Have a deep view into what people are curious about.

🔗 Physics

Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment".

Another way of phrasing Landauer's principle is that if an observer loses information about a physical system, the observer loses the ability to extract work from that system.

A so-called logically-reversible computation, in which no information is erased, may in principle be carried out without releasing any heat. This has led to considerable interest in the study of reversible computing. Indeed, without reversible computing, increases in the number of computations-per-joule-of-energy-dissipated must come to a halt by about 2050: because the limit implied by Landauer's principle will be reached by then, according to Koomey's law.

At 20 °C (room temperature, or 293.15 K), the Landauer limit represents an energy of approximately 0.0175 eV, or 2.805 zJ. Theoretically, room‑temperature computer memory operating at the Landauer limit could be changed at a rate of one billion bits per second (1Gbps) with energy being converted to heat in the memory media at the rate of only 2.805 trillionths of a watt (that is, at a rate of only 2.805 pJ/s). Modern computers use millions of times as much energy per second.

🔗 Physics 🔗 Philosophy 🔗 Philosophy/Metaphysics

The Boltzmann brain argument suggests that it is more likely for a single brain to spontaneously and briefly form in a void (complete with a false memory of having existed in our universe) than it is for our universe to have come about in the way modern science thinks it actually did. It was first proposed as a reductio ad absurdum response to Ludwig Boltzmann's early explanation for the low-entropy state of our universe.

In this physics thought experiment, a Boltzmann brain is a fully formed brain, complete with memories of a full human life in our universe, that arises due to extremely rare random fluctuations out of a state of thermodynamic equilibrium. Theoretically over a period of time on the order of hundreds of billions of years, by sheer chance atoms in a void could spontaneously come together in such a way as to assemble a functioning human brain. Like any brain in such circumstances, it would almost immediately stop functioning and begin to deteriorate.

The idea is ironically named after the Austrian physicist Ludwig Boltzmann (1844–1906), who in 1896 published a theory that tried to account for the fact that we find ourselves in a universe that is not as chaotic as the budding field of thermodynamics seemed to predict. He offered several explanations, one of them being that the universe, even one that is fully random (or at thermal equilibrium), would spontaneously fluctuate to a more ordered (or low-entropy) state. One criticism of this "Boltzmann universe" hypothesis is that the most common thermal fluctuations are as close to equilibrium overall as possible; thus, by any reasonable criterion, actual humans in the actual universe would be vastly less likely than "Boltzmann brains" existing alone in an empty universe.

Boltzmann brains gained new relevance around 2002, when some cosmologists started to become concerned that, in many existing theories about the Universe, human brains in the current Universe appear to be vastly outnumbered by Boltzmann brains in the future Universe who, by chance, have exactly the same perceptions that we do; this leads to the conclusion that statistically we ourselves are likely to be Boltzmann brains. Such a reductio ad absurdum argument is sometimes used to argue against certain theories of the Universe. When applied to more recent theories about the multiverse, Boltzmann brain arguments are part of the unsolved measure problem of cosmology. Boltzmann brains remain a thought experiment; physicists do not believe that we are actually Boltzmann brains, but rather use the thought experiment as a tool for evaluating competing scientific theories.

🔗 Aviation 🔗 Marketing & Advertising 🔗 United Kingdom 🔗 Guild of Copy Editors 🔗 Retailing 🔗 Home Living

The Hoover free flights promotion was a marketing promotion run by the British division of the Hoover Company in late 1992. The promotion, aiming to boost sales during the global recession of the early 1990s, offered two complimentary round-trip plane tickets to the United States, worth about £600, to any customer purchasing at least £100 in Hoover products. Hoover had been experiencing dwindling sales as a result of the economic downturn and a sharp increase in competing brands. Hoover was counting on most customers spending more than £100, as well as being deterred from completing the difficult application process, and not meeting its exact terms.

Consumer response was much higher than the company anticipated, with many customers buying the minimum £100 of Hoover products to qualify. It was perceived as two US flights for just £100 with a free vacuum cleaner included. The resulting demand was disastrous for the 84-year-old company. Hoover cancelled the ticket promotion after consumers had already bought the products and filled in forms applying for millions of pounds' worth of tickets. Reneging on the offer resulted in protests and legal action from customers who failed to receive the tickets they had been promised. The campaign was a financial disaster for the company and led to the loss of Hoover's Royal Warrant after the airing of a 2004 BBC documentary. The European branch of the company was eventually sold to one of its competitors, Candy, having never recovered from the losses, the promotion and the subsequent scandal.

🔗 Mathematics

In number theory, the Pólya conjecture stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors. The conjecture was posited by the Hungarian mathematician George Pólya in 1919, and proved false in 1958 by C. Brian Haselgrove.

The size of the smallest counterexample is often used to show how a conjecture can be true for many cases, and still be false, providing an illustration for the strong law of small numbers.

🔗 Architecture 🔗 Greece

The Tunnel of Eupalinos or Eupalinian aqueduct (Greek: Ευπαλίνιον όρυγμα, romanized: Efpalinion orygma) is a tunnel of 1,036 m (3,399 ft) length running through Mount Kastro in Samos, Greece, built in the 6th century BC to serve as an aqueduct. The tunnel is the second known tunnel in history which was excavated from both ends (Ancient Greek: ἀμφίστομον, romanized: amphistomon, "having two openings"), and the first with a geometry-based approach in doing so. Today it is a popular tourist attraction.

🔗 Novels 🔗 Novels/Science fiction

The Drowned World is a 1962 science fiction novel by British writer J. G. Ballard. The novel depicts a post-apocalyptic future in which global warming has caused the majority of the Earth to become uninhabitable. The story follows a team of scientists researching ongoing environmental developments in a flooded, abandoned London. The novel is an expansion of a novella of the same title first published in Science Fiction Adventures magazine in January 1962, Vol. 4, No. 24.

In 2010, Time Magazine named The Drowned World one of the top 10 best post-apocalyptic books. The novel has been identified as a founding text in the literary genre known as climate fiction.

🔗 Russia 🔗 Philosophy 🔗 Transhumanism 🔗 Alternative Views 🔗 Russia/science and education in Russia 🔗 Russia/language and literature of Russia 🔗 Russia/religion in Russia

Russian cosmism is a philosophical and cultural movement that emerged in Russia in the turn of the 19th and 20th centuries.

🔗 Computer science

In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which a probability distribution is represented as an element of a reproducing kernel Hilbert space (RKHS). A generalization of the individual data-point feature mapping done in classical kernel methods, the embedding of distributions into infinite-dimensional feature spaces can preserve all of the statistical features of arbitrary distributions, while allowing one to compare and manipulate distributions using Hilbert space operations such as inner products, distances, projections, linear transformations, and spectral analysis. This learning framework is very general and can be applied to distributions over any space ${\displaystyle \Omega }$ on which a sensible kernel function (measuring similarity between elements of ${\displaystyle \Omega }$) may be defined. For example, various kernels have been proposed for learning from data which are: vectors in ${\displaystyle \mathbb {R} ^{d}}$, discrete classes/categories, strings, graphs/networks, images, time series, manifolds, dynamical systems, and other structured objects. The theory behind kernel embeddings of distributions has been primarily developed by Alex Smola, Le Song , Arthur Gretton, and Bernhard Schölkopf. A review of recent works on kernel embedding of distributions can be found in.

The analysis of distributions is fundamental in machine learning and statistics, and many algorithms in these fields rely on information theoretic approaches such as entropy, mutual information, or Kullback–Leibler divergence. However, to estimate these quantities, one must first either perform density estimation, or employ sophisticated space-partitioning/bias-correction strategies which are typically infeasible for high-dimensional data. Commonly, methods for modeling complex distributions rely on parametric assumptions that may be unfounded or computationally challenging (e.g. Gaussian mixture models), while nonparametric methods like kernel density estimation (Note: the smoothing kernels in this context have a different interpretation than the kernels discussed here) or characteristic function representation (via the Fourier transform of the distribution) break down in high-dimensional settings.

Methods based on the kernel embedding of distributions sidestep these problems and also possess the following advantages:

1. Data may be modeled without restrictive assumptions about the form of the distributions and relationships between variables
2. Intermediate density estimation is not needed
3. Practitioners may specify the properties of a distribution most relevant for their problem (incorporating prior knowledge via choice of the kernel)
4. If a characteristic kernel is used, then the embedding can uniquely preserve all information about a distribution, while thanks to the kernel trick, computations on the potentially infinite-dimensional RKHS can be implemented in practice as simple Gram matrix operations
5. Dimensionality-independent rates of convergence for the empirical kernel mean (estimated using samples from the distribution) to the kernel embedding of the true underlying distribution can be proven.
6. Learning algorithms based on this framework exhibit good generalization ability and finite sample convergence, while often being simpler and more effective than information theoretic methods

Thus, learning via the kernel embedding of distributions offers a principled drop-in replacement for information theoretic approaches and is a framework which not only subsumes many popular methods in machine learning and statistics as special cases, but also can lead to entirely new learning algorithms.

🔗 Mathematics 🔗 Physics

Shor's algorithm is a polynomial-time quantum computer algorithm for integer factorization. Informally, it solves the following problem: Given an integer ${\displaystyle N}$, find its prime factors. It was invented in 1994 by the American mathematician Peter Shor.

On a quantum computer, to factor an integer ${\displaystyle N}$, Shor's algorithm runs in polynomial time (the time taken is polynomial in ${\displaystyle \log N}$, the size of the integer given as input). Specifically, it takes quantum gates of order ${\displaystyle O\!\left((\log N)^{2}(\log \log N)(\log \log \log N)\right)}$ using fast multiplication, thus demonstrating that the integer-factorization problem can be efficiently solved on a quantum computer and is consequently in the complexity class BQP. This is almost exponentially faster than the most efficient known classical factoring algorithm, the general number field sieve, which works in sub-exponential time — ${\displaystyle O\!\left(e^{1.9(\log N)^{1/3}(\log \log N)^{2/3}}\right)}$. The efficiency of Shor's algorithm is due to the efficiency of the quantum Fourier transform, and modular exponentiation by repeated squarings.

If a quantum computer with a sufficient number of qubits could operate without succumbing to quantum noise and other quantum-decoherence phenomena, then Shor's algorithm could be used to break public-key cryptography schemes, such as the widely used RSA scheme. RSA is based on the assumption that factoring large integers is computationally intractable. As far as is known, this assumption is valid for classical (non-quantum) computers; no classical algorithm is known that can factor integers in polynomial time. However, Shor's algorithm shows that factoring integers is efficient on an ideal quantum computer, so it may be feasible to defeat RSA by constructing a large quantum computer. It was also a powerful motivator for the design and construction of quantum computers, and for the study of new quantum-computer algorithms. It has also facilitated research on new cryptosystems that are secure from quantum computers, collectively called post-quantum cryptography.

In 2001, Shor's algorithm was demonstrated by a group at IBM, who factored ${\displaystyle 15}$ into ${\displaystyle 3\times 5}$, using an NMR implementation of a quantum computer with ${\displaystyle 7}$ qubits. After IBM's implementation, two independent groups implemented Shor's algorithm using photonic qubits, emphasizing that multi-qubit entanglement was observed when running the Shor's algorithm circuits. In 2012, the factorization of ${\displaystyle 15}$ was performed with solid-state qubits. Also, in 2012, the factorization of ${\displaystyle 21}$ was achieved, setting the record for the largest integer factored with Shor's algorithm.