| | If a plane is infinite...Page 1 of 2 (1, 2) | If a plane is plane is infinite and thus has no true beginning or end, then how can you record a point with any certainty?
and if the universe is the same way and thus our galaxy is a point in the universe then how can we record our existence with any certainty. | |
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| If a plane is infinite...
Posted: 3/22/2012 10:40:32 AM | If a plain is infinite, then people set an arbitrary point in space or time an start measuring and counting from there. (Greenwich, BC/AC and such)
Without people, it 's all irrelevant anyway, because who else cares. | |
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| If a plane is infinite...
Posted: 3/22/2012 11:51:21 AM | Recording a point on an infinite plane does not require a degree certinity on positioning as there will be an infinite length to go in each direction i.e. you will always be in middle.
Confusing concepts Such as infinity have only made there way through maths and physics mainly because humans have been incapable of providing a more simpler or detailed explanations about some hard questions, thus it does not mean it is an accurate account of practicality. | |
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| If a plane is infinite...
Posted: 3/22/2012 3:29:22 PM | Best way I can think of to explain it is:
Find one of those maps that has a red sticker on it saying "You Are Here." Notice that though you don't know where in space you are in an absolute way, that you do now know where you are, relative both to the sticker, and to everything else shown on the map.
In the same way, when a mathematician refers to s specific point, they are referring to it in relation to an established location. That location, and thereby the point being discussed, remain entirely lost, as far as the functionally infinite universe is concerned, but since the discussion in progress isn't ABOUT the infinite universe, it doesn't matter. | |
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| If a plane is infinite...
Posted: 3/22/2012 3:50:17 PM |
...then how can you record a point with any certainty?
As already noted, with reference points. | |
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| If a plane is infinite...
Posted: 3/23/2012 8:24:22 AM | | The universe, or rather this universe, appears not to be infinite. But even if it was you can still map things relative to each other. I know my drink is next to my laptop, even if I am not entirely sure where I am meant to place this galaxy amongst all the others. | |
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| If a plane is infinite...
Posted: 3/23/2012 8:35:24 PM |
" ... If a plane is plane is infinite and thus has no true beginning or end, then how can you record a point with any certainty? ... "
DUH ... ! You stick a PIN in it at the spot you want to remember ...
Jeez. Some things are just so OBVIOUS ... | |
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| If a plane is infinite...
Posted: 7/27/2012 5:04:32 PM | I love discussions about the properties of infinity!
With a recorded message using symbols with predetermined values we will define something that is boundless!!!
Can you take a point from infinity? If I take a point in an infinite plane, how big is the point? Couldn't you point to an infinite number of points within my point and ask- which of these points is the point you were pointing to! Then we take a point relative to the said point and measure the distance between them, we make a measurement again this time of a much closer point, we compare the results and find the distance.... it's exactly infinite!! In this way we have surely created an equilateral triangle? Three points all with a distance between them which is identical... Yea I don't actually know the answer to your question just thought I'd confuse things further, sorry about that | |
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| If a plane is infinite...
Posted: 7/27/2012 9:40:38 PM | I'm a Surveyor by trade. The absolute most fundamental rule of Surveying is that perfection does not exist. My every attempt at accuracy is an attempt to solute the lowest amount of error acceptable within the parameters of what is being designed.
Absolute points are never obtained. This is explained very well in Zeno's Paradox. Which basically states that if you always travel half the distance from you to your target you'll never actually reach your target. Richard Dawkins would probably say that because we live in a 'middle-world' what we consider close or far is relative only to our middle-world and that to an Atom. To the Atom the distance from your eyes to your nose would be immense or 'far'.
Certainty isn't a very good word for it. I'm certain that when I pick up a phone to make a phone call that I am holding it. But in actuality the cells that make up my hand are never touching the molecules that make up the phone.
But don't fall too deep down the Rabbit Hole. Just be certain that you aren't certain. :p | |
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| If a plane is infinite...
Posted: 7/27/2012 10:51:21 PM | Ridiculous.
Nothing is infinite, all things within existence have an origination, and a destination - Otherwise they would be outside the realm of the 4th dimension, in which case due to a stance of absolution they would not adhere to ANY spatial dimension, and cease to exist.
Problem solved - Nothing that -exists- is infinite.
Also - i forgot.
Planes are 2 dimensional, meaning they adhere to spatial dimensions by their existence, ergo they have both origin, and destination in according with the 4th dimension.
They are not infinite, and all measurements are just best case guess as they are dependent on the fractional of the tool being used to measure.
By that measures, nothing is fractal either. | |
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| If a plane is infinite...
Posted: 7/28/2012 5:52:36 AM | | Only humans measure in fractions because it is relevant to how we define our environment. Matter is otherwise always whole. So long as we continue to see smaller (and larger) it should be perceived as infinite. Only the religious think in finite terms. Which is ironic when you think about it. | |
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| If a plane is infinite...
Posted: 7/28/2012 10:35:28 AM | | Yeah nothing that exists is infinite. If I had a row of balls that stretched out infinitely but there was a pattern one red, two blue, one red, two blue, there would always be twice as many blue balls. Infinite when talking about something physical is impossible. You can have an infinite amount of numbers because they are an idea. | |
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| If a plane is infinite...
Posted: 7/28/2012 2:51:59 PM | | If when we think of this theoretical plane it does not exist, even in our mind, then it does at least say a lot about the nature of the universe that we can think of such a plane. If the plane cannot exist, then perhaps it is thought which is infinite. | |
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| If a plane is infinite...
Posted: 7/28/2012 4:11:10 PM | | Any distance is infinte. There is no evidence that inner-space or outer-space has any finite boundary. So whether theoretical, imagined or measured any plane is infinite. Just because you can see both ends of a ruler does not make it finite. | |
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| If a plane is infinite...
Posted: 7/28/2012 4:20:13 PM | | Well the OP also mentioned the universe as a plane so I was referring to that. If you are talking about an idea such as a theoretical plane it can be infinite because it is just an idea, with numbered measurements. It's impossible to know with absolute accuracy if the universe is infinite because while the universe could be infinite the matter that fills it could be finite and the evidence they have so far suggests this. | |
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| If a plane is infinite...
Posted: 7/28/2012 9:38:19 PM | I remember reading about Plancks Length. It's easy for us to fathom a Planck because it is by design a theory attempting to make absolute of a distance (or one so close no difference can be measured). Our brains are comfortable by default with finite lengths. As Dawkins said it favors our evolution to think in terms of a middle-world. Where everything is distinctly finite.
We're all being theoretical I'm simply saying that you can't prove mathematically or physically that any distance is finite. That's why I agree with Krauss in that it is safer to assume infinity since it doesn't cap our ability to imagine.
P.S.
I looked up the Wiki and I think this quote says it best:
"In string theory, the Planck length is the order of magnitude of the oscillating strings that form elementary particles, and shorter lengths do not make physical sense." | |
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| If a plane is infinite...
Posted: 7/28/2012 11:56:41 PM |
Yeah nothing that exists is infinite….Infinite when talking about something physical is impossible. You can have an infinite amount of numbers because they are an idea.
What if the universe is open (asymptotic) and expands "forever"?
Are you asserting that there would have to be an end of the spacetime expansion at some point, or only that there can be no such thing as "forever" since the limit of the expansion disallows infinity and is "always" finite?
This problem is a physically real analogue to (say) the "idea" of natural numbers for which we can say that any value "n" will always have a successor such that there cannot exist a highest "n" (but if we disallow a highest "n", then we must logically disallow all it's predecessors, which creates a paradox if we don't allow the limit to proceed to infinity)
If we don't allow an open spacetime to expand to infinity, is it not logical to assume the paradox of an expanding universe that cannot logically expand from the first instant and therefore always remains a pseudo-singularity (not really a singularity owing to QM limitations)?
The analogue between the physical space and the naturals does differ if we think of spacetime as continuous (an assumption belied by QM), but QM would suggest a "stepped" spacetime not unlike the naturals anyway (so I suspect the analogue would be a valid comparison). If in fact spacetime were to be continuous, we would have to make a comparison to the Reals, which is another "idea" with an even higher cardinality (cardinality of the continuum) than the countably infinite naturals.
I strongly suspect that unless you have a rational explanation for the vexing dilemma raised by the analogy, your assertion that "Infinite when talking about something physical is impossible." may well be fallacious.
Would you say that the speed of light can be attained with a finite amount of accelerating force applied to an object (especially in light of the fact that Quantum uncertainty would probably make "close enough" good enough)? | |
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| If a plane is infinite...
Posted: 7/29/2012 12:51:24 AM |
Any distance is infinte. There is no evidence that inner-space or outer-space has any finite boundary. So whether theoretical, imagined or measured any plane is infinite. Just because you can see both ends of a ruler does not make it finite.
You made one key statement here as to WHY you are wrong :
There is no evidence that inner-space or outer-space has any finite boundary
Now, why you are wrong is more a bad call of pragmatism rather then actual scientific process.
Example.
You can not prove universal spatial displacement has finite boundary, by that logic you can not disprove it doesn't.
Nor can you prove that it's infinite. Those statements render one truth - You can not prove, or disprove spatial finitity.
That leaves you no-where, except somewhere. - That being our ability to measure space always will be limited by our ability to measure 1/2/3/4 dimensional spatial measurements. Ergo it's the -safest- route to say in theory that no space is infinite because to say "Any distance is infinite" is to say you can prove that, which we can not.
We can only prove the finity of space that falls within our ability to measure -
This is a binary argument. Either it is or is not - You can't prove it is - so it must not be. Infinity is immeasurable, so it will never be.
I know the wording is confusing, a hard idea to articulate - But just because you can not measure it (due to the potential the measuring devices being exceeded), does not mean you label infinity, you do not know, and make the claim is weak science, and a lazy philosophical out. Every time you find the length to continue beyond your realm of measurement, you simply repeat the process of not being able to disprove finity.
For all we know the universe is a large puddle that is 4th dimensionally engulfed by matter, perhaps dark matter of such a great density it's solid at absolute zero leaving no atomic vibrations.
The fact the universe expands is pretty much encourages (does not prove), that it's finite, an infinite space can not expand. | |
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| If a plane is infinite...
Posted: 7/29/2012 2:22:10 AM | Dukky(msg22)
you must have missed the nugget from his follow on post (msg 18):
It's impossible to know with absolute accuracy if the universe is infinite because while the universe could be infinite the matter that fills it could be finite and the evidence they have so far suggests this.
An infinite universe with a finite amount of matter; I would like to take that to peer review.
What if the universe is open (asymptotic) and expands "forever"?
A "flat" universe also has a limit of infinity for the expansion, as well.
And since in both metric solutions to the Friedmann–Lemaître–Robertson–Walker model (asymptotic and flat) have the limit of expansion as infinite, the is no dilemma as they treat "infinity " as for what it is: a limit and not an entity.
Would you say that the speed of light can be attained with a finite amount of accelerating force applied to an object (especially in light of the fact that Quantum uncertainty would probably make "close enough" good enough)?
Of course, you attempt to draw into the trap that when conjecturing a thought experiment to violate relativity by accelerating to the speed of light, by setting the focus on velocity, when the real limiting factor is energy.
Special Relativity states for an object with non-zero rest mass to travel at the speed of light, it will then have to acquire an infinite mass. So, to resolve your question, if you want to quantum tunnel to the speed of light by means of the Uncertainty Principle' then you would have to be within:
delta(Energy) x delta(Time) > (Dirac's Constant)/2
of Energy=infinity (the mass that you are required to obtain).
In other words, you would still have to 'borrow' an infinite amount of energy in order to 'tunnel' to the speed of light, regardless of how close you manage to approach the speed of light.
Good luck! | |
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| If a plane is infinite...
Posted: 7/29/2012 9:15:53 AM | The inability to measure a perfect distance is proof enough that infinity is possible. That's my point. So it's safer to assume any distance is infinite and that we humans attempt to pinpoint as little as we can to set a visually finite distance. After all it doesn't serve me to know what one ten-thousandths of an inch is if I'm making a chair. However it would matter if I was building a particle collider.
The expansion of the universe is a very shady theory. In my opinion. It works fine and dandy for us but couldn't our viewable universe just as easily be a spec on a stretching and retracting space? I mean, if that was the case it would very easily appear as though our universe was expanding. Maybe it could be compared to humans that once believed the Sun went round the Earth simply because from where they were standing it appeared that way. | |
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| If a plane is infinite...
Posted: 7/29/2012 12:43:45 PM | Another way to answer this OP's question:
The specified infinite plane, is an imagined construct by a certain person. That person also designates the specific point on the plane. Therefore, the fact that the plane is defined as being infinite, has no pertinence to the question of the certainty of the position of the designated point on said plane.
The person who specified the plane, specified the point as well. Therefore it's position is known by definition.
The OP then tried to extend his misapprehension of how that little thing came to be confusing to him, and extended his confusion to allow for doubts about all existence. That's an entirely separate discussion, neither supported nor refuted by anything anyone might say about some imagined mathematical example. | |
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| If a plane is infinite...
Posted: 7/29/2012 9:56:44 PM | @ gedanken
An infinite universe with a finite amount of matter; I would like to take that to peer review.
It would be interesting…Would the density be reduced to an infinitesimal non-zero value or zero in the limit as "t" goes infinite? Not being much into physics or QM, I couldn't say, but my intuitive suspicion (if the Big Bang is true and the universe open) would be that the density would drop to some minimum threshold and "wink out" of existence.
A "flat" universe also has a limit of infinity for the expansion, as well.
And since in both metric solutions to the Friedmann–Lemaître–Robertson–Walker model (asymptotic and flat) have the limit of expansion as infinite, the is no dilemma as they treat "infinity " as for what it is: a limit and not an entity.
I see the physicists' view, but sometimes wonder if physics itself isn't doing itself a disfavour in taking the (sort of) constructivist view that infinities cannot be allowed. While I appreciate that introducing them might (in some cases) make physics as "unstable" as mathematics (with all of its antimonies & such), I still have a sneaking hunch That working with infinities as actual entities could go a long way in explaining much of physics.
Good luck!
Thanks. I kinda figured there would be a rational explanation, but my unfamiliarity with both relativity and QM prompted the question since I know that while both theoretical constructs are empirically valid in their respective domains, they have yet to reconcile the opposing differences where those domains overlap. | |
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| If a plane is infinite...
Posted: 7/30/2012 5:07:58 PM | @Dukky
It would be interesting…Would the density be reduced to an infinitesimal non-zero value or zero in the limit as "t" goes infinite?
My read on his statement, was that he was suggesting that the universe could literally be infinite, as opposed to being "flat/open". There is certainly no evidence for this, and the idea has not been seriously entertained since the Steady State theory finally petered out 45 years ago. But then again, who knows what he meant; clarity is often a fleeting beast in the forums.
I see the physicists' view, but sometimes wonder if physics itself isn't doing itself a disfavour in taking the (sort of) constructivist view that infinities cannot be allowed. While I appreciate that introducing them might (in some cases) make physics as "unstable" as mathematics (with all of its antimonies & such), I still have a sneaking hunch That working with infinities as actual entities could go a long way in explaining much of physics.
Au contraire, I would suggest one of the goals of physics is to eliminate the possibility of infinities. In classical physics, the universe was (potentially) infinite, and there was reason to assume that a rocket couldn't be built that would travel to many times the speed of light, right up to infinite speed. Relativity solved both of these issues. On the other side of the coin, the ultraviolet catastrophe associated with blackbody radiation in accordance with the Rayleigh–Jeans law, which predicted that radiation output from a blackbody would approach infinity for shorter wavelengths of light. Plank's Law resolved this issue, which eventually led to the quantum theory.
Today, ironically, we work with infinities on a regular basis. QED integral equations which calculate the mass or charge of an electron, for example, are divergent and thus lead to infinite results. This is resolved by renormalization, or factoring out the infinities. It is ugly, and technically illegal by math policing standards, but it works. The replacement theory for QED, once it comes, will almost certainly provide tidier math. The other case of infinities arise with singularities of black holes and of the universe itself. This will be easier to resolve, I believe, as I think that the answer already lies in the field equations, it is just a matter of coming up with the right solution.
Math is a family of languages and as such is a human invention. We use these languages to find proximate solutions for how things in the universe work. Infinity is an ugly concept, which is exacerbated by those who want to treat it as a number. The goal of physics is to find the proper math language in which infinities either don't exist, or can be duly accounted for and eliminated.
Thanks. I kinda figured there would be a rational explanation, but my unfamiliarity with both relativity and QM prompted the question since I know that while both theoretical constructs are empirically valid in their respective domains, they have yet to reconcile the opposing differences where those domains overlap.
This is mostly just a plain Relativity issue.
If I tell you to accelerate away from me until you reach 99.99999% of the speed of light, the issue you have is to even know (for yourself) when this speed is reached.
One solution is to look back at me, and stop accelerating once you see me moving away from you at 99.99999%. But once achieved, you realize that nothing has changed for you: flashlights work the same, balls bounce off the wall the same, your heart beats at the same rate.
"What", you say?! You measure the speed of the photons coming from your flashlight, and they are still moving at the speed of light, and you think to yourself "man, I have a long way still to go!".
So you look back at me (and I haven't moved an inch since you blasted off) and you say "hey, nothing has changed for me and I don't think I am able to quantum tunnel to the speed of light, but since you are moving at 99.99999% the speed of light, why don't you try?". Therein lies the dilemma.
The corollary is that the protons flying around the LHC at CERN at a considerable percentage of the speed of light, are in reality no closer to attaining the speed of light than you are sitting at your computer! | |
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| If a plane is infinite...
Posted: 8/1/2012 8:46:50 AM |
The corollary is that the protons flying around the LHC at CERN at a considerable percentage of the speed of light, are in reality no closer to attaining the speed of light than you are sitting at your computer!
Ahhh haaa,... that's funny! I liked this post! Hey OP there's a reason why imaginary math exists, its because we still don't fully understand these things yet, and says who that we're on a plan, or that there isn't an end to everything. | |
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