In which case you actually can't prove anything at all... ever. For instance, the entire world (yourself included) could be figments of my imagination. Or maybe we're both characters in a book, and just don't know it.
For the strictest definition of "prove", indeed we cannot. As Decartes so eloquently stated, the only thing I can be sure of is my own mind. (After all, if my mind didn't exist in some form, then I wouldn't be able to even contemplate not-existing.) But just because I am sure of my own mind's existence, does not mean that I can definitively extend that to other people.
"Truth" is commonly accepted to be something that is so likely that to withhold provisional belief would be irrational. Sure everything (with a single exception) cannot be proven definitively, but at some point things are so likely true that not believing in them just makes you crazy.
So, proving this whole issue and claiming the prize money would involve demonstrating that believing in practical quantum computers would be unreasonable. And that is perfectly reasonably possible.
But one has to realize the ambiguity of the word "prove" here. There is absolute proof of certainty (for instance most mathematical proofs), while just about everything else lies in a range of "yeah, probably." Newton's Laws of Motion were proven correct time and time again, until we eventually started noticing very small errors, and even yet today, while we know that Newton's Laws of Motion aren't the most accurate model, we still know that it's often "good enough".
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