On Sat, Sep 24, 2011 at 5:56 PM, meekerdb <meeke...@verizon.net> wrote:
> On 9/24/2011 1:54 PM, Jason Resch wrote: > > > > 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, > > > You have too narrow a view of mathematics. Infinite series are one way > sine and e can be defined, but not the only ones. > I'm not aware of any definitions of them which do not involve infinity directly, or otherwise infinite objects, or infinite numbers of objects. E.g., you could say e = ( 1 + (1 / infinity) ) ^ infinity, which uses infinity directly. > > > 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. > > This only reinforces my point. If we can only approximate objects mathematics, then how can it be a human construction? > > > >> >> >> 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). > > Bruno's shown how the physical world is part of the same model that includes the integers. > > This view of existence seems rather egocentric; > > > It's not egocentric if other people share the same model. > > A bunch of different people each individually believing that only the here and now (to each of them) is real. Each will have a different view of the here and now, and each will be wrong in denying the existence of what the here and now happens to be for other people in other places. > > 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. > > > Then your philosophy of mathematics differs from Roger's. You accept the existence of primes not yet known by humans, and primes so big we never could know them. > > >> >> 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. > > We know things about Pi, certainly. We know its first trillion or so digits. This enables us to use it for solving physical or engineering problems within tolerances that are acceptable for any intent or purpose yet imagined. But it is important to remember we don't know everything about Pi, for examples, we don't know if it is a normal number ( http://en.wikipedia.org/wiki/Normal_number ) or not. 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