this is the tiny piece of child's play that haunts the dreams of physicist and mathematician.
at first, it appears that this is a statement of the English language. but if English were the only system used in the statement's evaluation, we
will have to simultaneously admit its legitimacy and illegitimacy.....exploding the computer parsing it. but, your mind
does not explode. to
resolve its painful simplicity, your mind makes an appeal to a system outside of
English.....a system which is capable of unifying something
which is both true AND false. (more info: here
tell me: what system? you are the one that is using it, so surely you must be able to define it......right?
the answer to this question, and the appeal to a "outside system", is identical to the central problem in the push and pull between classical and
quantum physics. in order to understand the profound importance, let us look at the problem of counting numbers.
does 0.999999999.... = 1.0 ?
no one will argue that we do not live in a world of countable things. but where, exactly, at the tiniest level imaginable, is the boundary between my
apple and the table it sits on?
after just a moment of pondering we realize the futility of the question. we, yet again, make an appeal to a system outside of
larger than) the apple/table....draw a line....and state quite simply that the boundary is.....riiiiiiiiiiiight THERE!
TADA! we now have a "thing". (image source
the method used by modern physics, known as Renormalization
, is not any more sophisticated
than your own resolution to the problem: they simply draw a line, and .9999 becomes 1.
When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, the
continuum limit has to be taken carefully.
you mean, like a statement that is at once true AND not true? yeah buddy, you better be real careful
when taking that limit.....you might
accidentally (or conviniently?) leave out the most important part!
there sure are a lot of bizzare and unanswered questions around here:
- what is the definition of "observer" in quantum mechanics?
- entanglement, faster than light communication, nonlocality
- superposition (ill-formed true/false statement)
- a bajillion extra dimensions and exotic string-like beasts
- the indistinguishability of particles (re: entropy)
- ....hey. where did all that extra (dark) energy go?
- consiousness (appeal to a system outside of
i do not have an infallible answer to any of these, but i would bet my life that they can be found......
thanks for reading.