Re: socially challenged???!!??



Duane Rettig wrote:
Ken Tilton <kennytilton@xxxxxxxxxxxxx> writes:


<sigh> So close, yet so far. You failed to connect this deep insight
with my original response to the riddle: it ain't about set theory.


I agree here.


As with statements such as "I always lie.", an attempt to determine
the truth leads to an infinite recursion.


I disagree here. But first, some background: As an ex-hardware guy, I
am always amazed at programmers and logicians alike who take these
paradoxes as being an issue. Like you, I recognize them for what they
are and dismiss them, but others must agonize over the horrible flaw
in logic that makes the whole field of logic suspect. However, in the
hardware world, and especially in the world of digital electronics, we
have a specific term for these paradoxical situations, and we have
compartmentalized them very nicely and made good use of them: they are
called oscillators. In simplest digital logic terms, an oscillator is
an inverter (a NOT gate, if you will - if the input is a 1 the output
is a 0 and vice versa) whose output feeds back into its input. What
happens, during its operation, is that the natural delays (and usually
some elements are added to force longer delays) in the electronics
will cause the output to oscillate between 0 and 1, usually at regular
intervals. What is such a device good for? Well, when you talk about
your 2.3Ghz laptop, you are describing the frequency at which the
basic system's oscillator, or clock, changes from 0 to 1 and back to
0. So almost everyone (not only hardware geeks) refer to such
oscillators once in a while.

Finally, the statement of the previous poster that there is no time
element is naive; in pure logic there is theoretically no delay
between the input and output of a logic element, but in real life
there is always a delay. In hardware I have seen inverters that will
oscillate between 0 and 1 at some rate which depends on the natural
delay within its gate (this is the most common case, because in
digital logic pains are taken to ensure that there are only two
states; in technical terms the transistors are biased to ensure
saturation in both directions), but I have also seen inverters which
have a very strong analog component to them; when these are hooked up
as oscillators (or, more frequently, when a flaw in the circuitry
causes them to be joined in that way accidentally, they don't
oscillate, but instead they will settle into a stable state somewhere
in the no-mans-land of voltage that is between a 0 and a 1. Obviously,
these aren't as useful.

Now, back to my issue; it is true that recursion and iteration are
essentially the same, but recursion implies depth, and iteration
implies passage of time, so this is really an infinitely oscillating
iteration.


Well, to determine the truth of "I always lie" I must examine all my assertions to determine if each is true. No problem, I am a man of few words. One of my assertions is that I have a pack of hounds for troll hunts. Fine, I lied. Another is that I always lie. Ok, let's see if that one is true...

kt

--
http://www.theoryyalgebra.com/

"Algebra is the metaphysics of arithmetic." - John Ray

"As long as algebra is taught in school,
there will be prayer in school." - Cokie Roberts

"Stand firm in your refusal to remain conscious during algebra."
- Fran Lebowitz

"I'm an algebra liar. I figure two good lies make a positive."
- Tim Allen

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