Prime numbers in 4D structure

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[neondata]

There are nice cristalls based on primes. How do you understand "impedance"?

[fbunc]

Hi,

Impedance is just the context in wich I got familiar with complex numbers $z=a+i·b$ or like engineers write it $Z=R+j·X$.

The most basic impedance is pure resistor (real part) where $Z=R$

A pure inductance has a pure imaginary value of $Z=j·\omega·L$

A pure capacitance has a pure imaginary value of $Z=\frac{1}{j·\omega·C}$

$\omega = \frac{2·\pi}{T}$ where $f=1/T$ is the frequency of the signal present in the circuit being analyzed .

It's a simplification of all the differential equations that need to be solved for understanding/designing circuits, where all the heavy lifting involved in solving an ODE is avoided after a Laplace or Fourier transformation. In the jargon it is said that this kind of transformations take all the analysis to the 'frequency-domain', and then you can do an anti-transformation to bring back your conclusions to the 'time-domain'.

You can combine multiple impedances in series and in parallel to create, for example, analog filters used in electronics.

But this concepts, for example Laplace transform and Fourier transform are used all across math and science to model dynamical systems.

In the 'discrete-time' world you have discrete versions of this transformations called Z-transform(Laplace transform in the discrete world) and many others as the DFT (Discrete-Fourier-Transform) and modifications as (Fast Fourier Transform) FFT.

All this brings you to the concept of wavelets and digital filters.

https://en.wikipedia.org/wiki/Analogue_filter

https://en.wikipedia.org/wiki/Shannon_wavelet

https://en.wikipedia.org/wiki/Digital_filter

FIR https://en.wikipedia.org/wiki/Finite_impulse_response

Wheel Theory and HSV:

https://en.wikipedia.org/wiki/Wheel_theory

[neondata]

While I can not follow to all you say it looks interesting and I like the map of math that shows that all the topics are interlinked. The concept of "impedance" indeed is mostly used by electr***l engineers, indeed as a HAM I used this in the context of transmission lines: cables, antennas, free space were we have the wave resistance of about 380 Ohm. So it's always about impedance matching and energy transfer. I use this term to describe the ability to transfer energy from one system to another. As you seem to think out of the box: The question is: is there impedance at the outside of the universe or does the wave front (light) just create something that can carry itself ;-) I heard there was something as superexpansion after the big bang where the universe expanded and then shrunk again what could in terms of impedance be interpreted as there is a short-cut or open end of the "transmission line" which is the universe itself we know. Funny things may come from the impedance.

[fbunc]

Gottfried Leibniz Monadology:

https://en.wikipedia.org/wiki/Monadology

Sabine without the 'gobbledygook' :

https://www.youtube.com/clip/Ugkx4SNmXpF5TiPRNqGvQB3_E0gBCsqCQ8XR

History of the universe - Space and Time recommended by youtube:

https://www.youtube.com/watch?v=yPVQtvbiS4Y

[neondata]

If you meant me, I have to admit there are lot of references to a context I don't know .. But do you agree that impedance gives you an insight as it is a measure how something (energy) is a product of something else (voltage) (current)

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[neondata]

It will take at least 1/2 an hour to watch the video, but as I like veritasium I'll have a look to see where I agree and where not. As I looked to stackexchange and saw the politeness of the answers, I'm positively surprized. That doesn't happen often when you ask simple questions that look stupid to the "knowing". The concept of "impedance" is introduced whenever the simple "ohmic law" doesn't apply. That is, when a 2-pole shows changing current when the voltage is constant or changing voltage, when the current is constant. It turns out that three cases are sufficient to describe everything: voltage and current are proportional, voltage change is proportional to current and current change is proportional to voltage. As an electrical engineer you know in a resonance circuit energy is stored and continuously changes from magnetical to electrical state. When an antenna is connected, energy is radiated and then electrical and magnetical field are in phase. That is: travelling waves show in phase e-m-fields while in a cavity they are shifted by 90°. So an antenna is something that is able to shift the phase of e- and m- components of the field, but how? Is one shifted by 90°? Are both shifted by 45° into opposite direction, if yes: which one into which direction. At my time we just calculated the near field and the far field, and left the gap open. Maybe now this has changed, but I doubts, otherwise such questions should not arise or answered quickly. So you ask as "kurt"?

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[neondata]

I myself closed two issues, one: https://github.com/leios/SoME_Topics/issues/205 which no longer has any content, I decides this after some "moderators" kicked me of discord while I was writing. I only asked: what is the double slit made of? And can you explain why an electron should interfere with itself? Social media are so strange as they open the world to everybody and as we have seen what happens in the "real world" I still believed that this was not the case in science, that questions are allowed and "alternative facts" are just the same facts from another perspective. So as you are asking questions I also do: can you imagine a switch without losses? Me not. I can only imagine a dooms day switch. Imagine to pinpoints at the end of a wire connected to a voltage source. If you bring the tips in proximity they obviously form a capacitor. Every time the distance is laved, the capacity is doubled and current flows driven by voltage into the capacitor and the energy is stored there. So if you change the distance in such a way, that the current flowing constantly, this setup looks like an ohmic resistor. Only it you widen the gap you will see, that the energy comes back. But: If you one time decide to close the gap, what happens to the energy stored in the cap? It is dissipated. And there is no way to close a contact connected to a voltage source, without dissipating the energy stored in the electrical field between the once separated contacts. This is even true for a semiconductor or a diode. The only ways to limit the losses are to have a resistor in series to limit the current as an R-C-filter or to have an inductance in series for the same purpose, this inductance stores energy and when the contact is closed, this energy will go to the sink. But you started to plot prime numbers and I showed, that prime numbers can be cristals with defects.

[fbunc]

I myself closed two issues, one: #205 which no longer has any content, I decides this after some "moderators" kicked me of discord while I was writing. I only asked: what is the double slit made of? And can you explain why an electron should interfere with itself? Social media are so strange as they open the world to everybody and as we have seen what happens in the "real world" I still believed that this was not the case in science, that questions are allowed and "alternative facts" are just the same facts from another perspective. So as you are asking questions I also do: can you imagine a switch without losses? Me not. I can only imagine a dooms day switch. Imagine to pinpoints at the end of a wire connected to a voltage source. If you bring the tips in proximity they obviously form a capacitor. Every time the distance is laved, the capacity is doubled and current flows driven by voltage into the capacitor and the energy is stored there. So if you change the distance in such a way, that the current flowing constantly, this setup looks like an ohmic resistor. Only it you widen the gap you will see, that the energy comes back. But: If you one time decide to close the gap, what happens to the energy stored in the cap? It is dissipated. And there is no way to close a contact connected to a voltage source, without dissipating the energy stored in the electrical field between the once separated contacts. This is even true for a semiconductor or a diode. The only ways to limit the losses are to have a resistor in series to limit the current as an R-C-filter or to have an inductance in series for the same purpose, this inductance stores energy and when the contact is closed, this energy will go to the sink. But you started to plot prime numbers and I showed, that prime numbers can be cristals with defects.

Perfect opportunity to drop the right formulas to express what you mean:

You are saying, kids lets consider :

$$Z= R+j(\omega L-\frac{1}{\omega C})$$

And lets solve for resonance:

$$\omega L-\frac{1}{\omega C} =0$$

I know everybody reading this can arrive to:

$$\omega^2 = \frac{1}{LC}$$

$$\omega = \frac{1}{\sqrt{LC}}$$

About this and I quote you: ...prime numbers and I showed, that prime numbers can be cristals with defects...

You feel you have shown that, and as I understand the spirit you had to share it I can agree with you using empathy. But didn't you consider that these defects are just higher (degrees-of-freedom/dimensions ) projections/shadows?

[neondata]

Just to post-it: https://www.youtube.com/watch?v=OFI1FJcGLeM Interesting to watch a scientist realizing what every gear shaper knows : 15:00 . On the other hand: gear shapes don't imagine there knowledge to be relevant to science.

[fbunc]

Just to post-it: https://www.youtube.com/watch?v=OFI1FJcGLeM Interesting to watch a scientist realizing what every gear shaper knows : 15:00 . On the other hand: gear shapes don't imagine there knowledge to be relevant to science.

Amazing explanations!!

Have you seen these two Mathologer videos and tried to connect them?

for sure many of us did playing while watching youtube

Discrete Newton and what's next? (methods for investigating sequences) https://www.youtube.com/watch?v=4AuV93LOPcE

Mathologer FlowerPhi https://youtu.be/_GkxCIW46to?t=54

[neondata]

OK, I have to turn a part on my lathe. So let me now pause with an idea: the physical concept "action" (behind the famous quantum of action) in dimension is energy times time. (like impedance: voltage over current) So what is the impedance of action?

[neondata]

Have you seen these two Mathologer videos and tried to connect them?

I've seen a lot and learned a lot or became aware of a lot, but I tried to connect and ask two things but didn't get an answer.

So I can point you to something that to me is a fascinating relationship:

The equation I^N + J^N = K^N, as we all know has no solution for integers I, J, K, N if N>2. The question I rise is: is this equation mathematically equivalent to the question if the function z = f(x,y) = x^N + Y^N can have the same value z for two 2-tuples (I, J ) and (K, 0) I raised this question multiple times and never got an answer.

[fbunc]

My level of physics is too basic, for my answer to be useful.

But as I said, I'm just playing with the ideas the online community shares. We all do that, but if we don't find the right context, good ideas or proposals go to waste because of lack of formality.

What I loved during my career was control theory and the introductions to signal processing and dsp (MIT published the bible on all these topics freely available online), so... not really my place to introduce physics topics/paradoxes .

Because what I think you just tried to say using the wrong words is this:

(now I will use E for energy not electric field)

$$E=P·t$$

What would be a first simplification of an integral we both know that energy is the area under the curve of the rate on which that energy is generated/consumed during a certain time-period. This is also related to -work- , usually measured in Joules and E in the context we are talking about, but for people not familiar with this : Energy units are what you pay for your electricity bill each month plus some taxes and different time-peaks-based-cost-matrices ( $kWh/month$ )

Going on with the basics of the simple-impedance-model :

$$P=V·I$$

Being by a simplification of ohms law:

$$V=I·Z$$

Being V the Voltage (measured in Volts) , I the current (measured in Amperes) and Z the Impedance where we deal with some circuit components that integrate the current and others that differentiate the current (over time) . Now I ask, which one (considering the simplification with L's and C's) is the 'differentiator' and which one is the 'integrator'?

This is where you are trying to get?. I follow your lead. What is it that you are trying to point out?

[neondata]

As an electrical engineer you learned different concepts.As a physicist you would have learned about the same topic from a different view point. As a mathematician you learn about abstract structures and there is no need to apply them to anything if only you are paid ;-) So I can show you something that should be an eye opener if they are not open already. To prepare it: do you know the Clarke-Park transform? And if yes, can you tell me with simple words what it means ? (Just to synchronize)

[fbunc]

Nope, you sent me to google: https://es.mathworks.com/solutions/power-electronics-control/clarke-and-park-transforms/_jcr_content/mainParsys/band_copy_1227855798/mainParsys/columns_1606542234_c/1/animation.animation.mp4/1614705044699.mp4

But I mean, I work with solar energy and next month I'm installing a solar system 16kWp in 3 phases, so yeah it's all about context. If that is what you mean.

COOL! https://es.mathworks.com/solutions/power-electronics-control/clarke-and-park-transforms/_jcr_content/mainParsys/band_copy_1227855798/mainParsys/columns_1606542234_c/1/image_1765388138.adapt.full.medium.jpg/1657542801360.jpg

[neondata]

My solar panels work for me just now! 20 kWp, 3ph, but I plan to develop a 48V system to have every panel MPP-tracked and go to a 48V battery to then drive a heat pump at winter time. Do you work professionally in this field.

So I googled https://www.youtube.com/watch?v=9jBwIlTEa9M as a short video not to waste your time. As you may follow the math, (not the money) you will for sure miss a deeper insight. I'll come up with this later..

[fbunc]

Just a quick note: If your hint is that, if you want to call it that way imaginary-golden-ratio, and you see just the complex number, you just get $\frac{2\pi}{3}$ . That simple fact just like that, doesn't tell much. It takes people that really know math not like us like all reading this that really know math could laugh about this conversation. But I mean, to see that this ratios(not only these, but the infinite many that exist and we didn't take a look) all this games bring you connections between different fields of math, emotion of discovery is just a feeling you can have while you play, but the second you think your ideas are great you lose direction and purpose.

[neondata]

You worked as a teacher and did you ever laugh about someone who knew less then you do? So why should anybody care about being laughed at. OK with the heat pump: 1kW electricity in average creates about 4 kW of heat. You have to store the heat in a "(thermally) stratified storage tank" (hard to even find the english expression to the well known "Schichtspeicher") As solar power on your roof is for free (you can feed it to the grid for 0.08€/kWh) such a solution is just fine. I produce about 25 MWh a year. So if there is around a person who can explain the Park-Clarke-Transform in simple terms and why it is used as it is, reading this conversation, jump in and answer the question raised :-)

[fbunc]

Also, I don't know if in my previous post you read this question: Being V the Voltage (measured in Volts) , I the current (measured in Amperes) and Z the Impedance where we deal with some circuit components that integrate the current and others that differentiate the current (over time) . Now I ask, which one (considering the simplification with L's and C's) is the 'differentiator' and wich one is the 'integrator'?

This is where you are trying to get?. I follow your lead. What is it that you are trying to point out?

[neondata]

sorry, I in no way intended to embarass you, Maybe it's using a foreign language or even bad experience, I had enough myself.

[neondata]

What I wanted to show is: knowledge is not less worth, when it turns out to be not sophisticated. The opposite is true. Progress is reached when knowledge can be aquired by more people. In the past it was the privilege of an elite to read and write, this is no longer the case and so we can communicate. So now let me show you what is the secret of the Clarke-Park transform: from 3 sinusoidal voltages or currents you create a single sinusoidal voltage/current (Clarke) and then a DC voltage current (Park). What we need is Kirchhoffs law: ths sum of currents/voltages is zero. So e.g. U+V+W = 0. Then U1 + V1 + W1 = 0. We can write this as the inner product of two vectors: (U, V, W) (1, 1, 1) = 0. All vectors with an inner product of zero are perpenticular and all vectors perpenticular to a given vector are in a plane. You can designate the axis of this plane as X, Y, or d, q. If you take the phase angle of U as a reference, and line it with the d-axis, the vector formed by the 3 values (often called "space vector) lies in this d/q plane. And that's it, without any imaginary number and matrices.

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[leios]

Sorry I saw this conversation so late. @fbunc Would you say that @neondata is going far offtopic for this thread?

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[leios]

Ok, good. I realize that this discussion is quite offtopic and might discourage people from actually collaborating on this post. I can delete the comments on this thread so that people do not see the spam, if you want. Otherwise, we can leave it as is.

[fbunc]

If you think is better to remove the comments please do. (edited)

[neondata]

Do whatever is needed

[fbunc]

I will publish a more organized Idea soon, thank you neon and leios and sorry if any problem.

[fbunc]

I Reopen this issue, because first time I was in a conversation with neondata and I got too tired and that caused a misunderstanding from my side. Neondata insights where brilliant, and really useful, and also one of latest Sabine videos was a great introduction to some of neon questions. Next proposal I'll try to include some MIDI music in the same sequence, maybe some musician jumps to the rescue.

If off-topic comments should be removed, let me know. Sorry for any confusion and Thanks!

[fbunc]

Please @leios delete everything here. Posting a clean version with a summary. Thank you