Key Experiments of Physics: The Photoelectric Effect

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  • Опубликовано: 28 сен 2024
  • Performed first by Heinrich Hertz in 1887, the experiment became famous due to Einstein's interpretation in 1905...
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Комментарии • 80

  • @Dyslexic-Artist-Theory-on-Time
    @Dyslexic-Artist-Theory-on-Time 5 месяцев назад +3

    Could light be an electromagnetic wave over a ‘period of time’ with particle characteristics as a probabilistic future unfolds relative to the atoms of the Periodic Table?

    • @jaydenwilson9522
      @jaydenwilson9522 5 месяцев назад +1

      yeah i think the waves get knotted into linked donuts or something.... and the 2 little dudes get locked into tracing an outline/perimeter of a sphere to create the illusion of balls.

  • @clmasse
    @clmasse 5 месяцев назад +2

    Planck thought that the origin of quantization was in the interactions of radiation with matter, not in the electromagnetic field itself.

    • @TheMachian
      @TheMachian  5 месяцев назад +3

      I agree with Planck here, though I haven't emphazised it in this video.

  • @curiousmind9287
    @curiousmind9287 5 месяцев назад +6

    Is there any explanation of photoelectric effect that does not need quantum?

    • @zyxzevn
      @zyxzevn 5 месяцев назад +7

      My answer seems hidden (due to link).
      There is indeed an explanation that uses thresholds. Even supported by Max Planck. It was historically removed from memory due to bias for particles.
      This explanation states that the EM-waves are resonating with electron-shells. These resonances can be measured and are verified. At certain resonances the electron-shells start absorbing the energy and electrons can be released.
      In history the electron shells were not known, so they assumed that an electron was shot out of orbit. And to do that they needed to come up with a bullet, the photon-particle.
      But if you look deeper in electromagnetic waves, nowhere and never a photon can exist. It is always a wave. The photon only exists in mathematical models to describe a change.
      This change is never sudden. Not even at atomic levels. It is resonance that makes an electron-shell break and a new electron-shell form.

    • @graemenicholls2836
      @graemenicholls2836 5 месяцев назад

      I've not mentioned it specifically here - but it is in the book: dconstructionmodel.wordpress.com/2024/03/22/what-electricity-actually-is-super-conductivity-and-lightning-explained/

    • @radiofun232
      @radiofun232 5 месяцев назад

      The question is troublesome, because it is all about the description of a physical phenomenon.

    • @curiousmind9287
      @curiousmind9287 5 месяцев назад +1

      @zyxzevn Thank you so much! Do you have a reference?

    • @dicktracy3787
      @dicktracy3787 5 месяцев назад

      @@zyxzevn Hear hear

  • @rogerscottcathey
    @rogerscottcathey 5 месяцев назад

    Interesting. Vortices can sustain waves within their Faraday rings. The only way to get progress in this question is to begin incorporating C.F. Krafft's vortex atom model both theoretically and experimentally.

  • @PerScientiaAdAstra
    @PerScientiaAdAstra 5 месяцев назад +1

    ...the fact remains that we only have a mathematical description (a model) of the underlying phenomena. What physical "reality" these models represent constantly evolves with time and insight. What's important is that we mustn't constrain physical intuition by the "models" but rather use that intuition to refine them.

  • @someone3533
    @someone3533 5 месяцев назад +1

    Astroturfed superstar Einstein did not interpret the Ph.e. Effect "the right way". That's the problem. He, amongst others, derailed Physics off its course. Light is a transverse EM wave and as such, it requires a dielectric medium to propagate in the vacuum. There is no particle aspect to light (or any other frequency EM wave). However its interaction with the atomic structures that compose ALL physical bodies and materials of all kind (which interaction is NOT understood and not even described(!) at the moment) is such that it is absorbed and emitted by said atomic structures: atoms, ions and lattices of all kind in quantums of energy (according to for ex. Einstein's equation for the Ph.e Effect in case of the Ph.E. Effect). The problem is that the HOW exactly is said absorption/emission happening is not described and the WHY it is happening in a quantised manner is not understood (I guess, if one correctly describes the HOW, he will understand the WHY). It all has to do with the mainstream's erroneous description of the electric force (Maxwell/Heaviside's Electrodynamics is very problematic and incomplete and it should be substituted with Weber's Electrodynamics ASAP to start), of the particles that compose the atomic structures: electrons, protons and neutrons, of the atomic (and nucleic) structures themselves and last but not least of the very dielectric medium of the vacuum EM waves propagate in and also of the HOW exactly they propagate in said medium.

  • @leonhardtkristensen4093
    @leonhardtkristensen4093 5 месяцев назад +1

    As I understand it Planck's constant multiplied with the frequency hf gives an amount of energy over one second. That means that a photon has to be one second long. I find that unbelievable. I would rather believe that the frequency has to be right (high enough) to show the effect.
    We know from solar panels that they are sensitive to specific frequencies and with those frequencies also the intensity of light but outside the frequency range any intensity won't work.
    I would there fore say that the photon is a measurement for the energy of a frequency over one second and not at all a particle. The energy send from an electron jumping in an atom from a higher energy level to a lower one gives out an energy pulse at a certain frequency for some time but but I don't think it is bound to our time keeping of seconds.
    I also believe that an electron is more like a standing wave of some frequency and when it jumps it changes frequency to gain a new energy level.

    • @nonplayercharacter6478
      @nonplayercharacter6478 5 месяцев назад

      I would agree with that. I've also heard it suggested that the proton is itself, a standing wave, albeit a much more stable and self sustaining one.

  • @xxxYYZxxx
    @xxxYYZxxx 5 месяцев назад

    Wave-particle duality is straightforwardly described by the CTMU. The wave/particle duality respectively represents the design and actualization phase of reality. The wave-like design function distributes attributes over space-time domains while the actualization phase is associated with particle collapse internal to the distributed domain. Thusly, the attributes of a given object/event can be differentially "collapsed" according to each and every observer's (measurement tool's) unique frame of reference.
    "Incoversion carries global structure inward as state-recognition and state-transformation syntax, while coinversion projects syntactic structure outward in such a way as to recognize existing structure and determine future states in conformance with it. Incoversion is associated with an operation called requantization, while coinversion is associated with a complementary operation called inner expansion. The alternation of these operations, often referred to as wave-particle duality, comprises the conspansion process. The Principle of Conspansive Duality then says that what appears as cosmic expansion from an interior (local) viewpoint appears as material and temporal contraction from a global viewpoint...". C.M.Langan, "Intro. to the CTMU"

  • @ovidiulupu5575
    @ovidiulupu5575 5 месяцев назад +2

    If a half planck constant îs a vortex at quantum level of quantum microspaces, a foton are 2 vortexes combine, all particles are some mathematical structures of this kind of vortexes. Charge conservation îs due to cinetic moment conservation integrating over structures, mass îs quantum conection between structures and whole quantum univers. Mass can be made zero if we cut this enthengelment.Energy is related to The flow of time. Must reconstruct all, useing quantum microspaces, some mathematical lows of interraction between them. No virtual particles. We will have space curvature, unified forces, teleportation în every move, inertia, gravity, all particles are quantum condensate light. That is why atoms absorb or emite light. Because are The same nature structures.

    • @r3yv944
      @r3yv944 5 месяцев назад

      Matematical codes, With energy going through it and making it vibrate?

    • @andymouse
      @andymouse 5 месяцев назад

      "Must reconstruct all" sounds like a proper plan.

    • @ovidiulupu5575
      @ovidiulupu5575 5 месяцев назад +1

      He 4 îs some kind of macro replication of foton. Very stable.

    • @andymouse
      @andymouse 5 месяцев назад

      @@ovidiulupu5575 where can we hear more please ?

    • @ovidiulupu5575
      @ovidiulupu5575 5 месяцев назад

      The way în wich mater and antimater anihilate and become light mins that are în antifaze. Mind can resonate with frames of world histories. Mind is above mater reality. When we born we are enthengeled with this world. By meditation we can do many things. Resolution în Time, concentrated mind on present, mins lot of energy. An ordinary human only fallow The frames... I belive în superior realities, soule, mind, persons spaces, lows of material space îs în conection with superior lows. To understand this reality must first understand The human interdimensional structure. With all implications. But clues are. Humans are like interdimensional molecule. With ego like comand central. Sole and mind are controled by personal ego or from others ego s, more strong.

  • @walterbrownstone8017
    @walterbrownstone8017 5 месяцев назад +6

    To pretend the photon is a thing is just as preposterous as pretending a water wave is a thing. I'm this day and age it's counterproductive and profitable.

    • @atheistaetherist2747
      @atheistaetherist2747 5 месяцев назад

      Nope. Everything that we see & feel is photons. The opposite of your silly idea(s).

    • @walterbrownstone8017
      @walterbrownstone8017 5 месяцев назад

      @@atheistaetherist2747 nope. Electrostatic mass is what we are made of. Without the former there is no latter.

    • @atheistaetherist2747
      @atheistaetherist2747 5 месяцев назад

      @@walterbrownstone8017
      Gravity (& mass) has been explained by Prof Reg Cahill (Adelaide).
      EM is not a basic cause.

    • @walterbrownstone8017
      @walterbrownstone8017 5 месяцев назад

      @@atheistaetherist2747 From the outside in our the inside out, which makes more sense? One particle, one vector is the simple mathematical truth. Matter, therefore the universe and not The Universe therefore matter. Matter is all that matters. Citing doctrine will not get you there.

    • @atheistaetherist2747
      @atheistaetherist2747 5 месяцев назад

      @@walterbrownstone8017
      Yes, i agree. And that one particle or quasi-particle is the photon. Which makes proper particles, eg electrons. (See Williamson)(See Conrad Ranzan).

  • @teragreg2927
    @teragreg2927 4 месяца назад +1

    Hi Mr. Unzicker,
    I have a question for you:
    Do we know why a moving negative charge has a field that points in the anticlockwise direction, rather than the other?
    To be clear, I’m not asking why we named the conventions this way. I’m asking why does the field always point this way, as opposed to the other way. What about our universe causes the field to be this way, not the other way?
    Thanks for your time,
    TG

    • @obiwanduglobi6359
      @obiwanduglobi6359 4 месяца назад +1

      The anticlockwise direction of the magnetic field around a moving negative charge (like an electron) is a consequence of the fundamental properties of electromagnetic interactions and the conventions we use to describe them. The direction of the magnetic field generated by a moving charge is determined by the right-hand rule, a mnemonic that aligns with the definitions of current and magnetic fields in Maxwell's equations.
      Scientifically, there isn't a deeper "why" for this directionality beyond the consistency of these rules and equations. The universe doesn't inherently favor one direction over another; these rules are a way to consistently describe observed behaviors of electromagnetic forces. If the conventions were defined differently, the descriptions would still need to be consistent with observed phenomena, but the actual direction labeled as "anticlockwise" could be opposite. Thus, it's the consistency and predictability offered by these conventions and rules that dictate the field direction we observe and utilize in physics, rather than an intrinsic property of the universe itself.

    • @teragreg2927
      @teragreg2927 4 месяца назад +1

      @@obiwanduglobi6359 Thanks for the reply. The simplest explanation I've concluded on, thanks to your reply and a few others, is this:
      Negative charges produce a field with north pole pointing anticlockwise, positive charges produce clockwise north poles. Since electricity is associated with the flow of electrons, which are negative, it means live wires *always* have a field with anticlockwise north given direction of electron flow.

    • @obiwanduglobi6359
      @obiwanduglobi6359 4 месяца назад

      @@teragreg2927 The statement contains some inaccuracies and misconceptions about electric fields and magnetic fields.
      1. Electric Charges and Fields: Negative charges (electrons) and positive charges (protons) create electric fields, not magnetic fields. The direction of an electric field produced by a negative charge points towards the charge, whereas the field from a positive charge points away from it.
      2. Magnetic Fields and Current: Moving charges (current) create magnetic fields. According to the right-hand rule, if you point your thumb in the direction of the conventional current (positive to negative), your fingers curl in the direction of the magnetic field lines. For electron flow (negative to positive), the field direction is opposite to the conventional current direction.
      3. Poles and Field Direction: The concepts of "north pole" and "south pole" pertain to magnetic fields, not electric fields. In a current-carrying wire, the magnetic field forms concentric circles around the wire. There are no distinct north or south poles in this context.
      4. Live Wires: In alternating current (AC) systems, the direction of electron flow changes periodically, so the associated magnetic field also changes direction.
      I hope that helps. Have a nice day.

  • @atheistaetherist2747
    @atheistaetherist2747 5 месяцев назад

    Finding the true nature of the PEE depends on having a true idea of (1) what a photon is, & a true idea of (2) what a conductor (say metal) is, & (3) a true idea of what electricity is.
    ......... Electricity is due to photons propagating (at the speed of light) on/along/over the surface of the conductor, hugging the surface.
    ...........Metals are metals koz they have photons propagating on/along/over their surface, hugging the surface.
    ............A photon is not a wave, but it has wave-like propertys. A photon is not em, but it produces em.
    Now we can have a good think about the true nature of the PEE.
    I will give u another clue. PEE has zero to do with electrons orbiting in an atom.
    Why is it that i know more than everyone else around here combined??????????

  • @obiwanduglobi6359
    @obiwanduglobi6359 4 месяца назад +1

    Ein fetter Daumen nach oben, Herr Unzicker. Physikgeschichte ohne jegliches Geschwurbel. Weiter so und danke für den interessanten Beitrag!

  • @radiofun232
    @radiofun232 5 месяцев назад

    We all (perhaps not everyone...) know this 28 April 2024

  • @JamesEdwardTracy
    @JamesEdwardTracy 5 месяцев назад +7

    Really like your channel, great stuff. Years ago I ran project omicron which was later taken over by Dr jurgen Schultz in Germany. Out of the project we showed that electromagnetic waves have no electric component, they're purely magnetic. The electric component only shows up when it hits whatever detector or measurement system you're using. Anyway great channel really appreciate it. You remind me of Dr schultz, he was a great guy. Oh yeah we have an experimental apparatus called the Benzel, which I hope one day to get constructed. It would really be not that expensive. This device came out of the research. There were quite a few physicist and mathematicians involved in the project. I wrote a book about it in 1995 or was it 1998? I'm an old guy now, forgive me.

    • @zyxzevn
      @zyxzevn 5 месяцев назад +2

      Wait. Static charge is well tested. Do you claim that it does not exist?

    • @JamesEdwardTracy
      @JamesEdwardTracy 5 месяцев назад +2

      @@zyxzevn
      If you move a charge past a magnetic field detector you will find a magnetic field. We think that if you move the detector pass an electric charge, no magnetic field. I don't think we were ever able to find an experiment that bore this out to my knowledge. I don't know if this helps answer your question, alas I was merely the Creator and administrator for the project. I remember that proposition 13, which escapes my memory at the moment, caused quite a stir as relates to electromagnetic waves and I remember Dr Schultz getting quite excited about it along with many others. From that the Benzel experiment emerged. A properly constructed benzyl, tuned properly, could then project an accelerated Force. Oddly, I have been consistently sabotaged in trying to do this experiment. I'm not saying it's in a conspiracy theory but it just seems that life has conspired to shut the whole thing down. But that's probably just my oldness talking. LOL

    • @zyxzevn
      @zyxzevn 5 месяцев назад +1

      @@JamesEdwardTracy I think that you are describing the homopolar generator experiment in the beginning. There are some interesting historical discussions about it. But it seems resolved to me, as you can also describe it as the effect of Lorentz-forces.

    • @JamesEdwardTracy
      @JamesEdwardTracy 5 месяцев назад

      @@zyxzevn
      Oh yes I remember the homopolar motor came up quite a lot but forgive me I don't recall specifically how it fit in . I have my book in PDF format Although I'm not sure if it's on a hard drive or if I was smart enough to put it on a cloud drive but but you would be welcome to it if you are so inclined. I don't know how soon I could located comama at the moment I am having some family problems.

    • @JamesEdwardTracy
      @JamesEdwardTracy 5 месяцев назад +1

      @@zyxzevn
      Oh yes, I left out the most important piece of all period this project Was an attempt to throw out all of the conclusions in standard physics, and start Fresh period the result was neo Aetherics. I've been watching a channel called Dialects Which I believe is steering people into that direction. Our overall conclusion was that there wasn't ether and quite a bit of math was worked out in math cab buy our resident mathematician. Sorry I neglected to bring this up, I find most people unwilling to accept an ether theory although I have heard lately that it's making a comeband I would count myself among among the first to go in that direction. In a new direction that is to say As in neo etherics or a retry of an old theory. The ether always made perfect sense to me and and all the equations are just as accurate by looking at an ether as it is curb space for instance period it makes no difference accept to describe that which isn't fully understood.

  • @pdaniel97675
    @pdaniel97675 4 месяца назад

    It would be wonderful to see a video on what *causes* the Lorentz Force. There are so many videos explaining what it is, but I've never seen or read anything on the causes behind it.

    • @2tehnik
      @2tehnik 4 месяца назад

      What do you mean “what causes the Lorentz force”? As in, why it’s true in the first place?

  • @johnlord8337
    @johnlord8337 5 месяцев назад

    What Einstein, Hertz, and Planck were defining what are the "3" photons (particles) of the matter universe (tau electron photon, muon electron photon, and electron photon) and the "3" photino particulates (waves) of the Aether universe (small electron photino, electrino photino, and graviton photino).
    The matter particle photons are full light speed, while the aether particulates are variable light speed. This for these 6 photons and photinos, there are "6" light energy (particle angstroms) and (particulate frequencies). Knowing what are the tau, muon, electron, small electron, electrino, and graviton energy levels, you then have the dual electro-gravitic electron (electrino) and the electro-gravitic positron (positrino) composite (EG-EG) of the photon (photino) and its angstrom or Hz frequency with absolute clarity.
    This proves that the particle photon box of Einstein only shows the matter particle photons of the electron, muon, and tau, ... while the wave photino box only shows the wave (frequency) Aether particulates photinos of the small electron, electrino, and graviton.
    It is that simple. Don't make it more complex !!! This shows that the matter universe and the (dark) Aether universe are 2 established domains. It also solves more than 31+ of the common anomalies, disruptions, and disparencies between the various physics realms can be ABSOLUTELY RESOLVED, corrected inaccurate information in those sectors, and showing the Grand Unified Field Theory (GUFT, TOE) !!!

    • @obiwanduglobi6359
      @obiwanduglobi6359 4 месяца назад

      The concepts described, including distinctions between "matter particle photons" and "aether particulates" like "small electron photino," do not align with mainstream scientific understanding as established by Einstein, Hertz, Planck, or modern physics. Photons in standard physics are massless particles associated with electromagnetic force, not classified into types linked with matter particles like electrons, muons, or taus. The idea of an "Aether universe" comprising variable-speed "photinos" is speculative and not supported by empirical evidence within the framework of quantum mechanics or general relativity. These descriptions seem to mix conceptual elements of physics without recognition by the scientific community.

    • @johnlord8337
      @johnlord8337 4 месяца назад +1

      ​@@obiwanduglobi6359The Standard Model is self-negating the real truths of the sub-quantum realm - thus denying their own status of making authoritative comments.
      The electro-static (ES) and electro-gravitic (EG) model shows that your comments are partially true and partially false. Photons and photinos are EG-EG composites. They do have electro-gravitic force (quit saying magnetic, it is a bogus word). They APPEAR massless, because their composite structure has a photon neutron sphere as its outer structure, while the gravitational force is still viable inside. The same applies for the EG-EG aether particulate composite structure.
      Einstein's gravitational lensing proves the ES and EG mnodel, as the Tau, Muon, and Electron particles are light speed and gravity escape velocity - thus gravitational lensing. Einstein's variable light can only be validated within the Aether domain, and the photinos of the small electron, electron, and the graviton electro with less-than-light-speed velocity, thus they are gravitationally captured. Matter photons are "light is a particle" in the light box experiment. Aether photinos are "light is a wave" in the wave box experiment. The Aether and its particulates MUST BE there - no matter how pizzy and screaming the self-negating Standard Modellers have tantrums about. The Aether exists. The ES and EG model resolves 31+ anomalies and problems that the many different physics sectors can't resovle amongst themselves. Each claims their truths, but can find no mutual interactions. The only interaction can only be solved by the Aether sub-quantum realms.
      Even so, much more, the ES-ES composite structure of these 6 levels of 3 neutrons and 3 neutrinos have the same structure as the photons and photinos ! But as a dual ES of the neutron, versus the dual EG of the photon, they have the same neutron shell, appearing as a massless particle, while the interior has no gravitational force. Thus, neutrons and neutrinos can fly through 30+ light years of steel and not stop as they have no aspects of an interior gravitational force like the photons and photinos. You really need to ask questions about the model, before opening lips and making statements that are not valid. 40+ years of study and research is continually proving this model is correct.
      The same for explaining in simple terms the entire stellar engine, where the photosphere is composed of the Aether domain particulates and their tensor bosinos as the actual fusion producers of Hydrogen into metallic flow metal Hydrogen into Helium up to Iron. The chromosphere is composed of matter particles and their tensor bosons as the actual fusion producers of Cobalt up to Element 118. Stellar collapse is easily explained that anything conventionally explained now. Also nuclear fusion has no relevant million degrees of thermonuclear fusion properties as these tensor bosinos and tensor bosons (composed of alternating electrical force and gravitational force = i.e. Birkelund currents) give and take back all electrical forces (overwhelming the Van der Wahls radius of the eletron shells) and the gravitational forces (overwhelming the Coulomb boundary of the nucleus) fusing the 2 nucleus together, then retreating the tenson bosons/tensor bosinos allowing the electron shells to merge into the new singular fusion atomic structure.
      The same for Einstein's paradox of the sun disappearing and the Earth gets the last sunlight in 8.33 minutes, while the Sun instantly disappears, and the Earth instantly shoots off (and all other planets as well) into deep space. The sunlight model is matter quantum entanglement, while the tangental event happens at the Aether domain sub-quantum entanglement.
      Your generic (and sweeping ?) statements that QM and GR does not support the ES and EG model is negated (and shown inaccurate) when you have the FULL UNDERSTANDING of the whole ES and EG model (which you DO NOT know). Negating the Aether of dark matter, dark energy, and these particulates and sub-quantum entanglement DOES SOLVE all these issues.

  • @albertperson4013
    @albertperson4013 5 месяцев назад +1

    Since light is expressed as frequencies of the electromagnetic spectrum, then that should indicate its 'wave nature' as the aether being excited at those frequencies. If photons actually do exist, then they could be 'bundles' of energy travelling along those waves simultaneously with the waves. Perhaps neutrinos could be the missing link between these two phenomenon. Just a thought.

    • @nonplayercharacter6478
      @nonplayercharacter6478 5 месяцев назад

      Maybe the energy wave just discharges at that point, it doesn't need to carry particles, the detector or particle it interacts with 'creates' them, in effect, by absorbing the energy at that frequency in that spot. I think it's like digital sampling of an analog signal.

    • @obiwanduglobi6359
      @obiwanduglobi6359 4 месяца назад

      There's absolutely no evidence for an "aether". Why bringing old, falsified elements into the equation?

  • @zachariaszut
    @zachariaszut 5 месяцев назад +1

    This still boggles my mind... big time.

    • @EternalSearcher
      @EternalSearcher 5 месяцев назад

      everything boggles your little mind... big time

    • @zachariaszut
      @zachariaszut 5 месяцев назад +1

      @@EternalSearcher Define little.

    • @EternalSearcher
      @EternalSearcher 5 месяцев назад

      @@zachariaszut it's when you only have 2 brain cells yet they are competing for third place

    • @zachariaszut
      @zachariaszut 5 месяцев назад +3

      @@EternalSearcher ...and fail at that. You described yourself perfectly, thank you. I'll leave it here. Hasta la vista, baby.

    • @obiwanduglobi6359
      @obiwanduglobi6359 4 месяца назад

      @@EternalSearcher Small minds usually search for truth eternally without finding anything. And now, back to your cellar!

  • @Chris.Davies
    @Chris.Davies 5 месяцев назад +1

    I have downvotes showing, and it appears 3 idiots have been here.
    Thank you, as always, Dr. Unzicker.

  • @williamsvisualeffects1520
    @williamsvisualeffects1520 5 месяцев назад +1

    Trumps uncle has got to release the whole classified physics theory! Which we have from aliens

  • @markmartens
    @markmartens 5 месяцев назад +1

    I can find nothing in physics, actually in any science, that IS understood, I mean under the current paradigm. Perhaps least of all quanta. Am I missing something?

  • @davidwilkie9551
    @davidwilkie9551 5 месяцев назад

    I keep wondering why the Institute of Art and Ideas hasn't discussed the "artisimal" functional phenomenon of self-defining vertices in vortices, nodal-vibrational crystallisation and the properties of logarithmic condensation-coordination vanishing-into-no-thing Perspective. Odd. Singularity-point positioning holography-quantization doesn't seem as if it should be very strange to one who can picture coherence-cohesion operations of Lasers in projection-drawing.