Thanks a lot for caring, jambaugh. Further thinking and a look into Pedrottis' Introduction to Optics solved the problem. It turned out what I sought after was the usual refraction matrix: a11 = 1, a12 = a21 = 0, a22 = n1/n2. This constitudes the tensorial form of Snell's law. I even managed to...
Thanks a lot, jambaugh. Very nice explanation. Though, I am rather familiar with tensor analysis in coordinates. Perhaps I haven't stated clearly where my understanding fails.
Assume you have a Riemannian metric g, e.g. the one induced by the existence of a transparent medium, you can simply...
Dear readers,
In my recent study of dyadic products I found out that physical quantities expressend as 2nd rank tensors can also be expressed as a dyadic product of two vectors. Similarly 2nd rank tensor fields can be expressed as pointwise dyadic products of two vector fields.
One such...
Greetz,
As you possibly know, there's a book by Arthur C. Clarke with the same name. The movie and the book were made with cooperation of Clarke and Kubrick in a period from 1964 to 1968.
The book later became part of a series, even though Clarke refused to do a sequel at first. The books...
Greetz,
1. For Mentat:
You mean this situation is inevitable? Inbound Aristotelian logic, you're right but we could simply use another logical system capable of expressing Existence. This new logical system will have its own deficiency but this one may be located somewhere less controversial...
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"Fairness," "precision and "clarity," all my criteria of preference, are part of my current paradigm, and the remnant of my previous ways.
I know that I'll always be biased someway, why not determine part of my biases consciously. Most individuals are...
Greetz,
1. For Preator Fenix:
I guess you're a bit late for this thread but anyway you're welcome. I got problems reading your post but I managed to get something out of it.
For the part where you addressed me, I think, you're making a mistake in thinking that an AI entity can be "made...
Preamble: Some of these quotes aren't specifically by those who're usually called Philosophers. Some of the quotes belong to individuals who may seem naive to many. Yet I found all of them interesting and related enough to post after RageSk8's worthy quotes...
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Some of these many questions:
00. If the paradigm is all that is available to a human observer, where does common experience of human observers come from? Is there anything independent of observers?
01. Could it be that common experience comes from one...
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Deductive method gives "proofs." Inductive method gives "theories."
That's indeed a characteristic of a free thinker.
For "good" is still a reserved keyword for many. "Goodness" as an absolute quality still prevails in many human minds and one would better...
Greetz,
1. For Mentat:
I see, but then don't you mean Descartes, and his mates, were somehow biased right from the start? :wink:
I'm kidding. It's all right; you can have "further" there if you like it.
No, there's no problem with "pre-assuming" Q = T. That's the process of postulation...
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Stop right there, please :wink:. First, who is associating "goodness" with what I said?
I, personally, would be happy if "absence of distinguishing" could be proven existent or non-existent but don't associate my "happiness" with "goodness," "truth,"...
Greetz,
1. For Mentat:
All right but for the usage of the phrase "further validates" which is a reference to an illogical background. It sounds like Descartes' existence had been validated before and the Demon's challenge has only "further" validated it, while this isn't true for the Demon's...
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A similar case is with a statement like: "through every two points passes one and only one line." This is an axiom of Euclidian geometry and perfectly logical. It doesn't matter that there's no definition for a "point" and a "line." And it doesn't matter...