root, base - fruit
throat, crown - water
natal, solar - spf/aloe
sacral, heart - sunlight/heat of many colors
it's interconnectedness and intellectual upbringing that can aspire you to be still to figure things out, yourself and others out.
Inverse Square Law ✍️
Here is one of the most beautiful
unifying ideas in physics: five phenomena that seem completely unrelated, the brightness of stars, the loudness of sound, the illumination of surfaces, the force between electric charges, and the gravitational pull between masses, all weaken with distance in the same way. They follow the same pattern for the same underlying geometric reason. This reason has nothing to do with the specific nature of these phenomena but is all about the shape of the three-dimensional space we live in.
The core idea is almost embarrassingly simple once you see it: any influence that spreads equally in all directions from a single point forms an ever-expanding sphere. The total amount of influence emitted is fixed and cannot disappear. This fixed total must spread across the surface of this growing sphere. Here is the crucial geometric fact that drives everything: the surface area of a sphere grows with the square of its radius. When the radius doubles, the surface area quadruples. When the radius triples, the surface area grows ninefold. When the radius grows tenfold, the surface area grows a hundredfold. As a result, the influence available per unit area shrinks by the same factor. This gives you one quarter the intensity at twice the distance, one ninth at three times the distance, and one hundredth at ten times the distance.
The diagrams on the right side of the image make this perfectly clear. At the closest distance, one small square receives the full intensity. At twice the distance, the same cone of spreading influence now covers a two-by-two grid of four squares, so each gets one quarter. At three times the distance, it covers a three-by-three grid of nine squares, so each gets one ninth. The visual makes the geometry undeniable.
For sunlight and all electromagnetic radiation, the sun's total energy output spreads over an ever-growing sphere as it travels through space. This is why Mars receives less than half the solar intensity per square meter that Earth does, simply because it is farther out on that expanding sphere. This also explains why Mercury receives about seven times more solar intensity than Earth. The discovery that the universe's expansion is accelerating was made possible by measuring how dim distant supernovae appeared compared to their known true brightness and using the inverse square law to calculate how far away they must be.
For sound, a loudspeaker's fixed acoustic power spreads over the same expanding sphere. Doubling your distance from a speaker drops the sound intensity to one quarter a six decibel reduction. This is why outdoor concerts require large distributed speaker systems to make up for the dramatic inverse square drop that would leave the back rows barely able to hear.
For the illumination of surfaces, moving a photography light from one meter to two meters away from a subject reduces the light on that subject to one quarter. This is why portrait photographers must either quadruple their flash power or dramatically increase their aperture when they move their light back. It also explains why plants at twice the distance from a grow light receive only one quarter of the radiation they need for photosynthesis.
For electric force between charges, the electrostatic attraction or repulsion follows the same inverse square pattern. The electric field lines spreading from a charge distribute over a growing spherical surface in the same geometric way. This single fact underlies all chemistry. It explains the force holding electrons around atomic nuclei, the bonds between atoms that form molecules, the folding of proteins, and the properties of every material all resting on the inverse square law at tiny atomic scales where the distances are small and the forces are large.
This study describes a new physical mechanism that overcomes a big limitation in topological wave manipulation: narrow k-space of flat Landau levels. Scientists achieved it by artificially synthesizing pseudo-magnetic and pseudo-electric fields.
🔗 https://t.co/MnQMrVX3Ww
In 1785, French physicist Charles Augustin de Coulomb showed that the force between two electric charges depends on their charges and the square of the distance between them.
F = k(q₁q₂)/r²
This simple relationship explains why opposite charges attract, like charges repel, and why electric force weakens rapidly as distance increases. It became one of the foundations of electrostatics and later helped shape the development of modern physics and electrical engineering.
A matrix can do something surprisingly dramatic. It can collapse an entire dimension into nothing. The null space captures every direction that is completely eliminated, making it one of the most fundamental ideas in linear algebra, geometry, and countless areas of physics.
Rihanna is actively working on new music, A$AP Rocky reveals:
“She in the studio right now.[..] Like, bro, she working. She cooking, no funny sh*t. Damn, I’ma get in trouble for this.”
(https://t.co/ObdYsidNEP)
A classification framework based on differential geometry introduces geodesic and torsional scalar spin chiralities — revealing a quantum geometric effect that modifies electron equations of motion in complex magnetic textures.
Read the study: https://t.co/JoBiPC9sU9