## Made a Small Book on Complexity

Complexity is a complex thing. This thin book is about NP vs. P amongst other things. Some insight into analytic continuations and complex problems with direction to forms algorithms might take with some strength reduction by applying integral calculus.

## Statistics and Damn Lies

I was wondering over the statistics problem I call the ABC problem. Say you have 3 walls in a circular path, of different heights, and between them are points marked A, B and C. If in any ‘turn’ the ‘climber’ attempts to scale the wall in the current clockwise or anti-clockwise direction. The chances of success are proportional to the wall height. If the climber fails to get over a wall, they reverse direction. A simple thing, but what are the chances of the climber will be found facing clockwise just before scaling or not a wall? Is it close to 0.5 as the problem is not symmetric?

More interestingly the climber will be in a very real sense captured more often in the cell with the highest pair of walls. If the cell with the lowest pair of walls is just considered as consumption of time, then what is the ratio of the containment time over the total time not in the least inescapable wall cell?

So the binomial distribution of the elimination of the ’emptiest’ when repeating this pattern as an array with co-prime ‘dice’ (if all occupancy has to be in either of the most secure cells in each ‘ring nick’), the rate depends on the number of ring nicks. The considered security majority state is the state (selected from the two most secure cell states) which more of the ring nicks are in, given none are in the least secure state of the three states.

For the ring nick array to be majority most secure more than two thirds the time is another binomial or two away. If there are more than two-thirds of the time (excluding gaping minimal occupancy cells) the most secure state majority and less than two-thirds (by unitary summation) of the middle-security cells in majority, there exists a Jaxon Modulation coding to place data on the Prisoners by reversing all their directions at once where necessary, to invert the majority into a minority rarer state with more Shannon information. Note that the pseudo-random dice and other quantifying information remains constant in bits.

Dedicated to Kurt Godel … I am number 6. 😀

## Winter is Coming!

Hi

Things are going real slow on the electronics front due to space constraints of capital. But the good news is that uncertain geometry is a good predictor of 12 fermions. The bosons will have to wait for some fancy 4 velocity put into a relativistic solution of the mass independent free space equation, so as to show how each velocity flow (up, down, electron, neutrino) interacts with mass flowing relative to it. This gives in a real sense the interaction of matter as it sees matter, and the deviation is bosonic.

Couldn’t help the topical title on this post. Weather proofing is moving slow, and is very cash restricted. As with these things almost always, having some cash help to obtain more. It’s a “bad listed” working “class” thing. They’ve got to make their paranoia pay you know.

The good news is the ides keep flowing. The dark matter telescope using atomically timed WC break door open/close sensing for example was such a laugh, and perhaps even app feasible.

## MaxBLEP Audio DSP

```TYPE void DEF blep(int port, float value, bool limit) SUB
//limit line level
if(limit) value = clip(value);
//blep fractal process residual buffer and blep summation buffer
float v = value;
value = blb[port] - value - bl[((idx) & 15) + 32 * port + 16];//and + residual
blb[port] = v;//for next delta
for(int i = 0; i < 15; i++) {
bl[((i + idx + 1) & 15) + 32 * port] += value * blepFront[i];
}
value += bl[((idx) & 15) + 32 * port];//blep
float r = value - (float)((int16_t)(value * MAXINT)) / (float)MAXINT;//under bits residual
bl[((idx) & 15) + 32 * port + 16] = value * (blepFront - 1.0);//residual buffer
bl[((idx + 1) & 15) + 32 * port] += r;//noise shape
idx++;
//hard out
_OUT(port, value - r);//start the blep
RETURN
```

Yes an infinite zero crossing BLEP. … Finance and the BLEP reduced noise of micro transactions

## Disection of the Roots of the Mass Independent Space Equation

 (v^2) v ‘ ‘ ‘ −9v v ‘ v ‘ ‘ 12(v ‘ ^3) (1−v^2/c^2)v ‘ (wv)^2 3 Constants 2 Constants 1 Constant 1 Constant Square Power Linear Power Cubic Power Square and Quartic Power 3 Root Pairs 2 Roots 1 Root and 1 Root Pair 1 Root Pair and 2 Root Pairs Energy and Force of Force Momentum, Force and Velocity of Force Cube of Force Force Energy Potential Inertial Term Kinetic Inertial Term Strong Term Relativistic Force Energy Coupling Gravity Dark Strong Weak EM

The fact there are 4 connected modes, as it were, imply there are 6 cross overs between modes of action, indicating that one term can be stimulated to convert into another term. The exact equilibrium points can be set as 6 differential equation forms, with some further analysis required of stable phase space bounds, and unstable phases at which to alter the balance to have a particular effect. Installing a constant (or function) of proportionality in each of the following balance equations would in effect allow some translation of one term ‘resonance’ into another.

 v v ‘ ‘ ‘=−9 v ‘ v ‘ ‘ 3 Const and 1 root point (v^2) v ‘ ‘ ‘=12(v ‘ ^3) 3 Const and 6 root points v ‘ ‘ ‘=(1−v^2/c^2)v ‘ w^2 3 Const and 2 root points −9v v ‘ ‘=12(v ‘ ^2) 2 Const and 2 root points −9 v ‘ ‘=(1−v^2/c^2)(w^2) v 2 Const and 2 root points 12(v ‘ ^2)=(1−v^2/c^2)(wv)^2 1 Const and 12 root points

Another interesting point is 3 of the 6 are independent of w (omega mass oscillation frequency), and also by implication relativistic dependence on c.

Posted on

## The 3D Flavour Tensor in Analogue to the 4D of Einstein, for a 3D, 4D Curvature in Particle Physics

I like to keep updated about particle physics and LHC things, to quite an advanced level. My interest is in fields and their previous engineering value in radio waves and electronics in general. It makes sense to move to a tensor algebra in the 2+1 charge space, just as was done for the theory of gravitation. In some sense the conservation of acceleration becomes a conservation of net mapped curvature and it becomes funny via Noether’s Theorem.

CP violation as a horizon delta of radius of curvature from the “t” distance is perhaps relevant phrased as a moment of inertia in the 2+1, and its resultant geometric singular forms. This does create the idea of singular forms in the 2+1 space orbiting (or perhaps more correctly resonating) in tune with singularities in the 3+1 space. This interconnection entanglement, or something similar is perhaps connected to the “weak phase”.

So a 7D total space-time, with differing invariants in the 3D and 4D parts. The interesting thing from my prospective is the prediction of a heavy graviton, and conservation of acceleration. The idea that space itself holds its own shape without graviton interaction, and so conserves acceleration, while the heavy graviton can be a short range force which changes the curvature. The graviton then becomes a mediator of jerk and not acceleration. The graviton, being heavy would also travel slower than light. Gravity waves would then not necessarily need graviton exchange.

Quantization of theories has I think in many ways gone too far. I think the big breaks of the 21st century will be turning quantized bulk statistics into unquantized statistics, with quantization applied to only some aspects of theories. The implication is that dark matter is bent spacetime, without matter being present to emit gravitons. In this sense I predict it is not particulate.

So 7D and a differential phase space coordinate for each D (except time) gives a 13D reality. The following is an interesting equation I arrived at at one point for velocity solutions to uncertainty. I did not incorporate electromagnetism, but it’s interesting in the number of solutions, or superposition of velocity states as it were. The w being constant in the assumption, but purtubative expansion in it may be interesting. The units of the equation are conveniently force. A particle observing another particle would also be moving such, and the non linear summation for the lab rest frame of explanation might be quite interesting.

(v^2) v ‘ ‘ ‘−9v v ‘ v ‘ ‘+12(v ‘ ^3)+(1−v^2/c^2)v ‘ (wv)^2=0

With ‘ representing differential w.r.t. time notation. So v’ is acceleration and v” is the jerk. I think v”’ is called the jounce for those with a mind to learn all the Js. An interesting equation considering the whole concept of uncertain geometry started from an observation that relative mass was kind of an invariant, mass oscillation, although weird with RMS mass and RMS energy conservation, was perhaps a good way of parameterizing an uncertainty “force” proportional to the kinetic energy momentum product. As an addition it was more commutative as a tensor algebra. Some other work I calculated suggests dark energy is conservation of mass times log of normalized velocity, and dark matter could be conserved acceleration with gravity and the graviton operating to not bend space on density, but bend space through a short distance acting heavy graviton. Changes in gravity could thus travel slower than light, and an integral with a partial fourth power fraction could expand into conserved acceleration, energy, momentum and mass information velocity (dark energy) with perhaps another form of Higgs, and an uncertainty boson (spin 1) as well.

So really a 13D geometry. Each velocity state in the above mass independent free space equation above is an indication of a particle of differing mass. A particle count based on solutions. 6 quarks and all. An actual explanation for the three flavours of matter? So assuming an approximate linear superposable solution with 3 constants of integration, this gives 6 parameterized solutions from the first term via 3 constants and the square being rooted, The second tern involves just 2 of the constants for 2 possible offsets, and the third term involves just one of the constants, but 3 roots with two being in complex conjugation. The final term involves just one of the constants, but an approximation to the fourth power for 4 roots, and disappearing when the velocity is the speed of light, and so is likely a rest mass term.

So that would likely be a fermion list. A boson list would be in the boundaries at the discontinuities between those solutions, with the effective mass of the boson controlled by the expected life time between the states, and the state energy mismatch. Also of importance is how the equation translates to 4D, 3D spacetime, and the normalized rotational invariants of EM and other things. Angular momentum is conserved and constant (dimensionless in uncertain geometry),

Assuming the first 3 terms are very small compared to the last term, and v is not the speed of light. There would have to be some imaginary component to velocity, and this imaginary would be one of the degrees of freedom (leading to a total of 26). Is this imaginary velocity consistent with isospin?

# Yang–Mills Existence and Mass Gap (Clay Problem)

If mass oscillation is proved to exist, then the mass gap can never be proved to be greater than zero as the mass must pass through zero for oscillation. This does exclude the possibility of complex mass oscillation, but this is just mass shrinkage (no eventual gap in the infinite time limit), or mass growth, and hence no minimum except in the big bang.

The 24 degrees of freedom on the relativistic compacted holographic 3D for the 26D string model, imply with elliptic functions, a 44 fold way. This is a decomposition into 26 sporadic elliptic patterns, and 18 generational spectra patterns. With the differential equation above providing 6*2*(2+1) combinations from the first three terms, and the 3 constants of integration locating in “colour space” through a different orthogonal basis. Would provide 24 apparent solution types, with 12 of them having a complex conjugation relation as a pair for 36. If this is the isospin solution, then the 12 fermionic solutions have all been found. That leaves the 12 bosonic solutions (the ones without a conjugate in the 3rd term generative), with only 5 (or if a photon is special 4) having been found so far. If the bosonic sector includes the dual rooting via the second term for spin polarity, then of the six (with the dual degenerates cancelled), two more are left to be found if light is special in the 4th term.

This would also leave 8 of the 44 way in a non existent capacity. I’d maybe focus on them being gluons, and consider the third still to be found as a second form of Higgs. OK.

# Displacement Currents in Colour Space

Maybe an interesting wave induction effect is possible. I’m not sure what the transmitter should be made of. The ABC modulation may make it a bit “alternate” near the field emission. So not caused by bosons in the regular sense, more the “transition bosons” between particle states. The specific transitions between energy states may (although it’s not certain), pull the local ABC field in a resonant or engineered direction. The actual ABC solution of this reality has to have some reasoning for being stable for long enough. This does not imply though that no other ABC solutions act in parallel, or are not obtainable via some engineering means.

## Implementation of Digital Audio filters

An interesting experience. The choice of FIR or IIR is the most primary. As the filtering is modelling classic filters, the shorter coefficient varieties of IIR are the best choice for me. The fact of an infinite impulse response is not of concern with a continuous stream of data, and coefficient rounding is not really an issue when using doubles. IIR also has the advantage of an easy Sallen-Key implementation, due to the subtraction and re-adding of the feedback component, with a very simple CR processing.

The most interesting choices are to do with the anti-alias filtering, as the interpolation filter, on up-sampling is an easy choice. As the ear is not really responsive to phase, all the effort should be on the pass band response levels, and a good stop band non response. A Legendre or Butterworth are the candidates. The concept of a characteristic sound enters the design process at this point, as the cascading of SK filter sections is conceptually useful to improve the -6 dB response at cut off. This is a trade off of 20 kHz to 22.05 kHz in the alias pass band, and greater attenuation in the above 22.05 kHz infinite stop desire. The slight greater desire of alias attenuation above pass band maximal flatness (for audio harmony) implies the Legendre filter is better for the purpose than Butterworth.

In the end, the final choice is one of convenience. and a 9th order filter was decided upon, with 4 times oversampling. The use of 4 times oversampling instead of 8 times oversampling increases the alias by an octave reduction. This fact under the assumption of at least a linear reduction in the amplitude of the frequency of the generator of an alias frequency, with frequency increase, just requires a -12 dB extra gain reduction in the alias filter for an effective equivalence to 8 times oversampling (the up to and the reflection back down to 6 + 6). The amount of GHz processing also halves. These facts then become constructive in the design, with the bulk alias close to the cut off, and the minor reflected alias-alias limit, not being too relevant to overall alias inharmonic distortion.

A triple chain of 3 pole Legendre filter sections is the decided design. The approximate -9 dB at the corner, allows for slightly shifting up the cut off and still maintaining a very effective stop band. Code reuse also aids in the I-cache usage for CPU effective use.  A single 3 pole Legendre is the interpolation up sample filter. The roll off for not using Butterworth does cut some high frequency content from the maximally flat, hence the concept of maximally flat, but it out performs a Bessel filter in this regard. It’s not as though a phasor or flanger needs to operate almost perfectly in the alias band.

Perhaps there is improvement to be made in the up sampling filter, by post up sample 88.2 kHz noise shaped injection to eliminate all error at 44.1 kHz. This may have a potential advantage to map the alias noise into the low frequencies, instead of encroaching from the higher frequencies to the lower, and for creating the alias as a reduction in signal to noise, instead of at certain inharmonic peaks. The main issue with this is the 44.1 kHz wave fundamental, seen as the amplitude ring modulation of the injected phase noise, by the 44.1 kHz stepped waveform between samples input. The 88.2 kHz “carrier” and the sidebands are higher in frequency, and of the same amplitude magnitude.

But as this is following for no 44.1 kHz error, the 88.2 kHz and sidebands are the induced noise, the magnitude of which is of the order of 1 octave up from the -3 dB roll at the corner, plus approximately the octave for a 3 pole filter, or about 36 dB cut of a signal 3/4 of the input amplitude. I’d estimate about -37 dB at 88.1 kHz, and -19 dB at 44.1 kHz. Post processing with a 9 pole filter, provides an extra -54 dB on down sampling, for an estimate of around -73 dB or greater on the noise. That would be about 12 bit resolution at 44.1 kHz increasing with frequency. All estimates, likely errors, but in general not a good idea from first principals. Given that the 44.1 kHz content would be very small though post the interpolation filter, -73 dB down from this would be good, although I don’t think achievable in a sensible manor.

Using the last filtered sample in as the reference for the present sample filtered in as a base line, the signal at 22.05 kHz would be smoothed. It would have a notch filter effect, by injecting quantization offset ringing noise at 88.2 kHz to cancel 22.05 kHz. The notch would likely extend down in frequency for maybe -6 dB at about 11 kHz. Perhaps in the end it is just better to subtract the multiplied difference between two up sample filters using different sinc spreading of a 1000 and a 1100 sample occupancy zero inter fill. Subtracting the alternates up conversion delta as it were.

There is potentially also an argument for having a second order section with damping factor near 0.68 and corner 22.05 kHz to achieve some normalisation from sinc up-sampling. This adds in an amount of Q such as to peak the filter cancelling the sinc droop, which would be about 3% at 4 times oversampling.

EDIT: Some of you may have noticed that the required frequencies for stable filtering are too high at 4 times oversampling. So unfortunate for the CPU load an 8 times oversample has to be used. The sinc error is less than 1% at this oversample, but still corrected in a similar way, and a benefit of 2 extra poles. Following this by a 0.1 dB 3 pole Chebyshev high pass which has been inverted, gives a reasonable 5 pole up sampling filter. The down sampling filter for code efficiency is a triple instance of the sample inverse Chebyshev, with the corner frequencies slightly offset to produce more individual zeros, and some spreading of the “ringing”. These 9 poles are enough to get the stop band ripple to be lower than a 16 bit resolution. Odd order inverse Chebyshev are essential for the reflected spectra to be continually decreasing in amplitude.

## JDeveloper and Intel Python

The JDeveloper environment looks good. Nice work Oracle, and some of the Borland classic JBuilder. This tool look more like how I’d use an IDE. I’ve been looking at other technologies for computer development, and a recent Intel offering (for personal use free) is the MKL backed Intel Python. It needs at least an SSE4.2 supporting chip, but does have all that is needed to run the development on Xeon Phi Knights Landing. 72 cores and 144 vector processing AVX-512 engines. Multi Tflops stuff. For the developer this is perhaps the easiest way to start HPC, as through Cython and eventually C, the best performance can be had. Maybe FPGAs will help, and tools are available for that too. I’ve seen some good demonstrations, and maybe some clients with complex or hard problems would need this.

All this parallel stuff got me thinking of Kahan sums, and simulation of incompressibles by having a high speed of sound in a compressible, and the doing a compulsory diffusion to damp oscillation, and a pressure impulse (Pa s) handling of inertial failure of containers. It might reduce the non-locality of certain simulations, and actually act to simulate pressure hammer effects.

I’ve also recently got back into the idea of using Free Pascal for some of my projects maybe. There is now good JNI support, and even JVM targeting. I maen it’s very possible to use C for this kind of thing, but the FPC IDE and Lazarus are quick to build, with incremental unit compilation and many other features which make it good competition for general coding. Some would think it old hat, but the ease of use is excellent with much type checking, and no insistence on everything being a class. Units are very modular that way. The support for quite a few Pascal flavours is also good.

## Power Systems Lot of free energy videos about but does it actually work, or is it just virtual vapour wares? Here’s a highly unstable circuit I designed a few years ago. The magnetic balance is so fine, that an external field can throw the circuit into an unstable power spike. Then I went for an inductance modulation of lower scale, using a 3 phase (+++), to 1 phase (++-) arrangement, for greater stability. The difficulty with such devices is not the working, but the switch off without raising volts potential to any unlucky hands. This safety aspect is the ultimate reason of non use, and not as some suppose the disruptive effect on oil and other nuclear markets. Those markets may shrink, but will always be. The chemical industry will always have need of basic oil produce, and the lower short term profits of non burn, actually extend the future profits of chemical building. Transport is minor compared to health. The nuke industry could easily shrink, and still be big. The power waste of removing rods with 90% still effective power is a white wash of the electric power from a military objective. Reactors would be different for pure civil use. Amazing colours, but what’s it really about? The Pu problem of fast breed, and somehow there will never be less of it, just does not add up for efficient too cheap to meter power promises of not too long ago. There seems to be no real research on gamma cavity down conversion technology. I wonder how long it will be before the nova bomb. The effective slowing of light to lower than the black hole threshold, at Sun core. I think the major challenge is getting super dielectrics far enough into the Sun without melt. I suppose this is some hyperbole focus problem. One day people will understand the simple application of button technology, and the boxes will judge and provide on intent or not. It’s not like they won’t have a self interest.