Re: Interesting math

In article <Scydne0nH7dpuQ7bnZ2dnUVZ_veinZ2d@xxxxxxxxxxxx>,
Purl Gurl <purlgurl@xxxxxxxxxxxx> wrote:
blmblm wrote:

Roland Hutchinson wrote:
Purl Gurl wrote:

Zero is both odd and even.

?????

Good catch. I think I (mis)read that as "neither odd nor even",
which seems already sufficiently wrong-headed to someone with a
modest amount of formal mathematical training. But both ....

Hm. Well, maybe there are definitions of "odd" and "even"
that allow zero to be both.

I have read your, plural, previous articles, although Roland
only speaks bullfrog, these days. I did not read this article.

I will set some scenes for you and the bullfrog.

We are at one of our universities, sitting and talking with
professors of mathematics. Roland knows to croak only the
appropriate and accepted words around mathematicians, just
as we know to do the same. In the company of mathematicians,
within an academic environment, we know to speak mathematics
as prior defined and as is customary. We do not croak out
weird metaphysical things. We play by the rules. One of
those accepted rules is, "Division by zero is undefined."

Oh, those poor mathematicians, constrained by the box of
logical thinking!

Later, we are all enjoying skinny dipping around our family
pool. We are sipping champagne and nibbling strawberries.
Roland is avoiding direct sunlight being bad for his frog skin.

I start up with thinking outside the box, sans the cat.

"Listen you two, no matter what number you divide by zero,
any numerical answer is correct. Six divided by zero can
be ten, can be one, can be the value of pi. No matter what
number you divide by zero, the answer is an infinite set
of numbers. Other words, are you listening?

Yes, but I'm not hearing anything that sounds like sense yet.
What I'm hearing sounds to me like the babblings of someone who
doesn't know much mathematics, but feels free to make fun of
those who do.

(Of course I could be wrong. You probably did have to take some
math courses to get that undergraduate degree in -- was it earth
science?)

But let's go on; maybe there will be some sense later ....

Other words,
zero can divide any number an infinite number of times,
both positive and negative, even fractional. This is why,
very precisely, academics say division by zero is
undefined; no set answer, no set formula."

Within an environment of hanging out naked, splashing around
in a pool, fattening up on champagne and strawberries, we can
speak outside the box. There are no hard core mathematicians
around to squash and quash thinking outside the box, again,
sans the cat.

We can define zero and mathematical operations involving zero
in myriad ways. Our number zero, in itself, is not defined
and cannot be defined. Zero is the absence of everything.
Zero is nothing, is the ultimate void, like between the ears
of some of the boys around here.

Zero can be manipulated any old way we like because we are
manipulating nothing. I say ten can be divided by zero a
million times. Roland croaks ten can be divided by zero
a negative million times. You, BLM, say ten can be divided
by an infinite number of imaginary numbers. We are all
quite and precisely correct.

Well, except that I appear to have said something more or less
sensible [1], and you and the frog you're calling Roland have
said things that don't seem to me to mean anything.

[1] Assuming you mean "imaginary numbers" in the sense in
which mathematicians use the term. Otherwise, who knows.

Ok, I whip out some graph paper from our poolside pool house.
"BLM, plot a graph of coordinates [0, 0, 0] for me." Where
do you place those coordinates? Anywhere! Actually, you cannot
place those coordinates anywhere; those coordinates do not
exist. The moment you touch a pencil tip to your paper, you
have made a mistake; your pencil fly speck is too large to
represent those zero coordinates.

Now this almost sounds like sense -- conventional, even.

Of course it would be the same no matter what the coordinates
were; there's nothing special about [0, 0, 0].

Zero is infinitely small, actually smaller. Our universe,
a brief moment before Planck's clock began ticking, is
infinitely larger than zero, although we have come to
accept our universe, just immediately prior to the really
Big Bang, is infinitely small. Zero is even smaller.

We can define zero anyway we like because zero does not exist.

We can only "define" zero in relationship to other numbers.
In the absence of other numbers, zero is meaningless.

Clearly there is another problem. I give you two dimensional
paper and ask you to plot a three dimensional point. This
third dimension, the "Z" point, we can only imagine, on paper.
Is this Z point positive or negative? Well?

I do try to answer direct questions, but I can't make any sense
of this one.

Multiply any number by zero. What is your answer? This answer
we know. Multiple by an even number. Multiple by an odd number.
Answer remains the same. Multiplication by zero is both even
and odd. When we multiple by zero, we violate the rule of
even and odd. Zero must be both or must be neither. Zero
cannot be something between even and odd. Zero must be both
even and odd to not violate our even and odd rule.

What rule is that? Please state it as carefully as you can.
I'm unable to imagine any "rule of even and odd" that
is consistent with how integers operate in the world of
mathematics as I know it but is violated by multiplication
by zero.

We slip our clothes back on, return to a university with
Roland hopping along behind, our zero operations again
become of strict definition for convention.

Poolside and naked, though, we can discuss zero outside of
customary boundaries. We can think outside the box and can
be creative which leads to better understanding and leads
to better knowledge.

We only need to worry if we imprison our minds within a
tiny box, or if our minds infinitely surround the box.


I do not believe, as you seem to, that rigorous logical
thinking and imagination are mutually exclusive, or that
mathematicians who accept conventional definitions are
doing so merely because they (the mathematicians) are, well,
conventional.

And I'm not sure champagne has much on Cantor's theorem
as a means of inducing a pleasant state of dissociation
from ordinary life.


Roland only needs to worry about where is that cat we
set free from the magical box; cats eat frogs.


--
Decline To State
(But the e-mail address in the header should work.)
.

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