|From:||Steven Ericsson-Zenith <steven@xxxxxxx>|
|Date:||Thu, 12 Feb 2015 19:43:10 -0800|
a. Recall that I spoke about the use of a proof. I did not include how a proof might make you feel.
b. Your concern over consistency relates to the question of boolean "truth" values. And I assume, you refer to Godel's incompleteness, Tarski's undefinability, and the Church or Turing thesis. Of course, these are demonstrated for truth systems.
c. My colleagues (actually, David Shepherd) successfully demonstrated the implementation of the IEEE 754 standard. They did this by converting the standard into Occam and then Occam to CSP, the language in which the machine microcode was specified. This was then demonstrated to be equivalent to the RTL hardware description from which the device was manufactured. This is electrical engineering and at this level there is no concern about quantum effects.
It is not widely appreciated that truth based systems are inherently, and necessarily, dualist. As a result it is hardly surprising that there are logical statements that are ambiguous or may only be specified by an external language. Essentially, and this deals with foundational matters. To overcome it you must eliminate the notion of truth in favor of direct and holistic behavior (or action) where such inconsistency is impossible (essentially because you are not speaking about the world, you are simply describing it).
Inconsistency is a long standing problem in logic but it is not insurmountable. The confusion came from holding truth to be something in the world. The moment we escape metaphysics the problem disappears.
d. Pure Mathematics draws necessary conclusions from premises of any kind and is not a natural science. Natural science applies pure mathematics (that is capable of telling us beautiful lies) and it is the role (in my world) of Logic to build the bridge between Pure Mathematics and the natural sciences (i.e., I do not hold with Logicism). There are certainly aspects of computer engineering that are pure mathematics but this does not make computer engineering a natural science.
There are, however, things in natural science that can inform the engineering of computing machines, and indeed, this is where I spend a good deal of time. Engineering is a fine profession and there is no shame in using the term, although this does seem to be a very European view.
Engineering is driven by human economics and gathering a proof (that a bridge will not fall down, for example) would be incredibly expensive. And this is why good engineers have good intuitions. It is also why few efforts of the kind I describe above for the IEEE standard have been funded.
At which point does engineering become science? I think this is a good question and it may well take place in coming decades in bioengineering. But my guess is that we will all need to have longer lifespans and longer careers before this happens.
e. I was being informal in my use of the term "compatible" - I mean only that a proof should be continuous through specifications.
On Thu, Feb 12, 2015 at 4:47 PM, William Frank <williamf.frank@xxxxxxxxx> wrote:
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