Yup. Infinity is a funny idea, but it's just an idea. 1 monkey's work in infinity is essentially 0 monkey's work.
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Yup. Infinity is a funny idea, but it's just an idea. 1 monkey's work in infinity is essentially 0 monkey's work.
Infinity only exists in theory. Like circles. Circles only exist in theory. Show me a perfect circle.
:facepalm: Ever used a compass? That's just one of the simple ways to make a perfect circle.Quote:
Originally Posted by OngBonga
Um... nope. I'll emphasise the word "perfect". A compass circle isn't even going to be close to perfect, I'd be able to find imperfections with a standard microscope.Quote:
Originally Posted by NightGizmo
At least force me to get to molecular level to refute you.
Best I can come up with is a wave propagating through a vacuum, but of course there's no such thing as a perfect vacuum, which means the medium the wave is propagating through is not perfectly uniform. Furthermore, gravity will influence the wave's propagation, meaning that not only do you need a uniform medium, you need uniform gravity from every direction.
It's a lot, lot harder than you might think to make a perfect circle. I'm curious if mojo has any suggestions.
I think making a perfect circle is exactly as difficult as precisely calculating pi.
I'll accept a perfect sphere as proof, by the way. A perfect sphere will be capable of projecting a perfect circle... that is, if it were viewed from above, its outline would be a perfect circle. So a perfect sphere is good.
Is the universe a perfect sphere? Maybe, but probably not.
The definition of a circle is "a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)". So a "perfect circle" depends on your desired precision. If I need a circle down to the millimeter level, I'm not going to care if it's a few nanometers off.Quote:
Originally Posted by OngBonga
By your absurd definition, you couldn't ever have a perfect circle because quantum mechanics.
There are multiple mathematical series that can be used to calculate pi without using a circle. Gregory-Leibniz series and Nilakantha series are two examples.Quote:
Originally Posted by OngBonga
Ok write down pi in decimal form, that's how hard it is to draw a perfect circle.Quote:
Originally Posted by NightGizmo
I would say that a perfect circle is a regular geometric polygon in which the diameter/circumference ratio is exactly pi.
A compass circle is not a perfect circle because it's not perfectly regular, just nearly, and as such its ratios will be very close to pi.
I've clarified my definition. Is it still absurd?Quote:
By your absurd definition, you couldn't ever have a perfect circle because quantum mechanics.
So define round.Quote:
"a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)"
Is a regular 1,000,000 sided polygon a circle? It will certainly fit the description of "round" if that's a loose term.
In your definition, you have defined "perfect" as an unphysical property, so no, I can't prove you wrong.Quote:
Originally Posted by OngBonga
(unlike the dark matter, which you took me too much at face value when I said we haven't observed it to interact in any way but gravitation. I should have said, we have observed that it does not interact electromagnetically - which includes chemically. It is through electromagnetic interactions that stuff has a surface to be grabbed and manipulated, which is how you move things into your digestive system and then digest it. Still can't eat dark matter in any meaningful way.)
I could take odds with the utility of your definition of perfect circle, as pertains to physics, but not as pertains to mathematics.
I wont do this, as it's stupid. The rigorous mathematical definition is so useful.
Mathematically, a circle is a perfect circle, 'cause that's the only kind of circle. Anything less than perfect is decidedly not a circle, no matter how circular.
The closest thing in physics would be something like the surface of a neutron star or the equator of a black hole's event horizon. The problem here is that you are kinda really talking about smoothness, and if you think circular has a tricky definition, then you'll find "smooth" to be even more fundamentally fun.
Gravitational orbits tend to become more and more circular over time. In general an orbit is elliptical. The measure of how much more of an ellipse it is than a circle is called the eccentricity. The orbit will shed eccentricity over many periods and will tend to circularize over time. This is, as you may have guessed, asymptotic behavior.
This is an nteresting read...
http://einstein.stanford.edu/TECH/technology1.html
The roundest thing we ever made... a gyroscope. This particular gyroscope has roundness so perfect that the only thing we know of that is more spherical is a neutron star.
There's an interesting point that says that if that gyroscope were to be scaled up to Earth size, then the tallest mountains would be 8 feet tall.
That shows both the incredible level of perfection they've achieved, and that the imperfections still exist in something so amazingly spherical.
Yeah that was the impression I got. Note that the gyroscope talked of in the article I linked is only surpassed in roundness by neutron stars.Quote:
The closest thing in physics would be something like the surface of a neutron star or the equator of a black hole's event horizon. The problem here is that you are kinda really talking about smoothness, and if you think circular has a tricky definition, then you'll find "smooth" to be even more fundamentally fun.
I think they omitted event horizons simply because of the uncertainty in that regard. Hawking has muddied the waters by suggesting there could be wild fluctuations going on.
Yes.Quote:
Originally Posted by OngBonga
Circles are not polygons. Absurdity still in effect.Quote:
Originally Posted by OngBonga
pfft I googled it in shock that anyone would be so absurd to suggest a circle is not a polygon, and it fucking well isn't because a polygon has straight edges, apparently.
I thought a polygon was simply a "many sided shape", from three to infinity, from a traingle to a circle.
Ok, but the ratio aspects are the key to my definition. It has to be exactly pi, and the shape has to be perfectly regular.
Lol.Quote:
Originally Posted by OngBonga
Made me think the phonetic combination of sounds, "monogon," which I'm now wondering if it's already a word that means circle.
***
Monogon sounds decidedly like some anatomical word.
... flows through the perpendicular arterial flagellum to the monogon region of the oblong hypothesis...
:rolleyes:
I agree that circles are infinity sided polygons and I don't much care if the words miss the meaning.
Compasses don't make perfect circles, neither do mathematical series. Nothing makes perfect circles because they don't exist but in our estimation of things.
Maybe an electron can somehow be a perfect circle.
Maybe sinusoidal waves like light are a kind of perfect circle.
Well, you're ignoring that those series are infinite, and that the infinite series do, indeed, equal what they claim to equal.
(Assuming they aren't complete nonsense.)
Don't get tripped up by the fact that any finite number, no matter how big, is an infinitesimal when compared to infinity.
Any polygon with a finite number of sides is def. not a circle. The idea that a polygon can have infinite number of sides is only meaningful in the sense of a limit. It seems reasonable that circle = limit as N goes to infinity of N-gon.
However, I'm not sure it's the best definition of a circle. Perhaps it has it's uses. There are many, many ways to define a circle mathematically and some are more robust than others, some are more useful for specific applications than others.
(Mathematical) Series are not things. They live in a space where the rules allow for infinite steps.
Oh shit, calculus.Quote:
Originally Posted by MadMojoMonkey
There is something to say about the idea of a perfect circle. It certainly comes up a lot and has many uses.
:/Quote:
Originally Posted by a500lbgorilla
Don't make me ask you to define "things." That sounds tedious. Can we agree that we're talking about series as a noun and just agree that, whether person, place, thing, or idea... it's one of those.
I'd gladly do it though.Quote:
Originally Posted by MadMojoMonkey
Whatever exists is a thing.
Zeno's paradox shows that we do indeed live in a similar space.Quote:
Originally Posted by a500lbgorilla
Although, having glanced at the wiki page... seems like my interpretation isn't the popular one.
I always assumed that the whole... in order to get anywhere, you have to first get half-way there. Then, in order to cover the remaining half, you must first get half-way across that... ad infinitum. The conclusion is that it takes an infinite number of steps to get anywhere and ain't nobody got time for that.
However, that conclusion is clearly false. People "get there" all the time. Not just people, even.
So a more appropriate conclusion would be that it's all too common for something modeled as taking an infinite number of steps to be concluded in a finite length of time. The only requisite is that the length of time it takes between completion of steps reduces "fast enough" to allow for a "reasonable" amount of time needed for completion.
EDIT: "Fast enough" means that it converges as x goes to + infinity.
(At some point, someone was wondering why they had to learn about convergence. Here's an example of usage.)
Zeno's paradox shows that we very much don't. Draw any finish line and watch me cross it.
I would say that is much more reasonable to see infinity as funny idea but just an idea.Quote:
Originally Posted by MadMojoMonkey
How can you claim to live in a paradoxical world?
Pick any paradox. How can it be true of the world that you're a part of? Paradoxes are just what happen when human brains try to put human rules to an inhuman universe.
I don't see how this couldn't be said for all of mathematics.Quote:
Originally Posted by a500lbgorilla
The number 1 is a funny idea, but just an idea.
OK, if a thing needs finite time to render, the only place that infinity ever pops up is in your head.Quote:
Originally Posted by MadMojoMonkey
Yeah, I agree completely.Quote:
Originally Posted by MadMojoMonkey
What is the number 1?
Seems easy enough. I could take those words you just used and slightly rearrange them, throwing in some personal pronouns.Quote:
Originally Posted by a500lbgorilla
I wouldn't do that, though. Just because a thing is called a paradox, that doesn't mean the universe is messed up. I cited Zeno's paradox, then explained how it's not a contradiction.
But you're just shuffling words. Words are the things we use to share ideas with one another.Quote:
Originally Posted by MadMojoMonkey
Zeno's paradox shows how people can stumble into problems that aren't there.
Infinity exists in the real world.Quote:
Originally Posted by a500lbgorilla
What's the density of a singularity with a mass of >0?
If I told you 12, how would you show me wrong?Quote:
Originally Posted by OngBonga
By showing that mass/12 does not = 0Quote:
Originally Posted by a500lbgorilla
Let me put it another way.
If you reject infinity as a real world thing, then you reject the singularity.
That's not absurd, in fairness. There's debate about that according to google.
Do you really want to parse all of this nonsense to see where our points lie?Quote:
Originally Posted by OngBonga
The math breaks down with the singularity. It's not the infinity that's a real problem, it's that our ability to describe the real problem is lacking.
PS mass/12 does = 0.
I reject our ability to describe the singularity.Quote:
Originally Posted by OngBonga
The singularity is pretty well defined, as far as I'm aware. It's a region of mass with zero volume in space. If it has volume, it ceases to be a singularity. And if it has no mass, then it has zero density, not infinity.
If the maths breaks down, and the singularity exists in the physical world, why do you not see this as evidence of infinity in the physical world?Quote:
The math breaks down with the singularity. It's not the infinity that's a real problem, it's that our ability to describe the real problem is lacking.
I'm not sure I follow you here.Quote:
Originally Posted by a500lbgorilla
Are you saying that if any (real) process is completed in a finite number of steps, then infinity is a human construct?
Whether or not math is a property of the universe or a construct of minds is a maddeningly philosophical debate. There's something interesting to the fact that people who have never met can have nonetheless worked out the same language (math) on their own.
Whether or not infinity is an invention of humanity, it is a wildly useful concept which we use to make real, observable predictions about the universe.
Seems pretty clear cut to me... for us to "invent" something so exact is absurd. We only create the system of which we understand maths... ie decimal, binary, etc.Quote:
Whether or not math is a property of the universe or a construct of minds is a maddeningly philosophical debate.
The concept one 1, 2, etc... the earth and the moon make two... there are two things there... whatever word or symbol you wish to use for two, however you interpret two, there will never be someone who sees three things there unless to them three is the word they use for two.
Maths is the language of nature.
OK, define it all you like.Quote:
Originally Posted by OngBonga
PS, your definition ain't right.
Man, I wanted to explain my understanding of the singularity by explaining protons all the way up the iron-burning stars then supernova then black holes but I just don't have the strength.
Calling it a singularity doesn't make it a singularity.Quote:
Originally Posted by OngBonga
So tell me what a singularity is.
Share them with me.Quote:
Originally Posted by MadMojoMonkey
I don't know.Quote:
Originally Posted by OngBonga
Who'd a-thunk I wouldn't understand whatever a singularity might be?
There's no reason to believe that because you understand everything you understand, that you therefore understand everything.
Sometimes, you've got to accept that you just don't know.
The mathematical notion of a singularity or "pole" is well understood.Quote:
Originally Posted by OngBonga
If we're talking black holes, then Einstein's field equations predict a singularity in spacetime. Bu... bu... but... that mass is there 'cause particles, right? And them's particles have an astoundingly well defined location, right? So how can they have well-defined momentum and just sit there... being a singularity, then?
huh
?
GR and QM just don't overlap well, and the only thing to say is ... dunno.
We don't need to go to black holes to find a singularity, though.
Electrons have charge, obv. Electrons have no discernible size. At best, though astoundingly thorough predictions and measurements, we can say that if the electron has a non-0 radius, it can not be more than 10^-18 m. So for all that we have measured, there is a singularity in the electric field at the location of the electron.
Bu... bu... but... Where is that electron? QM... you make me cry sometimes.
We haven't proven ourselves clever enough to actually measure the E-field that precisely. The universe has decided that electrons will not sit still for photos, and so it must be.
Ok let's invent a word.
ongbongularity - a gravitational presence (mass >0) with zero volume in spacetime.
The ongbongularity might or might not be the same as a singularity, that is irrelevant.
Do you believe such a thing can exist in the physical universe? Or is my definition amibuous in ways I'm not aware of?
Quote:
Originally Posted by MadMojoMonkey
Quote:
Originally Posted by MadMojoMonkey
Yeah, I'm a fan of non-human ideas. Like measuring things in terms of other things.
How much of what you just said misses that mark?
No. I don't give a hoot about definitions or words or the nonense of other people.Quote:
Originally Posted by OngBonga
As far as I'm concerned, this is a discussion about whether or not the singularity exists, not whether or not it can be defined. I feel like rilla is muddying the waters with philosophy.
I really enjoy philosophy.Quote:
Originally Posted by OngBonga
And I mean to say a check. How much of what you just talked about is an unchecked story?Quote:
Originally Posted by a500lbgorilla
None of it.
And I already said they exist they're just, right now, outside of reason!
I'm sure infinity must exist in a black hole simply because light can't escape.
Light itself also experiences infinity. It experiences infinite time dilation and infinite space contraction, thus, from the photon's perspective, the universe is a 2d plane, and the photon is motionless [citation needed].
But we see a 3d, or 4d if you count time, world, and we can see the light moves along a trajectory.
Philosophy is cool, until you basically say "what is clearly defined is not clearly defined because philosophy".Quote:
Originally Posted by a500lbgorilla
It's like saying 1+1 does not = 2. I'm thinking "but it does, don't be silly".
You won't escape Earth. Is Earth's grip on you infinite or simply over some threshold/limit?Quote:
Originally Posted by OngBonga
Also, to the idea of the photon and it's infinite experience of time - you're literally saying that
a PHOTON
EXPERIENCES
INFINITE
TIME
and that this idea passes effortlessly through your mind with no problems.
You keep simply saying that you know these things.Quote:
Originally Posted by OngBonga
Obviously there's infinity!Quote:
Originally Posted by a500lbgorilla
When a particle encounters a boundary, it has a probability of "quantum tunneling" through said barrier. The solution to the wave function describing the particle experiences exponential decrease in the "forbidden" region which is the barrier.Quote:
Originally Posted by a500lbgorilla
The solution for that region is of the form
A*exp(x) + B*exp(-x)
but we can immediately rule out one of the terms, because we are going to integrate the square of the solution of the Schroedinger (to tease out ANY measurable quantity from it) from -inf to inf, i.e. over all space. In math speak, "We require all physical solutions to the Schroedinger equation to have finite L^2 norm."
So if we decide the particle is moving in the positive x-direction when it encounters this boundary, then we can rule out that part of the solution with exp(x), since that "blows up" as x goes to infinity.
So right there, we assumed that x can go to infinity, and we ruled out an entire class of mathematically viable solutions.
Then again, when we integrate the square of exp(-x) from {ongbonga} to infinity, we solve the definite integral setting exp(-inf) = 0, and we get our solution.
The solution we find uses this assumption of infinity twice and yields results correct to absurdly high degrees.
This is for the most simple cases of the SE. In general, the solutions exist in infinite-dimensional space. For instance... What is the minimum energy the electron can have in a Hydrogen atom? -13.6 eV. What's the max? Well... if it's 0, then the electron is no longer bound to the proton and it's no longer rightly an atom. There is no theoretical "highest energy level" or "biggest shell" the electron can occupy. So the solutions to the state of an electron in a Hydrogen atom exist in infinite dimensions.
I guess I don't demand a full understanding of a concept in order for me to accept it as fact.Quote:
Originally Posted by a500lbgorilla
Light exists. I can see that. It travels at light speed, by definition. Our mathematical understanding of time dilation implies that at light speed, time dilation and space contraction are infinite. I'm not having a problem here. The only thing I might think is that maybe light speed is another theoretical concept, that actually the photon always travels at <c due to gravitational influences, and as such infinity is never actually attained.
But I don't have problems with accepting that light can experience time in a way that I can't understand.
None of it.Quote:
Originally Posted by a500lbgorilla
What?
:/
None of it?
whew.Quote:
Originally Posted by a500lbgorilla
No top. But also, no one ever gets to the top. We use infinity but that doesn't make infinity a thing.Quote:
Originally Posted by MadMojoMonkey
Well, I should say, if we use it...Quote:
Originally Posted by a500lbgorilla
Touche.
I don't have problems with ideas when I need to use them.Quote:
Originally Posted by OngBonga
But when I'm left to my dreams, I like thinking about thinking about thinking.
LOLQuote:
Originally Posted by MadMojoMonkey
Well, if you accept that 1 means 1, then you also accept that + is worth exploring, then math.Quote:
Originally Posted by a500lbgorilla
The labels and names may be whatever, but the sequence 1, 2, 3, 4, 5, ... is there.
So the argument that 1 + 1 = 2 is a universal truth is interesting.
The question of whether or not it would be true if there were no mind to learn it is also interesting.
I feel like this is the difference between physics and philosophy...
physics is the attempt to understand the physical world,
philosophy is the attempt to not understand the physical world.
Like, the physician observes something and thinks "how can I understand this better", the philosopher thinks "how can I interpret this differently to how I observed it".
There's definitely a place for philosophy, but I'm not sure it's here, in teh physics thread, because it's too fucking ambiguous!
Yes, I agree that math is worth exploring.Quote:
Originally Posted by MadMojoMonkey
But math is rules making where physics is rules-exploring (or some better term). And I much prefer exploring the rules of the working world than exploring what can be crafted with clever rules.
There still is a lot of overlap.
HAHAHA sameQuote:
Originally Posted by OngBonga
It's hugely important to physics that there are highly trained physicists who ponder the philosophical completeness of what they understand.
It's hugely important to science that there are highly trained scientists who ponder the philosophical implications of the scientific process as a method of revealing True statements.
This helps the rest of the world understand what the professionals are saying and what they aren't saying. This helps the professionals pinpoint what they do and don't understand and offers clues as to what may be explored to expand understanding.