tag:blogger.com,1999:blog-10614348.post8779314610174001786..comments2023-03-18T02:32:07.872-07:00Comments on TGD diary: Quaternions, octonions, and TGDMatti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger17125tag:blogger.com,1999:blog-10614348.post-16476409457992350282015-03-11T23:34:24.726-07:002015-03-11T23:34:24.726-07:00Interesting , it makes sense.. some theorem of Lan...Interesting , it makes sense.. some theorem of Landau says things can only be ordered or unordered, there is no partially ordered states?The physics of clouds..http://phys.org/pdf345300363.pdfAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-23046831818567398442015-03-10T20:53:06.585-07:002015-03-10T20:53:06.585-07:00There should be a connection between these two sin...<br />There should be a connection between these two since quantum groups and p-adicization are parts of TGD and both indeed relate to finite measurement resolution.<br /><br />Discretization is the space-time counterpart for the inclusion of hyper finite factors as description of finite measurement resolution and cutoffs. q-derivative might relate to discretized functions of angle variables. p-Adicization forces discretization of angle variables by representing the allowed angles by corresponding phases which are roots of unity exp(ipi/n) up to some maximal n. This would naturally give rise to q-spherical harmonics and their generalizations and group theory would generalise to p-adic context. <br /><br />"Radial" coordinates can be mapped by discretised version of canonical identification between real and p-adic (cognitive) realms. Finite measurement resolution destroys well-orderedness of real numbers below resolution scale and p-adic numbers are indeed not well-ordered. One would get simpler number field which would not have well-orderedness not possessed by measurement data below resolution. I propose p-adic manifold as formulation of this.Matpitka@luukku.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-66203569464827912652015-03-10T20:52:15.994-07:002015-03-10T20:52:15.994-07:00
b) Finite measurement resolution leads to hyper-f...<br />b) Finite measurement resolution leads to hyper-finite factors and quantum groups characterised by quantum phases. One can introduce derivative, which is discretised version of ordinary derivative and approaches it when quantum group parameter q= exp(i2pi/n) approaches unity. What is beautiful is that the theory of group representations generalises and one can define notions like q-special function. <br /><br /> The physical meaning of this mathematics has remained obscure: to my opinion the idea to regard it as Planck length scale exotics is not good: one example of sloppy thinking characterising recent day thinking about physics by theoretical physics that I have been talking about. To my opinion it could relate to the description of finite measurement resolution in all length scales, just as p-adic fractals would do. <br /><br />To be continued... Matpitka@luukku.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-25622553805398961992015-03-10T20:45:47.733-07:002015-03-10T20:45:47.733-07:00I know whether little about these things. I wonder...<br />I know whether little about these things. I wonder how many definitions of fractional derivatives exists or is the definition unique by some god argument.<br /><br /> Two things come however in my mind.<br /><br />a) p-Adic fractals are obtained by mapping real continuous differentiable functions suchs f=x^2 to its p-adic counterpart by mapping x to p-adic number canonical identification x= SUM x_np^(-n) <br />-->x_p =SUM x_np^n. Forming the p-adic variant F(x_p) = x_p^2 and mapping its back to the reals by the inverse canonical identification. I have plotted this kind of fractals at my homepage. See<br />http://www.tgdtheory.fi/figu.html .<br /><br />The special feature of these fractals is that when p-adic norm of p-add norm changes, the real counterpart develops discontinuity since the numbers (p-1)(1+p) and 1 are mapped to real number p under canonical identification (analogy: .99999..=1 so that decimal expansion is not unique for real number).<br /><br />One could also form p-adic derivative dF/dx_p and map back to the reals to get what one might call fractal derivative. Left-right asymmetry is characteristic since canonical identification is well-defined only for non-negative reals. I have speculated that number theoretical universality could be behind the positive Grassmannians found in the construction of twistor representation of scattering amplitudes: in this case it relates to projectivity of the amplitudes.<br /><br />To be continued...Matpitka@luukku.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-49374207004972198722015-03-10T15:07:51.368-07:002015-03-10T15:07:51.368-07:00Matti, do these non-commutative fractional derivat...Matti, do these non-commutative fractional derivatives come up in TGD? <br /><br />http://courses2.cit.cornell.edu/pp396/Patie_Simon.pdf<br /><br />"Intertwining Certain Fractional Derivatives" it seems like it might relate to some of the twistor stuff<br /><br /><br /><br />--anonymouscrow :)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-8402049698213231712015-03-09T16:43:31.420-07:002015-03-09T16:43:31.420-07:00correction, its the "compensator" aka th...correction, its the "compensator" aka the "dual predictable projection" of a Hawkes process conditioned on the (almost) maximum likelihood estimate of the paramaters to a particular realization of the symbol SPY(S&P 500) on halloween of 2014 .. if the Hawkes process removed all predictibility it should turn the resulting output into a homogeneous unit rate Poisson process (a martingale) but, the leftovers in this case has a Cauchy kernel remaining(unaccounted for), and then i just discovered this.. .and i research it, and its related to .... Lorentz... and brownian motion.. and maybe im off my rocker, but the riemann hypothesis is still involved somehow i am almost sure of it.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-62529530633721151382015-03-09T16:33:13.253-07:002015-03-09T16:33:13.253-07:00Matti, the data is "time between trades"...Matti, the data is "time between trades" in seconds (fractional real number line) modeled as a jump process and in this formalism it has an associated "stochastic intensity process" which is akin to a wavefunction which randomly jumps , so point process theory has very interesting relation to wave/particle duality i think<br /><br />http://arxiv.org/abs/1301.5605<br /><br />on page 22 of the pdf, it looks like the distribution is a mixture of Poissionion (shot 'noise' process) and a Cauchy process , reflected 2d 'brownian motion' aka (Wiener process) at the origin<br /><br />Reflected stable subordinators for fractional Cauchy problems<br />Boris Baeumer, Mihály Kovács, Mark M. Meerschaert, René L. Schilling, Peter Straka<br />(Submitted on 23 Jan 2013)<br /><br /> In a fractional Cauchy problem, the first time derivative is replaced by a Caputo fractional derivative of order less than one. If the original Cauchy problem governs a Markov process, a non-Markovian time change yields a stochastic solution to the fractional Cauchy problem, using the first passage time of a stable subordinator. This paper proves that a spectrally negative stable process reflected at its infimum has the same one dimensional distributions as the inverse stable subordinator. Therefore, this Markov process can also be used as a time change, to produce stochastic solutions to fractional Cauchy problems. The proof uses an extension of the D. Andr\'e reflection principle. The forward equation of the reflected stable process is established, including the appropriate fractional boundary condition, and its transition densities are explicitly computed. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-61552719855757916982015-03-07T21:13:39.908-08:002015-03-07T21:13:39.908-08:00
Stephen,
could you elaborate this stock market c...<br />Stephen,<br /><br />could you elaborate this stock market claim. I am not sure whether I understood. 10 Hz is fundamental biorhythm and in TGD corresponds to the secondary p-adic time scale for electron. The frequency spectra for EEG, sound, etc… are not co-incidences in TGD Universe. <br /><br />Cyclotron frequencies in the magnetic field of Earth (or in its dark counterpart) are in EEG range and hearing as also other forms of sensory perception relies strongly on magnetic flux tubes and associated cyclotron frequencies. Cyclotron energies for these photons are extremely small unless one has large Planck constant. <br /><br />The wavelength of 10 Hz dark photon is about size of Earth. One could imagine that these photons could relate very closely to collective levels of consciousness. Maybe they could even give a background rhythm for all these idiocies that stock market people are doing to destroy our civilisation! <br /><br />I have developed this idea in detail using the h_eff=n*h= h_gr= GMm/v_0 hypothesis. The flux tube connections with magnetic Mother Gaia would be essential for life. Even nutrients- typically biomolecules - could mediate this connections and this would make them nutrients. Matpitka@luukku.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-60543200968025279242015-03-07T11:37:14.141-08:002015-03-07T11:37:14.141-08:00Even though its stock market data(time between tra...Even though its stock market data(time between trades for the s&p500), intentionality and physical effects are there.. aa well as the interesting observation that the empirical distribution has inflection points at about 200ms, and 1 second, corresponding to cognition timeshttp://www.newscientist.com/article/dn27107-confident-your-voice-gives-you-away-in-milliseconds.html the LHC protons speed around the ring at approximately 11khz. . Human audible range is 20hz to 20khz... ?! I don't know if this is pure coincidence or not<br /><br />http://www.newscientist.com/article/dn27107-confident-your-voice-gives-you-away-in-milliseconds.htmlAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-21649301089297334002015-03-06T20:27:55.809-08:002015-03-06T20:27:55.809-08:00Thank you for the link. I must admit that I failed...Thank you for the link. I must admit that I failed to understand the point. <br /><br />In any case, quaternion holomorphy has been discovered long time ago as I discovered recently. The trick is to define left- and right analytic series consisting of terms a_nq^n reap. q^na_n. This allows to circumvent the problems due to non-commutativity. The definition of quaternion analyticity is not unique. One form gives analyticity in 2 complex variables. <br /><br />Second form gives what one expects from quaternion analyticity: in the first case one has CR involving on t and radial coordinate r and corresponding unit vector as imaginary unit. Same trick works for octonions too and one avoids complications due to non-associativity.<br /><br />The continuation to Minkowski signature indeed works since z^n is of same form as z and belongs to the M^4 subspace of complexified quaternions as is easy to verify. Same for octonions.MMatpitka@luukku.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-48489917036228257872015-03-06T09:52:00.617-08:002015-03-06T09:52:00.617-08:00Matti, that data came from the stock market... so,...Matti, that data came from the stock market... so, in an indirect sense it does have to do with intention as you say :)<br /><br />Interesting post here, http://math.stackexchange.com/questions/821881/riemann-zeta-function-quaternions-and-physics<br /><br />-crowAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-18398433154941994922015-03-04T22:37:33.190-08:002015-03-04T22:37:33.190-08:00To Anonymous:
I guess that you refer to a distri...To Anonymous:<br /><br />I guess that you refer to a distribution/ wave function for causal diamonds (CDs) defining<br />the perceptive field of conscious entities selves in ZEO - that is Lorentz transforms defining moduli space for quaternion structures). I can only try to formulate what this distribution/wave function means in the framework provided by zero energy ontology (ZEO).<br /><br />*Zero energy states are characterised by wave function in the moduli space for CDs (I call it M for simplicity). State function reductions form sequences. During them second boundary of CD remains located at light-cone boundary common to all CDs. That part of any zero energy state in superposition is unaffected just like the quantum state in repeated quantum measurement is not affected after the first measurement (Zeno effect).<br /><br />*The wave function for the position of the opposite boundary of CD changes and (lower<br />level wave functions at the opposite boundary). In other words, the wave function in M changes. This sequence gives rise to self/mental image/.. in TGD inspired consciousness theory. Also the average temporal distance between the tips increases during this period and gives rise to experienced flow of time. When the first reduction at the opposite boundary of CD occurs, situation changes and it becomes fixed. Self "reincarnates".<br /><br />In the first reduction to second boundary the moduli are partially "measured" in the sense that second boundary of CDs is localized to fixed light-cone boundary. The opposite boundary of CD represents degrees of freedom analogous to momenta in the sense that it cannot be localized. The analogy with position-momentum duality can be made much more concrete and is probably much more than only an analogy. This is like measuring position: momentum becomes maximally uncertain. Uncertainty Principle prevents the measurement of the moduli distribution.<br /><br />This is all I can say. Maybe we can return to this question after century or two;-).<br />Matpitka@luukku.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-47643231439753337002015-03-02T15:54:17.638-08:002015-03-02T15:54:17.638-08:00Matti, could Lorentz transforms show themselves as...Matti, could Lorentz transforms show themselves as a peak in some event time data having a Cauchy (Lorentz ) distribution? http://stats.stackexchange.com/questions/139790/does-this-look-like-a-cauchy-distributionAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-37495910541679555162015-03-02T15:10:52.312-08:002015-03-02T15:10:52.312-08:00For torus topology, see:
4] viXra:1103.0002
3 Di...For torus topology, see:<br />4] viXra:1103.0002 <br /><br />3 Dimensional String Based Alternative Particles ModelLeo Vuykhttps://www.blogger.com/profile/16285797359437018414noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-27116257918926561092015-03-01T19:09:56.952-08:002015-03-01T19:09:56.952-08:00Thank you for links. Quaternions have been lurking...Thank you for links. Quaternions have been lurking around already since Maxwell. The problem with quaternion formulations is that breaking of Lorentz invariance takes place. The selection of quaternion real unit selects preferred time direction. <br /><br />One should be able to interpret this breaking as only apparent. The preferred time direction could for instance correspond to the time direction in rest frame of the subsystem. In zero energy ontology (ZEO) it corresponds to the time-like line connecting the tips of the causal diamond (CD). <br /><br />Using the language of mathematicians, the CDs with different time direction correspond to moduli characterising different quaternionic structures and changing in Lorentz transformations. This kind of moduli characterise also different complex structures: for torus topology these structure are labelled by points of torus. <br /><br /><br /><br />Matpitka@luukku.comhttp://tgdtheory.fi/noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-13586391324408987322015-03-01T15:15:13.347-08:002015-03-01T15:15:13.347-08:00Fringe/Alt-Physics have long proclaimed that the H...Fringe/Alt-Physics have long proclaimed that the Heaviside tensor normalization of Maxwell's original 20 quaternion-based equations has hidden "new physics". A quick Google search turned up:<br /><br />http://en.wikipedia.org/wiki/Quaternion<br /><br />http://www.rexresearch.com/maxwell.htm<br /><br />http://arxiv.org/abs/math-ph/0307038<br /><br />http://visualphysics.org/de/node/144<br /><br />http://www.enterprisemission.com/hyper2.html<br /><br />http://www.cheniere.org/books/aids/ch4.htm<br /><br />Of course, the Bearden types could still be wrong and yours more fundamentally correct.K.R.A.M.noreply@blogger.comtag:blogger.com,1999:blog-10614348.post-40963844301543963992015-03-01T00:23:50.088-08:002015-03-01T00:23:50.088-08:00Beautiful, must let this soak inBeautiful, must let this soak inAnonymousnoreply@blogger.com