain situations) we
must make sure that they know how to think logically, creatively and
scientifically. And at the moment, humanities has too much trash in it,
for it to be possible from studying it alone.

I think that economists or literature critiques or philosophers or
photographers for that matter, who are able mathematicians are much better
than those who are not. And I don't think Elementary->High School studies
alone can make a man an able mathemtician and I wish to change that.

If you ask me, Math education did not significantly change in the past 50
, 100 or even more years. And troughout this time, our dependance on Math
has only increased. So I think a change is in place.
 
> don't think you realize what it takes to excel in humanities.

I was not too bad in humanities at High School. My main problem in success
was that I could not get myself to write answers that were long enough to
satisfy the teachers. Luckily, in Tanakh, which I liked the most, that
wasn't the criteria for success, which was one of the reasons I liked it
the most.

During and after High School I became interested in Ancient history of the
Near East and Europe, Linguistics and recently, Objectivist philosophy.
I also write stories, which is as humane a human can get. So, I know what
it takes to excel in such things.

I'm not sure if studying Literature in school contributed as much to my
writing ability as reading all the books I have read, watching the various
T.V. shows and films that interested me, and solving all those math and
logic problems. If you ask me in Literature, the students should be
instructed to pass a lecture about a book or story they read and _liked_
(or have written themselves), rather than everybody have to study the same
creations, which some may find fascinating but others may find boring.

Of course, there are some cases, where the book is boring but its analysis
was quite nice. The most prominent example for it on my part was "The
Crime and Its Punishment".

> Yes, otherwise they'll all become engineers and I'll commit suicide. ;-)

I don't think they will all become engineers. But it will be easier for
them to become ones _if_ they want to. And later on they may wish to
become something else than their initial choice.

My intention in starting the "Lightning Speed Math Studies" thread was to
find out how pre-academic studies can be made as efficient as possible. I
focused on Math, because it's the subject which I think suffers from the
most neglect, but if you wish to start a "Lightning Speed History Studies"
thread - be my guest.

Regards,

	Shlomi Fish

---

From: Shlomi Fish <[email-masked]>
Date: Thu, 4 Jan 2001 20:28:40 +0200 (IST)

> their neighbors, not (only) for spying on them.

I agree. And besides, all the political vocabulary I have studied could
drive a person mad. I would have been much happier, had they taught us
real-life examples.

I used to know Arabic well enough so I could translate an article in
"Al-Aharam" with the aid of a dictionary. But freely speaking it was
naturally, impractical. I wonder if there are good Arabic courses in
Israel for people who studied it for their Bagrut.
 
> I waited till I was 15 ;)), but most kids won't :(

Actually, I agree. I have in mind a different corriculum but I need to
work on it a bit before I post it here.

Regards,

	Shlomi Fish

---

From: Alex Shnitman <[email-masked]>
Date: Sun, 7 Jan 2001 03:52:48 +0200

Hi, Shlomi!

> for it to be possible from studying it alone.

I don't agree with you about the necessity of logical and scientifical
thinking for humanities, surely not for appreciating or creating art.
On the contrary, mathematical thinking is deterrent to art. That kind
of thinking is the only thing I can blame for the waste that comes out
of Hollywood in the last years (save for a few exceptions). Believe
me, no mathematical thinking or logic has anything to do with Fellini,
or Antonioni. It's the same about music -- mathematical thinking can
bring us Britney Spears, but it cannot bring us David Bowie. Perhaps I
was mistaken when talking about humanities in general, however I
maintain that we must leave some people untainted with mathematics so
that they can create art for us, for the world to be be worth living in.

Wear short sleeves! Support your right to bare arms!

---

From: Gaal Yahas <[email-masked]>
Date: Sat, 13 Jan 2001 15:39:22 +0200

Hello.

For lack of time, I couldn't participate in this important thread
until now.  Although I share some of Shlomi's feelings regarding the
unreasonableness of education, some of the claims he presents here
just don't make sense, or else are in dire need of qualification. I
also disagree strongly with some of his conclusions.

The strongest methodological move Shlomi makes is the distinction of
the humanities and the exact sciences. He thinks that the humanities
are less "crucial" to modern life, and implies that underlying
any successful humanistic work are skills that come from the exact
sciences.

> > > have anything against photographers, etc.

[Alex Shnitman]
> skills are later very beneficial for other areas.

So they are, but I don't see on what grounds you appropriated these
"skills" to the sovereign reign of Mathematics. Do you believe
imagination and creativity are any less a part of writing a novel,
painting a picture, or making a film than doing math? Logic, I think,
is also a part of these practices, although obviously it is called
upon more explicitly in Mathematics.

The question of where "Logic, Creativity and Imagination" belong to is
(to paraphrase Hilary Putnam) no more than the question of allocating
parking space in the Universities. You want to claim these "tools"
are fundamentally part of Mathematics and not something else? Prove it.

> humanities per-se.

If that's an opinion you hold, I suppose you must have reasons for
holding it. Please give them.

> Looking back, I am quite unimpressed by the pragmatism
> of many of my teachers in High School, and many of them have B.A.s.

What do you refer to by "pragmatism" here?

> If we wish to have proper intellectuals (i.e: persons who can reach
> logical, ethical, creative and integrated solutions given a certain
> situations) we must make sure that they know how to think logically,
> creatively and scientifically.

Interesting argument. I would have supposed that if we want persons
who can reach "logical, ethical, creative and integrated solutions"
we would need to teach them to think logically, ethically, creatively
and integratedly (whatever that is). Where did science come in?

What do you mean by "ethical", anyway? What is an ethical solution
to a certain situation? Morality is a profound object of study;
I don't recall it being studied (as such) in the auditoriums of the
exact sciences.

> And at the moment, humanities has too much trash in it, for it to be
> possible from studying it alone.

What do you mean by "trash"? Please exemplify.

Also, do you believe this "trash" is an essential (mis)feature of
"humanities", or that it is just the current state of the "humanities"?
(Please help me qualify my question better by stating whether you
think the "trash" is in the high school teachers, the university
teachers, the thinkers in the "humanities" or perhaps part of the
disciplines themselves.)

> alone can make a man an able mathemtician and I wish to change that.

I don't want any of my economists, literary critics, or philosophers
to be stupid, but I don't particularly need them to be able to solve
differential equations. (Well, maybe the economist needs that.) They 3
all have the intelligence and means of learning to do that if suddenly
they come across a specific problem that requires that of them, but
I don't see why they should have that knowledge readily at hand. If
you think otherwise I would ask you to show /what is it in solving
differential equations that would make a literary critic better/.

> If you ask me, Math education did not significantly change in the past
> 50, 100 or even more years. And troughout this time, our dependance
> on Math has only increased. So I think a change is in place.

Being factually ignorant on the history of math education "in the
past 50, 100 or even more years", I will not comment about this point.

> > I don't think you realize what it takes to excel in humanities.
> 
> I was not too bad in humanities at High School. My main problem in
> success was that I could not get myself to write answers that were
> long enough to satisfy the teachers.

Are you certain that length of the answers was the sole criterion for
success? If you, I think you had some lamentably bad teachers in your
high school. They certainly could not have been conducive to anyone's
excellence in the humanities.

> Luckily, in Tanakh, which I liked the most, that wasn't the criteria
> for success, which was one of the reasons I liked it the most.

Don't you mean disliked it least?

In a field of study, I believe there is value that is quite divorced
from the criteria by which high school teachers judge pupils' success.
Apart from "success", there is actual _content_ to the study. So far
you have explained why your teachers have made you hate the study:
they, and you as a result, employed unfruitful judgments in it. What
it takes to get a good grade in something is not a good criteria for
judging if the something is important, or useful, or beautiful in
itself, though.

> it takes to excel in such things. 

You became interested in several fields of the humanities so you
know what it takes to excel "such things"? Excuse me, but that's
a ridiculous inference. Since when is taking interest in something
sufficient for knowing what it takes to excel in it?

I just have to add that "Objectivist philosophy" has often come under
the attack that it is not very objectivist, nor much of a philosophy;
and it is pretty blatantly not humane.

> Crime and Its Punishment".

I don't quite see your point here. Do you assume the purpose of
Literature studies in school is to make you a good writer of fiction?
I don't think that it is. I think the primary purpose of these studies
(and I would agree that the schools I've been to do a lousy job in it)
is to make you develop those sensitivities to language and form that
will enable you to be a better /reader/ of fiction. I've never read
_Crime and Punishment_ myself, but perhaps your boredom with it is
due to your reading it mostly, or only, for plot (which I happen to
know on its simplistic level, and I agree that "a young man kills an
old lady and then regrets it" doesn't sound too interesting).

Your suggestion for student lectures has merit, because like any
activity that treats students as adults, it will increase their
involvement with the material, and encourage them to think about how
it relates to them. Pedagogically, though, I'm not sure how early
students may learn to speak effectively in front of an audience. I
agree generally with the principle of "the sooner, the better",
but am naturally suspicious of awarding doctorates to six-year-olds.

> become something else than their initial choice.

Here I agree with your calling for broad education. We should give
people the means to do what they will, or at least the potential to
set themselves on any course they will wish to take.

> most neglect, but if you wish to start a "Lightning Speed History Studies"

I think *speed* is a terrible focus. Why are you preoccupied with
it?  Education should take as long as it should take. Imposing a
substantive limit on it from the outside is irrelevant to the question
of how to do it well *while* you're doing it. I am reminded of those
detestable "Teach Yourself X [some programming language] in 21 Days"
books so notorious for their superficiality and the bad programmers
they produce.

All along your argument lies an instrumental approach to learning:
we study X to be better at Y; we want people to know W so they can
understand Z more fully; and so on. While I'd agree that "learning
for" consists with most of our aims in education, I maintain that an
important part of what we do as people has no direct goal in mind.
What are all those bridges and airplanes for, anyway? A world of
engineers is all very *efficient*, but what is it effective for?
You can't convince me that the trains are better there in order to make
me arrive at work on time. What do I work for? Making better trains?

We--all of us--constantly need to be aware of that question. More
precisely, we all *are* aware of that question. The dividing line
between the humanities and the sciences is not as clear as it is
often made. Being human is more complex than just solving problems.

-- 
Gaal Yahas <[email-masked]>

---

From: Shlomi Fish <[email-masked]>
Date: Sun, 14 Jan 2001 11:16:40 +0200 (IST)

> are fundamentally part of Mathematics and not something else? Prove it.

I did not say they were not part of something else. I just think that with
proper practice of mathematics they can be developed more rapidly. In Math
such tools are critical for one's success. In Literature, on the other
hand, one can interpret one story this way and another one may interpret
it the completely other way.

> holding it. Please give them.

Humanities are found at a much higher level of abstraction than
Mathematics is. Thus, those subjects have a greater degree of variablity
than math does. Humans are governed by other factors beside Logic, so we
also need to consider other factors in order to analyze them. This
consideration, gives us some space to manuever in, which also enables
different conclusions.

In Math, there's only one possible valid conclusion. People who expertise
in Humanities, can survive without developing their logic to its full
extent, because they can reach incomplete conclusions and still their
answers will be considered valid and "reasonable". In math you cannot do
that.

> What do you refer to by "pragmatism" here?

Forget it. That's just my personal opinion and it will not of interest to
this thread or the mailing-list.

> I don't recall it being studied (as such) in the auditoriums of the

Hmmppf. Let me ask you this: do you or do you not, think that logical
thinking has to do with being ethical or not? If you believe Ethics cannot
be deduced from Logic, then we have nothing further to discuss.

> teachers, the thinkers in the "humanities" or perhaps part of the

I believe it is the current state of the humanities. If we take
philosophy, for example, most philosophical systems contain so many
illogical rationalizations, that would not be accepted by any respectable
Mathematician. 

> differential equations that would make a literary critic better/.

What I meant that I'd rather have humanitarians which are good
mathematicians that humanitarians that are awful in it. In the same
manner, I'd rather have mathamaticians who are good artists than those who
are awful in art.

> excellence in the humanities.

It was proven to be a very good factor, at least with most History and
Literature teachers. But I cannot make myself write so much in tests. Why
write a 100-line program when a 10-liner can do?

> Don't you mean disliked it least?

No, I actually liked Tanakh. I did not hate History, and Literature, but
the tests were not to the point, IMO.

> sufficient for knowing what it takes to excel in it?

Sorry for that. Maybe I know what it takes to be good (not excel) in
writing Stories, because one cannot write a 40-page story out of thin air.
But I'm only interested in those other fields, so I leave it has that.

> and it is pretty blatantly not humane.

Not to start a flame-war here, but:
1. Attacked by whom? I, personally, think it's great and I'm entitled to
my opinion.
2. I think it is Objective and a valid Philosophy.
3. The fact that it is very uncompromising and also rejects Altruism, does
not make it non-humane. The object of these properties is that it wishes 
to prevent disaster (if you wish to know why it thinks so - RTFM), and I
think that preventing people to be killed en-masse is very humane.

> will enable you to be a better /reader/ of fiction. 

In part I think Literature studies should give students the tools to be
proficient writers. But naturally, a student who is not such, is not a
failure. Of course, being sensitive readers is also an important purpose.
But forcing people to read a lot of stories which do not interest the vast
majority of them, is not the way to do it, IMO.

> I've never read

When I read a book, the plot is what interests me the most. Later on, I
think about the various elements that appeared in it. The Crime and Its
Punishment has a two low Plot per Length ratio to be effective in
encouraging people to read it, IMO. Natuarally, it was well-written, but
it is way too slow-paced.

> but am naturally suspicious of awarding doctorates to six-year-olds.

Six-year olds don't study Literature.

> books so notorious for their superficiality and the bad programmers

OK, I think that all the time invested in teaching pre-academic 
Mathematics can be used to teach pupils more math and much more
effectively. Of course, sometimes to learn something thoroughly, 
one needs to invest a lot of time in it. And this time varies 
from person to person. However, I do believe that in Elementary School and
High School, the time dedicated to teaching Mathematics is not invested 
properly. And I mean it from both the sense of speed and the sense of
quality.

Regards,

	Shlomi Fish

---

From: Shlomi Fish <[email-masked]>
Date: Sun, 14 Jan 2001 17:33:47 +0200 (IST)

> think that preventing people to be killed en-masse is very humane.

It seems there is an equivocation here (=confusing between two different
meanings of the word). The word "humane" has two meanings:
(quoting the online Webster dictionary):

1. marked by compassion, sympathy, or consideration for humans or animals
2. characterized by or tending to broad humanistic culture : HUMANISTIC
<humane studies>
 
Now, this entire discussion is about Humanities, and I meant meaning #2
when I wrote it. However, Gaal obviously meant meaning #1. I seemed to
answer according to meaning #1, too.

Since this sub-discussion is irrelevant to the general theme of the
message, I suggest we drop it.

Regards,

	Shlomi Fish

---

From: Gaal Yahas <[email-masked]>
Date: Tue, 16 Jan 2001 00:16:09 +0200

> it the completely other way.

And since many interpretations are possible in literature then "Logic,
Creativity and Imagination" are *less* important there?  I would expect
the numerous interpretations to require *a lot of* (maybe even more)
creativity and imagination, if people in the field are required to
produce them.

As for logic, don't let the multitude of possibilities confuse you:
any given interpretation is committed to internal coherence. If I
propose literary theory T, T must not contain contradictions. Moreover,
if you are to understand T, you must understand what results from it,
and you also would do well to have the meta-logical skill of identifying
its presuppositions (that is often a ripe place to attack the theory).
These are perhaps not reduceable to first-order logic, but it would be
silly to insist they are not logical.

> consideration, gives us some space to manuever in, which also enables

("What is a number?" Give me a concrete mathematical answer to that
question, please.)

My eristic parenthetical question aside, let's accept for a moment that
Mathematics are less abstract than the Humanities. In difference from
humans, who as you say are "governed by other factors beside Logic,"
I take it you put Mathematics, which aren't. But if Mathematics aren't
"governed" by anything but logic, where did creativity and imagination
creep in from? From what you say, we should steer away from Mathematics
and study humans if we wish to learn of imagination and creativity.

(And again returning to logic, notice you are implicitly favoring
dual value logic, in which a proposition may be either true or false
and "different conclusions" are not possible. What makes you believe
this is somehow the "correct" logic to use? There are other logics
available, you know, just as there are alternative geometries to
Euclidian geometry.)

Even a strict adherent of classical logic need not be so idealist
about literature as to demand one "true" interpretation of a work.
(What is such a true interpretation supposed to stand for, anyway?
The "message" of the work? It's "meaning"? The intentions of the
writer? These notions are blurry at best.) An interpretation may
be seen as a hypothesis--a complex one--regarding a work. Criticism
will then be the exploration of this large "what-if" world that
results from the hypothesis. But critique can be a logical proccess,
the sketching of the boundaries of what the hypothesis allows us to
say about the literary work.

> answers will be considered valid and "reasonable". In math you cannot do

What is the "one possible valid conclusion" of "0=0"?

What is "developing" "logic to its full possible extent"? Is Goldbach
in fault for not having developed his "logic to its full possible extent"
and either asserting or denying the content of what is today known as
the conjecture to his name?

> this thread or the mailing-list.

Forgotten.

> be deduced from Logic, then we have nothing further to discuss.

To answer your first question, yes, I think logical thinking "has to do"
with being ethical. To confound your implied second one, I must admit
I don't *know* whether ethics may be "deduced" from logic, though I am
almost certain that they cannot.

The following block of paragraphs contains philosophy, and may be skipped
by whoever is so (dis)inclined.

Logic doesn't "know" about people. Nothing in its content pertains to
"The Good", or "Justice", or even human inclinations. So how can logic
alone be the basis of morality? We should, I think, give up hopes for
doing that. What we *can* do is accept some sort of assumption (or a set
of assumptions) about (say) the nature of man, *apply* logic to those
assumptions, and see what ethics result in this application.

The problem with this method, of course, is that we need some way
of basing the assumption at the root of the process. What's difficult
about *that* is that in doing so, we can't presuppose logic. Interesting
predicament, eh?

A beautiful moral system that addresses this problem is Immanuel Kant's.
If you're interested, read my short sketch at

     http://www.haayal.co.il/story.php3?id=62

or ask me to email an English version.

> illogical rationalizations, that would not be accepted by any respectable

Name three.

Better choose contemporary philosophical systems, by the way, or else
I may be annoying and say the old ones are being taught historically,
not as dogma to be taken as fact. Of course, I don't think the contemporary
ones are being taught dogmatically either, certainly not necessarily so,
and never in my experience at school.

Also note your claim is about "most" philosophies and "any respectable
Mathematician". To convince me you'll have to either prove intensionally
why this is true, or enumerate over half of the "philosophical
systems" that exist and show that none of them are accepted by
even one "respectable Mathematician". Are you really up to that,
hypothetically? Wanna requalify your claim?

> manner, I'd rather have mathamaticians who are good artists than those who

Well, that's great. I'd rather have people that are well fed than people
who are starving in Africa. What makes you think anyone *wants* to be
awful in math?

But my question is still relevant: what is it in solving differential
equations that would make a literary critic better?

> Literature teachers.

Did you try a control experiment? For example, in your situation I'd have
tried submitting seventeen pages worth of the word "moose", repeatedly. I
bet not many students handed in papers that long! I'd expect a high grade.

> But I cannot make myself write so much in tests. Why

Maybe it *doesn't* do--in this context?

Substantially: when writing about literature (I don't know anything about
history) many things need to be cared for. Call them formal requirements
if you like. Call them your "#include" block, if the analogy helps you at
all. They have to do with the fact that you are relating to an existing
text within a certain context, that you are interested, in your answer,
in certain aspects of the text or particular questions that have arisen
from your reading of it, and they (I believe) really are necessary
for the effectiveness of what you write. These things take space, but
are not fluff. In addition, when you have an idea about a text that you
want to bring forth, you must prove it, not with one reference, but with
as many as necessary, depending on (well, several things, but mainly)
on the depth of the idea. Complex ideas you use need explication, and in
explication you need to provide all the information that is relevant and
present it in such a manner that will help your reader understand what
it is that you are trying to convey. Writing is a matter of control,
pushing and pulling your reader into understanding something that is
not obvious to him or her (if it were, why write it in the first place?).

Of course, your teachers may not have been good enough to give you a sense
of these matters at high school. Mine weren't. But since you raised this
issue to prove you understand what it is to be good in the humanities,
how does having had bad teachers strengthen your claim?

> the tests were not to the point, IMO.

I would say that the tests were not (rarely are) *the point*, at all.
Why judge a discipline by the exams given in it in high school?

> proficient writers.

Of what?

> But naturally, a student who is not such, is not a failure.

Why is this natural? If a field "should" give a student some proficiency,
and the student ends up not having that requirement, hasn't the student
failed?

> Of course, being sensitive readers is also an important purpose.

I agree. But you see, the trick is developing the ability to understand
literature. Before you understand it, it doesn't do anything to you, so
it's no wonder you're bored by it!

> it is way too slow-paced.

Fine. Even a rich piece of art must have some apparatus for drawing
audience to it.

> Six-year olds don't study Literature.

That was an ironic statement meant to question the fruitfulness of
abstract algebra at early age.

> properly. And I mean it from both the sense of speed and the sense of

I understand you see a lot of wasted time in the present program. But
that doesn't mean necessarily that an alternative program ought to aim
for increased speed. If you're worried about quality, worry about that
first.

---

From: Shlomi Fish <[email-masked]>
Date: Tue, 16 Jan 2001 12:10:15 +0200 (IST)

Hmmm. It seems this thread is getting quite off-topic for Hackers-IL. I
can answer Gaal, but I'm not sure if anybody will be interested in a reply
to a reply that's already 20KB in size.

Gaal, do you want me to answer you in person?

Regards,

	Shlomi Fish

---

From: Alex Shnitman <[email-masked]>
Date: Tue, 16 Jan 2001 14:36:38 +0200

Hi, Shlomi!

> to a reply that's already 20KB in size.

I'm all for the discussion to continue, for what it's worth. It's not
as if hackers-il is going to burst under the load anytime soon, anyway.

A printer consists of three main parts: the case, the jammed paper tray
and the blinking red light.

---

From: Gaal Yahas <[email-masked]>
Date: Tue, 16 Jan 2001 15:38:30 +0200

> Gaal, do you want me to answer you in person?

I agree with Alex. Unless anyone voices vehement opposition, let this
forum serve.
-- 
Gaal Yahas <[email-masked]>

---

From: Gaal Yahas <[email-masked]>
Date: Wed, 17 Jan 2001 00:24:49 +0200

> that they can create art for us, for the world to be be worth living in.

For the record, I disagree with this view. Oh, sure, if some people
escape the institutions occasionally I won't consider that a bad thing
a priori: my claim does not spring from anxiety about control. But
I just don't think like Alex does that "mathematical thinking is
deterrent to art". Why should it be? Apart from time not spent on
developing art skills, how does developing mathematical skills ruin
art thinking?

(This discussion has to do with a picture of what these skills are
and how they are acquired. I don't know if we have a clear picture
of that.)

---

From: Omer Zak <[email-masked]>
Date: Wed, 17 Jan 2001 09:52:48 +0200 (IST)

One of the most important assets of a top-notch programmer is precise use
of language (according to E.W. Dijkstra).

Dijkstra suggested that people be screened for programming jobs according
to their usage of human language.

I find this to be true.  When one has good command of his language, he can
create, on the spot, concepts (design patterns, objects, clean interfaces,
etc.), which map well on the problem domain.  Using those concepts, he can
create better design for the software. 

Mathematics is all about precise use of language (exactly what is a real
number?).

So my question is:  do people actually learn precise use of language in
humanities?
                                             --- Omer
WARNING TO SPAMMERS:  see at http://www.zak.co.il/spamwarning.html

---

From: Gaal Yahas <[email-masked]>
Date: Wed, 17 Jan 2001 22:13:25 +0200

> So my question is:  do people actually learn precise use of language in

That depends on what you mean by "learn" and "precise use of language".

There is no course that I know of that explicitly puts precise use of
language as its object. However, much of the work in the humanities
pertains to analysing texts. These analyses are communicated by
articles that people have to write and read; in a way, the discussion
*is* the work (or at least a major part of it). So people practice
language all the time in the humanities, and one would hope that
through this practice they become good at it. (Precision is a
constituent of the adjective "good" in my use here.)

If you insist on didactics, I can't give you a full answer since
I don't have enough information about programs in faculties of
humanities all over the world. But specifically, I can report that
in the Tel-Aviv University, there are several courses that do put
improving use of language in relative focus. In the English department,
there are three terms of Composition required before you can sign up
for seminars. The teachers that I have met there are very intelligent
and competent in giving appropriate feedback to their students, who are
in turn required to take heed. These remarks may be about anything from
improper indentation or citation through spelling and grammar mistakes
to unclear phrasings, clutter, or ineffective arrangement of material.
The English language itself is not studied except in a few courses
dedicated to it (or in Mediaeval Literature, where Old and Middle
English texts are encountered and of course need to be dealt with).
Students are expected to write correct English. Gross mistakes are
not accepted after the first year.

In Philosophy, teachers are less picky on the editorial and linguistic
side, but precision in meanings is of course still crucial. It is
in the nature of philosophy that it deals in drawing distinctions
and articulating criteria. Precision is therefore essential in it,
and students who don't appreciate precision aren't appreciated.

And interestingly, many *philosophers* of the past century--or rather,
even as early as Frege and the _Begriffsschrift_ of 1879--would take
your statement that I quote at the beginning of this mail and apply
it to them, thus:

     Philosophy is all about precise use of language.

This is the essence of Analytic philosophy and the Linguistic Turn.

---

From: Gaal Yahas <[email-masked]>
Date: Thu, 18 Jan 2001 16:52:54 +0200

> So my question is:  do people actually learn precise use of language in

Oh, and another possible answer:

Of *course* people learn precise use of language in the humanities.
People in the humanities have big dictionaries.