I am cheating, as I had help with this recently....
But the Cobe when it confirmed Cosmic Microwave Background Radiation... and confirmed the expanding universe theory, with the most objective and solid evidence in the history of experimental science. It is an elegant example of why science works.... and is endlessly stunning and awe inspiring!
Anyhoo... I just got a shirt with the CMB equation on the back, and on the front it says "Science, it works bitches!"
So good. you guys?
www.xckd.com/store/
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Re: most elegant scientific concept or moment in recent history?
Thu, January 24, 2008 - 7:09 AMKick A-a-ass, man!
I want one too-oo-oo!
::)))))))))) -
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Re: most elegant scientific concept or moment in recent history?
Thu, January 24, 2008 - 8:07 AMThe store is closed ............! Oh well.
For elegant scientific concept I would also consider the basic starting point of quantum theory.
The universe is made of quanta and is not continuous.
I would rate this simple idea as one of our greatest discoveries off all time. -
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Re: most elegant scientific concept or moment in recent history?
Thu, January 24, 2008 - 10:07 AMhuge vector graphic.... takes a second to load
e8 math : the theory that suggests every particle in the universe can be mapped onto every point of the diagram.
upload.wikimedia.org/wikiped...raph.svg
so cool.
new theory, rough theory, but beautiful.
I like to think that the answer to GUT is something more elegant that superstring. -
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Re: most elegant scientific concept or moment in recent history?
Thu, January 24, 2008 - 10:16 AMTough choices.
I can't really determine what "recent" means for me either, so I'm gonna say anything by Ed Witten. I find that he has an almost vulcan-like elegance to his work.
Also Kip Thorne & the late Richard Fenyman have done some very outstanding things as well - though not as recently as Witten (who I think still works at the Princeton Institute for Advanced Study)
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Re: most elegant scientific concept or moment in recent history?
Thu, January 24, 2008 - 10:18 AMI just can't pick one concept at this time, sorry.
There are too many that take my breath away!
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Re: most elegant scientific concept or moment in recent history?
Fri, January 25, 2008 - 9:54 PM -
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Re: most elegant scientific concept or moment in recent history?
Fri, January 25, 2008 - 10:22 PMFabulous! Do you mind if I share the image? -
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Re: most elegant scientific concept or moment in recent history?
Sat, January 26, 2008 - 12:36 AMgo right ahead. -
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Re: most elegant scientific concept or moment in recent history?
Sat, January 26, 2008 - 12:38 AMThank you, most obliged! -
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Re: most elegant scientific concept or moment in recent history?
Sat, January 26, 2008 - 10:37 AMAs a geometrician, I find this amusing,... somewhat interesting, yet the allegations that it represents a monstrous amount of dimensions folded or otherwise creased, is a mathematician's fantasy. I've drawn very similar diagrams from time to time over the years in my analysis of symmetries. It's being used as a 2-d visual prop, although, no doubt there is a 3-d computer model it represents.... and the computer model represents higher dimensions.... but that's as far as the modeling can go. I actually build 3-d models of original geometry. Also, I know there are higher dimensions, but nowhere near what is being theorized. I would call it an attempt to describe the 'string of theories that has led us into this confusion' with evermore elaborately condensed complexified singularities. (actually I'm building a superbly elegant model of my 360-dimensional universe theorem in my backyard.... it's a case of measuring stick envy) -
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Re: most elegant scientific concept or moment in recent history?
Sat, January 26, 2008 - 10:58 AMWhy the 30-fold division? That's the key to understanding the concept. I've played with much higher divisionism to attempt to create a fully universal diagram, but there are limits to this process.
Do my achievements with supersymmetrical geometry count as "scientific evidence"? It would appear that other people with a stake in the concepts of quantum physics are venturing into a domain where I am one of the world's experts, at least in terms of "Designed & Built" or "designed and buildable". There are people with high powered computer programs generating extremely complex 3D virtual models... and some with 3d stereolithography systems to create very convoluted models. My resources are far too limited to be able to create what I have conceptualized at present. I need "evidence! of interest & support" in the form of money to build in 3-d. Evidence!
Art is an essential element in my approach that is generally overlooked by purely mathematical interests..... yet art is part of the equation of supersymmetric elegance & aesthetic consciousness that sets my approach apart from others. Art (creative aesthetics) is the solid and sustainable path towards full integration of concepts into consciousness. It is the subtle element of consciousness which is the essence of the greatest and most intricate system of creation.... life and biospheres of life such as this one we are seeing being eroded by humans who dismiss aesthetics as "superfluous & illusionary".
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Re: most elegant scientific concept or moment in recent history?
Sat, January 26, 2008 - 11:19 AMWhat you are looking at is a, as in one of many, projection of the E8 group, with lines indicating relations between the nodes, onto a plane. This is really no different then looking at a shadow of a person. As for what it means in relation to physics, we have theories. What we do know is that subsets of E8 are important in explaining the relationships between elementary particles. -
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Re: most elegant scientific concept or moment in recent history?
Sat, January 26, 2008 - 8:01 PMCan you direct us to a site that explains the logic behind E8, without requiring us to be fluent mathologists? If it's going to be a truly universal theorem, it Has to make sense to other levels of consciousness outside of that possessed by left-brains trained in symbolic language .....there must relatableness to actual realities, even if those realities are partially or totally of an aetheric-energetic sort. The same holds true if we are speaking of interdimensional relationships-dynamics, which tend towards aetheric, rather than material physics. Is this strictly a way of explaining the 'relationships' between elementary particles?
Now for the jokey serious ..... can we call some particles "togethericles" ? If so, maybe particles would be more accurately called "aparticles".
(Is this where I get the George Carlin Award for Physics?)
brood-moody footnote: How is it we can understand so much about the basic nature of reality, and yet are compelled to live under such unsatisfactory circumstances? We know enough to make our own forms of power and money. Free energy technology has been trying to surface since the early 1900s, yet it is still regarded as a violation of an arbitrary law of physics since that law fails to do more than describe closed and limited systems of mechanics.... and that's just one excuse used by "thems thats got all the monies & power" to not even consider granting patents and do bad things to people who challenge oil interests.
But I digress...... if you want to go deep into this E8 group with someone who knows their way around geometry, I'm all: punch a link and see if what I throw at it sticks to the wall... -
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Re: most elegant scientific concept or moment in recent history?
Sat, January 26, 2008 - 8:08 PM"If it's going to be a truly universal theorem, it Has to make sense to other levels of consciousness outside of that possessed by left-brains trained in symbolic language .....there must relatableness to actual realities, even if those realities are partially or totally of an aetheric-energetic sort."
That is a very Ego-centric line of thinking, Leslie. Why should it matter to the universe, if a bunch of monkeys can understand its nature? -
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Re: most elegant scientific concept or moment in recent history?
Sat, January 26, 2008 - 9:13 PMI acknowledge I have an egoic level of consciousness, as well as many orders of magnitude of higher levels of consciousness with which I keep the whole system of my mind in balance. Only by way of unbalancing, which is side-effect of unnatural ways of living and thinking (witness the world of human dysfunction), does one fall into egoically directed consciousness. Ego is a defense mechanism which should not be overexercised. Humanity possesses all the tools for potentially realizing divine nature. We are the means by which the consciousness of the universe is able to awaken to its own full potential. The universe itself is the creation of divine beings (aetheric) of essentially humanistic form (overall and primarily) . That very divine awareness may take incarnation in these amazing but fragile physical vessels, whose apeish tendencies anchor us in this biosphere and link us with all its lifeforms. -
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Re: most elegant scientific concept or moment in recent history?
Sat, January 26, 2008 - 9:20 PM"The universe itself is the creation of divine beings (aetheric) of essentially humanistic form (overall and primarily) . That very divine awareness may take incarnation in these amazing but fragile physical vessels, whose apeish tendencies anchor us in this biosphere and link us with all its lifeforms."
Jon, thiis total BULLSHIT, man. I am sure if some Christian was doing this shit, he would have been booted long ago. What the hell kind of Moderator are you? -
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Re: most elegant scientific concept or moment in recent history?
Sat, January 26, 2008 - 10:20 PMI'm not parroting any doctrine, I'm speaking from direct personal experience and knowledge. It has nothing to do with any religion per se.... religions may speak of spiritual matters, and hold some related truths,.... as well as many distortions. I'm speaking of my consciousness, which is more similar to that of other humans than it is different. If consciousness is to be segregated from this discussion... there will be neither discussion nor anything with which to do so. The notion we are nothing but monkeys and the universe gives not a rat's ass about what we think..... smells of bovinity to me. One can live in as limited a field of being as they choose, and invent the physics that define the cage of limitations thereof, .... and the universe may oblige them even as it grants bliss to those who prefer to live in blissful dynamics,.... bliss physics, verifiable through the consciousness-directed evidentiary findings of quantum physics experimentation. But we're in this together, so when the vibes turn nasty,its better to spell out the reasons for discord than to be pushed around by that from whence it may emanate. Savvy? -
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 12:50 AMPerhaps some well-establish physicist should make this elegant postulation :
There is no consciousness without consciousness. There is (for all practical purposes), or this is, not a universe operating 'sans consciousness' (or in a purely mechanistic manner) unless one is willing to assert that we scientific aspirants have no real consciousness ... which some may, but which the likes of I will look upon as the antithesis of reality. That there is not a totally physical universe (devoid of non-physical existence) seems apparent. To equate sheer physicality alone with that state known as "Existing" is proven to be illusory, given that the roots of that very physicality reduce to non-physicality in essence, yet existence persists, and plays into and out of the physical realms.
Consciousness is non-physical, yet it is existent. There may be physical manifestations connecting to consciousness, yet the essence is more than just electrical activity in a brain. Even those who would call electricity 'consciousness' would only do so in terms of brain electricity. Does lightening and electrical power then possess consciousness? The electricity itself would not appear to be fully conscious as what we experience as our own minds... The mind is more than electricity, or computers would achieve self-awareness. In any system of thought.... such inconceivably complex systems of consciousness and being as the human organism would not self arise (not in a quadrillion years) out of a consciousness devoid universe.... except in the rationalistic fantasies of those irrational lovers of pseudologic. It is ridiculously absurd to imagine it all self-assembling into exquisite perfection that is as unmeasurablely sublime as what we see as the fantastic evidence of life around us........ or maybe that's just my brain electricity coding through this system to other brain electricities "out there". A lot of people actually may see the world in this way.... just a perception of their brain activity, the consciousness of which utterly ceases upon cessation of brain function. We are electricity perceiving electricity until the DNA chains fizzle entropically.... and that will be the utter end to anything resembling "awareness". What an indulgence in bleak fatalism. A fountainhead of cynicism. This inelegant and unscientific evaluation of an emotionally fatalistic sort of consciousness of being is the function of the spirit of consciousness stuck within the linear logic zone of the left brain. It's inevitable that in such a complex system as the human nervous system, there would arise syndromes of dysfunction that seek perpetuation of culturally cultistic dominionism over all other human hierarchies; even if logic as the ultimate form of consciousness defies most other forms of logic,.... which would place logic itself as a tool for the use of creative consciousness of a much higher order. The irony of the compulsion towards the Dominion of the Purely Logical, is that it negates all other forms of logic which are "tainted" by appearance of such corrupting influences as "emotionality", "personality", self-knowledge", and "common sense".
Oh how Twisted the mental games may be, yet Mind does not require a body-brain network in order to BE. We call consciousness that is evident beyond the electricity of the body,... Spirit! No violation of science to speak this word and know its truth! Only if there is a call to subjugate the evident science of your personal spirit to another hierarchy,... only then can the accusation of non-science aka religiousity be invoked! -
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 12:53 AM"Perhaps some well-establish physicist should make this elegant postulation : "
dont worry about it, Im leaving this tribe
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 12:48 AMDustin,
Please PM Jon with things like this instead of posting them.
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 12:46 AME8 is a Lie symmetry group as in Lie algebra. Lie algebra is the continuous differentiable version of point groups and fields (mathematics not physics). The short version is that E8 is a set of symmetry operator. When one applies a symmetry operator to something the result looks the same as if nothing was done - sounds pointless at first but isn't. A simple example of a symmetry operators is rotating a cube 90 degrees about its central axis or reflecting the cube through a plane that runs through opposite edges. For a more complete explanation, you will have to learn the math and Lie Algebra is generally considered a graduate level course. -
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 1:22 AMThanks Troy, for your explanation of Lie Algebra, which I grasp intuitively, and in that grasping there is a knowing that I have no inclination towards working my way up into a graduate course just to be able to comprehend what the complete explanation is. It serves the purpose of expressing mathematical functions of a high level of symmetry for those given to this method of exploring the universe. I understand the concept of mathematical elegance and perfection, although I made a judgment call years ago that in devoting oneself to such pursuit, there is a disengagement with the bigger experience of life that for me seemed restrictive and imbalanced, even if for others it might be the bee's knees.
As far as whether we can interpret it into terms for the less mathematical approach of understanding 3D and higher symmetries of existence by way of both 2d & 3d geometries (with some extrapolating into several higher dimensions).... and do so without violating the base knowledge represented in Lie Algebra,....... remains to be seen. I'm of a practical, as well as aesthetic, mindedness, so my interest is in exploring the actual creative potentials of geometry & symmetry more than exhausting the systematic algebraic knowledge base in search of an Eureka that only thorough facility with, and familiarity of Lie Algebra can potentiate. My personal view is that I've chosen the far more fun, meaningful, relevant , and useful path, but others may not see it as so and resist my enthusiasm for building sculpture, giving voice to my own geo-theorizations, and the like. Even so, the merits of fiddling with solid geometry rather than algebra may prove to be substantial. -
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 3:07 PM"Thanks Troy, for your explanation of Lie Algebra, which I grasp intuitively, and in that grasping there is a knowing that I have no inclination towards working my way up into a graduate course just to be able to comprehend what the complete explanation is."
Leslie, if this is so then you are the most intelligent person who has ever lived... there is no intuitively grasping Lie Algebra. Please, ... never mind you would just try to argue with me. -
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 4:12 PMI think, what he means with "intuitively understanding", or is trying to say, better said, is that he got the basic idea of where it might lead - the general direction, so to speak; but, of course, in order to "U"nderstand it, there is only one way - long, long hours, days, and months with (a) book(s). An the earlier one starts the sooner he will get there.
I.E., I think, he meant it in this way: "Where's mount Everest? - It is between China and Nepal. Where's Nepal? - It is between China and India. Oh, I see."
Smth. like that...
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 4:33 PMIf it is impossible to even get an intuitive sense of what Lie Algebra is "all about".... then it amounts to just a highly symmetrical system of relativities that relate to nothing in particular, but "could" fit a pattern as a model of how interdimensionality would possibly map out if it was even understandable in mathematical terms. If something can't be explained in plain English to a point of getting the gist of it (admittedly not getting the full concept without years of algebraic study) ..... I get to go "yeah, its an elegant system that, someone is hopeful, describes more than a lovely algebraic symmetry,.... and has speculated that it describes a 248 dimensional model of the universe due to that multifaceted manifold property it has."
A 248 dimensional universe is an extreme departure from the multi-dimensionality I'm familiar with.... which is more in the range of 8-26 dimensions, depending upon how it is reckoned.
I know hyperbole, and I lived with a theoretical mathematician (Robin Hur) who constructed an elegant system describing a circularity using original mathematical methods.... but he lack the imagination to conjecture what the significance of it might be, so his work was published, but he never got any financial support, and is now destitute. Hyperbole is a survival strategy, and you have to take that into account in evaluating the real significance of a mathematical system that is anything but transparent to outside evaluation by people in a related field (solid geometry, supersymmetry, and aetheric physics) who would have an inkling of what is being described, if anything actual. -
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 9:17 PMDude - are you now attacking a branch of mathematics because you don't understand it and don't want to try?
I'd have thought that with all your supersymmetry aetheric ramblings, you'd be less critical when mathematicians started looking into models involving symmetry in multiple dimensions. It really sounds up your alley - big deal if you don't understand the math language, others do.
Should those who don't understand your language attack your efforts? Quite honestly I wonder what you really mean with half of what you say - does that in of itself mean you're spouting nonsense?
At any rate, nice hijack -
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 10:24 PMI generally am responding in defense to such admonishments as that which you have added to, and rightfully so, Mike, dear apprenticemaker.
I'm all about getting to the truth rather than political posturing, or sidling up with and conceding to the claims being made (premature to any reason for doing so) by the mathematicians whose work strays into territory in which i hold a measure of expertise. Why I'm continually having to defend my character, and remind those that accuse me of hijacking, that they themselves are as much responsible for putting matters offtrack as I, ....has more to do with the gravity of "connecting the dots" in ways that challenge conventional thought, than any deficiency in my demeanor or in the need for me to devote myself to what I consider a bureaucratic system of categorizationings. If there are no explanations outside of this extremely Tedious, (albeit valuable as a technical thought system), and abstract menagerie of purely analytical exploration (for those of an inclination to endlessly explore in such a Ponderously Abstract system) of the endless permutations of possibilities that do not necessarily have direct analogs in actual reality in terms of the Entire Universal System of Being (everything of this universe).... if no one has made more than the conjectures that I have thusfar seen... then my views are as valid (as any others that may exist) in their critical analysis of and to such fair game as E8.
I'm not "attacking a branch of mathematics"..... absurd.... I'm offering valid criticism and perspectives on Output that is being Pushed by what is otherwise an apparently valuable exercise in abstract algebraic exploration which bears the odd name "Lie Algebra". (We are first to ignore the face value that is glaring, yes please) Exactly where have I presumed to "attack" their basic discipline? No, not but a totally Valid critique of that which has Emerged from the cryptic and obscure and declared itself to be something akin to "The Answer" to the question "what is the architecture of this universe?" There may be some validity to some of the concepts, yet there's far too little information being given while we're Supposed to Accept blindly the assertions on faith in the impenetrable complexity thereof.
At any rate, the rate and manner in which I present information is accessible, and I'm accessible to explain it, and I've certainly not called Lie Algebra, or its claim to the Answer to a Very Big Question, "nonsense". On the other hand, that others may understand the math language is no insurance at all that it is more than an understanding of a description of an imagined network of relationships built up out of a partially abstract systemology of a closed and not directly (in obvious ways) co-relative (to less abstract systems of knowledge) nature. Those systems to which direct co-relativeness is implied are highly theoretical in themselves.... something that is easily lost sight of in the need and desire to make sense out of what has become a network of uncertainties. -
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Re: most elegant scientific concept or moment in recent history?
Sun, January 27, 2008 - 11:57 PMok, forgive me - you're not "attacking" something that you do not understand. You are "validly criticizing" something that you do not understand. More fair? :)
Don't worry though - these math gurus aren't trying to convince you of anything yet. All I read from this is a big geeky "hey guys! Check this out - it's pretty neat!"
Far from a "We and We Alone have found the One True Theory of Everything that all you lower humans must now bow down and worship" that you seem to be reading from this...
(what's up with your capitalization anyway? Is there a difference between a very big question and a Very Big Question?) -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 10:18 AM"do not understand" is inaccurate in that I have a degree of understanding, yet lack the information to have a fuller understanding.... and that lack of information is due to the Extreme Opaqueness of this Information System called Lie Algebra.
I capitalize for emphasis and clarity, attributes and qualities which many don't dare to risk attempting due to fear of nonconformity to the Rules of Grammar that forbid such radical behavior. Rules are for those who don't understand natural boundaries ... so they "follow" ,.... and that's a good plan, except that when someone outgrows the rules they may be socially attacked. Hence, if you move towards more expansive and expressive states of consciousness, .... some will find it objectionable.
E8 uses 8-fold symmetries (apparently) which work more commonly with physical-base non-organic systems, and less so with organic and consciousness-of-a-high-order systems.
The universe is a system of systems of systems (enfolded synchronously) ..... and E8 is a system model. Its multi-dimensionalities (which may be multi-dimensional only within frameworks of 8-fold symmetries) are relative to 1,2,3,5,8 systems and their factors. I'd like to see where 7, 11, 13, 17, 19 and up the primes, fit in (not just 1,2,3,5,8 factored by primes, as the underlying structural limitations still hold).
Thusfar I see E8 as tailored towards conventional science, grounded in non-organic determinist modeling. It may serve a purpose of sparking those who are fully functional in & invested in mechanistic science ... and if it takes hold, there will be a need to radically update the concept as it shows its limitations (such as that which I see in the structure). -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 12:47 PMLeslie,
One point we do argee on, is that the language of math often makes it needlessly difficult for many to learn math. On the other hand, that same language carries a great deal of information in a very small package, which is greatly useful to those who use it daily.
E8 is the name of a group; the "8" has nothing to do with the symmetry of the group. 8-fold symmetry would be the symmetry of an octagon. An 8x8 matrix can have a huge number of symmetries because it is an 8-D object.
The problem with saying one has an intuitive understanding of Lie Algebra, is that Lie Algebras allow for more types of symmetry then just rotations, reflections and translations.
To say that one has an intuitive understanding of Lie Alebra is the same as saying that one understands that it has something to do with symmetry groups and nothing more. That is ok, until one expounds (sp) upon what it all means... -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 2:21 PMSo you dispute what Mike has said regarding 8-fold symmetry as a core characteristic? An 8x8 matrix may have a huge number of symmetries, yet they will all have an underlying 8-foldness.... which "misses" and bypasses other possible symmetrical orders. As for as to whether I am capable of intuiting the general purpose, intent, or symmetries of Lie Algebra, I might actually do benefit if someone would explain it better than just assure me that this is the most accurate model yet for mapping every point in the universe. When the Hype gets Mega, I start using my intuition, and it serves me well, even if it doesn't download the whole picture show necessarily. I say if the claims overrun all other territories.... they better anti-up their cards or expect people like me to second guess the sheer brilliance that is supposedly embedded. No doubt it is brilliant, but does it function as advertised, and what could I learn from it without needing to invest years of training only to possibly discover it is either useless for my purposes, or redundant to my own methods?
So, what do we have beyond rotations, reflections, and translations (a term that could use more definition itself) ? Where do curve and spiral symmetries, vortex dynamics, spheres, and such fit into this scheme? -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 2:58 PMTHESE WORDS, Leslie:
<<Rules are for those who don't understand natural boundaries ... so they "follow" ,.... and that's a good plan, except that when someone outgrows the rules they may be socially attacked.>>
Your words.
Thank You for them. -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 5:07 PMThanks Serge for your appreciation.... as too often my words are taken in an altogether different way. -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 5:28 PMSure Leslie. ::))
Life is a school, and this is how we learn. Little-by-little, from each other, from our own mistakes, from those of others.
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 3:49 PM"...I might actually do benefit if someone would explain it better than just assure me that this is the most accurate model yet for mapping every point in the universe."
I'd be interested in that myself... but what the hell do you mean by mapping every point in the universe? E8 by itself is just a mathematical object, there are physics theories that use the symmetries of E8 to explain/predict the forces of nature, well 3 of the 4, at the subatomic level.
"An 8x8 matrix may have a huge number of symmetries, yet they will all have an underlying 8-foldness.... " This is simply incorrect. For example a triangle has at most a 3-fold symmetry.
"... and what could I learn from it without needing to invest years of training..." Likely very little.
"So, what do we have beyond rotations, reflections, and translations (a term that could use more definition itself) ? Where do curve and spiral symmetries, vortex dynamics, spheres, and such fit into this scheme?"
For starters there are inversions. An object who's nodes at (x, y, z, ... how many dimensions you what) have an equivalent node at (-x, -y, -z, ...) is said to be symmetric under inversion.
Translations are exactly what they sound like (look-up the definition of translation, skipping the one about changing from one language to another), they move the system from (x, y, z, ....) to (x+a, y+b, z+c, ...) without visibly changing the appearance of the system. Try this exercise: Take two sheets of graph paper and lay one on top of the other such that the gridlines match, now slide the top sheet over the bottom such the when you are done the gridlines match-up again. What you did is a translation.
There are other types of symmetries: For example, EM has charge inversion (if one flipped the signs on the charges of all objects then one couldn't tell the difference; the same isn't true of mass btw).
Curves are not in general symmetric.
Spirals (helices) of constant radius are symmetric under a combined operation of rotation and translation.
Vortex dynamics: Depends on what type of vortex one is talking about. Dynamics refers to a process of change; unless that process is symmetric with respect to time (and very very few are) then it really doesn't make sense to talk about symmetries of dynamics as a general issue.
2-Spheres, yeh the things we can hold in our hands, belong to the C_infinity point group. They have an infinite number of axis of rotation the preserves their symmetry. They are also symmetric under inversion. BTW an axis of rotation is defined by the intersection of two-planes of reflection. -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 4:14 PMSounds like Calculus III, to me. :) -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 4:23 PMOne sees a bit of symmetry in Calculus but nothing along the lines of what I'm talking about. The study of symmetry groups is an area of mathematical analysis by itself even though it proves damn useful in solving problems in other areas. -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 5:30 PM<<... it proves damn useful in solving problems in other areas.>>
Totally.
We did use it in Linear, in Physics II, etc. -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 7:10 PMThe question remains: Will the twain ever meet twixt the likes of Lie Algebra (& the purely abstract mathematical approach to modeling solutions to problems) and the other, more humanistic side of the equation, ....also called such things as Analytical Creative Intuition (?)
I have an interest in quantum physics, yet am seeing a lot of doors closed to anyone who is not proficient in particular forms of mathematics. One of my best friends is a graduate math student/teacher at UNM, and also one of the few other total raw fooders (besides me) in the Albuquerque area. He, like me, has come to realize the limitations and wrong turns that have been taken in physics in general (along with wholesale dissolution of integrities in the popular culture). Perhaps I'll sort out a lot of issues with his help. Anyone else concerned that quantum physics (as an institution supported by big money interests), and other forms of science, are structurally opposed to involvement with non-establishment approaches, regardless of merit?
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 11:50 PM"I have an interest in quantum physics, yet am seeing a lot of doors closed to anyone who is not proficient in particular forms of mathematics."
There is a good reason for this, namely the advanced mathematics is the language of physics. If one wishes a deep understanding of the subject then one needs to spend the time and learn it. Period, same as any other subject one truly wishes to understand.
"He, like me, has come to realize the limitations and wrong turns that have been taken in physics in general..."
Look, like any other human endeavor, the sciences are full of wrong turns. Unlike most human endeavors it is self correcting even if it takes many years. -
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Re: most elegant scientific concept or moment in recent history?
Tue, January 29, 2008 - 12:25 AMI will maintain that matters relative to quantum physics are discernible without everyone who might have an interest being required to devote themselves to the study of advanced mathematics. The mathematics could be necessary for theoretical work and experimentation, but this is technical specialization .... specialty tools not to be confused with the tools of Applied Wisdom. If the technologists fail to communicate their work to specialists in applied wisdom, but prefer to imagine the special language of mathematics is a wisdom unto itself rather than a technology, then we have grounds for distortions in human values in favor of the mechanistic aesthetic and associated mental orientations. Peer iod -
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Re: most elegant scientific concept or moment in recent history?
Tue, January 29, 2008 - 12:44 AMWisdom comes from knowing when to be quiet...
And yes, people can have a basic understanding of any subject without spending much time studying it but that is all it will ever be, a basic understanding. -
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Re: most elegant scientific concept or moment in recent history?
Tue, January 29, 2008 - 1:36 AMStudy and know yourself first and foremost, and all else may become perceptible in its true light and proportion. -
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Re: most elegant scientific concept or moment in recent history?
Tue, January 29, 2008 - 5:53 AMWho sayes I haven't? -
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Re: most elegant scientific concept or moment in recent history?
Tue, January 29, 2008 - 7:27 AMWho & what, knew & know, is now the opposite of not? -
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Re: most elegant scientific concept or moment in recent history?
Fri, February 1, 2008 - 9:28 AMThat sound like some bonafide frontier gibberish to me. -
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Re: most elegant scientific concept or moment in recent history?
Fri, February 1, 2008 - 10:22 AMIt's certified pallelalian poetics..... if you want to get technical, .......which should be the next thread.... (sort of like "Are you ready to Rumble?") ... "Do you want to Get (transcendently) Technical?"
It's a spring-loaded frontier, and of course you can't really play very well without resiliently dynamic quantum froth of the non-rabid savage kind. -
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Re: most elegant scientific concept or moment in recent history?
Fri, February 1, 2008 - 11:07 AMRight, blanderdash... -
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Re: most elegant scientific concept or moment in recent history?
Fri, February 1, 2008 - 11:21 AMMore like savorysplash. Creativity is the stuff of "creation".... so surreal sequesterations of scienautic naughterisms from the ebb & flow of ecstadynajuicy mentations (as per) could account for said blandpercepts and gibbernegations of what seems well-lusciously viable in any open-ended conjugationary congress of linguisms. Relevance is in the eye of the beholding. (there's an eyewash station in Lab 7) -
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Re: most elegant scientific concept or moment in recent history?
Fri, February 1, 2008 - 1:59 PMusing scientifically imbued poetic nonsense is the first step in brainwashing people into a cult. Worked for L Ron Hubbard, why not others.
You know... looking at the above words I will leave them... but I am done feeding the deconstructionists.
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Re: most elegant scientific concept or moment in recent history?
Fri, February 1, 2008 - 1:59 PMIs this a last word contest?
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Re: most elegant scientific concept or moment in recent history?
Fri, February 1, 2008 - 4:20 PMCoherent wit relevant to the climate and discussion can be poked with the stick of nonsense and associated with widely verifiable nonsense, yet it may not reflect well upon those who do so in apparent disregard for the creative spirit.... not to say this is necessarily the case, but to indicate that such may be the perception amongst some of the subscribers who are here to do more than adhere to a narrowly defined agenda of strict tech to-the-letter talk. If you feel this is a last word contest, simply turn out the light upon completing your final word and we'll know it's time to go home.
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 5:29 PMThe claim that E8 is a system that can "map every point in the universe" is what I read in one of the press releases or articles, not my words, nor does it make sense to me.
As far as the issue of 8-fold symmetry, I think we must be on different pages or interpretations of geometry. I'm not able to make heads or tails of the view you are expressing, with seeming certainty. I mean, yes a triangle has 3fold symmetry, and 8fold symmetry is also predominant when multiplying 8s. Multiply 8x3 and you have both 8 and 3 fold symmetry...... but only by multiplying with a 7 will 7fold symmetry be shared with other symmetry. All I'm saying is this system doesn't tell thusfar how it involves prime number symmetries of 7 and above in its graphic fundamental layout diagram.
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 6:20 PM"As far as the issue of 8-fold symmetry, I think we must be on different pages or interpretations of geometry. I'm not able to make heads or tails of the view you are expressing, with seeming certainty. I mean, yes a triangle has 3fold symmetry, and 8fold symmetry is also predominant when multiplying 8s. Multiply 8x3 and you have both 8 and 3 fold symmetry...... but only by multiplying with a 7 will 7fold symmetry be shared with other symmetry."
First off, you used "all" when you said "An 8x8 matrix may have a huge number of symmetries, yet they will all have an underlying 8-foldness...." which is disproven by the example of a triangle which can't have an 8-fold symmetry.
Next, multiplication does not necessarily imply symmetry. Larger groups can be created from smaller ones, such that the number of elements in the new group is equal to the product of the number elements in each of the smaller groups. There are special rules for how the larger group gets constructed, it is not simple multiplication.
"I think we must be on different pages or interpretations of geometry."
Probably. -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 7:23 PMApparently you are following the rules of math logic, whereas I'm the sort of person who can construct a triangle with both 3fold and 8fold symmetry.... but it isn't a Simple triangle.
So, the implication is that math based on an 8x8 matrix can describe a simple triangle, right? This would be a matrix that enfolds 3ness somehow, not a purely 8fold matrix, unless your definition of a matrix goes beyond my more common use of the term. My geomath work is concerned with real results in terms of 3d realities, rather than virtual mathematical abstractions with virtual proofs, although I try not to make an issue of this because I also have a presence in other dimensional work as well. -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 8:41 PM<<... somehow ... >>
And THAT is what makes A-a-a-all the difference, Leslie.
It's the "SOMEHOW" thing that fundamentally separates "mental diarrhea" from Method. -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 9:03 PMAssuming the somehow is relevant to more than its own self-referentialities.... which is typical of closed systems (the tendency towards excluding other valid approaches that are actually not to be dismissed as "of lesser logic or methodology") There is a tendency with ultralogical systems to fail to accommodate real world systems due to perceived flaws.... all the while failing to appreciate the functional genius of seemingly imperfect methods. I'm sure many of Da Vinci's home-brewed methods and philosophies would be considered "mental diarrhea" in some modern science circles if presented sans his moniker. Beware of swallowing whole prescribed methodologies that are overly structured and inflexible. -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 9:24 PMAgree absolutely.
It is the Ratio of one to another that matters. Too much of one or another and the semiconductor looses its properties. However, if the ratio (read, ablitiy to connect things in the head right in order to know when to stop with one or the other), is right , then we get ... a technological revolution. Yep, no more, no less. -
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 10:11 PMI have an admiration for the work being done in geometry and related fields of topology and dimensional mathematics, along with supersymmetrical systems .... as great advances have been made in our lifetime in catagorizing many of the possibilities for reference (once the information is made available in a far more accessible form than what is for most people a cryptic symbological language).
The technological revolution is fantastic in many, many ways, if we can salvage it from the negative consequences that have precipitated as a side effect.
Any mechanistic system pursued overzealously and without regard for the larger context of such things as effects on the human & natural environment can become a serious problem. This hasn't happened, necessarily or specifically, with quantum physics, as it is not so much a direct influence on the applications of technology. However, a lot of the same attitudes that bear some responsibility for damages caused by the misapplication of technology, in other related forms of science, are apparent in and among those involved with quantum physics. That's why I feel compelled to present philosophical ideas involving issues of 'consciousness' in discussing science and technology. It's an extremely timely issue that can no longer be conscientiously set aside.
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 2:12 PM<<Rules are for those who don't understand natural boundaries ... so they "follow" ,.... and that's a good plan, except that when someone outgrows the rules they may be socially attacked.>>
Oh, boy... speaking of a nail....
These words, in quotes, go straight to my profile.
Thank You, Laslie.
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Re: most elegant scientific concept or moment in recent history?
Mon, January 28, 2008 - 12:09 AMSomething just struck me - E8 makes use of 8x8 matrices to form 64 values. Another cryptic tool being used to unlock secrets of the universe is the i ching, which uses 8 symbols in pairs to form 64 hexagrams
The ancient Chinese were pretty good with math - maybe they really were on to something?? :)
</trippy>
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