Test_Interesting Flashcards
What is Benford’s law?
The law of anomalous numbers, or the first-digit law, is an observation that in many real-life sets of numerical data, the leading digit is likely to be small.[1] In sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. If the digits were distributed uniformly, they would each occur about 11.1% of the time.[2] Benford’s law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.
What is Benford’s distribution?
The leading digits in such a set thus have the following distribution:
1 30.1%
2 17.6%
3 12.5%
4 9.7%
5 7.9%
6 6.7%
7 5.8%
8 5.1%
9 4.6%
Euler’s Equation?
e^iπ + 1 = 0
Gödel’s incompleteness theorems?
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.
What is Euclidean geometry?
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid’s approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these.
Schrödinger equation?
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system.[1]: 1–2 It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.
Who is Max Karl Ernst Ludwig Planck?
Max Karl Ernst Ludwig Planck ForMemRS[1] (English: /ˈplæŋk/,[2] German: [maks ˈplaŋk] (listen);[3] 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.[4]
Planck made many substantial contributions to theoretical physics, but his fame as a physicist rests primarily on his role as the originator of quantum theory,[5] which revolutionized human understanding of atomic and subatomic processes.
Fredonian Rebellion?
The Fredonian Rebellion (December 21, 1826 – January 31, 1827) was the first attempt by Anglo settlers in Texas to secede from Mexico. The settlers, led by Empresario Haden Edwards, declared independence from Mexican Texas and created the Republic of Fredonia near Nacogdoches. The short-lived republic encompassed the land the Mexican government had granted to Edwards in 1825 and included areas that had been previously settled. Edwards’s actions soon alienated the established residents, and the increasing hostilities between them and settlers recruited by Edwards led Víctor Blanco of the Mexican government to revoke Edwards’s contract.
What are Bach’s Inventions?
The Inventions and Sinfonias, BWV 772–801, also known as the Two- and Three-Part Inventions, are a collection of thirty short keyboard compositions by Johann Sebastian Bach (1685–1750): 15 inventions, which are two-part contrapuntal pieces, and 15 sinfonias, which are three-part contrapuntal pieces. They were originally written as “Praeambula” and “Fantasiae” in the Klavierbüchlein für Wilhelm Friedemann Bach, a Clavier-booklet for his eldest son, and later rewritten as musical exercises for his students.
Base-Ten System
The decimal numeral system (also called the base-ten positional numeral system and denary /ˈdiːnəri/[1] or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system.
Rules of counterpoint
Imaginary Numbers
Vigesimal System
A vigesimal (/vɪˈdʒɛsɪməl/) or base-20 (base-score) numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten). Vigesimal is derived from the Latin adjective vicesimus, meaning ‘twentieth’.
Mayan Number System
Twenty is a base in the Maya and Aztec number systems. The Maya use the following names for the powers of twenty: kal (20), bak (202 = 400), pic (203 = 8,000), calab (204 = 160,000), kinchil (205 = 3,200,000) and alau (206 = 64,000,000).
Sexagesimal System
Sexagesimal, also known as base 60 or sexagenary,[1] is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates.
asymmetric systems of cryptography - examples
Examples of asymmetric systems include Diffie–Hellman key exchange, RSA (Rivest–Shamir–Adleman), ECC (Elliptic Curve Cryptography), and Post-quantum cryptography. Secure symmetric algorithms include the commonly used AES (Advanced Encryption Standard) which replaced the older DES (Data Encryption Standard).
Symmetric-key cryptography
Symmetric-key cryptography refers to encryption methods in which both the sender and receiver share the same key (or, less commonly, in which their keys are different, but related in an easily computable way). This was the only kind of encryption publicly known until June 1976.
Symmetric key ciphers are implemented as
Symmetric key ciphers are implemented as either block ciphers or stream ciphers. A block cipher enciphers input in blocks of plaintext as opposed to individual characters, the input form used by a stream cipher.
The Data Encryption Standard (DES) and the Advanced Encryption Standard (AES)
The Data Encryption Standard (DES) and the Advanced Encryption Standard (AES) are block cipher designs that have been designated cryptography standards by the US government (though DES’s designation was finally withdrawn after the AES was adopted).
asymmetric key cryptography
In a groundbreaking 1976 paper, Whitfield Diffie and Martin Hellman proposed the notion of public-key (also, more generally, called asymmetric key) cryptography in which two different but mathematically related keys are used—a public key and a private key.[46] A public key system is so constructed that calculation of one key (the ‘private key’) is computationally infeasible from the other (the ‘public key’), even though they are necessarily related.
Cryptographic hash functions
Cryptographic hash functions are cryptographic algorithms that generate and use keys to encrypt data, and such functions may be viewed as keys themselves. They take a message of any length as input, and output a short, fixed-length hash, which can be used in (for example) a digital signature
kryptós
“hidden, secret”
Semantics
In English, the study of meaning in language has been known by many names that involve the Ancient Greek word σῆμα (sema, “sign, mark, token”).
In linguistics, semantics is the subfield that studies meaning.[10] Semantics can address meaning at the levels of words, phrases, sentences, or larger units of discourse. Two of the fundamental issues in the field of semantics are that of compositional semantics (which pertains on how smaller parts, like words, combine and interact to form the meaning of larger expressions, such as sentences) and lexical semantics (the nature of the meaning of words).
Neuroscience
Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions and disorders.[1][2][3] It is a multidisciplinary science that combines physiology, anatomy, molecular biology, developmental biology, cytology, psychology, physics, computer science, chemistry, medicine, statistics, and mathematical modeling to understand the fundamental and emergent properties of neurons, glia and neural circuits.