On Sat, Sep 24, 2011 at 2:22 PM, meekerdb <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> 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,
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.


>
>
>  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.).  This view of existence seems rather egocentric; 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?


>
> 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.

Jason

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