The Feynman Technique
I’m reposting this. I was looking through my old notes and stumbled onto this oldie. It really is such a superb way to dive into a subject. A four-step …
Read →Org-mode cheatsheet
Tags Search tags: SPC n m or SPC o a m Add tag: SPC m q Links Insert link: SPC m l l File links have the structure [[file:relative_link_to_file][some_title]] …
Read →Curl a GraphQL API
1 2 3 4 5 6 7 curl -0 -v -X POST https://some.api.com/graphql \ -H 'Content-Type: application/json' \ -d @- << EOF { "query": "query { …
Read →Function Overloading
Take a function like below… 1 2 3 4 5 6 7 8 type Combinable = string | number function add(a: Combinable, b: Combinable): Combinable { if (typeof a === …
Read →Nullish Coalescing
1 2 // say you have some var hangin' around called `name` let x: string = name ?? '(no name)' ?? is the nullish coalescing operator. It differs from …
Read →Recursive Type Aliases
In TS@4 a type can reference itself, e.g. 1 2 3 4 5 6 7 8 9 type JSONValue = | string | number | boolean | null | JSONValue[] | { [k: string]: JSONValue } …
Read →Labeled Tuple Types
1 type Address = [number, string, string, number] Say you now have a function printAddress which takes an Address type as its arg. 1 2 3 function …
Read →Variadic Tuple Types
1 type Foo<T extends any[]> = [boolean, ...T, boolean] Before TS@4.0 ...T would need to be the last element, but now we can spread the T type nested …
Read →Composite Builds
TypeScript has a way of describing a build process as multiple subpieces of a project. This saves from having to build every piece, and instead build …
Read →Jest Setup for a Monorepo
Out of the box, Jest mostly works in a Monorepo environment, with the exception of a few Babel plugins so that (as an example) TypeScript works. Needs: …
Read →Monorepos
Read →Colocation
“colocation” is a pattern wherein you keep the query/mutation as close to the consuming component as possible. In many instances, it’s in the …
Read →Yarn-NPM
package.json resolutions field yarn specific Allows you to force the use of a particular version for a nested dependency. e.g.: 1 2 3 4 …
Read →Cipher
A cipher is defined over the spaces of: All Keys, All Messages, All Cipher texts, Cipher (defined as a triple, …
Read →Distribution Vector
A vector with non-negative components (representing specific probabilities) which add up to one e.g. \begin{equation} (P(x_{0}), P(x_{1}),…,P(x_{n})) …
Read →Uniform Distribution
Where is the size of the universe (set). In Probability Theory, a uniform distribution …
Read →Point Distribution
x0: P(x) = 1,∀ x ≠ x0: P(x) = 0 In Probability Theory, a point distribution is a distribution which assigns all the probability to a given point (set element).
Read →Cryptography
Digital Signature
Read →Digital Signature
A function of the content being “signed”
Read →Cost Function
The measurement of accuracy of a hypothesis function. The accuracy is given as an average difference of all the results of the hypothesis from the inputs …
Read →Machine Learning
Gradient Descent Cost Function Hypothesis Function Artificial Neural Network
Read →Gradient Descent
An optimization algorithm for finding the local minimum of a differentiable function. (The red arrows show the minimums of , i.e. …
Read →Hypothesis Function
A function which maps values to an output value . Historically, in ML, hypothesis functions are denoted .
Read →Artificial Neural Network
Artificial Neural Network (ANN) Layers All learning occurs in the layers. In the image, below, there are three layers, but there could be only one, or many …
Read →Covectors
A linear mapping from a vector space to a field of scalars. In other words, a linear function which acts upon a vector resulting in a real number (scalar) …
Read →Differential Geometry
Tensors Tensor Product
Read →Linear Algebra
Bases Bases Transformation Coordinate Transformation Covectors Dual Space Identity Matrix Invertible Matrix Invertible Matrix Orthonormal Basis Tensor Product …
Read →Linear Mapping
A mapping from that preserves the operations of addition and scalar multiplication. Also known as Linear Map Linear …
Read →Multilinear Map
A function of several variables that is linear, separately, in each variable. A multilinear map of one variable is a standard linear mapping.
Read →Tensor Product
Read →Dual Space
The space of all linear functionals , noted as The dual space has the same dimension as the corresponding vector space …
Read →Dual Vector Space
The space of all linear functionals , noted as The dual space has the same dimension as the corresponding vector space …
Read →Heliosphere
The bubble, created by the Sun’s plasma (see Solar Wind), which encompasses the Sun itself. Outside of this bubble, the Sun’s plasma is overwhelmed …
Read →Solar Wind
TODO
Read →Tensors
As a linear representation A tensor can be represented as a vector of x-number of dimensions. Basically, a generalization on top of scalars, vectors, and …
Read →Kronecker Delta
Read →
Bases
a basis for an n-dimensional vector space is any ordered set of linearly independent vectors (\mathbf{e}_{1}, \mathbf{e}_{2},…,\mathbf{e}_{n}) …
Read →Orthonormal Basis
An orthonormal basis is a basis where all the vectors are one unit long and all perpendicular to each other (e.g. the Cartesian plane)
Read →Bases Transformation
Consider two bases and , where we consider the former the old basis and …
Read →Identity Matrix
Where any matrix is established via the Kronecker Delta, e.g. \begin{equation} …
Read →Invertible Matrix
A matrix, which when multiplied by another matrix, results in the identity matrix. e.g. …
Read →Vector Space
also known as a linear space A collection of objects known as “vectors”. In the Euclidean space these can be visualized as simple arrows with a …
Read →Coordinate Transformation
Read →Axioms (Vector Space)
To qualify as a vector space, a set and its associated operations of addition () and multiplication/scaling () must adhere to the below: …
Read →Invariance (Mathematics)
An property (of a mathematical object) is invariant if, after some operation(s) are applied, that property remains unchanged. For instance, in a geometrical …
Read →Cosmology
The Inflationary Universe Standard Model Cosmic Inflation Cosmological Constant Cosmic Microwave Background
Read →The Inflationary Universe
source The Inflationary Universe: A Possible Solution To The Horizon And Flatness Problems (Guth, 1980) Questions I still have DONE WHY#1: why is that …
Read →Standard Model (Cosmology)
This refers to the Cosmological “Standard Model”, i.e. the CDM. This is not the same as the Standard Model of Particle Physics Lambda-CDM …
Read →Cosmological Principle
The Cosmological Principle states that at large enough scales (>100Mpc) the universe’s matter distribution is isotropic and homogeneous and should not …
Read →Cosmological Constant
TODO
Read →Cosmic Microwave Background
TODO
Read →The Structure and Interpretation of Computer Programs
Table of Contents Chapter 1 Predicates/Expressions Functions v. Procedures or Imperative v. Declarative Chapter 1 Predicates/Expressions Taking the following …
Read →Programming
The Structure and Interpretation of Computer Programs (SICP)
Read →Manifold
A manifold is a topological space that locally resembles Euclidean space near each point. As defined in Physics An N-dimensional manifold of points is one for …
Read →Symmetric Relation
This definition is more clearly described sybollically: Tao’s definition: Given any two …
Read →Transitive Relation
A relation over a set is transitive if for all elements x, y, z in , whenever relates to and to , then also …
Read →Reflexive Relation
A binary relation over a set is reflexive if it relates every to itself. An …
Read →Learning
The Feynman Technique
Read →Physics
Articles Black Holes as Primordial Dark Matter Papers The Inflationary Universe (Guth, 1980) Concepts Configuration Space Cosmic Inflation Equations of Motion …
Read →Science
Branches Physics Articles Phosphine, Life, and Venus (Biology, Chemistry) Black Holes as Primordial Dark Matter (Physics) Papers The Inflationary Universe: …
Read →Set Theory
Concepts Relations Cardinality Binary Relation Symmetric Relation Transitive Relation Cartesian Product Reflexive Relation Surjective Function
Read →Teaching
The Feynman Technique
Read →Math
Real Analysis Differential Geometry Linear Algebra Topology Set Theory General Concepts Bijective Function Injective Function Surjective Function Transitive …
Read →Chemistry
Articles Phosphine, Life, and Venus
Read →Biology
Articles Phosphine, Life, and Venus
Read →Triangle Inequality
For any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
Read →Topology
Concepts Metric Space Open Balls Neighborhood Manifold Topological Space
Read →Topological Space
An ordered pair , where is a set and is a collection of subsets of satisfying: The empty set () and belong …
Read →Surjective Function
A function is surjective or “onto” if For every , there exists such that .
Read →Statistics
Concepts Null Hypothesis
Read →Shape of the Universe
Open/Closed/Flat TODO
Read →Relations (Sets)
Definition A relation from the elements of set to the elements of set is a subset of . …alternatively… Let …
Read →Real Analysis
The theoretical foundation which underlies calculus Peano Axioms Surjective Function Bijective Function Injective Function Cartesian Product
Read →Principle of Relativity
The Principle of Relativity states that: The laws of physics take the same form in every intertial frame. No exception has been found to this principle, and it …
Read →Phosphine, Life, and Venus
Source: Phosphine, Life, and Venus Regarding the released report that Venus was found to “possibly harbor life” (see this Nature article) …
Read →Peano Axioms
A natural number is any element of the set \mathbb{N} = \{0, 1, 2, 3…\} I 0 is a natural number. II If is a natural number, then n++ is also a …
Read →Oxidation
A type of chemical reaction in which electrons are lost
Read →Open Balls
Let be a metric space. Let and \delta > 0. The subset of consisting of those points such that \(d(a, x) < …
Read →Olber's Paradox
The Problem People used to believe that the Universe was infinite (in age and size) and static. If this were true Why is the night sky not as bright as day? …
Read →Null Hypothesis
Denoted H_0 (subscript 0) The position that there is no relationship among two measured phenomenon or among groups. The central task of science is to prove that …
Read →Newtons Laws of Motion
I In an intertial frame of reference (i.e. a frame of reference undergoing zero acceleration), an object at rest stays at rest (or, similarly, keeps its initial …
Read →Newtonian Spacetime
Newtonian Spacetime differs from Relativistic spacetime in that time is considered an absolute (i.e. ). Transformations between reference …
Read →Neighborhood
The set of points surrounding a point in a set , such that , within a radius \epsilon > 0 See also: Open Balls
Read →Metric Space
A set and a function which defines the distance between two points on that set An ordered pair , where is an arbitrary set and is a metric …
Read →Mechanics
Read →Locality (Math)
Locality refers to: A property , of a point , which holds true near every point around . As an example: A sphere (and, more generally, a …
Read →Isotropy (Physics)
Isotropy means that direction is not preferred, and that there is uniformity in any orientation. Specifically, in Astrophysics and Cosmology, it means that …
Read →Injective Function
A function is injective (“one-to-one”) if i.e. Given a set and a set , no …
Read →Inertial Frames
Above are two frames in Cartesian coordinates, and . We have coordinates , which define our dimensions. Inertial Frame An …
Read →Homogeneous (Physics)
Homogeneous means that location is not preferred, that the physics are the same at any point. Specifically, in Astrophysics and Cosmology, it means that there …
Read →Generalized Coordinates
Generalized coordinates are useful when calculating Lagrangians or Hamiltonians. The term itself, refers to the parameters that describe the configuration of a …
Read →General Relativity
Concepts Inertial Frames Newtons Laws of Motion
Read →Galilean Transformations
In Newton’s formulation of spacetime, time is an absolute; meaning that every observer experiences the same flow of time. Assuming an inertial frame with …
Read →Flatness Problem
Overview In the Big Bang model there are multiple parameters which appear to be “fine tuned” in that, small changes to a given parameter have …
Read →Equations of Motion
Linear Motion (under constant ) \begin{equation} \mathbf{r} …
Read →Emacs Notes
Emacs notes (doom emacs) Org handy cheatsheet: https://orgmode.org/orgcard.pdf To get a TODO item created on the same level as the one in which you’re …
Read →Degenerate Coordinate Systems
Any coordinate system which cannot describe an entirety of a space As an example, polar coordinates are degenerate at
Read →Curvature
TODO
Read →Cosmic Inflation
Inflation Inflation (Cosmic) is a theory put forth (originally, by Alan Guth in his 1980 paper) to explain why, if the universe is full of mass, is it not …
Read →Configuration Space
The vector space defined by generalized coordinates. Example: The position of a particle in Euclidean 3-space is defined by the generalized coordinate \(q = (x, …
Read →Cartesian Product
If and are sets, then we define the Cartesian Product to be the collection of ordered pairs, e.g. , whose first component …
Read →Cardinality
Equality in Cardinality Two sets and are equal iff there exists a bijection from to .
Read →Black Holes as Primordial Dark Matter
source: Physicists Argue That Black Holes From the Big Bang Could Be the Dark Matter Primordial Black Holes A “Primordial Black Hole” (PBH), is a …
Read →Black Hole Information Paradox
High-level The result of the marrying of QM with GR. (Initially, Hawking’s) calculations suggested that information would permanently disappear in a black …
Read →Binary Relation
A binary relation over sets and is a subset of the cartesian product of . Where is the domain, or set of departure of …
Read →Abiotic Process
An abiotic process is a process which occurs via abiotic resources (non-living physical/chemical elements) in the environment
Read →Abiotic Process
An abiotic process is a process which occurs via abiotic resources (non-living physical/chemical elements) in the environment
Read →Bijective Function
A function is bijective or “invertible” if it is Both one-to-one and onto (injective and surjective) In other words: each element of one set is …
Read →Set Theory
Concepts Relations Cardinality Binary Relation Symmetric Relation Transitive Relation Cartesian Product Reflexive Relation Surjective Function
Read →