Index WHAT'S INSIDE:
00:00:00 The Circular Trap00:02:07 Buffon's Needle00:04:56 The Staircase Paradox00:07:56 Pi in High Dimensions00:10:40 The BBP Formula00:11:53 The Beautiful Equation00:12:44 Einstein's Equations00:15:04 The Eigenvalue Problem00:17:00 The Price of Symmetry
Notes:
Pi is the mathematical constant of rotational symmetry.Pi is the price that the Universe pays when it tries to treat all directions the samePi is the normalization constant for rotation. It's the mathematical reward for continuous smooth transition (If the turn is not smooth (ie. not stepped/ quantized) then the Pi is not there)In multidimensional space the volume of the numerator (where pi resides) is exponential, but the denominator (gamma function) is a factorial. In mathematics a factorial eventually outpaces any exponential, no matter how large the base is. As the number of dimensions goes towards infinity, the volume of a unit hypersphere goes to zero. Meanwhile the volume of the hypercube it sits inside approaches infinity. In 2D, a circle fills 78% of the area of a square, In 3D a sphere fills 52% the volume of a cube, In 5D its fills 16%, 10D 0.25%, 20D ~0%. Pi is a constant that dictates how fast that symmetric center disappears (and moves towards the limiting edge ie- Event horizon)Most Beautiful Equation: Using e and i and pi: e^(i*pi) +1 = 0
Constants capturing natural architectures: e of Growth, i of Rotation, and Pi of Symmetry
Smooth symmetry vanishes in high dimensions.Gravity is isotropic. Pi is the reason that gravity spreads uniformly in all four space-time dimensions (Einstein's field equations). 8pi is 4pi x2... to cover tensors in the energy density + tensors in the Pressure (in all directions). It's a structural requirement, not a choice.If space were directional (jagged/stepped/quantized), gravity would behave differently. Instead of round stars and smooth orbits, mass would clump along a preferred axis. This uniformity is a hard-coded property of how fields behave in a vacuum. It leads us to a single mathematical operator that explains why pi keeps appearing in the equations.The Eigenvalue problem. Pi is the fundamental frequency of any continuous isotropic space. It is the lowest possible vibration of a coordinate system that has no bias. Pi is not just a measurement of a circle's edge. It is the lowest-energy state of any universe that treats all directions the same.Pi is not a property of the circle. The circle is just one possible expression of Pi.Pi is the price of symmetry. What it costs for a system to be perfectly fair to every direction simultaneously. It's the numerical signature of a Universe that hasn't picked a side.
Folding Space into the Edges
and calculating the Resulting Probabilities
Principle of Least Action
Direction of Spin? Chirality Bias?
Broken symmetry in physics occurs when a system’s underlying physical laws are symmetric, but the actual, realized state is not, leading to ordered, lower-energy states. Spontaneous symmetry breaking, critical in quantum field theory and the Standard Model, allows symmetric laws to produce non-symmetric, ordered outcomes.
Key Concepts and Types
- Spontaneous Symmetry Breaking: The Lagrangian (physics law) possesses a symmetry, but the ground state (vacuum) does not, such as a pencil falling in a random direction (symmetric tip to asymmetric lying down).
- Explicit Symmetry Breaking: The underlying physical laws themselves contain terms that violate the symmetry.
- Significance: This concept explains the emergence of structure, ordered phases (like crystals or magnets), and particle mass generation.
Examples in Physics
- Particle Physics (Higgs Mechanism): The electroweak symmetry is broken, allowing and bosons to acquire mass while keeping photons massless.
- Condensed Matter Physics: Superconductivity occurs when the electromagnetic gauge symmetry is spontaneously broken.
- Phase Transitions: As a liquid cools, it freezes into a crystal, breaking translational symmetry, as noted by.
- Magnetism: In a magnetic material, the magnetic moments align in a specific direction below the Curie temperature, violating rotational symmetry.
Broken symmetry is deeply related to Noether’s theorem, where a symmetry is linked to a conservation law; in many cases of broken symmetry, the symmetry is hidden rather than absent, often with key implications for fundamental particle interactions
What Kind of Physics Are we Talking About, Holmes?
23 comments:
It all depend of POV.
Like... what way you used to make and read blueprints? Isn't it ISO standart? ;-)
But I, was trained to do it in GOST.
So? How we know that there ONLY ONE math? Only "one ring to rule am all"? ;-)
What if math attached to universe it describes? Isn't it would be natural thing to assume? ;-)
All is depends on POV
You said you see Demn propaganda up close, but do you see what's not right(pun intended);-p in this flic???
Naaah. Not comparation of demns with deamons. ;-p
But the very idea "fathers founders have found USA for USAians"
Hello there. You all, your ancestors are "illegal immigrants that came to kill native... ehm, north-americans"
And that thing never have stop to continue (like in that "Gangs of NewArk" movie. ;-p
POV's are only possibilities which can be summed to determine the principle of least action. That's the lesson of symmetry (Pi), of the universe. The "universal" law.
The principle is resolved in the application of the "constant" (Pi)
The perspectives (humans/demons) cancel (balance of powers). Only the prevailing bias (principle of least action) materialize in the summation of the perspectives (democracy).
There are no "final solutions" to the problem, only proportiionally greater imbalances that generate a "backlash" (the power of calling someone an anti-semite or racist today). After a while, the charge and hyperbole wear off, and the "demons" reveal themselves.
They will always attempt to "over-reach". Hubris.
As my former red-diaper baby antagonist (mr. ducky) used to frequently exclaim, "The struggle is eternal!"
Well... like humans do not kill humans, like in that fantasy world, like in our mundane one.
And well, like opposite setup, more usual one -- humans and deamons clearly separated and fight bloody war -- any better, less bloody(sic?),lower casualities.c. @@
And by the way -- that innocently looking flic. About deamons and anime -- is propaganda spread by internet trolls/bots.
AND "author" of that link, with seamingly white cisgender male name -- have just that flic in his channel.
But I just found yet one such "authir".
And who knows -- WHO do it?
Some white USAian? Rightwing?
Or some RFia, Iran or North Korea troll farm? ;-p
PS Predicted by Lem -- idea that instead of fighting with enemy/controlling people through force -- one can just manipulate their POVs. ;-)
Yes. Foucault called it "Bio-Power". Byung-Chul Han calls it "PsychoPolitics". It's what happens when the Hyper-real distorts the individual's natural "Ordo Amoris". When the Post-Modern Father is substituted for the old "Authoritarian" one.
all politics... need to be idiots
Ah, still dreaming of the single bullet solution...
Dreaming? That cinical bastard???
Sin-ical? ;p
The phrase "cynical bastard " is commonly used to describe a person who is extremely skeptical of the sincerity and kindness of others, often combining this with a rude or dismissive manner of communication.
resistance is futile ;-p
psychological kung-fu -- how to deal with "mind bullets" ;-)
Ah... kynical!
Google AI:
Kynicism (or kynical) refers to an ancient philosophical practice, often associated with Diogenes, that embodies resistance through shameless, bodily gestures (laughing, farting, public action) to critique power and official ideology. It differs from modern cynicism, which is often passive, intellectualized, and self-repressive.
Key Aspects of Kynicism:
Embodied Critique: Unlike intellectual argument, kynicism uses the body and public performance to expose the "egoistical interests" behind polite, ruling ideology.
"Playfighting" and Subversion: It functions as a popular, often vulgar, rejection of "official" truth, turning subversion into a form of artistic or political practice, as noted in the ProQuest dissertation on Kynismus.
Diogenes vs. Lucian: Early kynicism (Diogenes) was a live-in opposition to idealism, while later forms (Lucian) began to blend with modern, detached cynicism.
Modern Examples: It can be seen in "smark" engagement in professional wrestling, where fans use ironic cheers and chants to disrupt the narrative they are watching, as analyzed in the Xavier University study on Smarks.
Slavoj Žižek's Analysis: Žižek, in his analysis found on The Autodidact Project, often compares modern "cynical reason" (which retains an ideological mask) with the classical "kynical" exposure of that mask.
Note: In some academic texts, "cynicism" and "kynicism" are deliberately differentiated using the letter 'K' for the original ancient practice to avoid confusion with the modern definition.
Like certain French kaniggets!
Not interesting? :-(
Not into New Age/ Human Potential Motivational stuff...
...I'm more nto gnothi seauton. Know thyself.
And? How it not???
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