Numbers, representation, nature and foundational myths.

[Y]

I'm writing with reference to this article...

http://mathforum.org/library/drmath/view/54660.html

There is a very common misunderstanding that numbers are somehow
derived from nature. This arises from an idea that numbers are
innately natural, and are somehow 'built' into natures workings.

In my opinion numbers aren't natural. While they are ultimately
something in nature (as a part of peoples minds and brains), the
emergence and presence of numbers in nature is limited to the domains
of mental ideation. This is contrary to the many numerological claims
which are purported commonly in the sciences. Such numerological
claims (especially common in physics) would have numbers as being
derived in some way from the nature of the universe.

Numbers are phenomenal representations of human ideas. In many ways,
numbers are a primitive and enduring form of technology (like
language). Numbers are enduring technologies, simply because it is
difficult to design them to be better, unlike other forms of
technology. For example, where the design of a car or it's parts can
be improved, numbers cannot necessarily or easily be improved upon.
This is not to say that new mathematical systems cannot be developed
or 'improved' using these parts.

If you're reading this and I'm still confusing you about what I mean
by nature, the best example I can give to illustrate my definition of
'nature' is the purple dragon. Purple dragons are not 'naturally'
occurring beings, but they are a part of nature and thus exist in the
sense that brains and thoughts are natural. Thus, the difference
between what I regard as natural versus representational can be summed
up by this purple dragon illustration. Bear in mind, numbers are an
emergent phenomena of the human mind, which is a biological and thus
natural thing.

There is also a misconception that numbers are 'inaccurate',
particularly when it comes to irrational numbers. I often hear
something like, "no matter how you try to acquire the diameter of a
circle with a circumference of 1, you'll never get an accurate
measurement." I think rather that the contrary is true. Numbers are
perfect. When I assign a number to something in nature, I reduce it's
actual physical properties and differentiation to other objects to the
perfect phenomenal 'shape' of that number. Pi is such a perfect
phenomenal shape, and it's endless string of decimal places mirrors
the perfection of the integer. It is only when we compare or assign
these perfect things to the unbounded variations in nature, either the
integer or pi, we have some level of suspicion with regards to their
value do we not ? This does not entail that perfect circles do not
exist. Of course perfect circles exist, quite comfortably in nature,
both in representation and in the minds of those who can imagine them.

There is also the foundational issue with the unit. The unit is an
attempt to improve upon the technology of numerals, in a way that
corresponds numerals with naturally occurring objects. For example, 1m
corresponds with a length of space, or matter. It is here that
measurement becomes inaccurate and abstract, not within the world of
numbers.

In the space of representation, if I assign the circumference of a
perfect circle to be 1 (without any particular unit, and thus no
particular need to correspond to a natural circle), it's diameter
yields a perfectly irrational number. This is not due to an inaccurate
process of natural measurement, but a function of the numerical
representational process. Irrational numbers are not a consequence of
nature. Irrational numbers are a consequence of the perfection of
numbers. The irrational number is no less perfect than the integer,
they are equally perfect. This is why studies into perfect Euler
Bricks are meaningless. Every Euler brick is perfect. It is the
distinction between numbers that are integers and numbers which have
fractional components that is the source of this problem. Therefore
anyone in their right mind might consider taking these ideas into
account before attempting anything such as the perfect Euler brick
problem.

http://answers.yahoo.com/question/index?qid=20091023120520AAXGRtm

-y

[AMiews]

"Y" <yana...@hotmail.com> wrote in message
news:388dfc21-1555-4b38...@be10g2000pbd.googlegroups.com...

> I'm writing with reference to this article...
>
> http://mathforum.org/library/drmath/view/54660.html
>
> There is a very common misunderstanding that numbers are somehow
> derived from nature. This arises from an idea that numbers are
> innately natural, and are somehow 'built' into natures workings.
>

<snip confused part>

> In the space of representation, if I assign the circumference of a
> perfect circle to be 1 (without any particular unit, and thus no
> particular need to correspond to a natural circle), it's diameter
> yields a perfectly irrational number. This is not due to an inaccurate
> process of natural measurement, but a function of the numerical
> representational process.

wrong.

> Irrational numbers are not a consequence of
> nature. Irrational numbers are a consequence of the perfection of
> numbers.

which means what ?

>The irrational number is no less perfect than the integer,
> they are equally perfect.

which one is a "perfect number" ? (google it first)

> This is why studies into perfect Euler
> Bricks are meaningless. Every Euler brick is perfect. It is the

> distinction between numbers that are integers and numbers which have
> fractional components that is the source of this problem.

there is no problem.

> Therefore
> anyone in their right mind might consider taking these ideas into
> account before attempting anything such as the perfect Euler brick
> problem.
>
> http://answers.yahoo.com/question/index?qid=20091023120520AAXGRtm
>
> -y

well, you are using base 10 but you forgot about it,

try base e, base Pi, or some other base number and see how irrational,
rational, and fractions move around.