On 7/31/2011 8:15 AM, Craig Weinberg wrote:
Reblogging myself here, but curious to see what you think of the idea
that 1 cannot be proven greater than 0.
Someone’s comment on the previous chart mentioned the difficulty
(impossibility?) of proving that 1> 0. It’s an interesting kernel
there, and it reminds me of the whole “time does not physically exist”
realization. On one level, I can think of zero as having no different
relation to 1 than it has with any other number. Zero does the same
thing to any number as it does to one and should be thought of more
properly as the hub of the decimal spiral.
I’m no mathematician, but I suppose that 0 is also formally defined as
an integer between 1 and -1 or something. Still it exposes the
question of whether the elemental underpinnings of our ability to
count is really anchored in anything at all other than our own
anthropological conventions of counting. Beyond numbers themselves, it
appears that the whole quantitative notion - of greater than or less
than, and of ‘equal’ is nothing but a figment of our feelings about
order. There may not be any inherent moreness to something than the
absence of something. If it’s the same thing, it actually seems more
palatable to see the absence of something being a condition predicated
upon the things’ a priori presence, no?
Even if we want to get into quantum atopoietic craziness where things
come out of nothing, rendering such a possibility discretely seems to
threaten the whole notion of mathematical coherence. If any or all
quantities, variables, and formulas can be generated arbitrarily from
0, then 0 would seem to be the same thing as ∞, and greater than 1 or
any other arithmetic expression.
Maybe it’s time to create a new numberline, without all of the
repetitive decimal numerals. Instead there could be a Wiki of new
quantitative symbols and names which anyone can add to and own as a
permanent vector in the schema. It would be easy to translate them to
and from Arabic numerals online and some interesting possibilities for
informal encryption and unanticipated mathematic-linguistic
By removing the aspect of repetition, we would unmask the semantic
bias of the math logos and arrive at a pure generic linear calibration
defined only in it’s own idiosyncratic a-signifying terms. Sort of
like breaking the mantra of math, it’s trance-like rhythms that
disguise it’s human neurological origin from us. By adding more unique
qualitative sense to the thing, the quality-flattening power drains
out and the system seems to disqualify itself.
Umm, what would be the point of coming up with yet another
representation system for quantities? We already established that a
description is not its referent even though for every referent there is
at least one description and for every description there is at least one
referent. Zero, 0, null, the empty set is an absence of sorts; a
placeholder. So in that sense it is a referent and just as space is 'the
place where referents could be but are not', so too is 0.
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