[ExI] Belief in maths (was mind body dualism)

[Adrian Tymes]

Welcome to the conversation.

--- On Tue, 7/6/10, Mike Dougherty <msd001 at gmail.com> wrote:
I am a software developer during the day.  Most of my time is spent anticipating the extremely unlikely cases and making sure the program does not encounter those conditions.  If I defend against 99% of the truly absurd cases of should-never-happen inputs, my boss (or QC, etc.) will surely try something from the 1% that I did not imagine.  Most code can be broken (whether cryptographic or procedural)  I can't be sure enough to say that all code can be broken - because that supposes that I have the time/patience to prove that to be true.  I dare not say one example of code is unbreakable (the exception to the previous statement) because I am unable to guarantee or warrant that assertion.  
Actually, it is possible to completely prove the functionality of small pieces of
code, given certain assumptions.  For instance, assuming the following is run
via a standard Perl interpreter in the normal sense (with a stdout, et al), the
following code will always output the string "2" followed by a newline:
---
my $foo = 1;
$foo = $foo + 1;
print $foo . "\n";
---
The trick is, how far can one go with this, while still being economical about
the effort involved?  NASA's coding procedures - and the astronomical costs
involved - are a good example of what happens when one tries to apply this
to very complex programs.  (And even that sometimes fails, though for lack
of communication and strict adherence to model instead of for theoretical
break in the model itself.)

What you're used to is the standard heuristic, where less than complete
proof is accepted because it would simply cost far too much to do said
complete proof.  ("Cost" not just in money, but also in commitment and
effort that the stakeholders often refuse to put forth.  How often have you
been given vague requirements, where the giver refused to write them
down into something formal that you could prove whether or not you've
met?)
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