Yes I'm experimenting!
Every time I hit a new notation I stumble for a while.
I studied mathematics. Each new notation was torture. I only
learned that I was dyslexic when I tried learning linguistics and
stumbled over the new phonetic alphabet. My first exam I translated
everything from Roman alphabet to standard phonetic alphabet then was
completely unable to check my work. My linguistics professor
diagnosed me after several tests at age 36. Somehow no-one noticed
as I learned to read by myself at age three--but not phonetically.
When I first met Ken Iverson I had worshiped him for years as APL was
the first thing I saw that was consistent and simple and allowed you
to acquire the language naturally as needed.
I asked him how he had the nerve to throw away the notation of Euler
et al and he couldn't stop laughing.
still working on b
What the heck is it meant to be for? perhaps that would be a clue
Donna
[EMAIL PROTECTED]
On 14-Jun-06, at 1:08 PM, Oleg Kobchenko wrote:
Donna,
If you are dyslexic you probably should especially stay away
from the Dictionary. Seriously. At least for a while.
That I can tell as a victim of the same ailment.
As a student I was keen on AI-sy stuff and had
LISP books, but never actually got to learn LISP or
understand how it works: it was an image of a bunch
of parenthese on the one side, congnitive frames
on the other and a big void in between. Until I had
a class-full of time in a computer lab to find something
to prevent from going to sleep. I wandered the disk drive
and found a muLISP folder. It contained the labs (it actually
had a different name) and I learnt LISP in one hour.
In a later semester when the professor said that
the basic structural element of LISP is a list -- no, it's
a CONS pair, I corrected -- she was very surprised.
There is a paragraph at the beginning of Dictionary of APL, which
I could not find in Dictionary of J, that specifically warns
against using it as a learning source for beginners. Instead,
learning is suggested with practical activity by examples in the
subject area close to the learner. Whereas the dictionary
is meant to be a reference source.
This approach is in accordance with the analogous learning
of a natural foreign language (note: the native language is learnt
without any dictionary at all.): you cannot learn a foregn language
using a dictionary. Or, similarly, with any other theoretical book.
It is believed by modern lingvo-psychologists (Chomsky?) that formal
instruction (books) do not cause language learning. What they
do is confirm what you already learnt. Learning happens with
massive exposure to samples and activity, immitation is a big factor,
plus our inborn code cracking ability, which rebuilds our own
dictionary
and grammar in the head. Then the book can help reorganize that
a little, but every person will have their own unique set of rules
in their heads.
That's actually confirmed in your examples below: you discovered
that the 'base' symbol and immediately formed your own rules,
which were not completely confirmed by the book and produced
contradictory experience. Then you corrected your rule and now
it's closer to the one in the book.
Learning is induced by positive reinforcement, which comes
from successes, possible wi th small incremetal tasks and
the pleasure of little discoveries and positive confirmations.
This is why gradual and hands-on labs are very productive,
as well as books like primer.
Frustration inhibits learning, which comes from attempting
too steep tasks or prematurely exposing to theoretical
material, which does not relate to any prior experience.
A special case is profound experience in a related, but
significantly different area, like you have a vast experience
in APL and expect J to be just another dialect.
That is similar to what happens to experienced skiers
who attempt snowboarding: most of those who tried
did not switch or even liked it for the reason that they
had so many bruises and pain that they simply could not stand it.
At the same time, that snowboarding is considered easier
to learn when you are a complete alpine novice.
----- Original Message ----
From: dly <[EMAIL PROTECTED]>
To: General forum <[email protected]>
Sent: Wednesday, June 14, 2006 11:56:14 AM
Subject: Re: [Jgeneral] Mathematical Roots of J & more musings
wow?
if b is base
why is
11b2
2
not
11b2
3
or
12b2
2
not
12b2
domain error
33bg
16
not
33bg
51
Constants and results are displayed in the default base 10 (a)
why
11ba
10
not
11ba
11
Scientific notation raises the default base 10 by powers of 10 as in
1e1
10
3.45e6
3450000
Napier's constant which he denoted e in honour of Euler is given by
1x1 in J which similarly can be raised by powers of e
(Not to be confused with Euler's constant which he denoted C and
Macheroni denoted γ=0.5772156649)
1x1
2.71828
2x2
14.7781
∏ is given by 1p1 in J which similarly can be raised to powers
of ∏
1p1
3.14159
2p2
19.7392
So why confuse the student with this?
Negative integers following p and x indicate the use of reciprocals.
For example, 2p_2 is two divided by π squared, and 2x_2 is two
divided by the square of Euler's number.
Why not just say that for e (exponent of 10), p (exponent of ∏) and
x (exponent of e) can be negative or decimal numbers?
Donna
[EMAIL PROTECTED]
On 14-Jun-06, at 9:42 AM, John Randall wrote:
dly wrote:
I get imaginary numbers 3j4 but at a loss why 1x1 for e
I see 1r1 but where did this x come from? it doesn't say but it
somehow seems to follow that 1p1 is PI
Donna:
The exponential numeric constants are explained in the system
documentation
http://www.jsoftware.com/books/help/dictionary/dcons.htm
and in Henry Rich's book
http://www.jsoftware.com/books/help/jforc/
applied_mathematics_in_j.htm#_Toc129570854
I guess e would have been better than x except that it had already
been
used for base 10 exponential notation.
Best wishes,
John
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