Posted as requested,
Don
_____________________________________________________________________
----- Original Message -----
From: chris burke
To: Don Watson
Sent: Monday, December 07, 2009 11:58 PM
Subject: Re: Number Machines
Hi Don
I agree with your idea - it would be a ideal use of J. However, we ourselves
(i.e. Jsoftware) do not have the time, and probably not the talent, to do a
really good job of this. We do have users who may be interested enough in
this idea to run with it. Actually, J is already used in education at
various grade levels and this would be a very nice supplement to existing
use.
Can I encourage you to post this idea to the chat forum?
Regards
Chris
________________________________________________________________________
On Mon, Dec 7, 2009 at 11:21 AM, Don Watson <[email protected]> wrote:
Hi Chris,
You may remember me. I stimulated some debate in February and March of
this year in your General Forum. I made suggestions for changes to J. In the
end, no one agreed with me. Since then, I have been doing other things.
However, the world needs a mathematical calculator that could be used
consistently from elementary school to graduate school and beyond. In
elementary school, they call it a number machine.
1. There are simple, inexpensive physical number machines with buttons for
"plus", "minus", "times", "divided by" and "square root".
2. There are more complex calculators with buttons for functions that are
frequently used in Science and Engineering, such as sin and cos.
3. There are computer packages, such as J and Maple, that seek to manipulate
and calculate many other complex expressions.
The process could be described as a two step one:
1. Translate the Mathematics expressions to a computer language.
2. Execute the computer language with a calculation engine (or number
machine).
J's strength is probably its calculation engine. I would trust Ken
Iverson to ensure a good design. Its weakness is the process of translating
Mathematics to a computer language, which is done manually by its users.
According to supporters, it takes 18 months to learn how to do this
translation. J is also still fighting 1960s battles that are no longer
relevant:
1. In the 1960s, computer entry was one dimensional (Each new line was just
a
continuation of the last, with a logical break). Today, applications allow
the entry of two dimensional Mathematical expressions. J has not adapted.
Your competitors, Maple and others, already have front ends that simulate
Mathematics in this way.
2. Program entry was restricted to the symbols marked on a keyboard. Today a
pull-down menu can allow any symbol to be entered. Again, J has not adapted.
A second strength that you have is your free download for individuals.
This allows easy downloads for educational applications. If students
graduate understanding and valuing your package, they will seek your package
in their professional life. By contrast, applications like Maple see
themselves as an expensive sledgehammer, rather than a gradual educational
tool, which is why they don't spread far into education.
If you had an inexpensive package (where your money came from School
Boards and State Education Departments, not individuals), that can translate
1 and 2 dimensional Mathematical expressions into J and then execute them
through your calculation with a documentation package that addresses the
needs of children as well as experts:
1. It could be used consistently from elementary school to graduate school
and
beyond.
2. It would have a short learning curve - because learning is incremental -
a
little more each year - and minimal.
3. It would become an essential package for businesses hiring graduates.
4. The understanding of Mathematics in the population would be much higher.
5. Your package could be implemented in specialized micro form - a
"Math-pod"
or even as an application on an I-pod, Blackberry or cell phone.
You could have a good and widely used product if you build on your
strengths and address your weaknesses. If you don't produce it, someone else
will fill the need.
Best Wishes,
Don Watson
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