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From: Archimedes Plutonium on 13 Feb 2010 15:59


FredJeffries wrote:
> On Feb 10, 8:43 pm, Transfer Principle <lwal...(a)lausd.net> wrote:
>
> > There's a discussion about the mathematician Yessenin-Volpin, a
> > famous ultrafinitist. When asked the question "Is n a natural
> > number" (for some Peano natural n), Y-V would wait until an
> > interval of time elapsed -- an interval in proportion to the
> > magnitude of n -- before answering "Yes." So if Yessenin is
> > asked, "Is 1 a natural number?" he'd answer "Yes" after, say,
> > one second. He would then take two seconds to answer "Is 2 a
> > natural number?" and so on.
> >

Well, obvious in hindsight, a better questioning of Y-V would have
been to ask him flat out-- what is your definition of "finite-number".
His best answer would have been -- probably -- the same as what LWalk
and
Jeffries answer is, that is, their assumed definition of finite-number
is one that ends in zeroes to the leftward string. Such that 94 is
finite because it is .....0000094.

That is why I asked LWalk to formalize this widely assumed definition
of
"finite number". It is what LWalk-- probably-- walks into any
conversation of mathematics,
most likely carries with him as his understanding, his definition of
"finite number."

Same can be said for Y-V. That if pressed to divulging what his
working career in
mathematics was with a definition of "finite-number." Would-- probably
--spill out
as a "finite number is one that ends in zeroes leftward string."

In my survey in the 1990s of math professors of elite colleges, all of
them came down
to the same definition of "finite number" as one ending in zeroes in
the leftward string
of a Real Number. So that by definition a Real Number has a finite
leftward string of the
decimal point means that a "finite number" is finite because it ends
in zeroes leftwards
string.

That is-- probably -- the same definition that Jeffries enters this
conversation, holding.
If Jeffries disputes that he is entering this conversation by holding
an altogether
different definition of "finite number", well, here is your chance to
correct me
if I am wrong. But odds are that Jeffries is holding the same
definition of
"finite-number" that everyone in the history of math held from
Pythagoras
to 2009. They all believed a finite-number was finite because it ends
in
repeating zeroes in the leftward string of digits; so that 94 is
finite because
it is .....0000094. And although there were no decimal representation
of numbers
until far after the Ancient Greek mathematics, they probably still
reasoned that
zeroes has something to do with being a "finite" entity. And the
Ancient Greeks would
likely not have a worry over precision defining of "finite" anyway.
Only until
we come in contact with sequence and series and the calculus are we
required to
have a precision definition of "finite number".

I am not here to be distracted and diverted by Y-V and his nuances and
his irrelevant topic.

I am here to nail a precision definition of "finite-number".

So if Y-V, ever had a precise definition of "finite-number" he would
not have
been caught up in a silly discussion of yes or no. That indicates Y-V
never
had a precision definition of "finite-number" and that his working
definition
was -- probably-- that of a repeating zeroes leftward string.

Because Lwalk and now Jeffries brings up the irrelevant case of
Y-V, indicates that both Lwalk and Jeffries-- probably-- have a
assumptive working
definition of "finite-number" the same as Y-V and as "repeating in
zeroes leftward string."

So, if Lwalk and Jeffries disputes the contention by me that they both
have a working assumptive definition of finite-number as
"repeating in zeroes leftward string." Well, here is the chance and
opportunity
for both Lwalk and Jeffries, and even Y-V (if still alive) to deny
that they
have an assumptive working definition as I have outlined.


> > So obviously, if Y-V were asked, "Is 10^500+1 a natural number?"
> > he'd never be able to answer. He can't answer "yes" or "no" to
> > the question before his death (or the end of the universe), so
> > his response to the question would be unknown -- or "incognitum"
> > as one might say. (Notice that AP, unlike Y-V, is definitely
> > _not_ an ultrafinitist in any sort of way.)
> >
> > So a few interesting questions are:
> >
> > 1. Does Y-V's philosophy on the decidability of such questions
> > as "Is n a natural number?" for large n, make AP's philosophy
> > on the "finite" vs. the "incognitum" more respectable?
>
> I don't have time to read Mr Plutonium's work to figure out his
> philosophy and have no comments as to its respectability, but as to
> Yessenin-Volpin, read the original context:
>
> http://www.math.ohio-state.edu/~friedman/pdf/Princeton532.pdf
> pp 4, 5
>
> Yessenin-Volpin's point was "a defense against the defense of
> Platonists that asks for a place to draw the line between reality and
> convention". It seems to me that the anecdote demonstrates the total
> contrary of drawing a line in the sand at 10^500 and saying "On this
> side finite, on that side incognitum" (if that is what Mr Plutonium
> does).

I have no time to figure out how much math respectability that
Jeffries possesses,
whether he has any native talents in mathematics, but obviously he is
lacking in
logic in this post on these issues:

1) Apparently Jeffries has never asked himself what his working
definition of finite-number
was, because he would have then entered this discussion by saying that
an endless string of repeating zeroes leftwards such as .....0000094,
would have never made a Y-V discussion noteworthy of attention in the
first place.

2) Apparently Jeffries has never asked himself what his own definition
of "finite number" was, nor has LWalk asked himself what his
definition of "finite number" that he carries around in
life was, for if they had, they would have entered this thread with
their own. But, also, that neither of them, Jeffries or LWalk, seem to
have asked whether mathematics is above physics or whether mathematics
is a subset of physics.

So, can both of you, Jeffries and Lwalk, leave us with your impression
of your definition of
"finite number" and to what extent math is connected to physics? Or
are those too difficult
of questions.

3) So if you enter this thread that wants to precision define "finite
number" and you enter it
without ever having your own definition of "finite-number", seems as
though you are very
poor in logic and math. The winter olympics has just begun in
Vancouver, and to enter the
winter olympics without ever "expecting to do a sport activity" seems
rather as silly as
Lwalk, Jeffries, Y-V engaging in a conversation about "finite-number,
without ever able
to disclose their own definition of finite-number. Eh?

So, Jeffries, ask yourself, what is your own definition of finite-
number? Am I right when I say
that you have carried all your career under a definition of leftward
string of zeroes? Am I not
right that your whole career in math has been under that umbrella of a
definition of finite-number? And have you ever asked yourself whether
math is a subset of physics or that
math is independent and removed of physics?

From your post above you seem to be oblivious of these important
questions. You seem to run on opinion more than run on wisdom and
logic.

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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