“I don’t know what you are on about the identity thing.”
As a one step tier:
1+infinity = 1
5*infinity = 5
I can’t remember where my mind was when I dinged this, but i kept it, so it must have been reasonably thought out. I was pondering convergences I think… meditating probably upon 1/3 of all coincidences.
-Justhink
Well, there is a math of infinity, it is true, and if we try and treat it like a normal number we can end up with crazy results. But this just makes it different. For example, treating the number i as if it was an element of the reals will fail miserably and lead one to paradox.
“Guess” that
i < 0
ii > i0
-1 > 0
which is false, so then we must conclude
i > 0
ii > i0
-1 > 0
which is just as false here as it was before.
As you can see, i is not a “normal” number. But it has a very clear mathematical—and physical—use.
A good rule of thumb is: the only thing that all numbers have in common is that we call them “numbers”. 
Now I can’t remember… it was either an identity for every operater in one sequence OR in one sequence anything on the other side had to come back as 1, no matter what it was before.
Argghh… it’ll take a while to retrieve it, apologies.
As for my troubling ideas, I’m arguing that the pressure exists and that these systems are dynamically predictive when a few basic ‘truths’ are understood and applied. The explanitory power is incredible, but I’m still more interested in collapsing it as you well know. In talking about it, I’m interested in putting rationality on the line in a means where we can all reasonbly conclude the result, but needent actually go through with it to understand that the dynamic is true. After all, we haven’t nuked ourselves yet, so I’m fairly confident that people can learn systems which bridge communication without requiring the physical ‘bomb’ to be set which actually applies the pressure that they know is going to be there. More like that Eris.
As for reality collapsing; impossible =)
-Justhink
Ooo… thx for the RN <> explanation.
-Justhink
Of course, if this progresses, violence will soon erupt and soldiers will end up firing on innocent civilians who are only trying to teach math.
Yes, it’ll be the “Pi Lie Massacre.”
Frankly, this thread has gotten simply bizarre. Justthink, it would help if you were to write in something more than stream of thought.
Given that, the mathematics have been sloppy. There is no “number” called infinity. The statement “1 + infinity” is imprecise at best. And it certainly isn’t equal to 1.
lim[sub]x->inf/sub diverges (or grows without bound, or tends to infinity, etc.). It is also not proper to say it equals infinity.
lim[sub]x->inf/sub also diverges.
I’m not saying that the boundary has breadth; quite the contrary. Look at this picture; if I ask someone if they can see a vertical line anywhere in it, some or all of them will point to the vertical boundary between black and white; the width of the interface (in ideal terms, not on a computer monitor) is exactly zero and yet we can quite clearly understand the boundary as being a vertical line.
I maintain that it is possible to imagine a line of zero width (I’m sure that I’m doing it right now).
Now we could get into arguments about how it isn’t possible to draw a perfect line, or even to make a perfect circular disc of anything (even if we had perfect tools, the granularity of matter on the molecular/atomic level would defeat us), but the existence of atoms isn’t intuitive; we interact with matter on such a large scale (compared to the size of atoms) that it is (I believe) quite easy to imagine a material that has no granularity and can be formed into a perfectly circular disc.
To go back to my previous post; either the width of the disc and the measurement around it’s circumference have a constant relationship, or they don’t. If they don’t, why don’t they?
Having just scanned the entire thread, ** Justhink**'s problem with pi appears to boil down to:
Just because, for every circle so far ever drawn, its circumference divided by its radius comes out as the same number doesn’t mean that the * next * circle won’t give something else. He thinks that the value of pi has been found inductively.
He sees a mathematical definition as being as arbitrary as, say, defining God to be a retired machinist called Lloyd.
In (1) he is wrong: as many others have pointed out, pi is * defined * as the aforementioned ratio.
In (2) he is right. Mathematical definitions * are * arbitrary. We only keep the useful ones: - the ones which allow us to go more than a couple of steps further according to the similarly arbitrary rules of mathematics. I * could * define God = Lloyd = omniscient = bashful etc., but mathematically that wouldn’t get me very far.
Unfortunately, I now fully expect 200 lines of schizophrenic babble proving my presumptuousness from first principles.
Merry Christmas
-Justhink
I’m really struggling to understand why a definition needs to be proven; 12 eggs constitute a dozen; there’s no need to prove that a collection of a dozen always comprises 12 units*, because it’s a definition, not an observation.
“What if we found that one instance of a dozen only contained 11 units?” - it wouldn’t be a dozen - it’s that simple.
Certainly it is interesting that pi is defined as a ratio and yet cannot be expressed as the ratio of two integers, but so what?
(*no smartypants comments about bakers’ dozens please)
I already stated why I believe this to be the case (that they don’t). There is something fundamentally contradictory about associating one sided figures and lines with regards to absolutes.
The problem seems to creep up with regards to infinity; more precisely, motion. Instead of thinking about the decimal output of something like 1/3; I think we’re actually observing these types of loops in motion in these instances. As odd as it sounds, I have no clue how to solve for the millionth place of the decimal output for 1/3. I can’t figure out if the string is extended or if a single digit is being accessed for replication designation. If it is being accessed for replication, what is bisecting these coordinates to determine such place-holdings (to hold them there and to access them and allow them to be accessed)?
Part of me wants to speculate a single digit being accessed.
Part of me wants to speculate space just being totally wasted with these extended strings. (I’m not big on this part)
Another part of me believes that the repeating decimals are looping. But then you need a new system of undiscovered layers to determine where these loops are being cut for each given point. The looping part of me gets excited at the idea of decimal geometry being created through walls formed by these infinite feeds, which serve as the backdrop for an enclosed data field which they support.
I feel that these infinite loops of decimal output are creating mass by oscillating in rapid succession - slamming into eachother, like a bunch of 3’s all a much lighter shade but all converging upon blocks of placeholders within the sequence. I think of ‘space’ as coming from this phenomenon, allowing you to see the actual form of a 3. The more I think about light, it strikes me that if angled properly an infinite number of shadows should be ‘creatable’ without using mirrors like we do to multiply our image into infinite regression. Not the normal shadow, but the refractive shadow… this should extend infinitely. Those inverse place-holders are weird. Hmm…
Oh my, if anyone thought I was crazy before.
I definately sense corruption in the teaching of pi without equal time to teaching the God concept. I think I need to figure out what those symbols juxtaposed with infinity are conveying.
Mathematics seems odd to me, as the ‘transcendence proof’ seems as simple as a sentence to convey - and yet that link of it was just filled with symbols. I need to learn what type of thought went into those symbols to understand what that proof means. It shouldn’t be of suprize that I have no clue about their meaning. This pi thing was bugging me today. I’m tired. My sentences are terse and wandering, apologies… and many thanks for helping this inquiry with these responses. Feel free to explain the symbols if you like; otherwise I imgine it’ll take a bit for me to fully comprehend their meaning and context.
Contrary to Azael’s sentiment, the fear of me being some sort of super-genius can be laid to rest =)
G’night.
-Justhink
What, no comments on my brilliant joke?
taps microphone Is this thing on?
Justhink: I’ve seen you apologize for your lack of clarity on at least three seperate occasions, now. Shouldn’t you be taking that as a sign of something?
Justhink wrote:
Would that all my fears might be so tame. 
[nitpick]
It’s true that the ratio isn’t pi on curved surfaces, but pi still has a habit of popping up. The circumference of a circle of radius r in hyperbolic geometry, for example, is 2pisinh® (where “sinh” is the hyperbolic sine function: sinh(x)=(exp(x)-exp(-x))/2).
[end nitpick, as Math Geek runs screaming from the rest of the thread…]
Wait! Take me with you! :eek:
How many angels can dance on the head of a pin?
Explanation for the pie joke: Weebl and Bob
Justhink:
The way that this thread has gone so far is that you have expressed some weird point of view on pi that contradicts all of modern mathematics, science, etc.; others have tried to explain how you are wrong as best as we can understand; and, you have refused to give up your belief.
Now, I am all for democracy and not blindly accepting authority, but I think it can be taken a bit too far. If I came up with something that contradicted the Second Law of Thermodynamics, it would be much wiser for me to think really hard about where I might have made an error before I were to go around suggesting that the 2nd Law is wrong!!!
By the way, I think it is perfectly fine to say that
“1 + infinity = infinity”
and
“5*infinity = infinity”
as long as it is understood that “infinity” is not a number per say but means a quantity tending toward infinity.
As erl correctly points out, a quantity like “infinity / infinity” alas does not have one single well-defined limit when simply expressed in this manner. We have to know how the numerator or denominator are actually tending toward infinity in order to determine what it is in specific cases. erl gave an example where the limit is 1/3 but one can come up with examples where it is any other finite number (including 0) or it is infinity, or even where it is not well-defined (e.g., it oscillates rather than converging to a value).
Hmm… at home my limit expression displays correctly; here at work it does not.
The expression’s numerator is ln(2 + e^x) where the ^ is an exponent operator. One could also write exp(x) (a convention we used in my calculus class before we defined the number e). The denominator is just 3x.
And, indeed, there are ways of evaluating any number of strange expressions. (Using & for infinity here) One can evaluate
&[sup]&[/sup]
0[sup]&[/sup]
&[sup]0[/sup]
n/0
0/0
&/&
blah blah blah…
Very interesting stuff, IMO; but, unlike our friend SmileyDeath, I do like math. I just never went very far with it.
