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> David Hilbert famously argued that infinity cannot exist in physical reality. This statement reduces the problem to the definitions of "existence" and "physi
by techno_modus 8y ago
> David Hilbert famously argued that infinity cannot exist in physical reality.
This statement reduces the problem to the definitions of "existence" and "physical reality" which of course may have quite different interpretations. For example, the existence of particles (with finite mass and finite coordinates which can be "touched") and the existence of waves are rather different notions.
- subroutine 8y agoWhat aspect of waves as they exist in our universe is infinite?
- whatshisface 8y agoIf waves are continuous then they are over the real numbers, and there are an infinite number of reals between any two points.
- subroutine 8y agoThis is specifically addressed in the article - this is a function how our maths represent phenomena: "Physicists have found it convenient to use the concept as a mathematical idealization where infinity occurs as a limit of large numbers, even though in physical reality there is no infinity of anything. An example is the Fourier series: while mathematically an infinite number of terms are needed to give an exact representation of the function representing an arbitrary waveform, this does not in fact mean that there are infinite physical frequencies occurring in the real physical system."
- jamesrcole 8y agoIt seems to me that something can only have existence for us if it can have a transitive causal influence upon us, and surely both particles and waves exist in that same sense.
- whatshisface 8y agoIf by existence you also mean, "something that continues to exist upon closer inspection," then neither particles nor waves exist, you can always design an experiment to refract something around a corner and meausre individual quanta of it when it gets to the detector.
- simonh 8y agoThe comment gave a meaning of existence: "...if it can have a transitive causal influence upon us", so there is no need to imagine up straw ones.
- whatshisface 8y agoZeus and Sherlock Holmes could both be argued to have had transitive causal influences upon us - so in order to make that statement make sense there must be some other implied constraints on what is considered to "exist."
- jamesrcole 8y ago> Zeus and Sherlock Holmes could both be argued to have had transitive causal influences upon us There's some philosophers who'd argue that, but I think the arguments are pretty weak.
- simonh 8y agoThe fictional character Sherlock Holmes certainly exists.
- jamesrcole 8y agoIt all depends on what you mean when you say "The fictional character Sherlock Holmes". I believe that thoughts, memories and knowledge "about Sherlock Holmes" exist and are physical details, as are Sherlock Holmes books, etc. And that there's no other reality to "Sherlock Holmes", above and beyond these things. But really, this discussion is too large to satisfactorily deal with here.