Of interest:
a blog post from Wolfram Research:
http://blog.wolfram.com/2008/04/29/today-we-broke-the-bernoulli-record-from-the-analytical-engine-to-mathematica/
this illustrates, partially, the power of having a full set of
mathematical functions build in, as part of the language.
from the perspective in the evolution of computer languages, one
characteristics is that the language becomes easier to use with more
power. e.g., assembly-like, C, Fortran, to C++, Java, to awk, bash,
then Perl, Python, and tcl, PHP, VisualBasic, Javascript, NewLisp, and
Mathematica.
One way to put a language in a evolution class, is simply to think of
how many lines of code is typical to do one thing. Another way to
think of this is, what level of learning a language requires its user
to use it.
We could, for example, say that all languages in year 2020, will all
have full mathematcial functions build in.
See also:
What is Expressiveness in a Computer Language
http://xahlee.org/perl-python/what_is_expresiveness.html
Xah
···@xahlee.org
∑ http://xahlee.org/
☄
On 2 Mai, 07:37, ·······@gmail.com" <······@gmail.com> wrote:
> We could, for example, say that all languages in year 2020, will all
> have full mathematcial functions build in.
What exactly it means for feature x or y to be "built in" or whether
it makes any difference depends on the language itself. Most of the
time a user will see no difference anyway.
From: Florian Weimer
Subject: Re: the power of a language example: full mathematical functions buildin
Date:
Message-ID: <871w4jvgaa.fsf@mid.deneb.enyo.de>
* Ingo Menger:
> On 2 Mai, 07:37, ·······@gmail.com" <······@gmail.com> wrote:
>
>> We could, for example, say that all languages in year 2020, will all
>> have full mathematcial functions build in.
>
> What exactly it means for feature x or y to be "built in" or whether
> it makes any difference depends on the language itself. Most of the
> time a user will see no difference anyway.
And the intersting question is not how much code it takes to type B_2n,
but how to implement a system that can (a) infer a bound for the
denominator of B_2n, and (b) can use that knowledge to efficiently
compute B_2n based on a sufficiently exact approximation of
\pi^{-2n}\zeta(2n). If I read the article correctly, Mathematica can't
do that automatically, it's been told by a programmer: "But a few years
ago I programmed a quite different algorithm into Mathematica."
From: John Thingstad
Subject: Re: the power of a language example: full mathematical functions buildin
Date:
Message-ID: <op.uaivltubut4oq5@pandora.alfanett.no>
På Fri, 02 May 2008 07:37:57 +0200, skrev ······@gmail.com
<······@gmail.com>:
> Of interest:
>
> a blog post from Wolfram Research:
>
> http://blog.wolfram.com/2008/04/29/today-we-broke-the-bernoulli-record-from-the-analytical-engine-to-mathematica/
>
> this illustrates, partially, the power of having a full set of
> mathematical functions build in, as part of the language.
>
> from the perspective in the evolution of computer languages, one
> characteristics is that the language becomes easier to use with more
> power. e.g., assembly-like, C, Fortran, to C++, Java, to awk, bash,
> then Perl, Python, and tcl, PHP, VisualBasic, Javascript, NewLisp, and
> Mathematica.
>
> One way to put a language in a evolution class, is simply to think of
> how many lines of code is typical to do one thing. Another way to
> think of this is, what level of learning a language requires its user
> to use it.
>
> We could, for example, say that all languages in year 2020, will all
> have full mathematcial functions build in.
>
> See also:
> What is Expressiveness in a Computer Language
> http://xahlee.org/perl-python/what_is_expresiveness.html
>
> Xah
> ···@xahlee.org
> ∑ http://xahlee.org/
>
> ☄
If you actually want a general purpose language with supports
multi-paradigm programming why don't you check out a Oz implementation
like Mozart. I could mention: logic programming, pattern matching,
distributed programming, OO, functional programming with lazy evaluation.
--------------
John Thingstad
······@gmail.com wrote:
> Of interest:
>
> a blog post from Wolfram Research:
>
>
http://blog.wolfram.com/2008/04/29/today-we-broke-the-bernoulli-record-from-the-analytical-engine-to-mathematica/
>
> this illustrates, partially, the power of having a full set of
> mathematical functions build in, as part of the language.
There are two main problems with this:
Firstly, finding the 10 millionth Bernoulli number is of no practical
importance.
Secondly, the implementation is written almost entirely in C and is simply
called from Mathematica code.
IMHO, there are better illustrations of the power of the Mathematica
language.
> from the perspective in the evolution of computer languages, one
> characteristics is that the language becomes easier to use with more
> power. e.g., assembly-like, C, Fortran, to C++, Java, to awk, bash,
> then Perl, Python, and tcl, PHP, VisualBasic, Javascript, NewLisp, and
> Mathematica.
Subjective.
> One way to put a language in a evolution class, is simply to think of
> how many lines of code is typical to do one thing. Another way to
> think of this is, what level of learning a language requires its user
> to use it.
You can easily pick a task that Mathematica is very poorly suited to, which
completely inverts your notion of "evolution".
> We could, for example, say that all languages in year 2020, will all
> have full mathematcial functions build in.
There is a lot more to programming than mathematics.
--
Dr Jon D Harrop, Flying Frog Consultancy
http://www.ffconsultancy.com/products/?u
On May 4, 9:21 am, Jon Harrop <····@ffconsultancy.com> wrote:
> ...
> There is a lot more to programming than mathematics.
Second that.
From: Robert Maas, http://tinyurl.com/uh3t
Subject: Re: the power of a language example: full mathematical functions buildin
Date:
Message-ID: <rem-2008may06-002@yahoo.com>
> From: Jon Harrop <····@ffconsultancy.com>
> There is a lot more to programming than mathematics.
I say the same thing, only stronger: Most programming deals with
data processing, and most data processing is in fact processing
numerical values and/or text, and most of the rest of programming
is device control such as driving graphics displays. The fraction
of programming that deals with mathematical theorem proving is
infinitesimally small. The fraction of programming that deals with
any aspect of symbolic/abstract math in any form is microscopically
small. Mathematics (beyond arithmetic) is a tiny niche market, not
large enough to warrent inclusion in any general-purpose
programming language except as an optional add-on module.