The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Is this an exceptionally hard set of questions to answer?
Replies: 68   Last Post: Nov 11, 2002 7:54 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Alberto C Moreira

Posts: 266
Registered: 12/6/04
Re: Is this an exceptionally hard set of questions to answer?
Posted: Oct 29, 2002 7:25 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


Kevin Foltinek <foltinek@math.utexas.edu> said:

>Alberto Moreira <junkmail@moreira.mv.com> writes:
>

>> For example,
>> something as simple as a function to add two numbers would be f(a,b)
>> in mathematics. But inside a program, it means "load a, load b, add
>> them, put them in a register, and return that register to the
>> caller:

>
>I thought you were saying that modern programming is all object
>oriented. You seem to have forgotten one of the keywords:
>encapsulation.
>
>The program does not say "load a...". Even most of the non-object
>oriented languages do not say this. This level of detail is in the
>compiler (or interpreter), and quite possibly hardware-dependent.


Kevin, it's a COMPUTER, not an idealization inside a brainwave. Values
a and b, be them objects or whatever, reside in a MEMORY. If you use
an object, you have to READ it before you use it. If you update an
object, you must READ it, UPDATE it, then WRITE it. This is not about
hardware dependency, this is about the fundamental nature of computer
data: data just doesn't exist as abstractions, data inside computers
is concrete, it has LOCATION, LIFETIME, and SCOPE. In math, 3 is 3 no
matter what - inside a computer, 3 here and 3 there are NOT the same
3.

Say I have a function f to add two numbers:

f(x,y) = x+y;

Say I have two threads running concurrently, both use f( ) to bump the
value of a. One says

a = f(a,3)

The other says

a = f(a,1)

I'm already abusing of mathematical notation and writing a=a+b for the
statement that a *becomes* a+b, but let it be, there's more
fundamental stuff under this hood.

In mathematics, the result of those two operations, carried out in
either sequence, is a+4. Inside a computer, the result can be a+1, a+3
or a+4, not because of hardware or compilers, but because of the
intrinsic nature of stored data. If we blow the function out into its
atomic components, it really looks like this:

r1=a; r1=r1+3; a = r1;
r2=a; r2=r2+1; a =r2;

Where the ri are machine registers, and each operation that ends with
a semicolon is indeed atomic. The interweaving of atomic operations
takes care of the nondeterminism:

r1=a; r2=a; r1=r1+3; r2=r2+1; a=r2; a=r1;

and you get a+3.

r1=a; r2=a; r1=r1+3; r2=r2+1; a=r1; r=r2;

and you get a+1. So, it isn't enough to reduce things to mathematics,
we must go one level down.

So, Kevin, ANYTIME WE HAVE SHARED WRITABLE DATA WE HAVE
SYNCHRONIZATION PROBLEMS - that's the beginning of Operating Systems
101. That's why in computer science we have mutexes, semaphores,
message passing, channels, critical sections, events, monitors, and
all that other jazz. True, you can throw math at it, but by the time
you get to real results, the math has gotten pretty hairy and its
usability is limited to the most trivial cases because of the
combinatorial explosion of the model's complexity.


Alberto.



Date Subject Author
9/28/02
Read Is this an exceptionally hard set of questions to answer?
Karl M. Bunday
9/30/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
9/30/02
Read Re: Is this an exceptionally hard set of questions to answer?
Shmuel (Seymour J.) Metz
10/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Moufang Loop
10/7/02
Read Re: Is this an exceptionally hard set of questions to answer?
Shmuel (Seymour J.) Metz
9/30/02
Read Re: Is this an exceptionally hard set of questions to answer?
Stephen Herschkorn
9/30/02
Read Re: Is this an exceptionally hard set of questions to answer?
Magi D. Shepley
10/1/02
Read Re: Is this an exceptionally hard set of questions to answer?
Karl M. Bunday
10/2/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/2/02
Read Re: Is this an exceptionally hard set of questions to answer?
Karl M. Bunday
10/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Jim Hunter
10/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Herman Rubin
10/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Herman Rubin
10/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/6/02
Read Re: Is this an exceptionally hard set of questions to answer?
Virgil
10/6/02
Read Re: Is this an exceptionally hard set of questions to answer?
Herman Rubin
10/6/02
Read Re: Is this an exceptionally hard set of questions to answer?
Jim Hunter
10/6/02
Read Re: Is this an exceptionally hard set of questions to answer?
Virgil
10/7/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/8/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/8/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/9/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/10/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/11/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/14/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/15/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/15/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/16/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/16/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/14/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/16/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/16/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/12/02
Read Re: Is this an exceptionally hard set of questions to answer?
Shmuel (Seymour J.) Metz
10/14/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/25/02
Read Re: Is this an exceptionally hard set of questions to answer?
Van Bagnol
10/25/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/26/02
Read Re: Is this an exceptionally hard set of questions to answer?
Van Bagnol
10/27/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/27/02
Read Re: Is this an exceptionally hard set of questions to answer?
Herman Rubin
10/28/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/29/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/24/02
Read Re: Is this an exceptionally hard set of questions to answer?
Van Bagnol
10/25/02
Read Re: Is this an exceptionally hard set of questions to answer?
Van Bagnol
10/26/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/28/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/29/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/29/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/31/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
10/31/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
11/2/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/2/02
Read Re: Is this an exceptionally hard set of questions to answer?
David Redmond
11/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
11/2/02
Read Re: Is this an exceptionally hard set of questions to answer?
Virgil
11/4/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
11/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
11/6/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/7/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
11/9/02
Read Re: Is this an exceptionally hard set of questions to answer?
Alberto C Moreira
11/11/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/3/02
Read Re: Is this an exceptionally hard set of questions to answer?
Kevin Foltinek
10/5/02
Read Re: Is this an exceptionally hard set of questions to answer?
Magi D. Shepley

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.