Brownian motion Updated 2025-07-16
Small microscopic visible particles move randomly around in water.
If water were continuous, this shouldn't happen. Therefore this serves as one important evidence of atomic theory.
The amount it moves also quantitatively matches with the expected properties of water and the floating particles, was was settled in 1905 by Einstein at: investigations on the theory of the Brownian movement by Einstein (1905).
This suggestion that Brownian motion comes from the movement of atoms had been made much before Einstein however, and passed tortuous discussions. Subtle is the Lord by Abraham Pais (1982) page 93 explains it well. There had already been infinite discussion on possible causes of those movements besides atomic theory, and many ideas were rejected as incompatible with observations:The first suggestions of atomic theory were from the 1860s.
Further investigations eliminated such causes as temperature gradients, mechanical disturbances, capillary actions, irradiation of the liquid (as long as the resulting temperature increase can be neglected), and the presence of convection currents within the liquid.
Tiny uniform plastic beads called "microbeads" are the preferred 2019 modern method of doing this: en.wikipedia.org/wiki/Microbead
Original well known observation in 1827 by Brown, with further experiments and interpretation in 1908 by Jean Baptiste Perrin. Possible precursor observation in 1785 by Jan Ingenhousz, not sure why he wasn't credited better.
Observing Brownian motion of micro beads by Forrest Charnock (2016)
Source. Coordinate chart Updated 2025-07-16
Terrorism Updated 2025-07-16
Big Dipper Updated 2025-07-16
Ciro's ASCII art circuit diagram notation Updated 2025-08-08
This notation is designed to be relatively easy to write. This is achieved by not drawing ultra complex ASCII art boxes of every component. It would be slightly more readable if we did that, but prioritizing the writer here.
Two wires are only joined if but the following are:
+ is given. E.g. the following two wires are not joined: |
--|--
| |
--+--
|Simple symmetric components:
-,+and|: wireAC: AC source. Parameters:e.g.:If only one side is given, the other is assumed to be at a groundAC_1Hz_2VG.C: capacitorG: ground. Often used together withDC, e.g.:means applying a voltage of 10 V across a 10 Ohm resistor, which would lead to a current of 1 ADC_10---R_10---GL: inductorMICROPHONE. As a multi-letter symmetric component, you can connect the two wires anywhere, e.g.or:---MICROPHONE---| MICROPHONE |SPEAKERR: resistorSQUID: SQUID deviceX: Josephson junction
Asymmetric components have multiple letters indicating different ports. The capital letter indicates the device, and lower case letters the ports. The wires then go into the ports:
D: diodeSample usage in a circuit:a: anode (where electrons can come in from)c: cathode
Can also be used vertically like aany other circuit:--aDc--We can also change the port order, the device is still the same due to capital| a D c |D:--cDa-- | Dac-- | Dca-- | --caDDCDC source. Ports:E.g. a 10 V source with a 10 Ohm resistor would be:p: positiven: negative
If only one side is given, the other is assumed to be at a the ground+---pDC_10_n---+ | | +----R_10------+G. We can also omitpandmin that case and assume thatpis the one used, e.g. the above would be equivalent to:If the voltage is not given, it is assumed to be a variable voltage power supply.DC_10---R_10---GLED: same as diodeI: electric current source. Ports:P: potentiometer source. Ports:1: one of the sides2: the middle3: the other side
T: transistor. The ports aresgTd:Sample usage in a circuit:s: sourceg: gated: gate
All the following are also equivalent:---+ | --sgTd--| g --sTd-- | --Tsgd-- |- ports can also be separated by double underscores from the component names to increase readability. Single underscores can also be used to increase readability of longer multi-word component names e.g.:which is the same as:
RPI_PICO_W__1gp0__3gnd | | R_2k | | | +-aLEDc-+represents a circuit linking port 1 of a Raspberry Pi Pico W, which is GPIO pin 0, through a resistor and an LED, back to pin 3 of the board, which is ground.RPI_PICO_W 1gp0 3gnd | | R_2k | | | +-aLEDc-+
Numbers characterizing components are put just next to each component with an underscore. When there is only one parameter, standard units are assumed, e.g.:means:Micro is denoted as
+-----+
| |
C_1p R_2k
| |
+-----+u. Arsenide compound Updated 2025-07-16
Brightest natural objects in the sky Updated 2025-07-16
Precession Updated 2025-07-16
Separation of variables Updated 2025-07-16
Technique to solve partial differential equations
Naturally leads to the Fourier series, see: solving partial differential equations with the Fourier series, and to other analogous expansions:
One notable application is the solution of the Schrödinger equation via the time-independent Schrödinger equation.
Sine and cossine Updated 2025-07-16
Amateur telescope vendor Updated 2025-07-16
Superconducting temperature of aluminum Updated 2025-07-16
Alternating current source Updated 2025-07-16
Diacritic Updated 2025-07-16
Cyrillic script Updated 2025-07-16
Greek alphabet Updated 2026-10-18
Unfortunately, physicists and mathematicians keep using Greek letters in their formulas, so we just have to learn them.
A helpful way to remember is to learn a bit of their history/pronunciation: Section "Historical correspondence between Latin and Greek".
To learn the greek letters if you have a base latin alphabet, you must learn the sound of each letter, and which Latin letters they correspond to.
Symbols that look like Greek letters but are not Greek letters:
Is Ciro Santilli crazy (he is, but for this point specifically), or do many/most Greek letters represent the mouth position used in the pronunciation of the letter?
Latin alphabet Updated 2025-07-16
Annus Mirabilis papers Updated 2025-07-16
Work about Einstein Updated 2025-07-16
Satellite Updated 2025-07-16
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