All posts by jgmoxness

Updated My ToE Demonstrations to Wolfram Language (aka. Mathematica) 11

Please see the latest in .nb, .cdf demonstrations files and web interactive pages.

ToE_Demonstration-Lite.cdf Latest: 08/15/2016 (10 Mb). This is a lite version of the full Mathematica version 11 demonstration in .CDF below (or as an interactive-Lite web page) (4 Mb). It only loads the first 8 panes and the last UI pane which doesn’t require the larger file and load times. It requires the free Mathematica CDF plugin.

This version of the ToE_Demonstration-Lite.nb (13 Mb) is the same as CDF except it includes file I/O capability not available in the free CDF player. This requires a full Mathematica license.

ToE_Demonstration.cdf Latest: 08/15/2016 (110 Mb). This is a Mathematica version 11 demonstration in .CDF (or as an interactive web page) (130 Mb) takes you on an integrated visual journey from the abstract elements of hyper-dimensional geometry, algebra, particle and nuclear physics, Computational Fluid Dynamics (CFD) in Chaos Theory and Fractals, quantum relativistic cosmological N-Body simulations, and on to the atomic elements of chemistry (visualized as a 4D periodic table arranged by quantum numbers). It requires the free Mathematica CDF plugin.

This version of the ToE_Demonstration.nb (140 Mb) is the same as CDF except it includes file I/O capability not available in the free CDF player. This requires a full Mathematica license.

(The CDF player from Wolfram.com is still at v. 10.4.1, so still exhibits the bug I discovered related to clipping planes/slicing of 3D models).

Hofstadter’s Quantum-Mechanical Butterfly

Hofstadter’s Quantum-Mechanical Butterfly relates to the fractional Quantum Hall Effect, which is (IMHO) at the heart of understanding (interpreting) how QM really works!

I modified Wolfram Demonstration code by Enrique Zeleny to produce a short video of the emergence of the Hofstadter’s Quantum-Mechanical Butterfly

I found an interesting pattern. By modifying the integer used in the solution i=12, the Golden Ratio Ф=(1+Sqrt[5])/2=1.618 … emerges within the butterfly! Can you find it (or 1/Ф=.618…)?
Hint: Use the interactive version and mouse-over the red or green dots in the white space of the wings of butterfly.

A snapshot of the code and last frame@n=50:
HofstadterButterfly

If you have the

Visualizing Climate Data

I saw this post on the Wolfram blog.

I’ve enhanced the code to show some error bar indicators and visualized by year w/o the obfuscation of accumulation over time. It also uses parallel CPUs and binary packed arrays to speed up the computation. I also reduced the scale from +2.5C to +1C (since there was no data above it). I wonder if that anomalously larger scale was selected to “suggest” a placeholder for future warming (not appropriate as science – but typical for “influencing” public opinion).

I think my presentation more accurately shows that the recent data from the ’00s (with several El Nino’s), mid 40-60’s ocean temp bias adjustment increases, and more recent changes in (space) technology for collecting data may be a (the?) significant root cause for increases in temperature.

That may not be a politically correct thing to suggest – but I will do more work to substantiate based on the statistical analysis of the various data sets….

If you don’t have the Wolfram CDF Player on a non-Chrome browser for interactive UI, you can watch the YouTube video here or see below.

warming1

warming-1g

Interactive Reimann Zeta Function Zeros Demonstration

This web enabled demonstration shows a polar plot of the first 20 non-trivial Riemann zeta function zeros (including Gram points) along the critical line Zeta(1/2+it) for real values of t running from 0 to 50. The consecutively labeled zeros have 50 red plot points between each, with zeros identified by concentric magenta rings scaled to show the relative distance between their values of t. Gram’s law states that the curve usually crosses the real axis once between zeros.

A downloadable copy is available ZetaZeros-local-art-50.cdf Latest: 05/23/2016.

Note: The interactive CDF plug-in as required below does not currently work on Chrome browsers.

A Snapshot picture for those w/o Wolfram CDF interactivity:
RiemannZeta_Zeros.svg

Selectable example code snippet:
[wlcode]Show[ListPlot[Style[pts2, Red], PlotRange -> {{-2, 4}, {-3, 3}},
AspectRatio -> 1, ImageSize -> imageSize,
AxesStyle ->
Directive[Thick, If[artPrint && ! localize, Large, Medium]],
Graphics[{PointSize@.01,
tttxt := If[artPrint && ! localize, tttxt1, ttxt0];
If[ttxt0 = ToString[# – 1];
Abs@zeroY[[#, 1]] < 10 chop, (* Magenta Critical Line Zeta Zeros *) tttxt1 = Column[{ToString[# - 1], "t=" <> ToString@zeroY[[#, 4]]},
Center];
ttLoc =
zeroY[[#, 4]] If[artPrint && ! localize, 1, 2] imagesize/40000;
(* Flip Point Labels above/below the X axis *)
ttLoc1 = {-1, (-1)^Round[#/2]} ttLoc/Sqrt[2];
{Magenta, Point@ttLoc1,
Circle[zeroY[[#, ;; 2]], ttLoc, {1, 3} \[Pi]/2],
Black,
Tooltip[Text[
Style[tttxt, If[artPrint && ! localize, Large, Medium, Bold]],
(* Shift the Labels off the Point *)
ttLoc1 (1 – (-1)^Round[#/2] .05)], tttxt1]},
(* Orange Critical Line Imaginary zeros w/Real>0 *)
tttxt1 =
Column[{ToString[# – 1], “x=” <> ToString@zeroY[[#, 1]],
“t=” <> ToString@zeroY[[#, 4]]}, Center];
{Tooltip[{Orange, Point@zeroY[[#, ;; 2]], Text[Style[

Column[If[EvenQ[Round[(# – 1)/2]], Prepend,
Append][{“\[UpDownArrow]”}, tttxt], Center,
Frame -> True],
Black, If[artPrint && ! localize, Large, Medium],
Background -> White],
(* Flip Point Labels above/below the X axis *)

zeroY[[#, ;; 2]] + {0, (-1)^Round[(# – 1)/2]} If[
artPrint && ! localize, 1,
If[artPrint, 4/1, 3]] imagesize/5000]},
Column[{ToString[# – 1], “x=” <> ToString@zeroY[[#, 1]],
“t=” <> ToString@zeroY[[#, 4]]}, Center]]}] & /@
Range@Length@zeroY,
Magenta, Disk[{0, 0}, .03]}]][/wlcode]

More plots with various scaling functions and multi-color coding along with Tooltip on mouse-over. Bear in mind the last Smith Chart with a division by Abs@Zeta indicates where the increments go exponential near the 0.

A Snapshot picture for those w/o Wolfram CDF interactivity:
ZetaZeros

A ToE should…

An interesting post re:qualifications for a ToE prompted me to jot down my initial list of requirements. A ToE should inform, expand on, or rationalize, in a mathematically self consistent and rigorous way, the state of the current SM & GR confirmed experimental data:

1) Prescription (aka prediction, retrodiction or specific rationalization) for 3 generations of fundamental fermion and boson particles (and their resulting composite particles), including: charge, spin, color, mass, lifetime, branching ratio, and scattering amplitudes (aka. S-Matrix)
2) Prescription for CKM and PMNS unitary matrices and CPT conservation
3) Framework for the integration of QM and GR, including e/m, weak, strong and gravitational forces
4) Explanation for dark energy and dark matter in proportion to visible matter
5) Solution to the hierarchy problem
6) Provide a realistic computational model based on the above for the evolution of the Universe from BB to present
7) Explain an arrow of time that is consistent with GR and QM CPT conservation symmetries

Non-specific general appeals to the anthropic principle, landscapes, and/or multiverses tend to excuse or avoid prescription and thus become a benign point (or possibly even meta-physical or philosophical), such that they are not considered supportive of an actually verifiable (aka. scientific) theory.

If the theory says “we can’t know” or “we can’t measure” or “it just is that way” – it isn’t science or part of a ToE. again – my opinion and definition of “science”.

There is redundancy in this list, that is expected (even required). Of course, the beauty of the theory would be in conclusively demonstrating that throughout!

Until we can study an actual ToE that is put on the table – the list is only a guide to what might be needed. I am working on a ToE, but it doesn’t yet meet all the criteria (it’s hard work 😉

IF we have a ToE and really understand it, we should, as Feynman suggested, be able to explain it in plain language to anyone. But in the current state of physics, a completed ToE does not yet exist.

IMO, a ToE is about knowing the Universal Laws of Physics (ULPs). It isn’t, in detail, involved in knowing the Universal Initial Conditions UICs).

If you believe that the laws of “climate science” are known (don’t get me started…), then the only problem with predicting the weather is not so much about NOT knowing the laws – it is about not knowing with sufficient accuracy the initial conditions (location & momentum) of enough particles in the system. We’re missing the “butterfly flapping its wings in the Pacific” data points.

The Copenhagen interpretation of QM suggests that is impossible in principle to know any quantum system ICs (vs. the deterministic formulation of QM by DeBroglie-Bohm). Either way, my view is ToE=ULP.s w/o UICs. So prediction of all long term events specifically (like what I will think about next) is NOT the goal.

We just need enough of an idea about the UICs to initiate the computer model so it comes out close enough to get Earth like planets with weather and life forms thinking about this topic.

Easier, but NOT easy!