On 9/24/2011 1:54 PM, Jason Resch wrote:
On Sat, Sep 24, 2011 at 2:22 PM, meekerdb <meeke...@verizon.net
<mailto:meeke...@verizon.net>> wrote:
On 9/24/2011 11:56 AM, Jason Resch wrote:
On Sep 24, 2011, at 12:44 PM, meekerdb <meeke...@verizon.net
<mailto:meeke...@verizon.net>> wrote:
On 9/24/2011 12:07 AM, Jason Resch wrote:
A final consideration: do you believe Pi has such a value that
when
Euler's number is raised to the power of (2*Pi*i) the result is
1? Pi
has a value which no human has determined, as determinig it
requires
infinite time and memory. If only those mathematical things
known to
humans exist, then Pi's true value does not exist.
I think this is questionable. One can use the value of pi,
calculate with
it, determine it's relation with other quantities.
We can use an approximation of it's value, or a definition of how to
derive it's
value (given infinite time and memory), but we've never known or used
it's value.
Sure we do: sin(pi/4) = 1/sqrt(2) uses the value. So does e^(i*pi) = -1.
There we are using its definition or an approximation of its value. If you plug
e^(Pi*i) into google, you get 1 but that is because the limited precision that computers
use to represent floating point numbers gets rounded. For proof, try entering into google:
e^(Pi*i+1E-9)
The function Sine and the number e are both defined by an infinite series,
You have too narrow a view of mathematics. Infinite series are one way sine and e can be
defined, but not the only ones.
which have likewise never been physically realized. You can either dispense with the
infinities, or dispense with the idea that math is man-made.
All of it's definitions require infinities.
The circumference of a circle whose diameter is 1.
A circle's definition involves an infinite number of points having the same distance
from a center. There has never been a physical construction or representation of a circle.
Neither has there been of the number 2. All physical realizations are only approximately
described by mathematics.
If these infinities don't exist, because your philosophy of mathematics
is
constructivist, then it follows that Pi does not exist.
In one (of the many) senses of "exist".
The two senses I have seen you have articulate are the one in which existence implies
you can interact with something (your chair), and the sense in which you cannot interact
with it (numbers, past, beyond horizon, etc.).
I said explicitly that "exist" means to be in the ontology of some model, and so it is
always relative to that model (and similarly for nonexistent).
This view of existence seems rather egocentric;
It's not egocentric if other people share the same model.
I don't see how the existence or non existence of something can depend on one person's
point of view. There are billions of people on this planet I will never meet, see, or
know, but I should not consider their existence to be a different sense of the word.
So you can't write it's decimal expansion, how significant is that?
Sure everything is questionable. But according to Rogers theory the
unnown
digits of Pi do not exist and/or have no definite value since no human
has
determined them.
What this equation and reasoning suggests is that there can be certain
values
which are unknown to us. Such as the googolplexth digit of Pi.
I'd say almost all (in the measure theoretic sense) values are unknown to
us.
So is it fair to say you believe there are an infinite number of primes?
Yes, as defined in arithmetic.
Brent
"By habit, whenever a man sees a name, he is led to figure
himself a corresponding object."
--- Jeremy Bentham (1748-1832)
"You can know the name of a bird in all the languages of the world, but when you're
finished, you'll know absolutely nothing whatever about the bird... So let's look at the
bird and see what it's doing — that's what counts. *I learned very early the difference
between knowing the name of something and knowing something.*" -- Richard Feynmann
We might know the name "17" or the name "Pi", but we should not let these simple labels
fool us into thinking we know everything there is to know about these objects.
But note that Feynmann new how to use pi...without knowing it's decimal expansion or
having any other infinite amount of knowledge.
Brent
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