The area of a circle is
.
analytic: regular, holomorphic, having a complex derivative at every point of its domain; compare synthetic
conformal map: a function that preserves angles but not necessarily lengths
conjugate: join, a different form, a modified form, this word has many meanings so you should find something else to do
convolve: to roll up, twist, coil; two convoluted objects form a third object
deterministic: predictable, see non-deterministic
differentiate: to recognize or ascertain what makes (someone or something) different
dimorphic: occurring in or representing two distinct forms
E = mc2
Einstein's equation,
Energy = mass * the speed of light squared
from Newton's equation:
F = ma
Force = mass * acceleration
These are easy formulas, but think about before they were known by anyone.
empirical: derived from experience
epistemology: the study of knowledge, especially regarding justification, rationality and the difference between fact and opinion
holomorphic: "whole" + "form"
homothety: a linear transformation that involves no rotation, the composition of
a translation and a central dilation. It is of the form
x' = kx
y' = ky
and is a stretching if k > 1 and a shrinking if 0 < k < 1
iatrogenic: medically induced
idempotent: unchanged when multiplied by itself; equal to its own square; an idempotent operation
has no additional effect if it is called more than once with the same input
The matrix
[ 2 2]
[-1 -1]
is idempotent.
Set-theoretic intersection and union are idempotent,
because
S ∪ S = S = S ∩ S
Kármán line: a proposed conventional boundary between Earth's atmosphere and outer space
often considered to encircle Earth at an altitude between 50 and 62 miles above mean sea level
the Las Vegas Sphere
Lorentz transformation: the relationship between two different coordinate frames that move at a constant velocity
and are relative to each other
byjus.com
mutex: mutual exclusion lock; only one thread or user can hold the lock, thereby preventing concurrent access to the mutexed resource
napalm: a substance used in incendiary (fire-inducing) bombs and flamethrowers, made by forming a gel of petrol with aluminum soaps
naphtha: any liquid hydrocarbon or mixture obtained by the fractional distillation of petroleum
non-deterministic: unpredictable; when the same input is used for two or more separate calls to the same function,
non-determinism can cause unpredictable output, due to concurrent access or the use of randomness, see mutex to prevent this
potassium hydrogentartrate: cream of tartar, a white crystalline acid salt, HOOC(CHOH)2COOK, obtained from
deposits on wine vats (argol) and used in baking powders
reverse engineering: taking apart somthing in order to understadn how it works
Pixalytics - How many satellites are orbitting Earth?
similitude: a homothety that leaves the origin fixed; in vector terms, a transformation x → kx
where k is a positive number (the ratio of similitude) and the origin is the center of similitude.
Two figures related by such a transformation are homothetic.
synthetic: neither true nor false by virtue of meaning alone
therapeutic index: a comparison of the amount of a therapeutic agent that causes the therapeutic effect to the amount that causes toxicity;
a drug with a narrow therapeutic index can cause a detrimental effect when the dose is raised only slightly higher than the
therapeutic dose; a drug with a wide therapeutic index can be dosed much higher than the therapeutic dose without causing
a stronger effect
threshold: a point at which tolerance changes; breaking point
transformation: a change in position, scale, rotation, orientation, etc.; sometimes simply called a "transform", in computer
graphics: "to apply a transform"
Wirtinger derivative: a partial differential operator, maybe
"The operational principle of the model may now be succinctly stated: the regulatory-protein mosaic is an adaptor made of separate pieces, a
multiplex adaptor. On one end, the multiplex plugs into the DNA and, on the other, into the RNA polymerase. Information about the location
of the start of transcriptional units flows into the multiple plug-ins at the various promoter and enhancer sites, and is relayed from
protein to protein in the adaptor mosaic, to finally converge on the RNA polymerase.
This gives the why and wherefore of the solid-state apparatus of the genes."
~ Werner Loewenstein, "The Touchstone of Life"
Academic writing is like a foreign language. Don't get frustrated or pedantic about it, whether you're the reader or the writer. 😉
"In normal times, the movement of rain water downward through the mat lowers its salinity and assists
the growth of photosynthesizers at the surface, the primary providers of food and energy for the communities
beneath. Salt crystals at, or near, the surface are also coated with their own specific varnish and
protected against easy solution in rain water."
~ James Lovelock, "The Ages of Gaia"
"We have, namely, good ground for the assumption that the 'field-free' Minkowski-space represents a special case possible in natural law,
in fact, the simplest conceivable special case. With respect to its metrical character, such a space is characterized by the fact that
dx12 + dx22 + dx32 is the square of the spatial separation, measured with a
unit gauge, of two infinitesimally neighbouring points of a three-dimensional 'space-like' cross section (Pythagorean theorem), whereas
dx4 is the temporal separation, measured with a suitable time gauge, of two events with common (x1, x2, x3).
All this simply means that an objective metrical significance is attached to the quantity
ds2 = dx12 + dx22 + dx32 - dx42
as is readily shown with the aid of the Lorentz transformations. Mathematically, this fact corresponds to the condition that ds2
is invariant with respect to Lorentz transformations."
~ Albert Einstein, "Relativity"
So what does this mean in plain English? "temporal" has to do with time. "an objective metrical significance" ? Is time objective or subjective?
How much does time matter in these calculations? (It is the only variable being subtracted.) ?
I wonder if I'll understand this stuff better 10 years from now.
trying to determine the sizes of particles:
"It is especially important to note that with a standard Lorentz transformation the
width of the photon perpendicular to its propagation direction will be preserved under all
changes in the observer coordinate system. Thus, the width of a photon will be the same in any coordinate system."
scirp.org
electron = 10
-28mm? (there are many estimates)
Supplement_1 from a literature review I did on holography.
I needed to create this supplement to better understand holography
keywords pertaining to holography:
angular spectrum method (ASM): a propagation-modeling technique which expands a complex wavefield into a summation of plane waves of the same frequencies but different directions
astigmatism: non-sphericity; asymmetry
CCD sensor: a charge-coupled device in which capacitors transfer electrical charge
direl: direction element
entrance pupil: entrance aperture
étendue: a measure of the spread of light
exit pupil: exit aperture
Fienup techniques: optical techniques including unconventional imaging, wavefront sensing, phase retrieval and image reconstruction and restoration
Fourier optics: the study of classical optics using Fourier transforms
fovea: a small pit in the back of the human eye used for central focussing tasks such as driving and reading
Fraunhofer diffraction equation: a formula which models diffraction when the light beam is at a long distance from the diffracting object or when the light beam is viewed at the focal plane of an imaging lens
Fresnel propagation: describes light properties when incident on an interface between different optical media
Gerchberg-Saxton algorithm: an iterative phase retrieval algorithm for retrieving the phases from two separate sources
grating: a set of elongated elements
hogel: holographic element; a sub-hologram; represented by a primitive variable
incidence: point of contact; an incidence ray is a ray that touches some other object
Monte Carlo sampling: a broad class of computational algorithms based on random samplings
no-parallax point (center of projection): the center of the lens’s entrance pupil; the axis on a camera lens around which rotation will cause no parallax
oblique direction: slanted; not parallel nor perpendicular
paraxial approximation: an approximation of the small angle between a light ray and a reference axis of an optical system
phase retrieval: the process of algorithmically finding solutions to the phase problem
piezo: pressure
polarization grating: elements that alter the polarization state of the transmitted light in a periodic way, yielding a polarization-dependent diffraction
pupil-shifting: a function of the change in pupil position; may indicate the relative change in amplitude and phase of the light wave
pupil-shifting holographic element (PSHOE): a slab of material capable of being pupil-aware
ray-tracing: a method of graphics rendering that simulates the physical behavior of light
Rayleigh scattering: the scattering of light by particles with a size much smaller than the wavelength of the radiation. For below-normally dispersed light, the amount of scattering is inversely proportional to the fourth power of the wavelength. Blue is scattered much more than red, for example.
saccade: quick, jumpy, movement of both eyes (together, not independent of each other)
saggital: dividing an object into left/right regions; "the saggital suture on top of the human skull runs front-to-back"
spatial light modulator (SLM): a device which controls the intensity, polarization or phase of light; it is important to note that SLMs cannot modulate phase and amplitude simultaneously
surface relief grating: grating with ridges on the surface
total internal reflection (TIR): complete reflection (with no loss of brightness)
vergence-accommodation conflict: mismatching/conflicting cues regarding vergence (movement in opposite directions, apart or together) and accomodation (focus) of the human eye
volume Bragg grating: a volume in which there is a periodic change in the refractive index; can be used to transmit or reflect
wafel: wavefront element
zero-order diffraction beam (ZOD): If reflection grating is used, this is direct reflection. If transmissive grating is used, this is direct transmission.
more keywords pertaining to math:
Cauchy-Riemann equations: two partial differential equations used in complex analysis
convolution: an operation on two functions which produces a third function
differentiation (for beam splitting): calculating the rate of change
Fourier transform: an integral that takes as input a function and outputs a function describing the frequencies present in the input function
integration and summation (for final image): calculating an accumulation
Mahajan formula: a formula for the scaling of higher order aberrations by pupil size
modulation transfer function: measures a lens's ability to transfer the contrast of a sample to an image using spatial frequency (resolution)
point spread function: describes the response of a focused optical imaging system to a point source or point object
Rayleigh-Sommerfeld integral: an integral used to propagate a wavefield. The angular spectrum method equates to a multiplication by exp(izkz) in Fourier space, while the Rayleigh-Sommerfeld integral equates to a convolution. May be used with spherical waves.
Strehl ratio: a measure of the quality of optical image formation
Wigner function: a signal-processing transform used in time-frequency analysis
Wirtinger derivative: a type of partial differential operator
Zernicke polynomials: a set of functions used to classify aberration maps
more keywords pertaining to machine learning:
error back-propagation: output fed back as input
feed-forward process: the process of using information to predict future solutions
ReLu activation: rectified linear unit function whose output does not saturate, assisting gradient descent; it introduces non-linearity, aiding in complex pattern
recognition; the first layer of a neural network can receive errors from the last layer and adjust weights, for example
stochastic: random
stochastic gradient descent: an iterative optimization function that can be used to adjust weights
weighting/cost function: applying various weight (cost, penalty) values to similarly grouped objects; the weights may or may not be negative or adjustable during
processing
Note: AR augments a real-world setting while VR is completely virtual. AR users can influence their presence in the real world; VR users are influenced by the system.