Impossible things are definitely untestable.
However, I think it would be possible to have something that is both possible and untestable. Say, the total mass of the earth, circa 1 AD was W.xyz kilograms.
I am not referring to a particular Feynman video. As I suggested before, you can certainly find one yourself.
Sure, if you wish to qualify your thoughts into a valid idea with a proper essential characteristic, i.e., hubris, arrogance, fine, but still don't see any relevant link between me being certain that the impossible cannot happen, you thinking that I am arrogant and that this has something to do with God and faith, when I hail objectivity, reason, causality and noncontradiction. I will amend my philosophical commitment to causality and noncontradiction when another idea changes my entire philosophy as to make more sense as a whole. The way I see it, an objective universe where causality and noncontradiction are universal makes the most sense overall. I believe nothing without it being consistent with natural, not supernatural, law. There is no room for faith in my life. And you calling me arrogant and telling me I have a god complex is quite ad hominem and a demonstration of your weakness, no? Is my ego not actually and appropriately big enough to wax philosophical? Have I not done the requisite reading and consideration? What if I had an advanced degree or two in mathematics and/or physics? Why don't we stick to the material and not the person?
August, Fullerenes have always been logically possible. They were considered physically impossible by many people, perhaps, owing to the seeming difficulty in creating them, but there was obviously no logical reason they couldn't exist, since, in fact, they always have. That particular arrangement of carbon atoms in no way violates the principles of chemical bonding. This example is moot.
Wave-particle duality is a better example, but since wave-like behavior and particle-like behavior are not exhibited simultaneously, this doesn't constitute a logical contradiction. This is like saying flying cars are logically impossible because sometimes they drive and sometimes they fly.
Logic is not dependent on perspective. What a thing looks like is dependent on perspective.
It is nonsense by definition, because red != blue. Testing is not required, because testing can't possibly produce any other outcome than that red != blue, because they are not equal by definition. You guys are working waaaaaaay too hard if this is how you want to approach things. There is a vast class of things that we need not bother with, because we know for sure up front that we don't need to.
This is different from the case of things being considered extremely unlikely until found. Science is full of surprises. It is not full of contradictions and impossibilities.
And once again, you confuse logical possibility with widely held (and not-as-yet-informed) opinion. The Ptolemaic universe was never "true", apart from being a reasonable approximation given the data available. There's nothing inherently illogical about either a static or a dynamic universe. Your weird definition of logic is confusing the hell out of you, Cane. Logic does not simply mean "thought experiment" or "axiom" or "uninformed opinion arrived at solely by thinking".
Actually, Michael is correct. The "static universe" idea never made any sense, given the fact that we could always see things moving around. Why should they stay stuck on the same tracks forever?
Fullerenes were predicted before their discovery: http://en.wikipedia.org/wiki/Fullerene#History.
C-C bonds in diamond do not strike me as planar, though I may not understand the structure properly.
The point is that there is nothing logically contradictory about Fullerenes and our pre-existing knowledge of chemistry. As very large and relatively geometrically simple molecular structures (unlike say, proteins), they would have been considered unlikely, but I fail to understand your assertion that they would have been considered logically impossible. I think you, like Cane, persist in confusing logical impossibility with extreme unlikelihood.
As you say, "simultaneously" is not a good word to use in the context of quantum mechanics (few words are, apparently). But the Copenhagen Interpretation at least seems to suggest that you can get quantum effects to behave like waves or like particles, but not at the same time. It may be entirely a semantic distinction, but I think we could also say that measuring (resolving) a quantum effect forces it to exhibit one or the other behaviors, but not both. Either way, I think my flying car analogy is reasonably apt. I see no logical contradiction in quantum effects, just multiple behaviors. Surprising and weird, but I don't see why they would logically preclude each other.
And logic requires causality. A person's perspective affects that person's understanding, but the logic exists externally to be discovered by anybody. I do not subscribe to the "person creates his own reality" idea.