perhaps it looks more like a typical noise spectrum.

Have a bit further thought, remember exponential decay is a ratio against time thus not a flat distribution so is not going to look like WGN or similar distributions, (untill the decay has finally finished in which case zero).

]]>I visualize a broad maximum in the neighborhood of the mean frequency. Because the intervals between decay events are extremely scattered, I suppose there to be energy spread throughout the range of the spectrum, slowly diminishing according to distance from that peak.

I wouldn’t be surprised if I’m “all wet” — perhaps it looks more like a typical noise spectrum.

]]>The spectrum of isotope decay detection will make a better approximation to a “bell curve”.

And what is your reasoning for that statment?

]]>Within selected constraints (for example, choice of a city in which to record times of birth), Type 2 sequences will exhibit some mean frequency over a sufficiently long interval.

That frequency is an artifact of population size and probability density. To infer from the existence of such frequency that Type 2 sequences are in any way “periodic” is a mistake. Arguments valid for Type 1 can be false for Type 2.

]]>I’ll call a sequence of events determined by a common causation which constrains their relative timing a Type 1 sequence.

By contrast, the sequence of largely (or completely) independent events occurring in a population I’ll call Type 2.

Mundane examples of Type 1 include the ticking of a mechanical clock; an oscillator (even when chaotic); sheets of paper issuing from a copy machine or printer; the beating of our hearts.

Type 2 phenomena are also very familiar.

Sometimes at a large public event, you can see dozens (maybe even hundreds) of camera flashes per second.

Human births in a city are another example.

Earthquakes are Type 2 event sequences (as I mentioned on another thread); so are supernovas.

]]>The electronic chaotic oscillator is new to me, though the complex gyrations of its mechanical counterpart are not. I’m glad you introduced this gadget, because can serve as good illustration of how errors of classification can happen.

I suggest that the spectrum of such an oscillator (over a long integration time) would crudely resemble some statistical distribution curves, with a weakly defined “peak” and broad “shoulders”.

The spectrum of isotope decay detection will make a better approximation to a “bell curve”.

In this sense, these phenomena have a sort of family resemblance — *in the frequency domain*.

To infer from such frequency domain resemblance that one type of phenomenon (deterministic causally linked) is equivalent to the other type of phenomenon (events in a large population which are weakly linked or fully independent) is invalid.

]]>For an oscillator, each cycle is causally linked to the preceding cycle: timing the zero-crossings of its output can be used to make a fairly good estimate of when the next zero-crossing will occur.

Ever heard of a “chaotic oscillator”

http://www.scholarpedia.org/article/Transistor-based_chaotic_oscillator

Whilst they are not common in designed devices, they are in nature rather more present than the type of “periodic” oscillator you are talking about.

For instance your arm is fundementaly a structure to form a 2D chaotic oscillator due to the number of pivit points. It is only the fact that you cannot have fully universal joints due to blood supply, tendons etc that stop it being capable of reaching all points in a 2D surface and importantly continuous direction rotation.

But for a simple example of a physical chaotic oscillator you need two motors and two arms. If you fix one motor to a base and have the arm rotate parallel to the base the tip of the arm describes a circle. Now add the second motor to the tip of that first arm with a second arm above but parallel to both the base and first arm. This second arm describes a circle around the point of the first arm. However with regards to the base the tip of the second arm forms a complex pattern the shape of which is related to the speed of rotation relationship of the rotation of both arms. Because such a system is sensitive to that relationship if it varies in a determanistic fashion it is by definition chaotic.

Obviously the more rotation points you add the more interesting things get. You should realise from the likes of square, triangular, and sawtooth waves that under certain very distinct relationships when the relationships remain stable the final arm end point will trace out squares, trapezoids, triangles and even straight lines none of which to the observer have circular movments to an observers eye.

]]>For those interested in developing lithium battery technology,

It’s not a bad article as such, and it covers most of the bases…

But it misses out on a couple of important points.

Firstly, there is one heck of a difference between a consumer device drawing milliwatts of power and vehicals that can draw hundreds of kilowatts of power. Specifically the current in the anode of batteries. Heat generated in a battery being charged or discharged is related to I^2R losses. The easy way to get R down is to increase the “cross sectional area” of the conductor/battery, thus large area but very thin batteries would be favoured… However there are limitations on thinness, beyond a certain point it causes the energy density of the battery to drop thus battery size&weight to increase. Crazy as it sounds some people are looking at folded manifolds based around 3D fractals (don’t ask go look it up, I’ve enough trouble getting my head around fractal antenna).

The second problem not realy mentioned about vehicles is the “fill time”. When you work out the energy density of petrol/gas and how fast you can move it into a fuel tank you get a very very very high rate of energy transmission. Convert that to electrical energy and you quickly realise you are dealing with currents even big industrial spot welders can not reach. That is currents high enough to not just melt but turn into vapour all metals that would make practical conductors / connectors of usable cross sectional area.

]]>If some intelligence agency is bombarding your facility with high-power beams, you have a whole host of problems (including danger to human health) which I suggest belong outside the scope of this discussion.

Other than that, the clock for the correct radioisotope TRNG need not be exceptionally accurate or stable; its function is to discriminate among events occurring at unpredictable times.

Excepting cases where the circuitry is Just Plain Broken (happens sometimes), any clock based on a crystal oscillator will do fine.

The worrisome locking case is the reverse: in a poor design, AC energy might be coupled into the detector circuitry with the effect of shifting the detection edge significantly from its “undisturbed” timing. As I wrote, the hardware must be designed with great care.

]]>The argument is mistaken. Consider the assertion “you can regard the particle detector output as an oscillator.”

For an oscillator, each cycle is causally linked to the preceding cycle: timing the zero-crossings of its output can be used to make a fairly good estimate of when the next zero-crossing will occur.

Now suppose that you’ve clocked a pair of successive decay detections in a TRNG. *Every future nanosecond has the same probability for a detection: timing of recent events adds no further knowledge.*

No recurring event sequence can be more fundamentally different from an oscillator; reasoning premised on periodicity is invalid.

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