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First Observational Test of the "Multiverse"
An anonymous reader writes "The theory that our universe is contained inside a bubble, and that multiple alternative universes exist inside their own bubbles – making up the 'multiverse' – is being tested observationally by UK physicists, who are searching for disk-like collision patterns in the cosmic microwave background (CMB) radiation. Though CMB is generally thought of as a uniform schmear of radiation extending in all directions in our universe, in fact, they say if a multiverse exists, there ought to be imprints trapped in the muck like footprints of where our universe banged into others."
in this universe at least.
If universes can physically interact with each other, can each really be called a "Universe"?
How can I believe you when you tell me what I don't want to hear?
Yes. Inaccurately perhaps, but life goes on, the sun will still rise and fall.
"Flaming Error" is claiming the sun will rise tomorrow...
It reminds me of Hume.
Somewhere, an Irony Universe has just bumped into ours.
=)
-- IANAL, this isn't legal advice, and definitely isn't legal advice for you. Also, Squee!
This is why I love Physics. The mere fact that we are considering such a colossal hypothesis and devise a method to verify/falsify it by observing reality...
I rarely respond to comments. Also, don't ask for clarifications: a brain and Google are faster, believe me!
Hopefully we can pick up some new television channels and radio stations. I'm getting pretty bored with the universe our universe offers.
Or multinet. Think of the porn!
Slashdot needs Geekcode | Can anyone recommend any good SCIFI? My tastes: Foundation, Startide Rising, CITY, Ringworld,
goatse
Or maybe you just don't what what you're talking about, and think that playing a public game of semantics is a suitable replacement for knowledge.
The world's burning. Moped Jesus spotted on I50. Details at 11.
I'm way ahead of you.
Never say never. Ah!! I did it again!
There is nothing testable about any multiverse hypothesis and nothing being measured here. The.CMB's variability is indistinguishable from noise.
I hypothesize that the multiverse exists, and that the portion of it that is that portion of our universe which I observe will continue to exist even if I type squee.
squee.
Oh sh--
-- IANAL, this isn't legal advice, and definitely isn't legal advice for you. Also, Squee!
There are experiments in progress to determine if that is true or not, you have a functioning crystal ball?
You know, my 11-year-old son said something kind of interesting last night, on this subject. This month's article in Scientific American is about multiverse theories, and he asked me (paraphrase), "If the universe is contained among a bunch of other universes, and the universe is expanding, isn't it possible that the other universes are exerting pressure on our universe as it's expanding?"
I'd never really thought about that before, and it may be an unanswerable question (along the lines of, "what are the multiverses contain in"), but I thought that was an intriguing thought.
Sometimes it's best to just let stupid people be stupid.
The multiverses are hypothesised to have been a part of and able to interact with our universe in the past, but not now. The scientists wish to see if there is any lasting imprint on our universe from that past time
We are looking at the dents on the inside surface of our universe made by something that bumped into it from outside, way in the past.
And our laws of physics hold only inside our universe, and only after a certain time since the Big Bang. Before that time, anything could have happened. This is one hypothesis we can check.
My question is how they're supposed to tell what caused a particular distortion in the background radiation. A quick look at the COBE plot shows it to be a swiss cheese. So how do you differentiate between multiverses and sharp sticks poking into it?
That's what she said. You mom says that "she" says a lot too though. She also says "hi".
which is totally what she said
Only if we can devise another test to show that the other universes experienced the big band at the same time as us.
The point is that it isn't our space. That two manifolds can influence each other in some way doesn't somehow make them the same manifold, any more than two balloons colliding suddenly share the same internal structure.
This is pretty basic cosmological principles here.
The world's burning. Moped Jesus spotted on I50. Details at 11.
Complete with Les Brown and his Band of Renown?
Multiverses are considered one viable interpretation of quantum mechanics, why pass up a chance to check it out? Next to cost of another resource or power war against a brown-peopled non-christian country, the cost will be minuscule and no one will get hurt.
Well, I don't want to pay for any of the roads you drive on, or for the police and firemen that protect you.
So there.
(See how that works?)
The problem was that the Jeffersonian-Madisonian state tore itself to pieces and Lincoln came along and had to redefine it so there still would be a United States. Look at pictures of the Civil War. There's your fucking Libertarian state, lying their in ruins.
Libertarianism doesn't work.
The world's burning. Moped Jesus spotted on I50. Details at 11.
Well of course you wish that, because you're a selfish sociopath like all your fellow Libertarians. Well, actually, most of them are just plain stupid. I haven't decided whether you're clinically dangerous or just clinically moronic.
The world's burning. Moped Jesus spotted on I50. Details at 11.
In the same way the router that sits in most living rooms is called a "cable modem."
It's not technically accurate, but most people know what it means.
It only gets confusing when discussing philosophical issues conflate the definition used in one realm for the definition used in another realm.
then move to Somalia, you'll love it
Probably not so long ago, someone probably told the person experimenting with agriculture to stop that nonsense, and go find some nuts to feed the tribe for a day.
The economy was built in all sorts of ways. One of the chief ways from WWII onward was via defense contractors.
Oh, I forgot, you're the chronically confused halfwit who probably thinks the taxpayer didn't pay for the invention of such critical items like the Internet.
The world's burning. Moped Jesus spotted on I50. Details at 11.
This can't be right, how can we, "inside" our own universe observe anything else "outside"our universe? Wouldn't anything we observe withing our universe be our universe?
We can't, and it would.
What we would hypothetically be observing is the effect, in our universe, of interactions with another universe. Things in our universe from which we would infer the existence of others.
It is certainly possible that there are interactions between these universes that are not possible within them, and vice versa. For example we live within a (nominally) 4-dimensional space-time. This bubble of space time could interact in a higher dimension with other bubbles of space-time, having an observable effect on the nature of our space-time bubble, but not allowing us to directly look across into the other.
If we expand our notion of "universe" to include these extra interactions and ergo anything capable of producing them, then sure we've automatically ruled out any kind of falsifiable multiverse, because if we can observe it then it's not a multiverse, and if a multiverse exists we can't observe it. By definition. Meaning, not with any consequence for reality.
Meaning, it would still make sense to look for indications in the CMBR of such interactions, regardless of what you'd call it if they were found.
The enemies of Democracy are
Wow, you're just making it up now. Typical Libertarian. Go back to jerking off to pictures of Ron Paul, and leave serious historical and economic analysis to people who don't treat politics and economics like some sort of a religious statement.
The world's burning. Moped Jesus spotted on I50. Details at 11.
Morgan Freeman already told me all I needed to know about this a couple of months ago. Start around 14:14 in the video for the relevant info. Seriously - it's worth watching.
Person who doesn't understand something monumentally complex claims it can't be true, news at 11.
Stop taking the literal mean of the words which are just an abstract way to explain something incredible complex. If they jsut laid out the math and said 'there you do, that's why' would understand it?
OTOH, anyone who thinks that video in correct probably can't think more then two steps anyways.
The Kruger Dunning explains most post on
mumbo jumbo... OK, clearly you are a troll or an ignorant knuckle dragger.
The Kruger Dunning explains most post on
Two arbitrary lines in a 2D plane will meet with probability 1.0.
Two arbitrary lines in 3D space will meet with probability 0.0.
What you should be considering is:
Two arbitrary lines in a 2D plane will meet with probability 1.0.
Two arbitrary planes in 3D space will meet with probability 1.0.
Two arbitrary cubes in 4D space will meet with probability 1.0.
I don't think you listened to what he said, and your snarky and denigrating remarks are not constructive to a really interesting conversation we could all be having. This is most certainly not an issue of semantics.
The multiverse theory, as I have always understood it, posits that for every possible "choice", universes are created to express each on the possibilities, or "choices". This could be purely causality, or could be free will. Who really knows.
However, and this is not semantics, a universe is generally defined as " the totality of everything that exists".
If we use that definition, then he is correct about this being nonsense because then every newly created universe is in fact splitting into two universes. Quasi-Mitosis on a grand scale if you will. If this is true, then we have been expanding at an exponential rate since the beginning of the universe itself, and all of these "bubbles" are in fact, part of a single universe.
If there is a center bubble universe, it must split into two. So do all the other bubbles simply get pushed out of the way at speeds clearly above the speed of light itself? Think about it. In the space of a "choice", countless "bubble" universes must move to make way for the two "bubbles" that just got created.
It really is nonsense.
The multiverse theory, as I have always understood it, states that new universes get created. This strongly implies, by the definition of the words, that no interaction is possible between universes naturally . If we can travel from one universe to another universe, it won't be through conventional space travel, wormholes, or space folding, since the two universes are not actually connected.
I am more willing to accept the possibility that there are multiple, if not infinite, big bangs going on in the universe. What we understand to be the universe is really just a cohesive collection of galaxies and spaces between them that may, or may not, be in a constant state of expansion and contraction. Perhaps a "universe" expands without stopping and eventually the energy and matter of that collection of galaxies collides with another collection. Quite similar to how galaxies are colliding with each other now.
Who could ever really know?
I just know that roman_mir has a pretty damn good point, and I would hardly call it pedantic and solely based on semantics. There is some logical reasoning behind it, and if we are going to keep language and terms consistent in science, then this whole idea is nonsense on the face of it.
Perhaps a simple analogy is the search for extrasolar planets.
Although recently some have been imaged directly, the way to usually find them is not to look for the planets themselves.. they tend to be too dim and small ..but to look for the effect they have on their nearby star(s). Be it a periodic shifting in the star's velocity relative to Earth or a periodic dimming of its apparent output, etc.
So we don't observe the planet directly, but by looking for the signs we'd expect a planet to have on something else, we can infer their existence.
http://en.wikipedia.org/wiki/Extrasolar_planet#Detection_methods
The universe started as a point and is expanding. The event horizon of this expansion is the inside surface. We can't see it, but we can see just inside of it. The radiation reaching us from it was sent to us at an instant after the big bang, and has taken this long to get here, even though we started out less than a femtometer away from it.
At least, that's the theory. There's another theory that you can have it your way at Burger King. Both are testable.
I am going to make the assumption that you are living in the US (based on your other posts.)
Considering that the summary says that "UK Physicists" are researching this, my guess is that neither you nor I are paying for this as a US taxpayer.
Two arbitrary lines in a 2D plane will meet with probability 1.0.
Two arbitrary planes in a 3D space will meet with probability 1.0.
Two arbitrary N-1 dimensional slices through an N dimensional space will meet with probability 1.0.
But of course, universes are not lines, planes, or anything of the sort. And the question is not, "Will two arbitrary universes collide," but rather, "What is the average number of collisions a universe will experience with the infinite other universes in the multiverse?"
So what's your point?
"I'm too busy to research this and form an educated opinion, but I do have time to tell everyone my uninformed opinion."
Since the society you described has never existed, not even in the pre-Civil War United States, would you care to describe how you could possibly describe how your ideal society isn't the broken one?
The world's burning. Moped Jesus spotted on I50. Details at 11.
Just finished reading The Hidden Reality by Brian Greene, a respected string theorist. He explicitly mentions mining the CMB data for exactly this kind of observation.
Unfortunately, a planet is too "normal" to be of any use as an explanatory device in situations like this. I've tried using the example of inferring the existence of exoplanets from gravitational evidence to explain how we infer the existence of dark matter from gravitational evidence. But dark matter is "too weird", so even though it's relying on the same force, one is perfectly acceptable, but the other must just mean that our understanding of gravity is wrong.
A multiverse, inferred from evidence in the CMBR and created by a presumably unknown form of interaction? Yeah, not going to help.
But aside from that it is a good analogy about inference. :)
The enemies of Democracy are
For those who don't want to read the actual paper: they conclude that the average number of detectable collision events is <1.6, with a 68% confidence. Or to put it differently, the data is consistent with there not being any detectable collisions at all, and the number is certainly no more than a handful.
They should be able to say more once they get new data from the Planck satellite.
"I'm too busy to research this and form an educated opinion, but I do have time to tell everyone my uninformed opinion."
You've now proven you know nothing about physics, economics, or American history. That's quite an accomplishment for one thread.
that should have been a big bang
"Two arbitrary lines in a 2D plane will meet with probability 1.0."
y=1
y=2
Huh?
Multiverses are considered one viable interpretation of quantum mechanics, why pass up a chance to check it out? Next to cost of another resource or power war against a brown-peopled non-christian country, the cost will be minuscule and no one will get hurt.
Because they aren't really checking it out. No matter what they find, it will neither confirm nor deny the plausibility of the multiverse interpretation. If they do find the distortion in CMB they are looking for, it only means that the multiverse hypothesis is one possible explanation for it. If they don't, it doesn't prove that the multiverse hypothesis is wrong. It isn't even really evidence of it. They may as well say they are trying to prove that god exists by looking at the indentations in the CMB where he gripped the universe and tossed it in the waste bin after finishing it.
The authors even say this in the article - their data neither confirms nor rejects the hypothesis.
I also like this bit -
Basically, they've got lots of data but no real way of constraining what they are looking for - so they have developed an algorithm to go looking through all the data for all different sizes and shapes of anomalies, and wonder of wonders, they found a fit. If they bring a statistician or ten on board I might begin to give some credence to their methodology, but this very much sounds like a fishing expedition (but it's okay; their algorithm is advanced and won't get fooled like those other algorithms people use). Look for enough patterns in any given set of data and you will get a hit for any given level of confidence.
You're assuming that the abilities that make for a good cosmologist are the same as those of a good climatologist, politician, or genetic/agricultural engineer. They're not.
That's a common science fiction/fantasy theme (and so far as I know, nothing more) and not at all what they're talking about.
That is entirely semantics. The article is saying is that everything we've been considering the entirety of existence--i.e. the universe--may just be something that exists in a bubble beside other such bubbles with similar contents. You're complaining, not that they're wrong, but that instead of saying our universe is beside others in a 'multiverse', they should have said that 'the universe' might be much bigger than we thought and consists of lots of 'bubbles' that contain discrete regions similar to what we currently consider to be the universe but may have different laws of physics.
Also, there was no mention of universes splitting; I can only assume you got that from that choice-based multiple universe theory you thought they were talking about.
When someone says, "Any fool can see
Try reading just two more sentences...
If there is even a hint of order in the cosmic microwave background radiation then there is only one possible conclusion and that is that there was an intelligence at work in the creation of the universe. What other possible explanation could there be?
"...trapped in the muck like footprints, of where our universe banged into others."
This may be true, depending on the definitions of the (perhaps metaphorically used) words "trapped", "muck", "where", "universe", and "banged".
Also, wasn't the same phenomenon cited as evidence of structure that existed "before" the big bang by someone else recently? Roger Penrose?
Equine Mammals Are Considerably Smaller
Two arbitrary lines in a 2D plane will meet with probability 1.0.
Two arbitrary lines in 3D space will meet with probability 0.0.
(In each case, the exceptions are vanishingly few relative to the norm.)
Of course, given one arbitrary line in 3D space there are an infinite number of (non-arbitrary) lines that intersect it.
I guess it all depends on your arbitrariness.
Look,
If you wanted to observe multiple universes, I wish you'd have asked me earlier, mate. I'd have introduced you to my neighbour, Benny "The Shroom" Colforth.
"Flyin' in just a sweet place,
Never been known to fail..."
it's like saying when you try to extrapolate the end of the universe you say the...if the universe is indeed infinite then how what does that mean? How far is is t...is all the way and then if it stops what's stoppin' it and what's behind what's stoppin' it, so what's the end, you know, is my...question to you....
. .
Why doesn't the submitter link to the actual articles? Why don't the editors make sure those links are included before the story is posted? Why is there at all a link to ScienceBlog? All relevant information the blog post contains would fit into a Slashdot summary.
Does anyone have the links to the papers so we can actually read about this work?
Swedish plasma phys. PhD student; MSc EE; knows maths, programming, electronics; finance interest; seeks opportunities
cubes are not the projection of planes in 3d space
regards.
After all it's quite possible that multi-verses don't exist as separate entities but as overlapping entities. Even each possibility being expressed by the same energy but phase shifting in and out of different universes. Quarks being a snapshot of energy as it pops into and out of our universe along its geometric progression. Could explain our problem of measurement as well, when we confine energy to where we expect it to be (our universe) we can't know all its possibilities, likewise when we know what it is capable of we no longer know which universe its in.
Oh god, let's just hope that i don't start over-using primary colours, bold, and start talking about cubes and the natuew of time.
Give it a rest syntax/grammar nazis i'm typing this on my n900.
Don't complain about syntax, grammar, or spelling. There is no.hell like input on android.
Two arbitrary cubes in 4D space will meet with probability 1.0.
Two arbitrary cubes don't necessary intersect even in 3D space, why the hell would they in 4D space? The word you are looking for is not "cube" -- more like "3 dimensional subspace."
You could apply your objections to any law of science, that the model is false and an alternate explanation is possible. Regardless of the merit of this article's theory, there are many benefits to searching for patterns in the CMB anyway, as it was made during a very significant event in our universe's formation.
The universe is space that contains matter. If there were two, and then they bumped into each other, the only interaction would be when the matter floating in the space of universe A collides with the matter in universe B. I doubt this would create a uniform disk-like collision pattern as the matter in our universe is not dispersed that evenly. If universes are within bubbles, where did that much soap come from and why is there still so much dirt?
Philosophical Theory: Not to be taken literally
The Idea for a packet switched network came from a circuit switched network? No, no it didn't.
Also:
Baran developed the concept of message block switching during his research at the RAND Corporation for the US Air Force into survivable communications networks, first presented to the Air Force in the summer of 1961
Well shit. What was your argument again?
The multiverse theory, as I have always understood it, posits that for every possible "choice", universes are created to express each on the possibilities, or "choices".
Here's how you can test that theory. It's the Schrödinger's cat experiment, except YOU are the cat. If there are multiple universes where each possible outcome occurs, then now half of them have you alive and half have you dead. Of course, *you* will only perceive the alive half. Repeat until you reach your desired level of certainty. Of course, that doesn't really prove much for most copies of the rest of us, since we'll all mainly be in universes where you are quite dead.
(Author not responsible for dead experimenters)
Evidently who is not a smart ass has already thought of this: http://en.wikipedia.org/wiki/Quantum_suicide_and_immortality
This assumes the leading edge of the matter and radiation in the universe have reached the surface of this "bubble" and that the bubble isn't expanding in and of itself ahead of any sort of detectable edge.
Think "bubble inside a bubble".
The inner bubble represents the known universe, background radiation, matter, etc. The outer bubble represents the actual edge of our universe.
Now imagine being able to put a needle through the outer bubble and into the inner one, then introduce more air. The inner bubble gets bigger, but so does the outer one.
Chas - The one, the only.
THANK GOD!!!
That's a common science fiction/fantasy theme (and so far as I know, nothing more) and not at all what they're talking about.
I read the summary again, and you're right. They are specifically redefining the multiverse and then proposing a test. However, the multiverse is not a common science fiction/fantasy theme. It is used in science fiction, but first appeared in "religion". It's quite old. Although it started more philosophically, in recent times it did change its name to the many-worlds theory and is also known as the quantum multiverse theory.
Most people just say multiverse and don't add the quantum.
So I am speaking of science here and the mainstream definition does not include "bubbles".
I was not arguing semantics though, but the definition of the word, and once again, I did not notice they redefined it. So I get your point.
Also, there was no mention of universes splitting; I can only assume you got that from that choice-based multiple universe theory you thought they were talking about.
No, there is specifically mention of it *not* splitting. After reading the summary again they just say "alternate" and propose nothing that causes "alternate" universes to appear.
Yes, from my understanding of the many-worlds theory and my misreading of the summary, it would have to be universes splitting and pushing away from each other.
In any case, a lot of people will get confused with their use of the word multiverse since it really is commonly thought to be referencing quantum multiverse theory or many-worlds theory ( other posts indicate that), and if you assume that is what they mean, then it is fundamentally impossible.
From a mathematical point of view, this isn't actually true (although it is intuitive). The probability that two arbitrary lines in 2D space will meet is undefined. Going back to basics, there are an unbounded number of possible lines. Without loss of generality, select y=0. (We don't lose generality because we can translate, rotate, and scale the plane to make any other selection equivalent to y=0.) Then the probability that the second line selected meets the first is defined as the number of lines which meet it divided by the universe of lines. Both sets are unbounded, so the probability is undefined (infinity / infinity).
If you'd like to resort to an argument based on transfinite numbers, I don't think it's valid. But it still undercuts the statement. It turns out that the two sets are of equivalent (transfinite) cardinality[1], so I suppose you could argue that the probability is still 1.0. But the same argument applies to arbitrary lines in 3D, 4D, or N-D space[2], so those are also 1.0.
Anybody see any problems there? I'm not a serious math geek, just a professor of computer science.
[1] The set of lines y=mx+b which don't meet y=0 are all pairs m=0, b!=0. The cardinality of that set is equal to the cardinality of the reals. The lines which do meet y=0 are everything else, and has cardinality equal to the set of all pairs of reals. It's fairly straightforward to show by, e.g., interleaving digits of our pair values, that there's an injective function from the pairs of reals to the reals. By inclusion, there's also an injective function from the singleton to the pairs. By the Cantor-Berstein-Schroeder Theorem, this means that a bijective function exists and the sets are of equivalent cardinality.
[2] Lines in N-D space are defined by a set of N real coefficients. We've already shown that the cardinality of the set of reals is equal to the cardinality of the set of pairs of reals. By induction on the number of coefficients, the cardinality of lines in N-D space is also the same as the cardinality of the reals.
--Somebody infect me with a
It *is* turtles all the way down!
schmear of muck. And come on, who but Jewish people or deluded Seinfeld fans use the word 'schmear'. How bloody scientific is this summary. DNRTFA
http://www.acetonestudio.com
"Que" is not an English word.
Nobody has realized that the collision patterns might be from Superboy-Prime punching the walls of reality?
Others worked on more pressing problems, like preventing catastrophic global warming, trying to avoiding using the remaining oil by fighting over it and making sure we are all fed.
Sure, let's throw astrophysicists at economic problems. That's not inefficient and dumb at all. But, wait, we can head that problem off by forcing anyone who wants to be an astrophysicist to instead study something more practical. It's not like exploring esoteric physics has ever resulted in practical applications and the advancement of human well-being. /SARCASM
All that is necessary for the triumph of good is that evil men do nothing.
Ah, I see it. You're quite right, and I see the point. Using pure set cardinality leaves the probability undefined, but this gives a workaround. I'd have some difficult reading to prove whether the original assertion is correct under measure theory, but I suspect it is.
And here's the poison pill to demonstrate how far I missed the boat: the same arguments I used apply to something as simple as picking a number x from [0,2] and computing the probability that x < 1. Obviously that's 0.5, but the technique I outlined would claim it's undefined.
I'm so glad I don't claim to make my living as a mathematician!
--Somebody infect me with a
http://idle.slashdot.org/story/11/08/02/197239/Mysterious-Object-Found-In-Seabed
Table-ized A.I.
I sometimes wonder if a real universe comes out of existence, if only for a brief moment, whenever I dream of my own magical world inside of my head.
What if we're living inside the mind of a supercomputer right now?
...then it exploded.
An Indian-American Hindu committed to non-violent thought/speech/action alarmed by the global explosion of radical Islam
You first state 1D-2D; then 1D-3D, and then extrapolate to 3D-nD, having not modified the primary factor before.
Two arbitrary 2D objects in 3D space will also meet with a probability vanishingly close to 1.0. The same goes, then - if you *can* extrapolate that without knowing all the rules in place in higher dimensions - that two 3D objects will meet in 4D, and two 4D objects will meet in 5D; et cetera.
Thus, if our nD universe is encapsulated in an n+1D multiverse, they will certainly meet, according to your logic.
All of that, however, still assumes that said objects do not move around in the higher-D space. Two arbitrary lines moving around in a 3D plane may eventually meet, depending on their movements; and the more lines there are the more likely collisions become. Now, given that the multiverse is supposedly composed of an infinite number of universes, the probability of collisions is absolute 1.
What a depressingly stupid machine.
Ubuntu users have been seeing it for years
If I understand correctly, this is exactly what some string theorists think the big bang was.
The Tao of math: The numbers you can count are not the real numbers.
Only if we can devise another test to show that the other universes experienced the big band at the same time as us.
I think some of them experienced a symphonic orchestra instead.
The Tao of math: The numbers you can count are not the real numbers.
I think you're here confusing the multiverses of string theory with those of the many worlds interpretation of quantum mechanics. These are completely orthogonal concepts (it's an unfortunate fact that the term "multiverse" is used in both contexts).
The Tao of math: The numbers you can count are not the real numbers.
And people probably said the same about Planck, Einstein, Curie et al a hundred or so years ago.
And yet others wasted their time posting comments on Slashdot about it ...
The Tao of math: The numbers you can count are not the real numbers.
The usual term is "hyperplane". More exactly, in an n-dimensional space a hyperplane is an (n-1)-dimensional subspace.
The Tao of math: The numbers you can count are not the real numbers.
What I accept with much less enthusiasm is government spending on it or anything, actually.
From your other posts, I assume you're in the US, so it's not your government spending the money - it's mine. Thanks for your concern, but I'm happy for them to do so as I think fundemental science research, such as this, is an area that government should fund due to the lack of economic incentive.
If I have nothing to hide, you have no reason to search me
Ah, I see it. You're quite right, and I see the point. Using pure set cardinality leaves the probability undefined, but this gives a workaround. I'd have some difficult reading to prove whether the original assertion is correct under measure theory, but I suspect it is.
And here's the poison pill to demonstrate how far I missed the boat: the same arguments I used apply to something as simple as picking a number x from [0,2] and computing the probability that x < 1. Obviously that's 0.5, but the technique I outlined would claim it's undefined.
I'm so glad I don't claim to make my living as a mathematician!
Actually it is undefined, until you've decided on a probability distribution. In the interval, you'll usually assume an uniform distribution, which gives your result 0.5, but that's not mandatory. It might be that the number is the square of an uniformly distributed random variable from the interval [0,sqrt(2)]. In which case, the probability would be slightly above 0.7.
The Tao of math: The numbers you can count are not the real numbers.
I don't see the problem. All your points seem related to the problem that we need two earth for our resource consumption. Well, these scientists are looking for it!
Infinity over infinity can be well defined. Consider that by your same argument, I could not tell you that half the whole numbers are even. After all, there's an infinite number of odd ones, and an infinite number of even ones. All that matters is that we can define rules to map exactly one even number onto each odd number. Therefore, we can prove that half the numbers are even despite the fact that there are an infinite number of both. We can also prove similarly that 1/3 of whole numbers are divisible by three even though the cardinality of those that are and those that aren't is the same.
Doing similarly with the lines in a 2D plane, we can define rules that map onto each line that doesn't intersect (y = b for your reference line y = 0) an infinite number of lines that do intersect (y = mx + b, same value b, unlimited selection of m). Therefore, the ratio between the two classes of lines (those that intersect and those that don't) is well known even though there are an infinite number of them, and the probability can be calculated to be 1.
I'm just an organic chemistry professor, so it's been a while since I've thought seriously about math. Some terminology may be a bit off, and the style may or may not be textbook perfect, but the general sketch of the proof is solid.
Others worked on more pressing problems, like preventing catastrophic global warming, trying to avoiding using the remaining oil by fighting over it and making sure we are all fed.
Just out of interest, who is actually working on these things? How successful are they likely to be while the rest of the population are working in the opposite direction and moaning and screaming and having tantrums if they find that any of their money has been used to feed the poor, or redress global warming? These are problems of belief - for the theists amongst us, we might call it evil, or if you are a secular humanist, see it as an inherent flaw in the structure of our society. It is in any case not a problem solved purely by science - we already know the problem, and what to do to solve it, we just don't want to.
It doesn't matter in the end with which epistemological view you adhere, as they are two sides of the same coin. If you are a verificationist, you keep doing experiments that will verify your hypothesis until you find one that doesn't. If you are a falsationist, you keep doing experiments that will falsify your hypotesis while you wait for the one that succeed in doing that.
It does matter, actually, in the sense that even if you are a "verificationist", you must design experiments intended to falsify your hypothesis. If you do not, you could be ascending "an endless stair of confirmation" of the wrong hypothesis which a single attempt to falsify could have shown.
One could reasonably state that a properly designed experiment by a verificationist would do that, but that's my point: A properly designed experiment must include a serious attempt to falsify for it to have value as verification. Whereas a falsification experiment inherently provides verification, if falsification fails. The relationship between the two is non-symmetrical.
So sure, once you've conducted your experiment it may not make much difference if you view a positive result as "another failure to falsify" or "more verification". But when designing the experiment, if you aren't thinking like a falsificationist, then you're quite possibly not doing it right.
The enemies of Democracy are
I bet you personally aren't paying for shit, but receiving some government subsidy one way or another and just want others to pay for everything.
I'm gainfully employed and pay my taxes; I'm happy for a portion of those taxes to fund this project - what more do you expect from me?
As to my comments, they are general in nature,
As were mine; I'm quite happy for my taxes to fund fundamental scientific research that has no commercial merit, but expands our understanding of the way the universe works as the private sector has no incentive to do so. Another good example of this type of research is the LHC at CERN. Indeed, I would like a higher proportion of my taxes to go towards scientific endeavour, and less towards things like (for example) over-budget, under performing government IT systems.
If I have nothing to hide, you have no reason to search me
I wonder how silly the guy who found the first black swan felt.
Never mind him. Think how silly the guy who put the black makeup on the swan felt!
-- IANAL, this isn't legal advice, and definitely isn't legal advice for you. Also, Squee!
Back when I was a wee lad, my wonderful maths teacher taught us to consider aleph-0, aleph-1 etc values of infinity as follows...
There is an infinite number (A) of lines of constant y that don't intersect y=0.
There is a larger infinity of lines of non-constant y that do: For each value of y at the y-axis (an infinite number equal to A), there is an infinite number (B) of angles at which the line can be drawn. Thus the first infinity cancels out, giving the probability of an arbitrary line not intersecting y=0 to be A/AB == 1/B == 0 because B is infinite.
Alternatively: for any location in 2d space, there is one line that does not intersect, and an infinite number that do. Probability of picking one that doesn't intersect is therefore zero even though there is a line that doesn't intersect!
qv Hilbert's Paradox.
Justin.
You're only jealous cos the little penguins are talking to me.
This is only valid if you can prove the two A values are identical.
You're only jealous cos the little penguins are talking to me.
Those aren't arbitrary, they are carefully selected to be parallel. Which was his point- almost all lines in 2D would intersect.