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Re: Numerical accuracy/precision - this is a bug or a feature?

• To: mathgroup at smc.vnet.net
• Subject: [mg120289] Re: Numerical accuracy/precision - this is a bug or a feature?
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Sun, 17 Jul 2011 06:02:11 -0400 (EDT)
• References: <ius5op$2g7$1@smc.vnet.net> <ius7b6$30t$1@smc.vnet.net> <ivrmd0$82e$1@smc.vnet.net>

On 7/16/2011 2:41 AM, Noqsi wrote:
> On Jul 15, 1:10 am, Richard Fateman<fate... at cs.berkeley.edu>  wrote:

...

>> I think you may be confusing "computer science"  with "applications of
>> computers to whatever [e.g. physics, engineering, business]"  which is
>> usually taught in the department of 'whatever'.
>
> So, in your view, the substance is all in the departments of
> 'whatever'? Because without applications, what's left? Computers are
> not natural objects: they are artificial, so without applications the
> whole field is just a made-up story. A true science needs the
> discipline of relating to *something* in the real world. You're
> evading this discipline. Your view makes computer science
> indistinguishable from religious scholasticism.

I think your comment might be more aptly directed toward the study of 
pure math.  Since I've raised the hackles of the physicists, why not 
poke the mathematicians in the eye too.  (My Phd is in Applied Math, my 
bachelor's degree is in Physics [&math]).

It is true that computer science without applications is mostly dealing 
with the artificial. Artificial languages to use to communicate 
algorithms to computers. The design of algorithms, which by and large 
take (artificial representations of numbers/data/) and after some 
processing, return (artificial representations ..).  The design of data, 
by which one can take some external something and encode it.
Music, personnel records, signals from outer space, commodity prices, 
etc. Computer security, networking, operating systems, cryptography, 
graph theory, some theoretical areas.  Some "general" tools, like 
graphics, robotics, sensors.   While some familiarity with the 
application domain is sometimes helpful, a deep understanding of each of 
most of the application domains of computers is not part of "computer 
science".

If you want to know more about what is taught in a department of 
computer science, look in the online catalog of some school.

If you look at Berkeley's you might be surprised that courses "in 
programming in language X" are typically given only 1 unit, not 3 or 4.
Also, CS majors usually don't take them, and I think at most one can be 
counted toward graduation.  It is not that CS majors don't know how to 
program, it is that programming in a particular language per se is 
incidental to the topics of CS, like data structures, compilers, design 
of programming languages. In the course of their studies, majors 
typically write programs in a variety of languages including Java, C, 
C++, Lisp, assembly language, Python, perhaps some "toy" programming 
languages.  Maybe prolog, postscript, ruby, ..

Now it has been argued that any "science" that has "science" in its name 
is not a true science.  E.g. political science, social science, 
management science, and computer science.  So one could try, as some 
have, to call it "informatics". Or something else.  Maybe Wolframatics?

....

>>
>> (RJF) Do you know for a fact that the Russians didn't care what orbit the
>> first manned satellite had?
>
> (nosqi) I know the consequences of getting it wrong. Basically, they knew if
> they got the perigee high enough to go around once, nothing really bad
> could result from the other orbital parameters. The rocket wasn't
> powerful enough to do something silly like put Gagarin into an escape
> trajectory. The limitations of the rocket combined with very basic
> orbital mechanics guaranteed that about an hour and a half after
> launch, the spacecraft would return to a point near overhead to where
> the launch site had been. Consider the rotation of the Earth, and then
> all they had to do was fire the retrorocket in roughly the right
> direction at roughly the right time and Gagarin was guaranteed to come
> down about 23 degrees west of where he was launched. The Soviet Union
> was a huge place: they didn't need to do this accurately at all.

I'm sure it would have been a great comfort to Gagarin to be told, 
"don't worry, you'll probably land somewhere in the USSR".

>
> Satisfying a single inequality is enormously easier than rendezvous in
> orbit around a body with poorly known gravity, where you must satisfy
> six equations to high precision.
>
>> I think you are confusing application knowledge with computer science.
>
> Without applications, computer science is vacuous.

You know any mathematicians?  No?  How about theologians?
>
>> Of course there are many methods that can be programmed. You are
>> assuming that analysis of signals is done by some kind of particle
>> tracking?  I assume that programs are designed by persons familiar with
>> differential equations and electromagnetic radiation, as well as more
>> seat-of-the-pants stuff like antenna design and sun spots.
>>
>> Also I assume
>> that cell phones use signal strength and feedback, and do not need great
>> accuracy.
>
> How do you determine how large to make the transistors when
> manufacturing the cell phone? This requires calculation. How would you
> do that calculation?

I assume that would be done by electrical engineers perhaps using tools 
in the field of "computer aided design of integrated circuits". Not my 
area of expertise.
>
>> Though maybe GPS stuff is tricky if you have few
>> triangulation points.  Using 10 points, maybe not so tricky.  Not
>> something I've cared to look at.
>
> If von Neumann was alive, he'd understand the issues completely before
> you'd even finished describing the problem. He was a *real* computer
> scientist.

Wow, I didn't know you had such powers that you could predict what John 
von Neumann (died in 1957) would have understood.
>
>>> There is no universal method for tracking uncertainty that is accurate
>>> and practical.
>>
>> Ah, so you are saying that Mathematica is not accurate and practical??
>
> Not universally. However, given a specific problem, it is often the
> tool of choice.
>
>> I am primarily interested in building systems appropriate for a range of
>> applications.  (That's more computer science).
>
> Without knowledge of applications, you have no foundation to stand on
> here. And that's Wolfram's advantage: he and his people *do*
> understand a very wide range of applications.

Indeed some of the people he hired understood relevant parts of computer 
science.  Unfortunately, Wolfram himself, and some of the people he 
hired did NOT know relevant parts of computer science, and that's why 
some of the design turned out relatively weak.

Wolfram had an earlier design, SMP, which was even worse in this respect.

>
>>    From that perspective I
>> think that Mathematica falls short.
>
> Since many of us find Mathematica a very effective tool in real
> applications, this judgement is obviously based on nothing but
> ideology.

You bring to mind the old joke about the man falling off the top of the 
Empire State building.  Asked, as he passed floor 50, how he was doing, 
he said "So far, so good"..




> You have repeatedly demonstrated your complete lack of any
> useful perspective here, and your unwillingness to do the necessary
> studying to gain that perspective.

Um, you seem to think that in order to understand how arithmetic should 
be done, I should study low-earth orbits, GPS triangulation, and , and 
everything else?

Instead, you carefully define
> "computer science" in a way that excuses you from studying anything
> you don't wish to study.

See above. Computer science is pretty well defined these days.
>
>>   I don't see that as a threat, but I
>> am inclined to object to statements that claim (in my view incorrectly)
>> that Mathematica (arithmetically speaking) is the best, or even the only
>> way to do floating-point calculations.
>
> There is no best. It depends on what you're doing. Mathematica is very
> effective over a wide range of applications. It is not the right tool
> for every application. But you need the application knowledge to
> understand this.

OK, let's hear it from your experience: tell us what applications you 
know about for which Mathematica is not suitable.

And then if you believe your own stance, you would have to concede that 
for areas that you are not expert in, your opinion on what is best is of 
no value.

RJF
>
>

• Follow-Ups:
  • Re: Numerical accuracy/precision - this is a bug or a feature?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>