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Physicists Discover Geometry Underlying Particle Physics
New submitter Lee_Dailey sends this news from Quanta Magazine:
"Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality. 'This is completely new and very much simpler than anything that has been done before,' said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work. The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like "amplituhedron," which yields an equivalent one-term expression."
Almost there....
Is secretly a complex distributed particle physics computation!
Isn't this similar to the geometric structure that the 'surfing physicist' came up with - the one that predicts a bunch of undiscovered particles? Or is this completely different?
Roll for initiative...
God is playing dice with the universe
Guys, we've been down this road about a million times in physics. Just because a mathematical model simplifies certain calculations, does not mean that the actual underlying physical geometry matches the theoretical model. Mathematicians have been adding extra dimensions to equations and finding they simplify things for years. It doesn't mean we live in a 27 dimension manifold. All direct observations to date point to a 3D universe.
#fuckbeta #iamslashdot #dicemustdie
If this can be independently verified, I think they have just earned a trip to Europe! I wonder how it calculates the Higgs field vs. what the LHC discovered this year.
does the simplification that it mentions, mean that simulations will be way faster? does it in any way affect the n-body problem simulations ?
Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.
These things come up every so often and it always makes me facepalm in a RTFM moment. It is as if none of these advanced physics and mathematics people have ever read or understood why mathematics and physics was invented in the first place. The Greeks invented it to study forms, geometric at first, learning quickly that so much of our human perception is illusion based on these forms. Only later did abstraction of these forms come to be through a great many expressive number systems that have never stopped increasing in complexity to think that analytical quantitative thought has become bloated and inefficient compared to its forgotten origins.
Another excellent example is ignorance on Descartes. Mathematicians and physicists use Cartesian coordinate systems so frequently but have completely neglected the rest of the work by the man that invented it. Temporal relativity, the atomic idea of time later 'pioneered' by Planck, and time itself as merely a manifestation of the flow of consciousness within it can all be attributed to Descartes, but all that Oxford cares of him is his pretty graphs.
If people so high would have taken the time to learn why these thoughts and tools came to be instead merely how to use them, human understanding could be centuries more advanced. Instead we have to reinvent and rediscover ancient issues over and over with new tools designed to solve different problems in ways that require different efficiencies.
I have an impressions that the wall of fundamental laws is reached and further research of particles is useless. This is it. No way further. The impasse.
http://en.wikipedia.org/wiki/Amplituhedron
Since the N=4 supersymmetric Yang-Mills theory is a toy theory that does not describe the real world, the relevance of this theory to the real world is currently unknown, but it provides promising directions for research into theories about the real world.
The whole, "our understanding is a dim view of a more perfect geometry" thing gave me a very Neal Stephenson Anathem shiver.
We don't have a state-run media we have a media-run state.
Time is an illusion. Lunchtime doubly so.
-73, de n1ywb
www.n1ywb.com
xkcd's Purity. In the other hand, can't take out of my head that Kepler originally tried to match that the orbits of the 6 known planets at that time with the shapes of the platonic solids, and this could face the same risk.
I know some of you are thinking this, but it's not, ok.
It's not some complicated mess of geometrical shapes to describe the universe in kaleidoscopic glory as envisioned by a lunatic with a Spirograph.
Sig. Sig. Sputnik
Kepler was right
No sooner do I get over one, then you put a better one right next to me. Bastards.
EARTH HAS 4 CORNER
SIMULTANEOUS 4-DAY
TIME CUBE
WITHIN SINGLE ROTATION.
4 CORNER DAYS PROVES 1
DAY 1 GOD IS TAUGHT EVIL.
IGNORANCE OF TIMECUBE4
SIMPLE MATH IS RETARDATION
AND EVIL EDUCATION DAMNATION.
CUBELESS AMERICANS DESERVE -
AND SHALL BE EXTERMINATED
duh
There is no good reason to assume the universe is simple or elegant. Simple and elegant models can be usefull though. They can make calculations in special cases easier.
It looks like Wolfram was onto something in A New Kind of Science with his approach to replacing complex equations with simple rules.
Even a layman follower of the history of science could have come up with speculation like that.
Just as alchemy eventually led to chemistry the mystics win again. The logic in theology is that God by definition would be the ultimate craftsman. That means no errors and no waste and no undue use of effort or energy.
So just how God make a creation? Obviously endless universes could be set in motion by a science that resembles computer programs. Yes, humanity is nothing but the gorilla with a sledge hammer playing whack-a-mole on a monitor. We do be cyber bro!
Modern physicists have studied all of that, and more.
In fact the physicists I know are also the best read on the classics and have a tremendous breadth of knowledge about many subjects other than physics. Perhaps you should actually get to know them.
And incidentally, most Physicists don't use Cartesian corrdinats. Physicists use whatever coordinate system they need to use depending on the geometry, and the real world is far from Euclidian.
DUH!
I knew this my whole life.
This is either a major breakthrough or utter bullshit. It's too early to tell which. If it's real, it's a Nobel Prize in physics.
The publisher, the Simmons Foundation, is a project of a rich weirdo from Texas.
It looks like Wolfram was onto something in A New Kind of Science with his approach to replacing complex equations with simple rules.
I'd say Plato (perhaps Pythagoras) was onto something when he basically said that math is the fundamental everything of everything. Yep, the guy was wrong on the details, but what damn fine intuitions he managed to have 2400 years ago. No matter what we do we always end up referring back to him...
Conservatism: (n.) love of the existing evils. Liberalism: (n.) desire to substitute new evils for the existing ones.
And now all the textbooks will need to be rewritten. Should make theoretical chemistry, and particle simulations faster and easier, shouldn't it? Can this also be applied in some way to game rendering?
On a side note, I've been wondering when exactly this discovery was going to come.
Isn't an expression required to have two or more terms by defintion?
Lately, for whatever reason, I have been hearing about "sacred geometry" and especially about this "flower of life" figure that appears all over ancient human sites. To me it just looks like bits from the Led Zeppelin 4 album cover...
Sheldon Cooper is going to cry over this..a bright young mind has been wasting his career on string theory with all those superfluous dimensions. And Penny will get the Nobel prize because she's been wearing homemade amplituhedron earrings she created one night over too much Jägermeister with Raj. He'll get "honorable mention" at the ceremony in Norway and start talking to girls as a by product. Howard will be tremendously proud of his girlfriend and screw up the relationship again......and Howard will still not be a Doctor. The big question is whether Amy Farrah Fowler will ditch her now disgraced boy toy and fully come out to Penny or make a play for Raj.
If one assumes that Special Relativity and Quantum Mechanics are correct, and there is no observational evidence that they are not, then Yang-Mills theory, or something very much like it, is inevitable. It arises from the need for conservation of the various charges each force.
Just because you are paranoid does not mean that no-one is out to get you.
Wibbly Wobbly Timey Wimey... Stuff
"Proximity to wonder has blunted our perception and appreciation of it" --Tim Hartnell in 'Exploring ARTIFICIAL INTELLI
It's Plato all the way down...
“He’s not deformed, he’s just drunk!”
Logic. Logic is the firmament. Without it, math is just man's scribblings.
Time must exist, but the argument comes from computational theory rather than physics. Certain complex problems cannot be short-circuited by some efficiency, in that there is no known solution significantly better than try all possibilities. We can do such calculations and arrive at a solution in this reality, and thus this reality is at least as complex as computational models that can solve them.
A frozen hyper-reality with no real time element Time must exist, but the argument comes from computational theory rather than physics. Certain complex problems cannot be short-circuited by some efficiency, in that there is no known solution significantly better than try all possibilities. We can do such calculations and arrive at a solution. A frozen hyper-reality with no real time element simply could not exist without those calculations actually having been run. You can't just find a magical, hyperdimensional film strip with such calculations done already.
This could be some other time axis or higher complex reality in which we are embedded, but calculations must occur, which requires time, even positing godlike oracles and entities.
(-1: Post disagrees with my already-settled worldview) is not a valid mod option.
Why is this any different from the multitudes of other mathematical wrappers of reality?
:wq
The spherical cow in a vacuum.
Have gnu, will travel.
What's ironic about your post is you've only stuck to western science, neglecting to point out how those things were known even millenia before the greeks. Don't be too harsh on people ignorant of history, we all, like you have demonstrated, have blind spots.
I agree entirely. Currently I am contemplating a double major in philosophy and religion, being funded by my computer networking and security work as no one seems to take the study of knowledge, ethics and so on seriously. The field is ripe for better ideas and understanding through systematic analysis of eastern thought that is often mis-categorized as religious studies. My life, computer systems administration, networking, academics, it is all simply the synthesis of new, useful things from already existing tools. It is a wonderful world full of potential.
I firmly believe that time does not exist. It is just a creation of the human mind as we are aware of the past, the present and the future.
Yeah, I know about "time" slows down in a strong gravitational field or if you approach to the speed of light. But "time" slows down for you (which you do not notice of course) because the particles in your body do not have "time" to interact with each other. I mean, they are busy going into a particular direction and cannot go into another one as the resulting speed vector would be greater than c.
If there is no interaction between particles then there is no change in their states and the result will be as if "time" stands still.
The problem is, as you can notice in my explanation, that such words like "change" and "speed" implicate time. But that does not mean time is a real physical dimension. Reality does not execute our equations in order to work.
Government cannot make man richer, but it can make him poorer. - Ludwig von Mises
One of the things the article says is that space and time may not be fundamental properties of nature, but properties that emerge (i.e., are the result of) a more fundamental reality.
Warning: IANAP. But with some axioms, it is possible to reach the same conclusion.
Imagine a simple experiment with an electron source and a detector. An electron is emitted in the direction of a detector. The experiment is set up such that while travelling towards the detector, the electron does not interact. More precisely, in between the emitter and the detector, the electron does not exchange any energy. Then, the electron hits the detector and becomes detected (interaction two).
Has the electron physically travelled in the space between the electron source and the detector? May it be assumed that in between the interaction with the emitter and its subsequent interaction with the detector the electron is physically present?
Obviously, it is impossible to establish that the electron is present between the emitter and the detector without actually interacting with the electron. It is therefore herewith observed that any assumptions about physical presence of the electron in between the source and the detector can not be experimentally verified. More generally, it is observed that the assumption of physical presence of any elementary particle in between two interactions can not be falsified.
Equally impossible to falsify is the assumption that in between the emitter and the detector, the electron in the experiment was not physically present. This assumption implies that (in the reference frame of the observer) the electron disappeared at the emitter and reappeared at the detector, and did not take up any physical space at any time in between. In between interactions, the representation of the electron disappeared and became unobservable. For as far as an observer can tell, the electron disappeared from the universe completely in between interactions.
Since obviously, properties about the electron are preserved in between interactions, the electron must still somehow being represented – i.e., the representation of the electron has clearly not disappeared from the universe.
The notion “observable universe” is therefore being introduced to make the distinction between interactions which can be observed, and the herewith theorized part of the universe that is apparently capable of at least holding a representation of an elementary particle and which can not be observed.
Observable universe: The part of the universe in which an interaction manifests itself.
Let us formulate the following two axioms:
Axiom 1: An interaction is instantaneous, i.e., it lasts for an infinitely small amount of time.
Axiom 2: An elementary particle only exists in the observable universe at the moment of its interaction.
Notice that axiom 1 and 2 are unfalsifiable. Consider the reverse of axiom 2:
Reverse of Axiom 2: An elementary particle physically exists in the observable universe in the time that passes (in the reference frame of an observer) between two interactions.
This axiom is equally unfalsifiable, since physical presence of an elementary particle can only be proven by interacting with it. The reverse of axiom 1, which would postulate that an interaction lasts a non-zero amount of time, is equally unfalsifiable.
Elementary particles have no internal structure and are considered point particles. In other words, an elementary particle does not take up any physical space. If we assume that everything in the observable universe consists of elementary particles, then it follows that all particles that exist in the universe do not take up any space. The aggregate volume of all elementary particles is zero.
Combined, axioms 1 and 2 state that in between two interactions, an elementary particle is not present in the observable universe. A particle only manifests itse
My karma ran over your dogma
Anyone written an article that can explain what the heck I'm actually looking at?
The Slashdot headline, not the physics.
http://www.math.columbia.edu/~woit/wordpress/
My question is - does this get humanity any closer to the point at which I can build my own interstellar spacecraft? If not... why I should care?
An enigma, wrapped in a riddle, shrouded in bacon and cheese
This doesn't necessarily invalidate Feynman's approach. His problem was that he assumed a limitless supply of graduate students to calculate the various reaction path probabilities.
Have gnu, will travel.
The biggest problem with particle physics is that we call them particles when they clearly are not.
So are matter and energy. They're just properties of the (two-dimensional) surface of the Universe. They only look like they're particles/wavicles/waves (from in here) - they're really just dents in the surface of existence (from "out there", whatever that is).
Zelazny must be loving this!
But I'm hoping we never actually prove that souls exist. That's one door I'd prefer to remain closed. If science determined that souls exist, then we'd be figuring out ways to harness souls for energy. And then that'd bring up the whole question of what else is out there in that sphere of reality--and I'd really rather not draw a Nyarlathotep-analogue's attention.
Here's to hot beer, cold women, and Glaswegian kisses for all.
I think we should be told.
Won't any direct observation we make as 3D critters point to a 3D universe? Isn't that sort of inherent to us being only able to perceive 3D?
Nope. Actually there is evidence that the early universe had only one dimension and that the other two have only come into existence as the universe cooled.
http://phys.org/news/2011-04-primordial-weirdness-early-universe-dimension.html
Another paradigm in the string theory paradigm (that cannot predict anything) is not going to earn anyone a trip to certain part of Scandinavia until it is proven.
I would love to hear him discuss this in an our long lecture.
And if you go straight long enough you'll end up where you were.
If one assumes that Special Relativity and Quantum Mechanics are correct, and there is no observational evidence that they are not, then Yang-Mills theory, or something very much like it, is inevitable. It arises from the need for conservation of the various charges each force.
A Yang-Mills theory, based on {pick-your-favorite-group}, may be inevitable. Whether it would be the N=4 supersymmetric Yang-Mills theory is another matter; it won't be.
"All theories are wrong, but some are useful."
Are you serious!? I' m still spending a few hours a week trying to uudecode a gif from abpe! My mom stepped on the phone cord when I was getting one of the parts.
That "article" was made today, dipshit.
Could this really be that great? I remember how difficult quantum field theory was and I have always wished for an easier way to do it (so I could actually understand more of it). But, if these methods have been around since the 80s, why haven't I heard about them before?
So, first stop Wikipedia
"When the volume of the amplituhedron is calculated in N=4 supersymmetric Yang-Mills theory, it perfectly describes the scattering patterns of subatomic particles."
OK, sounds good.
"Since the N=4 supersymmetric Yang-Mills theory is a toy theory that does not describe the real world, the relevance of this theory to the real world is currently unknown, but it provides promising directions for research into theories about the real world."
Oh, crap. So, it's just another toy theory with promising properties which has not been applied to the real world yet? That's not very interesting since there are plenty of such toy theories. It would be really cool if one of them turned out to work for the real universe as well but that seems to be a very hard nut to crack. I personally hope Lisis E8 theory would be the right one just because Lie groups are fun and the pictures are pretty.
Math is a tool, nothing more. The universe doesn't give a damn about math - that's an abstract human model that happens to simplify things for us so we can understand abstract concepts. No, the universe follows its own set of rules and proportion, and we make math to describe it to ourselves.
Seven puppies were harmed during the making of this post.
As the wisdom goes, "You can make it with Plato"
Nope, he is wrong. Fell into the classic trap of 'I know how to apply something therefore it's what everything is'.
What we(humans) have done is invented a way to describe events around with accurate but context specific predictions.
Example:
I have to apples and you have two apples.
I give you my apples. You know have twice as many apples.
But do you have twice as much Apple? Probably note.
If you have 5 pounds of Apples, and I give you 5 pounds of apples, do you have twice as many apples? probably not. Do you have twice as much apple? yes.
Context specific.
The Kruger Dunning explains most post on
...awesome ganja you been smokin'.
This article made me think of the attempts by the ancient Greeks to understand the universe using geometry and of Kepler's Platonic solid model of the solar system.
:)
Maybe in a weird way Kepler had the right idea just at the wrong scale.
It would appear that you don't understand the term "meta-physical". In your defence, perhaps your mind thought one thing and your fingers typed another.
Hint: "meta-physical" does not mean "abstract", "conceptual", nor "representational".
Computers manipulate concepts above the level of abstraction of their substrate (gates, wires, signals, etc) all day long, in the same way that brains manipulate ideas above the level of abstraction of their substrate (neurons, synapses, and both chemical and ionic signals). The substrates of computers and brains are totally different, but they each have a similar relationship with the abstractions that they manipulate.
That doesn't mean that either computers or brains deal with anything meta-physical in actual reality --- they can only do that in films and other forms of fantasy. Both computers and brains manipulate representations of the world, and in both cases the things they represent can be real or imagined, but the representation is very concrete in both cases. You can't manipulate something that doesn't exist, but only a representation of it.
The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.
...And unitarity holds that the probabilities of all possible outcomes of a quantum mechanical interaction must add up to one.
I'm probably being very naive attempting to understand this article that has probably already been massively dumbed down, but, how can the probabilities of all possible outcomes of an interaction not add up to one? Surely they add up to one by definition, otherwise they are not probabilities? For example outcome X having a probability of 1/3 means, on average, you can multiply the number of times you observe the interaction by 1/3 and get the expected number of times you would see outcome X. If the probabilities in your statistical trials didn't add up to 1, doesn't that mean adding up the numbers of individual outcomes observed would give a number bigger (or smaller) than the total number of interactions observed? Obviously it cannot mean that, as that fails basic arithmetic.
I can imagine tossing a fair coin - heads has probability 0.5, tails 0.5, total 1. So now how about a 3 sided coin without unitarity? Let's say the probability of heads is still 0.5, tails 0.5 but it has a third side, bodies that also has probability 0.5 of occurring. That sounds mathematically impossible. It could be a mind-reading coin, where you pick heads and find that then occurs on half your coin tosses. Later you pick tails, and that occurs on half your coin tosses, but when you pick bodies, that also occurs on half of those coin tosses. OK, I give up! Can anyone who really understands unitarity enlighten me please? Is this anything like the uncertainty principle?
Your ad here.
Believing in 'souls' has nothing to do with the 'singularity'
The singularity as envisioned by Kurzweil and others is a complete figment...arising from making disctinctions where no differences are present.
man / machine: that's the key distinction in your line of logic and it is a false distinction...
first, by this logic all of nature is the same as any machine...if our brains are 'machines' then so are bees, flowers, thunderstorms, rocks, etc....this alone renders the distinction useless by your definition of terms...if **everything** is a machine then the distinction is **pointless**
2nd, the universe is more complex than mathmatics can describe by definition....humans invented math to communicate meaning...it is a **reflection** of the universe we see....all of science, even the speed of light itself is dependent on human perception...math will always be limited by the humans using it
3rd, All artificial intelligence is human will expressed by a programmed machine. AI is incapable of doing anything a human didn't decide for it first programtically in the code. just b/c some dude on a grant at MIT says that 'X' defines 'life' in computation doesn't mean you can then get a team of undergrads to program a box to do 'X' and call it 'Artificial intelligence'
is it possible to, one day in the far future, make a machine that mimics the human brain to such a minute detail that human society grants that machine with rights like humans...that sure is theoretically **possible**...but that is a question of politics and material science, not anything to do with the singularity dogma
singularity nuts confuse 'scratching the surface' with 'total understanding'...we've just scratched the surface on how the brain works...psychology still doesn't even have accurate language, and the best neuroscience can do is match brain waves with percieved stimulus...it's in its infancy and no matter how it progresses it will yield nothing more than a description of how the brain works as observed
Thank you Dave Raggett
right...good question
the 'Geometry' to which you refer is an expression of relationships
it tells us how matter and energy relate...which is how physicists say 'how things really work'
imagine a simple ratio: x/y
as x increases, y increases...that can be mapped on a graph...
now thrown in every fundamental particle relationship we've observed, graph it, and it comes up with this geometric figure
it's like using a stencil to paint a 'no smoking' sign vs painting each by hand
Thank you Dave Raggett
Logic just might be empirical....
right and it picks up when the Angel Moroni visits pre-Columbian Native Americans and gives them the formula for the World-Tesseract
yes, I get it...therefor (machination)->alchemy (?) -> lead + machination (alchemy) -> gold
totally makes sense...
lastly, you really nailed me here:
right, in your ridiculously far-flung hypothetical scenario, we could program machines to write programs...which exactly proves my point that AI is all an expression of human choices
in the end it just instructions executed on a box made by humans...doing nothing humans did not tell it to do
glad you agree?
Thank you Dave Raggett
It looks like Wolfram was onto something in A New Kind of Science with his approach to replacing complex equations with simple rules.
I'd say Plato (perhaps Pythagoras) was onto something when he basically said that math is the fundamental everything of everything. Yep, the guy was wrong on the details, but what damn fine intuitions he managed to have 2400 years ago. No matter what we do we always end up referring back to him...
And perhaps Zeno and the Eleatics who maintained that "Space and time can be neither continuous nor discrete. What could they possibly be if neither continuous nor discrete, these are the only options we can conceive of. Therefore space and time must be completely different to how we conceive of them and, perhaps, don't exist at all." (this was the purpose of the 'Zenos paradoxes'.
In the free world the media isn't government run; the government is media run.
Quantum computation won't make a dent in any NP-HARD problem. QC works brilliantly against problems that lie in BQP, but BQP is known to not include NP-HARD or NP-COMPLETE. Some NP problems (like factoring) live in NP and BQP, but all NP-HARD/NP-COMPLETES live outside of BQP.
Check out Richard Feynman's lecture regarding space-time and his analogy of bugs on a sphere. If you tell them that the rule for making a square is to go N units in one direction, then turn 90 degrees and repeat until you complete the square, they would find that they cannot actually make a square. This leads them to conclude that there is "something wrong" with their space.
I haven't actually seen the lecture you're talking about, but just from the description I can already start to understand his sense of humor, in that we humans literally are the bugs living on the sphere. We just don't notice that the squares we "draw" all the time basis are wrong, because we don't draw them big enough; which I suppose is analogous to the issue of physics wierd-ness being un-noticed until you zoom into the really small scale (or into the really high-energy scales).
Wait a second...yeah me to
Psst... the second "o" at the end there just happens to be tucked away in an extra dimension the rest of you can't see. :)
Not so.
Start with fundamental belief. "I think, therefore I am." This is a rational belief, but it is only a belief. The universe would need to be extraordinarily weird for this one to not be true. But it is still a belief.
Every scientific "fact" is a belief. These are educated beliefs, based upon scientific principles, observations, and methods. Yet they are still beliefs. Various scientific beliefs are challenged and changed on a daily basis. Knowledge of what science says still requires belief in those ideas. Action based on these beliefs is still a form of faith, even if it is entirely non-religious.
This article itself is on the cutting edge of doubting particular scientific ideas. It is a weakened belief in the status quo, and an exploration of an alternate theory. That's how science works.
Science cannot be separated from belief. To do so becomes fanaticism or fiction, and ceases to be science.
I won't join Slashcott. OTOH, If Beta goes live, I just won't be back until it's fixed. Sorry Dice.
For any given (specific) NP hard problem, a 1000x speed increase in computation will result in a solution in 1/1000th of the time. It will still need to complete the same algorithmic steps, but it will do them 1000x faster. What it does not aid with is making the problem of N+1 any closer to N in complexity, or making a general solution any more computationally feasible.
I won't join Slashcott. OTOH, If Beta goes live, I just won't be back until it's fixed. Sorry Dice.
It's turtlehedrons all the way down
Table-ized A.I.
Okay...that cannot predict anything TESTABLE.
> Do you believe in souls?
Do you believe in software?
great work by the artist.. I wish an interpretation of the graphic accompanied it tho.. is that art? or a graph of the theory?
Isn't this what the physicists hoping to "test" whether or not the universe is just a huge simulation, were saying would "prove" that theorem?
"Stratigraphically the origin of agriculture and thermonuclear destruction will appear essentially simultaneous" -- Lee
Every attempt to refer chemical questions to mathematical doctrines must be considered, now and always, profoundly irrational, as being contrary to the nature of the phenomena. . . . but if the employment of mathematical analysis should ever become so preponderant in chemistry (an aberration which is happily almost impossible) it would occasion vast and rapid retrogradation....
Auguste Comte, The Positive Philosophy, 1853
Achilles and the tortoise relies on space being discrete. It is essentially a calculus problem in the form of "the limit of distance as time approaches zero". If speed is rate over time, at some point the rate becomes incalculable due to division by zero. Solving introductory calculus problems removes this division by zero and you get an answer - two straight lines which cross. The failure here is implying that time is continuous, when it reaches infinitely small values and eventually zero.
Dichotomy paradox is basically the same thing, the limit as time approaches zero. Time gets cut in half when distance does, turning a straight line into a logarithm with one non-constant axis.
Arrow paradox is based on a misunderstanding of intertia, or moment. Stopping time for the durationless instance does not remove momentum - in fact it is impossible and only a thought experiment.
I didn't dig further - Wikipedia fouled up the others by quoting Aristotle's dissection rather than Zeno. I find one source for your quote - Jethro from sciforums - who lists these as 4 statements that, taken together, cannot be simultaneously true. (or two pairs, it's not clear)
If each is flawed, then there is no paradox. Zeno was brilliant for his time, and thought provoking, but it is pure philosophy and holds no water outside of that branch.
Comment removed based on user account deletion
In case of an electron - there is no "infinite amount of time" between two interactions. - Just because of finite speed of light: 299 792 458 m / s.
Vacuum is not equivalent of nothing just because of the same fact.
In case of an electron - there is no "infinite amount of time" between two interactions. - Just because of finite speed of light: 299 792 458 m / s.
Vacuum is not equivalent to nothing just because of the same fact.
In case of an electron - there is no "infinite SMALL amount of time" between two interactions. - Just because of finite speed of light: 299 792 458 m / s.
Vacuum is not equivalent to nothing just because of the same fact.
This seems to be a breakthrough and I would not be surprised if it would have an impact on cosmology. May be it would be worth looking at the Schwadron Retention Theory and on boundary layers in general: http://de.slideshare.net/ppalme/the-schwadron-retention-theory
probabilities always sum to 1, this is just basic axiom of probability theory. if we wanted to define probability differently, we could have it sum to something else, but why fuck with what is not broken.
Unitarity is property of operators. Since the probabilities must always sum to 1, it means that eigenvalues of operators must be unimodular so that the operators must be unitary.
Unitary operators are nice for other reasons, too.
Anyway, observables are self-adjoint, therefore have strictly real eigenvalues, and operators are unitary, therefore have strictly unimodular eigenvalues, and operators act on observables by conjugation, thereby preserving the strict reality.
if that was helpful, please send vodka to the physics department at the university of florida gainesville
Except. When a mathematical model emerges which massively simplifies something which has previously been hideously complex (as this one does), is both particularly elegant and simple (as this one is), AND works well (as this one apparently does), there is a very strong case for concluding that it is indeed accurately describing the properties of "the underlying reality" it is modelling (whatever that may mean). And in that context, at least until inconvenient reality intrudes with the discovery of phenomena that do not and cannot fit the model, it makes little sense to talk about "the actual underlying physical geometry" as though it is something entirely different.
(As others far more qualified than me have pointed out, one of the most surprising things about the universe is just how good a tool mathematics is for describing it - and how often, the deeper we get into studying something, the simpler and more elegant the mathematics becomes. Respectable physicists have speculated, in all seriousness, that the universe may fundamentally BE a mathematical object - e.g. Max Tegmark's Mathematical Universe Hypothesis - in which case there IS no "actual underlying physical geometry" separate from the maths. But at that point, if we're not very careful, we end up leaving the realms of science, and get trapped in the treacherous quagmires of philosophy. )
The clever bit is that current theories assume unitarity. The nyarlathohedron doesn't assume it, but everything comes out to 1 anyway. Unitarity, like spacetime, are emergenct properties.
Which fair bakes my noodle.
It's okay guys; just shout "Four-dimensional Time Cube!" and give over to the delicious madness.
Can somebody explain the classical two-slit quantum mechanic experiment in terms of these amplituhedron objects?
If Pandora's box is destined to be opened, *I* want to be the one to open it.
There is a lot to be said for diagrammatic solutions. One of things I enjoyed about Engineering Drafting was the way you could design a road to go up a mountain using only geometry. Doing this with just math and 3D survey data would be incrediby tedious and require a high level of detailed calculation. I was sold on the course when I saw the results.
I come here for the love
This reminds me of Peter Higgs work. He came up with his postulations because the math worked more elegantly. Fifty years later he was proven right. We now have a Higgs-boson - and more elegant particle physics math.
The revelation that particle interactions, the most basic events in nature, may be consequences of geometry
No. Someone invented (not "discovered") a geometry-inspired model that makes certain calculations on particles easier. That's nice if it holds, but it says nothing about the actual structure of the subatomic world. Platonism is so 400 BCE.
Unitarity is an assumption that physicists make about systems. It's a requirement we make of the math: all the probabilities have to add up to 1. If we do a calculation and they don't, then either A) we haven't included all the probabilities, or B) we normalize whatever number we get to 1.
Bazinga!!
Interesting way to look at it. I wouldn't have thought "consciousness" to be particularly awash with ambiguity, given that pretty much every person on the planet would seem to experience the phenomena on a daily basis. "Self awareness" is a little fuzzier, granted, but I'd still have thought the meaning was clear, given the context.
Still, you're quite right in that problem lies with the definitions. Without a definition of "consciousness" (your term, by the way) it's going to be very hard to point to any evidence that the phenomenon arises either "arises from individual particles interacting" or even "from a higher level of organization such as synapses signaling".
So feel free to define your terms and raise the level of the debate. Or if that's too much like hard work, maybe we can argue informally without carping about definitions. Either way is fine by me :)
I like that! I wonder if there are any other poorly defined sentences where we could apply that approach? :D
Great fun, but it doesn't really advance the argument, does it?
At the end of the day, "consciousness" is an intangible abstraction that defies any sort of physical measurement. The only evidence for its existence is either annecdotal or purely subjective. As such I still doubt that you have any evidence to support your assertions over any sort of MAGIC[1], or vice versa for that matter. Absence of evidence is not evidence of absence and all that.
[1] Where "MAGIC" can be taken to mean "self awareness" , "computational processes", "souls", "particle physics" or "Great Aunt Elsie's Fondue Cake".
Don't let THEM immanentize the Eschaton!
Take a look here, for starters: The Bell Inequality.
Well, let us know when this happens.
The term unitarity is not mentioned at all in that article. I see nothing in the article that suggests (to a layman) that the probabilities of all possible outcomes wouldn't add up to one. If they didn't, they wouldn't be probabilities.
I'm perfectly fine with idea that a theory might not account for all possible events and thus is flawed. That isn't saying that unitarity is broken - only that the theory doesn't correspond to reality.
What would it even mean for probabilities to not add up to one? They have to add up to something, so just stick the something in the divisor and magically they add up to one now. Or is the proposal that on an unlucky die roll we just kill the scientist so that he doesn't report his results? Of course, you could just state that as one more possible outcome. :)
I understand Einstein disliked the untidy nature of particle physics and the Standard Model, and wanted to discover an elegant, geometrical explanation for quantum phenomena. Is the current discovery a step in that direction?
First they ignore you. Then they laugh at you. Then they fight you. Then you win. -Gandhi
Can no one see the Hand of God in so Elegant a structure?
It appears reminiscent of another of my favourite contenders, E8 mathematics.
Feels like we are almost on the right track; exciting times...
A whole week goes by and no-one can answer that; I'd say there is 120% chance no one else here understands this either.