Posted on 02/12/2005 4:24:09 PM PST by snarks_when_bored
The space of a 2 dimensional area is flat, a plane. In three dimensions it is a cube. That much is pretty straight forward.
Add a fourth dimension (or more) and you have a hypercube which would look like this if the observer and it were standing still and the dimensions were 4 of space:
If the observer (or it) moved around so that the hypercube could be seen from different perspectives, it would look like this:
Add the perspective of time (space/time instead of just space) and it would look like this:
Getting back to communications for a second, Shannon's model looks at the message space as a sphere - the sum of which would look like a gumball machine before a selection is made by the receiver. That part is very well established in information theory and also as information theory is applied to molecular biology.
Shannon sphere: A sphere in a high dimensional space which represents either a single message of a communications system (after sphere) or the volume that contains all possible messages (before sphere) could be called a Shannon sphere, in honor of Claude Shannon who recognized its importance in information_theory. The radius of the smaller after spheres is determined by the ambient thermal noise, while that of the larger before sphere is determined by both the thermal noise and the signal power (signal-to-noise ratio), measured at the receiver. The logarithm of the number of small spheres that can fit into the larger sphere determines the channel capacity (See: Shannon1949). The high-dimensional packing of the spheres is the coding of the system.
There are two ways to understand how the spheres come to be. Consider a digital message consisting of independent voltage pulses. The independent voltage values specify a point in a high dimensional space since independence is represented by coordinate axes set at right angles to each other. Thus three voltage pulses correspond to a point in a 3 dimensional space and 100 pulses correspond to a point in a 100 dimensional space. The first `non-Cartesian' way to understand the spheres is to note that thermal noise interferes with the initial message during transmission of the information such that the received point is dislocated from the initial point. Since noisy distortion can be in any direction, the set of all possible dislocations is a sphere. The second `Cartesian' method is to note that the sum of many small dislocations to each pulse, caused by thermal noise, gives a Gaussian distribution at the receiver .
For a molecular machine containing n atoms there can be as many as 3n-6 independent components (degrees of freedom) so there can be 3n-6 dimensions. The velocity of these components corresponds to the voltage in a communication system and they are disturbed by thermal noise. Thus the state of a molecular machine can also be described by a sphere in a high dimensional velocity space.
A simpler way to consider how that might work would be to meditate playing Tic-tac-toe on a Hypercube and how a "solution" there might be akin to the message encoding structure of the DNA (not the DNA itself which is double helix).
Fascinating insight, Alamo-Girl! Thank you ever so much for the link -- I'll take the time to do the "Tic-Tac-Toe in a Hypercube" meditation this evening. Then we must compare notes!!! :^)
Thanks so much for writing!
AG:No. I would classify it as the effect of a cause.
Interesting. I am not sure science at this point and time can address what is beyond the cause of the electrostatic forces (which drive everything in biology).
How does one get more of a handle on this cause?
Electricity coupled with magnetism however (electromagnetism) is a field (and wave) which is propagated by electricity and magnetism creating each other. So an EM field would have adequate magnitude for the will to live. Some investigators evidently believe it holds a key to answering the "will to live" question.
However, as Right Wing Professor suggests in post 870, if the EM field were the host field for a will to live per se then we ought to observe repeatable changes in biological systems in the presence of different frequencies, etc. And Frankenstein's experiment would have some basis.
The first step of course is observation, analysis and definition - all of which is already in process. IMHO, it will be a natural extension of the work already proceeding wrt information theory and physics in biology: communications, complexity, autonomy, semiosis, etc.
I think Right Wing Professor's suggestion is right on the money. And so think that something more than "just" an EM field would be required -- although I do imagine that the presence of a "local" EM field may well be the factor that allows an organism to self-organize and govern itself as a unified, dynamic whole. In short, my speculation is the EM field is a facilitator, not source, of the information required for the organism to constantly monitor and modify its internal boundary conditions, to organize itself at the cellular and organic levels, to form "collective degrees of freedom" which, on the basis of research I've seen, is primarily responsible for the organism's ability to enhance its Gibbs free energy at the most economical "cost" to the organism. But the EM field does not itself supply the information required for the organism to be able to do any of these things. The EM field is a field of force, not a field of information.
Which is why I'm with you, Alamo-Girl, in suspecting that a vacuum field is, if not the source, then the carrier of biological information. And to the extent that a hypothetical primary universal vacuum field is the "field of all fields," perhaps it also provides the information necessary for all the other fields as well, thus "informing" matter -- e.g., non-living systems -- as well as living systems.
I read the fascinating "Hypercube Tic-Tac-Toe" last night, A-G. Thanks so much for that link! It was an ingenious study of multidimensionality, starting with observations that are easily made in our 3+1D world within the framework of a seemingly "pointless" game: tic-tac-toe, a game played by two players on a board with n = 3 cells per side in k = 2 dimensions. In short, tic-tac-toe deals with a "planar" reality. Varying k (and also n) leads to some surprising results. The article deals with extra dimensions as a stacking up of planes (each additional dimension regarded as a "plane" engrafted upon the lower-dimensional plane(s) below it. I thought that was a useful way to envision the possibility of extra dimensions beyond our 4D block. And it was interesting to see the behavior elicited by playing the game of tic-tac-toe in higher dimensions. I was fascinated by certain symmetries that seemed to emerge, and also the possibilities for "paired behavior" of the game players.
Anyhoot, the hypercube that emerges from this discussion expresses as geometrical form. To me, the implicit point of the exercise seemed to be that whatever the value of k is, the "highest k" "enfolds" all the other ks, be they of space or time. And this is directly analogous to the idea of a "field of all fields." One would think there is no field more ultimate than the primary vacuum of the universe. But in what "k" that "lives," I imagine will be very difficult to ascertain....
The point is, in my thought experiment, the ultimate k enfolds all within itself; it may be geometrical in form; and it may carry a sort of "cosmic information set" that can be accessed by living beings (e.g., variously called the life principle, the fecundity principle, the will to live). Living beings are living because they are in successful communication with this information source.
Right Wing Professor, I apologize for not pinging you to my posts from 872 forward. I had you in mind, even represented some of what you said and like an idiot, forgot to ping you.
I'm fixing to go paint again this afternoon but will be meditating on all of your points, betty boop - and look forward to furthering this investigation! See y'all later.
But you can't have a forest without trees in the first place, dear Alamo-Girl!
But then you do know how very intrigued I am with the problem of "the evolution of a population of one" -- as Rod Swenson so felicitously terms it in his article, "Thermodynamics, Evolution, and Behavior."
BTW, the crickets do not seem to be doing much chirping right about now. :^) It must be Winter.
Also BTW, I thought the "Hypercube T-T-T" article was truly extraordinary, A-G. On first reading, I think I have only scratched the surface of its meaning. I'll be consulting it again. Thank you ever so much!
It's all crickets all the time here - hopefully the conversation will pick up on the new thread when the article is finished.
Since we seem to always top off a long thread with a benediction, perhaps this will be appropriate for the final conversation here:
Let the words of my mouth, and the meditation of my heart, be acceptable in thy sight, O LORD, my strength, and my redeemer. Psalms 19
And he said, Go, and tell this people, Hear ye indeed, but understand not; and see ye indeed, but perceive not. Make the heart of this people fat, and make their ears heavy, and shut their eyes; lest they see with their eyes, and hear with their ears, and understand with their heart, and convert, and be healed. - Isaiah 6:9-10
Actually a 4-dimensional cube would be just an everyday cube. The 4th dimension being time and orthogonal to the space dimensions.
If it exists for any amount of time then it is 4-dimensional.
PZ is pretty clueless. Because design can be detected and Mt. Rushmore is an example.
There are two worldviews on the subject. One sees three spatial dimensions evolving over time.
The other sees four dimensions, one of which is time - x,y,z and t for time.
The first view allows no additional temporal dimensions, the second does, e.g. Vafa's F-theory and Wesson's 5 Dimensional Relativity, 2 Times.
The second view is also expressed in Max Tegmark's Level IV Parallel Universe:
The Platonic paradigm raises the question of why the universe is the way it is. To an Aristotelian, this is a meaningless question: The universe just is. But a Platonist cannot help but wonder why it could not have been different. If the universe is inherently mathematical, then why was only one of the many mathematical structures singled out to describe a universe? A fundamental asymmetry appears to be built into the very heart of reality.
Tegmark, Max, Parallel Universes, Scientific American, May, 2003
Celebrate by reading "Origin of Species". More like reading Ptolemy than Copernicus.
Waded thru Wesson and Vafa and Tegmark a little, till each spat on my Jib which made me tack away.... Wonder if Jesus considered these possible ramifications.. The human body is a wonderful bit of mechanics.. Most (of them(humans)) in time and history)) are clueless as to how it works in space/time.. It just does.. i.e the arm connected to the shoulder then to the backbone on down to the sphincter..
Humans bodys work fine not knowing how they work (usually).. it don't seem to be required (by God) to know how the body works(exactly).. It does however seem to be a requirement to know what and how the spirit works.. evidence: the Bible(written or oral even experiencial)..
What is required of the "frog in the well"(frog metaphore).. Cause it is certain we are all frogs in wells.. Few, it seems, could possibly understand the "tailings" of human fact mining.. and the "gold" thats been found could indeed be fools gold.. (math, geology, anthropology, even geometry.. etc.)
After a lifetime of wading thru the shoals and swamps and mountain peaks.. nugget hunting.. One thing is/seems certain to me.. When it gets complicated I'm probably on the wrong path.. Jesus does seem to make things "simpler".. as a matter fact he appears to operate on the "keep it simple stupid(K.I.S.S.) principle.
In my readings, he recognizes the human body but leads toward the spirit.. Theologically as in other "sciences" when it gets complicated the odor of BS is detected.. even if not seen.. Cynical?.. maybe..
Two dimensions "this one" and the "spiritual one".. seem to me to be quite practical.. Tacyons may be just a mental construct.. with marginal use.. After all a frog in a well seems to be limited to an either/or duality.. More than two options might be beyonds mans ability to comprehend.. It seems so.. beyond duality man seems to lose track chasing the maze..
Little wonder the Bible is so solid.. The spirit riding the donkey(mankind) is quite bibical.. Could be "the spirit" where all thought is generated will never under stand "this universe".. The human brain can't handle it and the human spirit don't really need to know.. If, as I suspect, human spirits will one day command "gifts" to manipulate "this universe" easily.. "We" won't "have" to know..
Meaning, as the human body operates easily in this "realm".. (not knowing the mechanics of it).. the spirit will operate in the other/different realm not needing to "know" the mechanics of "there".. This human experience just might be a mandatory test to spiritual suitabilty for that "there" experience.. Oversimplified?.. maybe..
But consideing "many" of these types of conversations.. it appears to me people do better with "simple".. All mannar of imaginings can come from that well in the ground(frog).. Counting the rocks on the wall(math) seems to be a common practice then to the shape((of the rocks)geometry).. True, its lonely in that well.. you must do something.. To think that, that, frog is not alone in that well.. the Holy Spirit is there to.. often/mostly ignored.. Theres a duality for you, the frog in the well ignoring the Holy Spirt.. Must think on that today.. Now theres a concept..
Sorry, Wesson drove me to it..
Oh well.... my memory ain't as good as it used to be!
Thanks for this informative essay/post, Alamo-Girl!
Seems that way hosepipe. Seems to have something to do with Aristotle's law of the excluded middle. This recalls what Einstein said: "If two descriptions are mutually exclusive, at least one of them must be wrong."
And yet his friend Bohr tried to point out to Einstein that "even though the wave and particle behavior of an object are mutually exclusive, we need both to completely understand its properties." This is Bohr's famous "complementarity principle." As a "classical physicist," Einstein could never accept this.
At bottom, the question of "either/or" basically goes to the issue of what the observer wants to see. Yet to choose one (is it a particle or a wave?) does not extinguish the other. To insist that it does is to not have the complete description of the system.
Thank you hosepipe for your inspirational essay/post!
We can and do certainly create all kinds of different reference systems and multi-dimensional mathematical equations.
One of the most widely used and generally useful system for physicists in relativity today is called Minkowski space which defines the world in the 4 dimensions of x, y, z, and -t. (negative t)
However, there are a variety of coordinate systems that can and are used depending upon the particular physics under investigation.
Some of the systems have verifiable relevance to real life (Minkowski for instance) where all the dimensions can be measured and proven.
Other systems are multidimensional; and usually have very limited ability to be proven, verified, in the real world. String theory and its variants for instance.
Mathematically we deal witn n-number of dimensions and can make the mathematics do all sorts of interesting tricks, but many of those tricks will have zero truth, or reality, if they could be experimentally investigated (which most cannot).
I personally get a little impatient with the theorists (though I am one myself) who get all wrapped up in their mathematics and may lose sight of the real world. They tend to make a large number of simplifying assumptions, which take their formulas out of reality (but can still illuminate if verifiable)
It is rather like using a language to write beautiful elegant poetry or elaborate fiction rather than using the language to write dull documentaries and non-fiction. both use the same language, it must meet rules of grammar, spelling etc...one defines a reality (and is correct linguistically) and the other defines vast worlds of fiction (but is also correct linguistically).
Just because the math is correct does not make it real. (though certainly at times it does illuminate paths to new realities since it is much more a modelling language than the written language)
So true.. I love Einsteins 2 x 2 = 4.. and if you come up with a different answer you're simply WRONG(this universe).. yet I love Bohr's if you're wrong that says something too.. Reciprocals are so often true in other than Math.. Reducing all to mathematics must be a second reality.. I think Bohr was righter than Einstein.. Albert was counting rocks in the well Bohr was gazing the sky.. Good froggies both..
Thought of the day- "If the bullfrog had wings he wouldn't bump his ass".. i.e. You Must be born again- Jesus...
I suspect we need to look at the molecules that comprise life to begin to measure a "life force".
All fields are measured by their effects on something else which we can then measure. We don't really measure any fields directly.
Effects of gravity are measured by its effects on all matter (which in turn is measure by scales, etc)
magnetism by effects on iron. (measured also by scales for force)
elctrostatics by effects on gold leafs for instance (they seperate based on the amount of charge, one of the simplest oldest staic measuring devices. Or the effects of the electron.
strong force by its effects on hadrons (which is measured by effects on other materials in particle experiments, and of course in nuclear reactions).
weak force by beta decay (which in turn is measured by some other effects on material in particle detectors)
Thus for life force we must look for unique properties of the life elements/molecules that distinguish them from other molecules, with similar chemistries, perhaps silicon based molecules (the popular silicon life form ideas in sci fi which i suppose evolutionary theories suggest should already have been established, but don't exist)
I finally made the time your long (but KISSed!) post, and it was a delight to my heart, as all your posts are, dear hosepipe. Thank you for pinging me to it.
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