Hi James,
I don't want to get into the Platonism discussion as I'm not of a
philosophical bent, but I would like to start discussion based on
something you wrote in one of your posts on the subject:
James N Rose wrote:
> The square root of a negative number has no physical
> reality (or so it is presumed, because no abject
> examples have yet been shown/proven) but it has a most
> definite platonic ideal existence.
>
The whole square root of a negative number question boils down to
the reality/unreality of a single number, the square root of minus one,
usually called i, as every other negative square root can be expressed
as a real multiple of this imaginary number. Now, I'd be the first to
accept that you can't have i oranges, so i does not have the same kind
of physical reality as the natural numbers, or even the positive real
numbers.
However, you also cannot have zero oranges, or minus five oranges
for that matter. So perhaps it is no less physically real than the
negative numbers or zero.
I'd also like to say that in a great deal of physics, the imaginary
number is indispensible, at least in doing the math - could this be
sufficient evidence to declare it physically real? Specifically, if we
have used i to predict the result of a particular experiment, and we
find that our prediction and the result match, is this evidence for the
physical reality of i?
I'm reminded of looking out of the window to watch the trees move,
and concluding that it is windy, even though I haven't seen or felt the
wind...
Just a thought,
Matt.
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When God plays dice with the Universe, He throws every number at once...
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