Hameroff (see this). To my humble opinion the news suffer from rather heavy hyping. If the observation of the group lead by Anirban Bandyopadhyay about detection of quantum vibration in microtubule scale - their lengths vary up to 50 μm - can be replicated, one can speak about breakthrough in quantum consciousness. The results do not however prove Orch OR, which involves poorly defined vision about quantum gravitational description of state function reduction so that most predictions are just order of magnitude estimates relying on Uncertainty Principle.
The biological half of the theory relies on microtubules and for this side of the theory the claimed finding would of course be a victory. Indeed, there is a meeting in Amsterdam devoted to Orch OR theory of consciousness motivated by this finding (see this) Unfortunately, I could not find any article about the findings of Bandyopadhyay in web. I managed however to find two years old Youtube talk of Bandyopahdyay summarizing earlier experimental results supporting the vision about microtubules as macroscopic quantum systems (see this) to be discussed below.
The findings reported in the talk give support for the general TGD inspired view about TQC and allow rather detailed model in the case of microtubules. The idea is that flux tubes from a 2-D coordinate grid consisting of parallel flux tubes in two different directions: say helical Fibonacci flux tubes and their mirror images. Crossing points would be associated with tubulins and the conformational state of tubulin could define a bit coding whether the braid strands defining coordinate lines are braided or not (swap or not). In this manner any bit pattern at microtubule defines a particular TQC program. If also conformations are quantum superposed one as "quantum-quantum computation". The flux tubes could form lattice of type A whereas microtubules form always a lattice of type B - a heavy objection against Penrose-Hameroff model. This picture generalizes in the fractal universe of TGD. One can form layers of 2-D coordinate grids and connect them by vertical flux tubes to obtain 3-D grid defining TQC. Brain is known to have grid like architecture and neurons could by quantum computation produce bit/qubit defining swap or not/superposition of swap and not-swap for a larger scale TQC. One would have fractal of TQCs.
One also ends up with a very crazy idea which turned out to have lifetime longer than the time it took to type it.
- If one piles up 2-D TQC:s one obtains 3-D TQC. In crossings one must have 4 bits to specify whether to swap or not since there are three planes for TQC and 4 pairs of crossing strands (12,13,23,23).
- If one further piles 3D TQC:s in 4-D one obtains 4-D one making sense in zero energy ontology because failure of strict non-determinism is basic element of TGD. Single crossing would in 4-D would involve crossings of four lines in orthogonal dimensions. TGD predicts also space-time regions with Euclidian signature in all scales (lines of generalised Feynman diagrams). I have proposed that any system corresponds to an Euclidian space-time sheet having its size and shape and behaving like quantum system. In these regions the fourth piling might really make sense!
- in 4-D This would make 6 crossing pairs corresponding to 6 planes in which particular TQC takes place - for which one must tell whether to swap or not (12,13,14,23,24,34). This makes 6 bits. DNA codons correspond to 6 bits! Could codons define crossing points of magnetic flux tubes arriving from 4 coordinate directions- perhaps at Euclidian space-time sheets? Could the planes correspond to 3 components of magnetic field and 3 components electric field. Magnetic flux tubes and electric flux tubes in 3 directions? In Euclidian regions magnetic and electric do not differ intrinsically.
This would fit very nicely with the general vision about frequencies as passwords inducing not only directed attention but activities in target - also TQCs! The increase of Planck constant could be associated with the phase transition to A-phase making possible high Tc dark super-conductivity for which evidence is observed! One can even deduce estimates for heff/h=n if one requires that AC photons have energy above thermal threshold: n= fvisible/fAC would be the estimate. For biophoton energies one would obtain something like n≈ 108-109, which pops up in different contexts in TGD framework.
For details see the chapter Quantum Mind, Magnetic Body, and Biological Body or the article "Orch-Or theory of Penrose and Hameroff and new experimental findings about microtubules".
49 comments:
http://phys.org/news/2014-01-symphony-life-revealed-imaging-technique.html
I just placed a microtubule-like net on a flaky Chinese modem to stop it overheating and loosing connectivity to the magnetic noise. Yawn. I think your point about Type A and B nets is a good one. One Goergiev in the Balkans was making bold claims along these lines ten years ago, but the details wouldn't pan out.
Meanwhile, Sennosides are the most symmetrical enzymes I've ever seen, and they are directly involved in peristalsis, the basic biological oscillation in the gut. This goes down to the level of cell hairs, and their rhythmic beating, which drives food particles into the absolutely primitive gut of Parmecium. Microtubules have a mechanical role at this level, so the interesting phenomenon is simply biological oscillators.
Even in the near-perfect 2-way mirror symmetry of sennosides C and D (hardly studied yet), the symmetry is broken by two hydrogen bonds -deviant as always.
To Orwin:
As a mathematician I find difficult to believe that A type microtubules would not be there at all. Probably so does also Penrose.
The resolution of the paradox would be that the 8 resonance frequencies transform B phase to A-phase claimed be optimal for TQC (I do not understand the argument). This would fit very nicely with TGD interpretation in terms of flux tube coordinate grids define basic architecture of TQC.
I have already earlier proposed that quantum critical super-conductivity and hbar changing phase transitions could occur only at specific resonance frequencies. Frequency would take the role of critical temperature. This interpretation seems to apply in this situation!
Hi, inspired by all this I'm slow by slow studying group theory and algebraic topology, and from philosophical background I'm now fascinated by the 'identity element' as definitive requirement for a group as much more refined approach than the brutal and questionable classical law of identity (that Hegel etc. have criticized). The deep philosophical motivation for some basic "sameness" remains also for identity element of group theory, but the beauty of it is that the value or appearance of identity element is context dependent, e.g. depending from operation - "zero" for addition and "one" for multiplication; or in other cases empty set or just identity function. So I'm now wondering and questioning, could we and should we consider (the idea and or function of) identity element of monoids, groups, lattices etc a kind of, or even the most basic "flux tube"? At least it seems that it is also formally correct to state that the identity element of a Lie group (at tangent space) is the flux tube or flux brane to the related Lie algebra. So in all this formal richness we could conjecture that all the ideas of flux tubes or branes goes back the basic idea of identity element of identity element of group theory?!
Matti, AC=Alternating Current here?
To crow:
AC refers now to alternating voltage between microtubule ends. AC potential induces AC current in Ohmian wire. Now the wire would have in conducting state ohmian resistances at its ends and would be super-conducting between them. This is consistent with the finding that the resistance does not depend on the length of the microtubule and is temperature independent.
If one looks only what happens inside forgetting the resistances at the ends of MT and regards the magnetic flux tube carrying the current as Josephson junction, the current would be of form
I= I_0sin( (Qe/h) Int Vdt)
The integral Int Vdt for AC voltage
V=V_AC*cos(omega*t)
would also oscillate sinusoidally and the outcome would be periodic function in time with AC frequency but rather complex. To get some idea you can plot function
sin[k*sin(omega*t)]
[k= QeV_AC/omega h]
Sinusoidally modulated sine with two perodicities.
By adding constant term to potential one obtains
sin[omega_0*t+ sin(omega*t)]
omega_0= QeV_0/h
containing the periodic Josephson correspond to which AC contribution is added.
To Anynymous.
intresting ideas. I have tried to learn category theory and written some chapters about TGD and category theory but I feel always myself equally stupid when I hear about categorifying of mathematics. Certainly in physics already finite measurement resolution allows to speak only about equivalence classes and one should define identify as isomorphism.
If I understand correctly, flux tube could be a physical realisation for the "arrow" of category theory. In any case, for me flux tubes are a manner are a phenomenological notion. Mathematicians usually try to get rid of all "flesh" in their formulations and leave only the skeleton. Category is basic example of this approach trying to leave only the structure. Magnetic flux tube contains a lot of "flesh";-). On the other hand, physicists like in turn are unable to think in terms of abstract structures only so that your idea might have something in it;-)
Thanks Matti. Calling magnetic bodies also flesh is highly observant phenomenology. :)
Structuralism can be taken as critical approach to find underlying generative categories and structures that lead up to formation of structures, and question their validity and function and origin in this dance of forms. Finite measurement resolution relates to presupposition of category of real numbers, which are not universally accepted, and are more like the flickering shadows on Plato's cave wall than "real". We are so used to them it's hard to imagine how it would be without presupposing them, but we do also like challenges :). Likewise, if the category of identity (element, function etc.) was replaced with a codependent dialectic (SUSY of ZEO) and or considered a/the basic morphism (chiral double arrow?!) where would such deconstruction lead? Both mathematicians and physicist respect and value the principle of simplicity and beauty, both create beautiful mandalas and then wipe them out - or should do more of the wiping out instead of getting attached and entangled to what is not... simple.
Yes, what is "flesh" depends on context;-).
I agree that real numbers are too restricted starting point even for the simple needs of physicist. I include both reals and various p-adic numbers together with their extensions as basis of physics and this leads to number theoretical vision about physics as fusion of real and various p-adic physics - the latter interpreted as physics of cognition.
And the notion of real number can be indeed challenged. For instance, the hierarchy of infinite primes inspires to consider an extension of the notion of real number. One outcome is the presence of infinite space of real units identifiable as numbers which are ratios of infinite integers which are equal to 1 as real numbers and have unit p-adic norms. One could think that single space-time point with the degeneracy implied by these units multiplying the coordinate values represents the entire Platonia: number theoretical Brahman =Atman or algebraic holography. One can even ask whether the simple and humble 8-D imbedding space with points having this degeneracy is able to represent the "World of Classical Worlds".
One can also consider the replacement of sum and product for real numbers with direct sum and tensor product for Hilbert spaces. This leads to calculus of Hilbert spaces but unfortunately this goes too much over my simple physicist's head:-) . This has not prevented me to write about this option somewhere in http://www.tgdtheory.fi/publc_html/tgdnumber/tgdnumber.html ;-).
Re "crazy idea". I assume that in this context it is not trivial that the _smallest_ non-abelian group (http://en.wikipedia.org/wiki/Dihedral_group_of_order_6) has six elements, and it is the permutation group of three objects. The idea of being just mental image of set of mental images inside a 4D or nD QC comes often to thoughts nowadays, when thinking in lines of mathematical physics, which according to Chalmers is isomorphic to Matrix (http://consc.net/papers/matrix.html)
On the other hand in the alliterative Finnish measurement resolution in this context, the isomorphism of "kuusi" (sex/six in germanic languages) and "kuusi" (spruce) cannot now be avoided, which associates with saying "joka kuuseen kurkoittaa, se katajaan kapsahtaa" (who reaches for spruce, falls back on juniper). Which saying is a subgroup of interpretations of the famous "kun Aaro Hellaakoski hellaa koski" poem or poppaa-laulu, known also as Pike's Song:
http://oulu.ouka.fi/kirjasto/kirjailijat/hellaak/hauki.htm
English translation:
http://www.fieralingue.it/corner.php?pa=printpage&pid=1137
On this lonely white and green day I'm grateful for you and your blog to share my silly musings. <3
To Anonymous:
I might guess who you are;-).
The Matrix problem is created by many questionable assumptions. Brain (not necessarily in vat) builds all mental image from input feeded directly into it. There is unique reality there obeying some dynamical laws. Brain is isolated from the target of observations creating the sensory percepts. And so on… All these assumptions can be challenged.
*At philosophical level the Matrix problem disappears if one accepts that only mental images exist subjectively. It does not make sense to ask whether the mental image represents objective reality or not. It is only about replacement of
reality with a new one, not about reality. In principle objects of sensory percepts are our creations - the laboratory containing the vat, Tucson, etc… are not "really real".
* Brain might not be so isolated as we think. If one believes that flux tubes connecting perceiver and perceived are necessary for sensory perception, it becomes more difficult to create Matrix illusion. Something must be there. It could of course be secondary representation for external world. Are p-adic cognitive space-time sheets be enough or do we experience them only as thought about sensory percepts?
*The assumption about brain as builder of the entire experience might be wrong. Even direct sensory percepts are impossible for the brain in vat if one accepts that sensory organs contain the primary sensory qualia. And it might be that
sensory percept requires flux tube connection to the target inducing the perception: the flux tube could be correlate for attention.
*Locality of sensory perception is assumed too. Remote sensory perceptions by using sensory organs of some other living creatures might be possible in TGD Universe unless brain in vat is deprived from this magnetic body. This kind of experiences might be stimulated by "hallucinogens" if flux tube connections to magnetic bodies somewhere in cosmos are created. Finite light-velocity would not be a problem is the signals can propagate in both time directions: in principle ZEO allows this. Should w regard these experiences as hallucinations or remote sensory experiences?
I believe in Chalmer's argument "brain", "vat" etc can and should be taken metaphorically, and the point is that the "metaphysical hypothesis" subsumes also mathematical physics (that can be computed?), therefore Matrix is "real" if we consider world(s) of mathematical physics "real". How this relates sadness and loneliness and Lonely God, I'm not at all sure, but perhaps the feeling is a loss of some of the poetry and mystery if all is computable at some level (even if only at the level of QM of tensor products and direct sums of Hilbert spaces?). The red cone at the top of the spruce could be interpreted to symbolize both poetry and mystery, as well as the archetype of Architect/Demiurge/Lonely God of computatable physics/Matrix/Maia. Another closely related aspect of the sadness and loneliness (dukkha) of observer-identity, separated from observed-theorized-created (WCW). And I don't mean that we should consider sadness and loneliness negatively (only), but there is much poetry and beauty in these existential feelings also. To conclude, however intellectually acceptable Matrix of Mathematical Physics may be, perhaps the best argument against that view is that explaining is unnecessary function vis-a-vis experiencing. You know and live that e.g. when you pick your guitar and let music flow. :)
So, some music: John Baez on number five, mentioning among others Penrose, spinors, and of course Ramanujan. :)
Sorry, forgot the link:
http://www.youtube.com/watch?v=2oPGmxDua2U
After five, it may be interesting and entertaining to listen also eight and twenty four:
http://www.youtube.com/watch?v=Tw8w4YPp4zM
http://www.youtube.com/watch?v=vzjbRhYjELo
In the last presentation (with ties between zeta function, harmonic oscillations of a string instrument, etc) the lecturer very deeply comments that 4*6=24
My question now is, what is the implication of the ability to think about 24D leech lattice to WCW and TQC?
And one more question about necessity of reals. The classical motivation for them is that rationals are "incomplete" in the sense that there is a gap at each irrational. However, if I understand correctly, p-adic field alone, without reals, is a completion of rationals. And can be used to prove that a number is not algebraic (ie transcendental): http://www.jstor.org/discover/10.2307/1971488?uid=3737976&uid=2&uid=4&sid=21103444373733
Also, intuitively, the absolute value of p-adics seems much closer to reality infinite primes than the shadow world of reals. ;)
Thank you for the links. I try to find time. It seems that I am loosing time with abnormally high rate. I have not been able to identify the hole where it leaks out.
About 24 D Leech lattice I cannot say anything interesting. In any case, arbitrarily high-D lattices can be represented in terms of algebraic extensions of p-adic numbers, which have arbitrarily high algebraic dimension. Topological dimension of imbedding space poses of course limitations but also here there are tricks.
Both reals and p-adic numbers are completions of rationals and number theoretic democracy requires accepting all of them. The p-adic topology is not natural for the physics of matter, for physics of thought it looks natural: why not use both so that physics can be extended to describe also thought bubbles.
As far measurements are numerical calculations are considered, one must be satisfied with rationals belonging to the interaction of all number fields. And also here finite measurement resolution makes the number of digits a available finite.
To my humble understanding infinite digits applies only to irrationals, but repeating Cauchy sequence "cuts of" after the repetition has become apparent and we know we have a ratio of two integers.
What is the relation of using reals (based on Euclidean metric) and the statement that "TGD predicts also space-time regions with Euclidian signature in all scales"? Does the latter follow by necessity from the former? In other words, when you think in terms of euclidean metric (via reals), you see euclidean spaces?! Similarly, every time when a physicist proudly states that QED has been proven to nth digit of a real number, an euclidian space has been created.
I assume the TGD predicition is not this trivial (or insightful ;)), so I would like to ask, do you mean exactly Euclidian, or would affine spaces do the same trick from your point of view? Better or worse?
To Santeri:
Yes, rationals have periodic binary expansion from some digit but I mean tthat there is cutoff to the length of the period.
Euclidian and Minkowskian signatures
do not follow from using reals or imaginaries although one can get formally signatures in this manner as is sometimes done. To my opinion this trick hides the difference of these geometries. In Minkowskian signature one can speak about wave propagation, in Euclidian signature about Laplace
equation: there is no propagation since one cannot specify time direction.
Euclidian signature results in very strong induced gravitational fields when CP_2 contribution to the metric is so strong that metric changes its signature to that of CP_2. TGD counterparts of blackholes would be Euclidian regions also identified as lines of generalised Feynman diagrams.
I did not mean exactly Euclidian metric: only that the metric in local diagonalised form has four components with same sign: -1-1-1-1 by my conventions. In Minkowskian signature the signs are 1-1-1-1.
To get back to number six, there is also article about Leech lattice on CP4 blog:
http://cp4space.wordpress.com/2013/09/12/leech-lattice/
And I'd like to quote the description of the blog:
"Complex projective 4-space, in mathematical terms, is a set of points described by a 5-tuple of complex numbers (v,w,x,y,z), where scalar multiples are considered equivalent. It is a geometry far more elaborate than our own boring, bog-standard, vanilla, common or garden, three-dimensional Euclidean geometry.
Informally, however, ‘complex projective 4-space’ was used in a joint Anglo-Hungarian IMO training camp to refer to a mythical world inhabited by unimaginable beasts. On reflection, these ideas are more similar than one might imagine: complex projective 4-space is indeed inhabited by such impossible-to-visualise objects as polychora, Klein bottles and an embedding of the E8 lattice."
Interestingly enough, ability to form projective spaces seems to stop at octonions, OPn for n=3 or larger cannot be defined: http://www.math.uwaterloo.ca/~karigian/talks/CUMC-2010.pdf
The above link to presentation of spheres and projective spaces ends up mentioning the open problem of whether S6 is a complex manifold. Could the speciality of A24 (or R24, if we allow reals), isomorphic to CP12 and HP6, if I'm not mistaken, have something to do with WCW limits of mathematical freedom? Rather than simply at A8 or R8, maybe the limit comes against more naturally where commutativity and associativity ends, whith octonions, and (iso)morphically related other projective spaces, e.g. HPn+1 < 8 or <16?
To continue, there are slightly less than 24 aminoacids involved in genetic code, and what unites numbers 5, 6, 8 and 24 is that they are operations of 2 and 3, smallest generative integers that do "something else" than identity element would do:
5=2+3,
6=2*3
8=2^3
24=3*2^3...
following both principles of informational economy and variety.
PS: 24 is, as to be expected, where division comes into play, it is highly composite having more divisors than any smaller number, exactly eight(!) divisors to be exact: 1, 2, 3, 4, 6, 8, 12 and 24. ;)
good lord, you guys are all over the map! at yahoo they tried "emulating" all this stuff with really really terrible facet. they had things called "facets" in each "object" and they had a "self" object and then a bunch of nerds got in a fight about "whether the self object should be deprecated". Suffice it say none of that crap worked out very well and they outsourced it all to india.. where, paradoxically their culture is becoming just as dumb as american culture. Anyway, I wrote some stuff about Clifford algebras... but im so tired... so very very tired. Matti, these time leaks.. .I know the feeling. You know these are classic symptoms of parapsychology(UFU abductions and such) ;) Anyway, I have anecdotal y noticed people taking the notion of time very seriously, as in, being stingy with their own, treating it like some sort of market... just got a new car... the previous owner lived on Euclid Avenue... heh. heh. heh.
Peace,
Crow (SC)
This *just* happened, I walked over to a book shelf, grab the Popular Oxford Urdu->English dictionary and immediately open to a "random" page. It just so happened to be the page that has the entry "barqi rau" which translates as "electric current". what. the. f....
To Anonymous:
thanks for reminding about S^6. I have been just thinking about S^6.
One can think of non-associative generalisation of the notion of group using octonions. In map x-->uxu^*, u any unit octonion, the image of product of octonions goes to product of images of octonions. By non-associativity the resulting group like structure analogous to rotation group for quaternions is however not a group. For instance, for Lie algebra Jacobi identity fails. Baez has talked about this. This pseudo group is topologically S^7, not S^6 as I though for day or two! Double thanks!
In any case, 6-sphere S^6 expressible as a coset space G_2/SU(3). One might ask whether one could imagine alternative for TGD with space-time surfaces replaced with 6-D surfaces in M^2xS^6. If S^6 allows complex structure on can forget this option. This option is excluded for other mathematical and physical reasons too.
Guys, as they say, lattices are all about kissing numbers. Kuß!
Baez on 6: http://math.ucr.edu/home/baez/six.html
With quick search, there seems to be quite a lot of group theoretical approaches to genetic code, as to expected, here is one example: http://www.iconceptpress.com/download/paper/100912111200.pdf
A question came to mind, perhaps related, probably as silly as usual: is it possible to form a group or group like structure of various identity elements and (other) operations in group theory generally, and specifically in genetic code, and if so, what would be the properties of such structure?
Thank you for the link. I looked the article.
It has become clear that genetic code codes also for the secondary structure of DNA and that this coding is inherited by amino acids so that different DNA sequences coding for the same amino-acid sequences code for them different spatial conformations.
The proposed model is based on rather nice idea that each nucleotide corresponds to a particular element of subgroup of rotation group which contains 4-element cyclic groups corresponding to rotations around 3 axes. To my view this fixes the group to be the group of symmetries of cube
(or equivalently tetrahedron). This group is identical with permutation group of 4 elements having 4!=24 elements. A, T, C and G correspond to 4 suitably chosen elements of this group so that they generate the entire group.
On can require that the rotations associated with nucleotide and its conjugate (in conjugate strand) are inverses of each other: the rotation sequences are carried out in reverse directions for strand and its conjugate. Simple check shows can generate the entire group in this manner.
To build amino acid one can start from amino-acid and reference direction associated with it. The rotation defined by the amino acid is the product of rotations associated with the nucleotides and tells to which direction next amino acid points. In this manner amino acid conformation is fixed uniquely.
The idea is very ice but the explanation contains several mistakes so that the above represents only my interpretation about what seems to be involved
Yeah, sorry for that link, it was just first that came up, and I also got the impression that the formalism was on the "lighter" side. This article by Mark White seems both more humble and more lucid, but same themes keep on coming up (platonic solids, especially dodecahedron, etc.):
http://www.codefun.com/Papers/IS7.pdf
To Anonymous:
Thank you for really interesting links. There is absolutely no reason to be sorry. The idea is really nice although the explanation contains errors and is difficult to comprehend. Same can be said about my scribblings. Biologists are finally learning mathematics: the saying that biologists's number system contains three numbers: one, two, and many ceases to be true! I believe that tte numerical calculations are probably correct.
Some further comments.
a) I claimed that the symmetries of cube are those of tetrahedron. This is of course not true. Octahedron is in question. Octahedron has 8 vertices as also cube and is dual of cube so that symmetries are same.
b) A good starting point is to take symmetry group of Platonic solid and require that the rotations associated with A,T, C, G generate it. A and T correspond to g1 and its inverse as conjugate codons. C and G to g2 and its inverse. One cannot get too big groups in this manner. The group must be generated by these 4 rotations g1, g_1^(-1), g_2, and g_2^(-1).
c) For cube and octahedron one has group permutation group of four objects. It can be generated by 3 suitably chosen elements and now one has four. Direct inspection shows that this should work.
d) Also the symmetry rotations of dodecahedron forming 60-element alternating group A_5 (even permutations of 5 elements) can be generated from 2 elements. See
http://brauer.maths.qmul.ac.uk/Atlas/v3/alt/A5/.
Hence this group is viable candidate. The bigger the better so that I would choose this group.
Rotations by multiplies of 2p/5, the angle associated with Golden Mean, appear as generators, and a good hint is tha Golden angle 2pi/5 is associated also with DNA winding!
I have the feeling that in the first link the 24-element rotational symmetries of cube were considered and found to produce something good looking in some cases. 60-element dodecahedral group is much more promising candidate.
I have written something about platonic solids and genetic code: See
http://www.tgdtheory.fi/public_html/articles/icosagene.pdf
but cannot recall it immediately. In any case, I did not have the coding of secondary structure in mind. The inability to recall the idea immediately is a good measure for its fuzziness;-).
ahh the golden ratio. it popped up in my zeta stuff some time back. piling up tqcs... quite the funny idea :) http://scienceasia.asia/index.php/ama/article/view/55
I thought I saw tesseract mentioned in either of the papers, but tesseract+DNA brings out this link:
http://www.scribd.com/doc/106779619/The-DNA-Tesseract
There is interesting relation between tetrahedron studied in your link and tesseract: "The tetrahedron forms the convex hull of the tesseract's vertex-centered central projection."
http://en.wikipedia.org/wiki/Tesseract
http://en.wikipedia.org/wiki/Convex_hull
Also, if tesseract is hung from one of its vertices and sliced horizontally through its center, the result is octahedron. http://www.daviddarling.info/encyclopedia/T/tesseract.html
Very nice visuals of 3D solids and tesseract:
http://www.bibliotecapleyades.net/geometria_sagrada/esp_geometria_sagrada_4.htm
squaring the circle: tesseract graph is isomorphic to 4-Hadamard graph.
http://mathworld.wolfram.com/TesseractGraph.html
http://mathworld.wolfram.com/HadamardGraph.html
Hadamard transformation or Hadamard gate is important in quantum computation:
http://en.wikipedia.org/wiki/Hadamard_transform
If I understand correctly, the "annoying" √2 in the transformation formula comes from doing it on 2D plane, in 3D it would be √3. In 4D tesseract 4D the distance between opposite corners is much tidier twice the length of a side than the corresponding irrational values of √2 for a square and √3 for a cube (from link mentioned above, http://www.daviddarling.info/encyclopedia/T/tesseract.html). This would be cruxial for DNA level error avoiding quantum computation?!
Another article about tesseract, tesseract Rubik's cube:
http://helm.lu/cube/tesseract.pdf
At one point the "players" use technique wich they call "far fetched analogy of gene splicing". Maybe the analogy is not so far fecthed?
im with sheldon. biology is "squishy yucky things". thought y'all might get a kick out of this. http://www.quantumconsciousness.org/
well, depending on the context, very yummy squishy things :) *rawr*
To Anonymous who wrote:
"Hi! Very interesting post!
Please take a look at the following new:
http://phys.org/news/2014-02-team-limits-famous-quantum-principle.html
Does it have any consequence on the quantum mind theories?
D. "
The comment is not visible for some reason nor are the other comments. In any case, the answer is that this is just nonsense hype. Almost every week some-one promises to demonstrate that quantum theory is somehow wrong. They of course claim that they have a new revolutionary theory. The recent period of superhype was initiated by super string community, and now everyone is doing the same to such research money from decision makers who do not understand.
Matti, we all know the world is terrible and fjlled with hype, what to do about it? or rather, how to live with the idea?
The link to Quantum mind, magnetic body and biological body does not work.
ulla, yah, they arent exactly synced up. and all these idiots with their wifi signals just adds noise go the mix
Thank you Ulla: corrected.
oh, I think u meant hyperlink, not link
Crow, your mind is not synched up. You add noise to this, and you are anon. Please stop.
I confess that my comments are not always synched up either :( But comments seldom are generally.
Sorry Matti,
but the article:
http://phys.org/news/2014-02-team-limits-famous-quantum-principle.html
is not about a new theory. It talks about experimental evidence. Maybe I'm just not able to give it the right interpretation. What do you think about?
Regards
D.
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