title: Battle of Kherson

text: On Russian social media, many troops appeared to be in panic as they sought to escape, with pro-Kremlin bloggers echoing panic, suggesting a collapse in morale and logistics. Many reports from journalists, Ukrainian civilians and authorities as well as individual Russian soldiers indicated that the withdrawal had been rather chaotic, with many Russian servicemen and materiel left behind on the right bank. DW reported that major equipment pieces such as anti-aircraft defence systems appeared to have been successfully transferred to the other bank, but this would leave troops stuck on the northern side vulnerable to Ukrainian artillery and drone attacks. Groups of Russian soldiers (some of them wounded) were reportedly captured, or voluntarily surrendered to advancing Ukrainian forces. Ukrainian official Serhiy Khlan stated that some Russian soldiers failed to leave Kherson, and changed into civilian clothing. One unidentified Russian soldier appeared to confirm that the last order his unit received was 'to change into civilian clothing and fuck off any way you want'. Some Russian soldiers reportedly drowned while trying to swim across the Dnipro. Ukrainian intelligence posted a Russian-language statement on social media, calling on remaining Russian soldiers to surrender. Footage on social media suggested that Ukrainian troops had captured several Russian tanks, armoured vehicles and crates of ammunition, contradicting the Russian Defence Ministry's statement that '[n]ot a single piece of military equipment or weaponry was left behind on the right [west] bank'.


title: Network topology

text: Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. Network topology can be used to define or describe the arrangement of various types of telecommunication networks, including command and control radio networks, industrial fieldbusses and computer networks.


title: Network topology

text: Network topology is the topological structure of a network and may be depicted physically or logically. It is an application of graph theory wherein communicating devices are modeled as nodes and the connections between the devices are modeled as links or lines between the nodes. Physical topology is the placement of the various components of a network (e.g., device location and cable installation), while logical topology illustrates how data flows within a network. Distances between nodes, physical interconnections, transmission rates, or signal types may differ between two different networks, yet their logical topologies may be identical. A network’s physical topology is a particular concern of the physical layer of the OSI model.


title: Network topology

text: Examples of network topologies are found in local area networks (LAN), a common computer network installation. Any given node in the LAN has one or more physical links to other devices in the network; graphically mapping these links results in a geometric shape that can be used to describe the physical topology of the network. A wide variety of physical topologies have been used in LANs, including ring, bus, mesh and star. Conversely, mapping the data flow between the components determines the logical topology of the network. In comparison, Controller Area Networks, common in vehicles, are primarily distributed control system networks of one or more controllers interconnected with sensors and actuators over, invariably, a physical bus topology.


title: Network topology

text: The transmission medium layout used to link devices is the physical topology of the network. For conductive or fiber optical mediums, this refers to the layout of cabling, the locations of nodes, and the links between the nodes and the cabling. The physical topology of a network is determined by the capabilities of the network access devices and media, the level of control or fault tolerance desired, and the cost associated with cabling or telecommunication circuits.


title: Network topology

text: In contrast, logical topology is the way that the signals act on the network media, or the way that the data passes through the network from one device to the next without regard to the physical interconnection of the devices. A network's logical topology is not necessarily the same as its physical topology. For example, the original twisted pair Ethernet using repeater hubs was a logical bus topology carried on a physical star topology. Token Ring is a logical ring topology, but is wired as a physical star from the media access unit. Physically, AFDX can be a cascaded star topology of multiple dual redundant Ethernet switches; however, the AFDX Virtual links are modeled as time-switched single-transmitter bus connections, thus following the safety model of a single-transmitter bus topology previously used in aircraft. Logical topologies are often closely associated with media access control methods and protocols. Some networks are able to dynamically change their logical topology through configuration changes to their routers and switches.


title: Network topology

text: The transmission media (often referred to in the literature as the "physical media") used to link devices to form a computer network include electrical cables (Ethernet, HomePNA, power line communication, G.hn), optical fiber (fiber-optic communication), and radio waves (wireless networking). In the OSI model, these are defined at layers 1 and 2 — the physical layer and the data link layer.


title: Network topology

text: A widely adopted "family" of transmission media used in local area network (LAN) technology is collectively known as Ethernet. The media and protocol standards that enable communication between networked devices over Ethernet are defined by IEEE 802.3. Ethernet transmits data over both copper and fiber cables. Wireless LAN standards (e.g. those defined by IEEE 802.11) use radio waves, or others use infrared signals as a transmission medium. Power line communication uses a building's power cabling to transmit data.


title: Network topology

text: The orders of the following wired technologies are, roughly, from slowest to fastest transmission speed.


title: Network topology

text: Price is a main factor distinguishing wired- and wireless-technology options in a business. Wireless options command a price premium that can make purchasing wired computers, printers and other devices a financial benefit. Before making the decision to purchase hard-wired technology products, a review of the restrictions and limitations of the selections is necessary. Business and employee needs may override any cost considerations.


title: Network topology

text: Both cases have a large round-trip delay time, which gives slow two-way communication, but does not prevent sending large amounts of information.


title: Network topology

text: Network nodes are the points of connection of the transmission medium to transmitters and receivers of the electrical, optical, or radio signals carried in the medium. Nodes may be associated with a computer, but certain types may have only a microcontroller at a node or possibly no programmable device at all. In the simplest of serial arrangements, one RS-232 transmitter can be connected by a pair of wires to one receiver, forming two nodes on one link, or a Point-to-Point topology. Some protocols permit a single node to only either transmit or receive (e.g., ARINC 429). Other protocols have nodes that can both transmit and receive into a single channel (e.g., CAN can have many transceivers connected to a single bus). While the conventional system building blocks of a computer network include network interface controllers (NICs), repeaters, hubs, bridges, switches, routers, modems, gateways, and firewalls, most address network concerns beyond the physical network topology and may be represented as single nodes on a particular physical network topology.


title: Network topology

text: A network interface controller (NIC) is computer hardware that provides a computer with the ability to access the transmission media, and has the ability to process low-level network information. For example, the NIC may have a connector for accepting a cable, or an aerial for wireless transmission and reception, and the associated circuitry.


title: Network topology

text: The NIC responds to traffic addressed to a network address for either the NIC or the computer as a whole.


title: Network topology

text: In Ethernet networks, each network interface controller has a unique Media Access Control (MAC) address—usually stored in the controller's permanent memory. To avoid address conflicts between network devices, the Institute of Electrical and Electronics Engineers (IEEE) maintains and administers MAC address uniqueness. The size of an Ethernet MAC address is six octets. The three most significant octets are reserved to identify NIC manufacturers. These manufacturers, using only their assigned prefixes, uniquely assign the three least-significant octets of every Ethernet interface they produce.


title: Network topology

text: A repeater is an electronic device that receives a network signal, cleans it of unnecessary noise and regenerates it. The signal may be reformed or retransmitted at a higher power level, to the other side of an obstruction possibly using a different transmission medium, so that the signal can cover longer distances without degradation. Commercial repeaters have extended RS-232 segments from 15 meters to over a kilometer. In most twisted pair Ethernet configurations, repeaters are required for cable that runs longer than 100 meters. With fiber optics, repeaters can be tens or even hundreds of kilometers apart.


title: Network topology

text: Repeaters work within the physical layer of the OSI model, that is, there is no end-to-end change in the physical protocol across the repeater, or repeater pair, even if a different physical layer may be used between the ends of the repeater, or repeater pair. Repeaters require a small amount of time to regenerate the signal. This can cause a propagation delay that affects network performance and may affect proper function. As a result, many network architectures limit the number of repeaters that can be used in a row, e.g., the Ethernet 5-4-3 rule.


title: Network topology

text: A repeater with multiple ports is known as hub, an Ethernet hub in Ethernet networks, a USB hub in USB networks.


title: Network topology

text: A network bridge connects and filters traffic between two network segments at the data link layer (layer 2) of the OSI model to form a single network. This breaks the network's collision domain but maintains a unified broadcast domain. Network segmentation breaks down a large, congested network into an aggregation of smaller, more efficient networks.


title: Network topology

text: A network switch is a device that forwards and filters OSI layer 2 datagrams (frames) between ports based on the destination MAC address in each frame.


title: Network topology

text: A switch is distinct from a hub in that it only forwards the frames to the physical ports involved in the communication rather than all ports connected. It can be thought of as a multi-port bridge. It learns to associate physical ports to MAC addresses by examining the source addresses of received frames. If an unknown destination is targeted, the switch broadcasts to all ports but the source. Switches normally have numerous ports, facilitating a star topology for devices, and cascading additional switches.


title: Network topology

text: Multi-layer switches are capable of routing based on layer 3 addressing or additional logical levels. The term "switch" is often used loosely to include devices such as routers and bridges, as well as devices that may distribute traffic based on load or based on application content (e.g., a Web URL identifier).


title: Network topology

text: A router is an internetworking device that forwards packets between networks by processing the routing information included in the packet or datagram (Internet protocol information from layer 3). The routing information is often processed in conjunction with the routing table (or forwarding table). A router uses its routing table to determine where to forward packets. A destination in a routing table can include a "null" interface, also known as the "black hole" interface because data can go into it, however, no further processing is done for said data, i.e. the packets are dropped.


title: Network topology

text: Modems (MOdulator-DEModulator) are used to connect network nodes via wire not originally designed for digital network traffic, or for wireless. To do this one or more carrier signals are modulated by the digital signal to produce an analog signal that can be tailored to give the required properties for transmission. Modems are commonly used for telephone lines, using a digital subscriber line technology.


title: Network topology

text: A firewall is a network device for controlling network security and access rules. Firewalls are typically configured to reject access requests from unrecognized sources while allowing actions from recognized ones. The vital role firewalls play in network security grows in parallel with the constant increase in cyber attacks.


title: Network topology

text: The study of network topology recognizes eight basic topologies: point-to-point, bus, star, ring or circular, mesh, tree, hybrid, or daisy chain.


title: Network topology

text: The simplest topology with a dedicated link between two endpoints. Easiest to understand, of the variations of point-to-point topology, is a point-to-point communication channel that appears, to the user, to be permanently associated with the two endpoints. A child's tin can telephone is one example of a "physical dedicated" channel.


title: Network topology

text: Using circuit-switching or packet-switching technologies, a point-to-point circuit can be set up dynamically and dropped when no longer needed. Switched point-to-point topologies are the basic model of conventional telephony.


title: Network topology

text: The value of a permanent point-to-point network is unimpeded communications between the two endpoints. The value of an on-demand point-to-point connection is proportional to the number of potential pairs of subscribers and has been expressed as Metcalfe's Law.


title: Network topology

text: Daisy chaining is accomplished by connecting each computer in series to the next. If a message is intended for a computer partway down the line, each system bounces it along in sequence until it reaches the destination. A daisy-chained network can take two basic forms: linear and ring.


title: Network topology

text: In local area networks using bus topology, each node is connected by interface connectors to a single central cable. This is the 'bus', also referred to as the backbone, or trunk – all data transmission between nodes in the network is transmitted over this common transmission medium and is able to be received by all nodes in the network simultaneously.


title: Network topology

text: A signal containing the address of the intended receiving machine travels from a source machine in both directions to all machines connected to the bus until it finds the intended recipient, which then accepts the data. If the machine address does not match the intended address for the data, the data portion of the signal is ignored. Since the bus topology consists of only one wire it is less expensive to implement than other topologies, but the savings are offset by the higher cost of managing the network. Additionally, since the network is dependent on the single cable, it can be the single point of failure of the network. In this topology data being transferred may be accessed by any node.


title: Network topology

text: In a linear bus network, all of the nodes of the network are connected to a common transmission medium which has just two endpoints. When the electrical signal reaches the end of the bus, the signal is reflected back down the line, causing unwanted interference. To prevent this, the two endpoints of the bus are normally terminated with a device called a terminator.


title: Network topology

text: In a distributed bus network, all of the nodes of the network are connected to a common transmission medium with more than two endpoints, created by adding branches to the main section of the transmission medium – the physical distributed bus topology functions in exactly the same fashion as the physical linear bus topology because all nodes share a common transmission medium.


title: Network topology

text: In star topology, every peripheral node (computer workstation or any other peripheral) is connected to a central node called a hub or switch. The hub is the server and the peripherals are the clients. The network does not necessarily have to resemble a star to be classified as a star network, but all of the peripheral nodes on the network must be connected to one central hub. All traffic that traverses the network passes through the central hub, which acts as a signal repeater.


title: Network topology

text: The star topology is considered the easiest topology to design and implement. One advantage of the star topology is the simplicity of adding additional nodes. The primary disadvantage of the star topology is that the hub represents a single point of failure. Also, since all peripheral communication must flow through the central hub, the aggregate central bandwidth forms a network bottleneck for large clusters.


title: Network topology

text: The extended star network topology extends a physical star topology by one or more repeaters between the central node and the peripheral (or 'spoke') nodes. The repeaters are used to extend the maximum transmission distance of the physical layer, the point-to-point distance between the central node and the peripheral nodes. Repeaters allow greater transmission distance, further than would be possible using just the transmitting power of the central node. The use of repeaters can also overcome limitations from the standard upon which the physical layer is based.


title: Network topology

text: A physical extended star topology in which repeaters are replaced with hubs or switches is a type of hybrid network topology and is referred to as a physical hierarchical star topology, although some texts make no distinction between the two topologies.


title: Network topology

text: A physical hierarchical star topology can also be referred as a tier-star topology. This topology differs from a tree topology in the way star networks are connected together. A tier-star topology uses a central node, while a tree topology uses a central bus and can also be referred as a star-bus network.


title: Network topology

text: A distributed star is a network topology that is composed of individual networks that are based upon the physical star topology connected in a linear fashion – i.e., 'daisy-chained' – with no central or top level connection point (e.g., two or more 'stacked' hubs, along with their associated star connected nodes or 'spokes').


title: Network topology

text: A ring topology is a daisy chain in a closed loop. Data travels around the ring in one direction. When one node sends data to another, the data passes through each intermediate node on the ring until it reaches its destination. The intermediate nodes repeat (retransmit) the data to keep the signal strong. Every node is a peer; there is no hierarchical relationship of clients and servers. If one node is unable to retransmit data, it severs communication between the nodes before and after it in the bus.


title: Network topology

text: The value of fully meshed networks is proportional to the exponent of the number of subscribers, assuming that communicating groups of any two endpoints, up to and including all the endpoints, is approximated by Reed's Law.


title: Network topology

text: In a "fully connected network", all nodes are interconnected. (In graph theory this is called a complete graph.) The simplest fully connected network is a two-node network. A fully connected network doesn't need to use packet switching or broadcasting. However, since the number of connections grows quadratically with the number of nodes:


title: Network topology

text: This makes it impractical for large networks. This kind of topology does not trip and affect other nodes in the network.


title: Network topology

text: In a partially connected network, certain nodes are connected to exactly one other node; but some nodes are connected to two or more other nodes with a point-to-point link. This makes it possible to make use of some of the redundancy of mesh topology that is physically fully connected, without the expense and complexity required for a connection between every node in the network.


title: Network topology

text: Hybrid topology is also known as hybrid network. Hybrid networks combine two or more topologies in such a way that the resulting network does not exhibit one of the standard topologies (e.g., bus, star, ring, etc.). For example, a tree network (or "star-bus network") is a hybrid topology in which star networks are interconnected via bus networks. However, a tree network connected to another tree network is still topologically a tree network, not a distinct network type. A hybrid topology is always produced when two different basic network topologies are connected.


title: Network topology

text: A "star-ring" network consists of two or more ring networks connected using a multistation access unit (MAU) as a centralized hub.


title: Network topology

text: The star topology reduces the probability of a network failure by connecting all of the peripheral nodes (computers, etc.) to a central node. When the physical star topology is applied to a logical bus network such as Ethernet, this central node (traditionally a hub) rebroadcasts all transmissions received from any peripheral node to all peripheral nodes on the network, sometimes including the originating node. All peripheral nodes may thus communicate with all others by transmitting to, and receiving from, the central node only. The failure of a transmission line linking any peripheral node to the central node will result in the isolation of that peripheral node from all others, but the remaining peripheral nodes will be unaffected. However, the disadvantage is that the failure of the central node will cause the failure of all of the peripheral nodes.


title: Network topology

text: If the central node is "passive", the originating node must be able to tolerate the reception of an echo of its own transmission, delayed by the two-way round trip transmission time (i.e. to and from the central node) plus any delay generated in the central node. An "active" star network has an active central node that usually has the means to prevent echo-related problems.


title: Network topology

text: A tree topology (a.k.a. hierarchical topology) can be viewed as a collection of star networks arranged in a hierarchy. This tree structure has individual peripheral nodes (e.g. leaves) which are required to transmit to and receive from one other node only and are not required to act as repeaters or regenerators. Unlike the star network, the functionality of the central node may be distributed.


title: Network topology

text: As in the conventional star network, individual nodes may thus still be isolated from the network by a single-point failure of a transmission path to the node. If a link connecting a leaf fails, that leaf is isolated; if a connection to a non-leaf node fails, an entire section of the network becomes isolated from the rest.


title: Network topology

text: To alleviate the amount of network traffic that comes from broadcasting all signals to all nodes, more advanced central nodes were developed that are able to keep track of the identities of the nodes that are connected to the network. These network switches will "learn" the layout of the network by "listening" on each port during normal data transmission, examining the data packets and recording the address/identifier of each connected node and which port it is connected to in a lookup table held in memory. This lookup table then allows future transmissions to be forwarded to the intended destination only.


title: Network topology

text: In a partially connected mesh topology, there are at least two nodes with two or more paths between them to provide redundant paths in case the link providing one of the paths fails. Decentralization is often used to compensate for the single-point-failure disadvantage that is present when using a single device as a central node (e.g., in star and tree networks). A special kind of mesh, limiting the number of hops between two nodes, is a hypercube. The number of arbitrary forks in mesh networks makes them more difficult to design and implement, but their decentralized nature makes them very useful.


title: Network topology

text: This is similar in some ways to a grid network, where a linear or ring topology is used to connect systems in multiple directions. A multidimensional ring has a toroidal topology, for instance.


title: Network topology

text: A "fully connected network", "complete topology", or "full mesh topology" is a network topology in which there is a direct link between all pairs of nodes. In a fully connected network with n nodes, there are formula_2 direct links. Networks designed with this topology are usually very expensive to set up, but provide a high degree of reliability due to the multiple paths for data that are provided by the large number of redundant links between nodes. This topology is mostly seen in military applications.


title: Bayesian inference

text: Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability".


title: Bayesian inference

text: Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference computes the posterior probability according to Bayes' theorem:


title: Bayesian inference

text: For different values of formula_2, only the factors formula_3 and formula_11, both in the numerator, affect the value of formula_23 – the posterior probability of a hypothesis is proportional to its prior probability (its inherent likeliness) and the newly acquired likelihood (its compatibility with the new observed evidence).


title: Bayesian inference

text: Bayesian updating is widely used and computationally convenient. However, it is not the only updating rule that might be considered rational.


title: Bayesian inference

text: Ian Hacking noted that traditional "Dutch book" arguments did not specify Bayesian updating: they left open the possibility that non-Bayesian updating rules could avoid Dutch books. Hacking wrote "And neither the Dutch book argument nor any other in the personalist arsenal of proofs of the probability axioms entails the dynamic assumption. Not one entails Bayesianism. So the personalist requires the dynamic assumption to be Bayesian. It is true that in consistency a personalist could abandon the Bayesian model of learning from experience. Salt could lose its savour."


title: Bayesian inference

text: Indeed, there are non-Bayesian updating rules that also avoid Dutch books (as discussed in the literature on "probability kinematics") following the publication of Richard C. Jeffrey's rule, which applies Bayes' rule to the case where the evidence itself is assigned a probability. The additional hypotheses needed to uniquely require Bayesian updating have been deemed to be substantial, complicated, and unsatisfactory.


title: Bayesian inference

text: If evidence is simultaneously used to update belief over a set of exclusive and exhaustive propositions, Bayesian inference may be thought of as acting on this belief distribution as a whole.


title: Bayesian inference

text: Suppose a process is generating independent and identically distributed events formula_31, but the probability distribution is unknown. Let the event space formula_32 represent the current state of belief for this process. Each model is represented by event formula_33. The conditional probabilities formula_34 are specified to define the models. formula_35 is the degree of belief in formula_33. Before the first inference step, formula_37 is a set of "initial prior probabilities". These must sum to 1, but are otherwise arbitrary.


title: Bayesian inference

text: Suppose that the process is observed to generate formula_38. For each formula_39, the prior formula_40 is updated to the posterior formula_41. From Bayes' theorem:


title: Bayesian inference

text: For a sequence of independent and identically distributed observations formula_43, it can be shown by induction that repeated application of the above is equivalent to


title: Bayesian inference

text: By parameterizing the space of models, the belief in all models may be updated in a single step. The distribution of belief over the model space may then be thought of as a distribution of belief over the parameter space. The distributions in this section are expressed as continuous, represented by probability densities, as this is the usual situation. The technique is however equally applicable to discrete distributions.


title: Bayesian inference

text: Let the vector formula_46 span the parameter space. Let the initial prior distribution over formula_46 be formula_48, where formula_49 is a set of parameters to the prior itself, or "hyperparameters". Let formula_43 be a sequence of independent and identically distributed event observations, where all formula_51 are distributed as formula_52 for some formula_46. Bayes' theorem is applied to find the posterior distribution over formula_46:


title: Bayesian inference

text: Bayesian theory calls for the use of the posterior predictive distribution to do predictive inference, i.e., to predict the distribution of a new, unobserved data point. That is, instead of a fixed point as a prediction, a distribution over possible points is returned. Only this way is the entire posterior distribution of the parameter(s) used. By comparison, prediction in frequentist statistics often involves finding an optimum point estimate of the parameter(s)—e.g., by maximum likelihood or maximum a posteriori estimation (MAP)—and then plugging this estimate into the formula for the distribution of a data point. This has the disadvantage that it does not account for any uncertainty in the value of the parameter, and hence will underestimate the variance of the predictive distribution.


title: Bayesian inference

text: In some instances, frequentist statistics can work around this problem. For example, confidence intervals and prediction intervals in frequentist statistics when constructed from a normal distribution with unknown mean and variance are constructed using a Student's t-distribution. This correctly estimates the variance, due to the facts that (1) the average of normally distributed random variables is also normally distributed, and (2) the predictive distribution of a normally distributed data point with unknown mean and variance, using conjugate or uninformative priors, has a Student's t-distribution. In Bayesian statistics, however, the posterior predictive distribution can always be determined exactly—or at least to an arbitrary level of precision when numerical methods are used.


title: Bayesian inference

text: Both types of predictive distributions have the form of a compound probability distribution (as does the marginal likelihood). In fact, if the prior distribution is a conjugate prior, such that the prior and posterior distributions come from the same family, it can be seen that both prior and posterior predictive distributions also come from the same family of compound distributions. The only difference is that the posterior predictive distribution uses the updated values of the hyperparameters (applying the Bayesian update rules given in the conjugate prior article), while the prior predictive distribution uses the values of the hyperparameters that appear in the prior distribution.


title: Bayesian inference

text: formula_74. That is, if the model were true, the evidence would be more likely than is predicted by the current state of belief. The reverse applies for a decrease in belief. If the belief does not change, formula_75. That is, the evidence is independent of the model. If the model were true, the evidence would be exactly as likely as predicted by the current state of belief.


title: Bayesian inference

text: If formula_76 then formula_77. If formula_78, then formula_79. This can be interpreted to mean that hard convictions are insensitive to counter-evidence.


title: Bayesian inference

text: The former follows directly from Bayes' theorem. The latter can be derived by applying the first rule to the event "not formula_80" in place of "formula_80", yielding "if formula_82, then formula_83", from which the result immediately follows.


title: Bayesian inference

text: Consider the behaviour of a belief distribution as it is updated a large number of times with independent and identically distributed trials. For sufficiently nice prior probabilities, the Bernstein-von Mises theorem gives that in the limit of infinite trials, the posterior converges to a Gaussian distribution independent of the initial prior under some conditions firstly outlined and rigorously proven by Joseph L. Doob in 1948, namely if the random variable in consideration has a finite probability space. The more general results were obtained later by the statistician David A. Freedman who published in two seminal research papers in 1963 and 1965 when and under what circumstances the asymptotic behaviour of posterior is guaranteed. His 1963 paper treats, like Doob (1949), the finite case and comes to a satisfactory conclusion. However, if the random variable has an infinite but countable probability space (i.e., corresponding to a die with infinite many faces) the 1965 paper demonstrates that for a dense subset of priors the Bernstein-von Mises theorem is not applicable. In this case there is almost surely no asymptotic convergence. Later in the 1980s and 1990s Freedman and Persi Diaconis continued to work on the case of infinite countable probability spaces. To summarise, there may be insufficient trials to suppress the effects of the initial choice, and especially for large (but finite) systems the convergence might be very slow.


title: Bayesian inference

text: In parameterized form, the prior distribution is often assumed to come from a family of distributions called conjugate priors. The usefulness of a conjugate prior is that the corresponding posterior distribution will be in the same family, and the calculation may be expressed in closed form.


title: Bayesian inference

text: It is often desired to use a posterior distribution to estimate a parameter or variable. Several methods of Bayesian estimation select measurements of central tendency from the posterior distribution.


title: Bayesian inference

text: For one-dimensional problems, a unique median exists for practical continuous problems. The posterior median is attractive as a robust estimator.


title: Bayesian inference

text: If there exists a finite mean for the posterior distribution, then the posterior mean is a method of estimation.


title: Bayesian inference

text: There are other methods of estimation that minimize the posterior "risk" (expected-posterior loss) with respect to a loss function, and these are of interest to statistical decision theory using the sampling distribution ("frequentist statistics").


title: Bayesian inference

text: The posterior predictive distribution of a new observation formula_63 (that is independent of previous observations) is determined by


title: Bayesian inference

text: Suppose there are two full bowls of cookies. Bowl #1 has 10 chocolate chip and 30 plain cookies, while bowl #2 has 20 of each. Our friend Fred picks a bowl at random, and then picks a cookie at random. We may assume there is no reason to believe Fred treats one bowl differently from another, likewise for the cookies. The cookie turns out to be a plain one. How probable is it that Fred picked it out of bowl #1?


title: Bayesian inference

text: Intuitively, it seems clear that the answer should be more than a half, since there are more plain cookies in bowl #1. The precise answer is given by Bayes' theorem. Let formula_88 correspond to bowl #1, and formula_89 to bowl #2.


title: Bayesian inference

text: It is given that the bowls are identical from Fred's point of view, thus formula_90, and the two must add up to 1, so both are equal to 0.5.


title: Bayesian inference

text: The event formula_91 is the observation of a plain cookie. From the contents of the bowls, we know that formula_92 and formula_93 Bayes' formula then yields


title: Bayesian inference

text: Before we observed the cookie, the probability we assigned for Fred having chosen bowl #1 was the prior probability, formula_95, which was 0.5. After observing the cookie, we must revise the probability to formula_96, which is 0.6.


title: Bayesian inference

text: An archaeologist is working at a site thought to be from the medieval period, between the 11th century to the 16th century. However, it is uncertain exactly when in this period the site was inhabited. Fragments of pottery are found, some of which are glazed and some of which are decorated. It is expected that if the site were inhabited during the early medieval period, then 1% of the pottery would be glazed and 50% of its area decorated, whereas if it had been inhabited in the late medieval period then 81% would be glazed and 5% of its area decorated. How confident can the archaeologist be in the date of inhabitation as fragments are unearthed?


title: Bayesian inference

text: The degree of belief in the continuous variable formula_97 (century) is to be calculated, with the discrete set of events formula_98 as evidence. Assuming linear variation of glaze and decoration with time, and that these variables are independent,


title: Bayesian inference

text: Assume a uniform prior of formula_103, and that trials are independent and identically distributed. When a new fragment of type formula_104 is discovered, Bayes' theorem is applied to update the degree of belief for each formula_105:


title: Bayesian inference

text: A computer simulation of the changing belief as 50 fragments are unearthed is shown on the graph. In the simulation, the site was inhabited around 1420, or formula_107. By calculating the area under the relevant portion of the graph for 50 trials, the archaeologist can say that there is practically no chance the site was inhabited in the 11th and 12th centuries, about 1% chance that it was inhabited during the 13th century, 63% chance during the 14th century and 36% during the 15th century. The Bernstein-von Mises theorem asserts here the asymptotic convergence to the "true" distribution because the probability space corresponding to the discrete set of events formula_98 is finite (see above section on asymptotic behaviour of the posterior).


title: Bayesian inference

text: A decision-theoretic justification of the use of Bayesian inference was given by Abraham Wald, who proved that every unique Bayesian procedure is admissible. Conversely, every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.


title: Bayesian inference

text: Wald characterized admissible procedures as Bayesian procedures (and limits of Bayesian procedures), making the Bayesian formalism a central technique in such areas of frequentist inference as parameter estimation, hypothesis testing, and computing confidence intervals. For example:


title: Bayesian inference

text: Bayesian methodology also plays a role in model selection where the aim is to select one model from a set of competing models that represents most closely the underlying process that generated the observed data. In Bayesian model comparison, the model with the highest posterior probability given the data is selected. The posterior probability of a model depends on the evidence, or marginal likelihood, which reflects the probability that the data is generated by the model, and on the prior belief of the model. When two competing models are a priori considered to be equiprobable, the ratio of their posterior probabilities corresponds to the Bayes factor. Since Bayesian model comparison is aimed on selecting the model with the highest posterior probability, this methodology is also referred to as the maximum a posteriori (MAP) selection rule or the MAP probability rule.


title: Bayesian inference

text: While conceptually simple, Bayesian methods can be mathematically and numerically challenging. Probabilistic programming languages (PPLs) implement functions to easily build Bayesian models together with efficient automatic inference methods. This helps separate the model building from the inference, allowing practitioners to focus on their specific problems and leaving PPLs to handle the computational details for them.


title: Bayesian inference

text: See the separate Wikipedia entry on Bayesian Statistics, specifically the Statistical modeling section in that page.


title: Bayesian inference

text: Bayesian inference has applications in artificial intelligence and expert systems. Bayesian inference techniques have been a fundamental part of computerized pattern recognition techniques since the late 1950s. There is also an ever-growing connection between Bayesian methods and simulation-based Monte Carlo techniques since complex models cannot be processed in closed form by a Bayesian analysis, while a graphical model structure "may" allow for efficient simulation algorithms like the Gibbs sampling and other Metropolis–Hastings algorithm schemes. Recently Bayesian inference has gained popularity among the phylogenetics community for these reasons; a number of applications allow many demographic and evolutionary parameters to be estimated simultaneously.


title: Bayesian inference

text: As applied to statistical classification, Bayesian inference has been used to develop algorithms for identifying e-mail spam. Applications which make use of Bayesian inference for spam filtering include CRM114, DSPAM, Bogofilter, SpamAssassin, SpamBayes, Mozilla, XEAMS, and others. Spam classification is treated in more detail in the article on the naïve Bayes classifier.


title: Bayesian inference

text: Solomonoff's Inductive inference is the theory of prediction based on observations; for example, predicting the next symbol based upon a given series of symbols. The only assumption is that the environment follows some unknown but computable probability distribution. It is a formal inductive framework that combines two well-studied principles of inductive inference: Bayesian statistics and Occam's Razor. Solomonoff's universal prior probability of any prefix "p" of a computable sequence "x" is the sum of the probabilities of all programs (for a universal computer) that compute something starting with "p". Given some "p" and any computable but unknown probability distribution from which "x" is sampled, the universal prior and Bayes' theorem can be used to predict the yet unseen parts of "x" in optimal fashion.


title: Bayesian inference

text: Bayesian inference has been applied in different Bioinformatics applications, including differential gene expression analysis. Bayesian inference is also used in a general cancer risk model, called CIRI (Continuous Individualized Risk Index), where serial measurements are incorporated to update a Bayesian model which is primarily built from prior knowledge.


title: Bayesian inference

text: Bayesian inference can be used by jurors to coherently accumulate the evidence for and against a defendant, and to see whether, in totality, it meets their personal threshold for 'beyond a reasonable doubt'. Bayes' theorem is applied successively to all evidence presented, with the posterior from one stage becoming the prior for the next. The benefit of a Bayesian approach is that it gives the juror an unbiased, rational mechanism for combining evidence. It may be appropriate to explain Bayes' theorem to jurors in odds form, as betting odds are more widely understood than probabilities. Alternatively, a logarithmic approach, replacing multiplication with addition, might be easier for a jury to handle.


title: Bayesian inference

text: If the existence of the crime is not in doubt, only the identity of the culprit, it has been suggested that the prior should be uniform over the qualifying population. For example, if 1,000 people could have committed the crime, the prior probability of guilt would be 1/1000.


title: Bayesian inference

text: The use of Bayes' theorem by jurors is controversial. In the United Kingdom, a defence expert witness explained Bayes' theorem to the jury in "R v Adams". The jury convicted, but the case went to appeal on the basis that no means of accumulating evidence had been provided for jurors who did not wish to use Bayes' theorem. The Court of Appeal upheld the conviction, but it also gave the opinion that "To introduce Bayes' Theorem, or any similar method, into a criminal trial plunges the jury into inappropriate and unnecessary realms of theory and complexity, deflecting them from their proper task."


title: Bayesian inference

text: Gardner-Medwin argues that the criterion on which a verdict in a criminal trial should be based is "not" the probability of guilt, but rather the "probability of the evidence, given that the defendant is innocent" (akin to a frequentist p-value). He argues that if the posterior probability of guilt is to be computed by Bayes' theorem, the prior probability of guilt must be known. This will depend on the incidence of the crime, which is an unusual piece of evidence to consider in a criminal trial. Consider the following three propositions:


title: Bayesian inference

text: Gardner-Medwin argues that the jury should believe both A and not-B in order to convict. A and not-B implies the truth of C, but the reverse is not true. It is possible that B and C are both true, but in this case he argues that a jury should acquit, even though they know that they will be letting some guilty people go free. See also Lindley's paradox.


title: Bayesian inference

text: Bayesian epistemology is a movement that advocates for Bayesian inference as a means of justifying the rules of inductive logic.


title: Bayesian inference

text: Karl Popper and David Miller have rejected the idea of Bayesian rationalism, i.e. using Bayes rule to make epistemological inferences: It is prone to the same vicious circle as any other justificationist epistemology, because it presupposes what it attempts to justify. According to this view, a rational interpretation of Bayesian inference would see it merely as a probabilistic version of falsification, rejecting the belief, commonly held by Bayesians, that high likelihood achieved by a series of Bayesian updates would prove the hypothesis beyond any reasonable doubt, or even with likelihood greater than 0.


title: Bayesian inference

text: The problem considered by Bayes in Proposition 9 of his essay, "An Essay towards solving a Problem in the Doctrine of Chances", is the posterior distribution for the parameter "a" (the success rate) of the binomial distribution.


title: Bayesian inference

text: The term "Bayesian" refers to Thomas Bayes (1701–1761), who proved that probabilistic limits could be placed on an unknown event. However, it was Pierre-Simon Laplace (1749–1827) who introduced (as Principle VI) what is now called Bayes' theorem and used it to address problems in celestial mechanics, medical statistics, reliability, and jurisprudence. Early Bayesian inference, which used uniform priors following Laplace's principle of insufficient reason, was called "inverse probability" (because it infers backwards from observations to parameters, or from effects to causes). After the 1920s, "inverse probability" was largely supplanted by a collection of methods that came to be called frequentist statistics.


title: Bayesian inference

text: In the 20th century, the ideas of Laplace were further developed in two different directions, giving rise to "objective" and "subjective" currents in Bayesian practice. In the objective or "non-informative" current, the statistical analysis depends on only the model assumed, the data analyzed, and the method assigning the prior, which differs from one objective Bayesian practitioner to another. In the subjective or "informative" current, the specification of the prior depends on the belief (that is, propositions on which the analysis is prepared to act), which can summarize information from experts, previous studies, etc.


title: Bayesian inference

text: In the 1980s, there was a dramatic growth in research and applications of Bayesian methods, mostly attributed to the discovery of Markov chain Monte Carlo methods, which removed many of the computational problems, and an increasing interest in nonstandard, complex applications. Despite growth of Bayesian research, most undergraduate teaching is still based on frequentist statistics. Nonetheless, Bayesian methods are widely accepted and used, such as for example in the field of machine learning.


title: Software design pattern

text: In software engineering, a software design pattern is a general, reusable solution to a commonly occurring problem within a given context in software design. It is not a finished design that can be transformed directly into source or machine code. Rather, it is a description or template for how to solve a problem that can be used in many different situations. Design patterns are formalized best practices that the programmer can use to solve common problems when designing an application or system.


title: Software design pattern

text: Object-oriented design patterns typically show relationships and interactions between classes or objects, without specifying the final application classes or objects that are involved. Patterns that imply mutable state may be unsuited for functional programming languages. Some patterns can be rendered unnecessary in languages that have built-in support for solving the problem they are trying to solve, and object-oriented patterns are not necessarily suitable for non-object-oriented languages.


title: Software design pattern

text: Design patterns may be viewed as a structured approach to computer programming intermediate between the levels of a programming paradigm and a concrete algorithm.


title: Software design pattern

text: Patterns originated as an architectural concept by Christopher Alexander as early as 1977 (c.f. "The Pattern of Streets," JOURNAL OF THE AIP, September, 1977, Vol. 32, No. 3, pp. 273–278). In 1987, Kent Beck and Ward Cunningham began experimenting with the idea of applying patterns to programming – specifically pattern languages – and presented their results at the OOPSLA conference that year. In the following years, Beck, Cunningham and others followed up on this work.


title: Software design pattern

text: Design patterns gained popularity in computer science after the book "Design Patterns: Elements of Reusable Object-Oriented Software" was published in 1994 by the so-called "Gang of Four" (Gamma et al.), which is frequently abbreviated as "GoF". That same year, the first Pattern Languages of Programming Conference was held, and the following year the Portland Pattern Repository was set up for documentation of design patterns. The scope of the term remains a matter of dispute. Notable books in the design pattern genre include:


title: Software design pattern

text: Although design patterns have been applied practically for a long time, formalization of the concept of design patterns languished for several years.


title: Software design pattern

text: Design patterns can speed up the development process by providing tested, proven development paradigms. Effective software design requires considering issues that may not become visible until later in the implementation. Freshly written code can often have hidden subtle issues that take time to be detected, issues that sometimes can cause major problems down the road. Reusing design patterns helps to prevent such subtle issues, and it also improves code readability for coders and architects who are familiar with the patterns.


title: Software design pattern

text: In order to achieve flexibility, design patterns usually introduce additional levels of indirection, which in some cases may complicate the resulting designs and hurt application performance.


title: Software design pattern

text: By definition, a pattern must be programmed anew into each application that uses it. Since some authors see this as a step backward from software reuse as provided by components, researchers have worked to turn patterns into components. Meyer and Arnout were able to provide full or partial componentization of two-thirds of the patterns they attempted.


title: Software design pattern

text: Software design techniques are difficult to apply to a broader range of problems. Design patterns provide general solutions, documented in a format that does not require specifics tied to a particular problem.


title: Software design pattern

text: Design patterns are composed of several sections (see below). Of particular interest are the Structure, Participants, and Collaboration sections. These sections describe a "design motif": a prototypical "micro-architecture" that developers copy and adapt to their particular designs to solve the recurrent problem described by the design pattern. A micro-architecture is a set of program constituents (e.g., classes, methods...) and their relationships. Developers use the design pattern by introducing in their designs this prototypical micro-architecture, which means that micro-architectures in their designs will have structure and organization similar to the chosen design motif.


title: Software design pattern

text: Efforts have also been made to codify design patterns in particular domains, including use of existing design patterns as well as domain-specific design patterns. Examples include user interface design patterns, information visualization, secure design, "secure usability", Web design and business model design.


title: Software design pattern

text: The annual Pattern Languages of Programming Conference proceedings include many examples of domain-specific patterns.


title: Software design pattern

text: Design patterns had originally been categorized into 3 sub-classifications based on what kind of problem they solve. Creational patterns provide the capability to create objects based on a required criterion and in a controlled way. Structural patterns are about organizing different classes and objects to form larger structures and provide new functionality. Finally, behavioral patterns are about identifying common communication patterns between objects and realizing these patterns.


title: Software design pattern

text: The documentation for a design pattern describes the context in which the pattern is used, the forces within the context that the pattern seeks to resolve, and the suggested solution. There is no single, standard format for documenting design patterns. Rather, a variety of different formats have been used by different pattern authors. However, according to Martin Fowler, certain pattern forms have become more well-known than others, and consequently become common starting points for new pattern-writing efforts. One example of a commonly used documentation format is the one used by Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides in their book "Design Patterns". It contains the following sections:


title: Software design pattern

text: It has been observed that design patterns may just be a sign that some features are missing in a given programming language (Java or C++ for instance). Peter Norvig demonstrates that 16 out of the 23 patterns in the "Design Patterns" book (which is primarily focused on C++) are simplified or eliminated (via direct language support) in Lisp or Dylan. Related observations were made by Hannemann and Kiczales who implemented several of the 23 design patterns using an aspect-oriented programming language (AspectJ) and showed that code-level dependencies were removed from the implementations of 17 of the 23 design patterns and that aspect-oriented programming could simplify the implementations of design patterns.


title: 070 Shake

text: Danielle Balbuena (born June 13, 1997), better known by her stage name 070 Shake, is an American rapper, singer, and songwriter. Aside from her solo career, she is also a member of the musical collective 070, who have released a mixtape together titled "The 070 Project: Chapter 1" (2016). Shake would release her debut EP, "Glitter", in March 2018.


title: 070 Shake

text: In 2018, Shake gained attention for her involvement with American musician Kanye West's production work in Wyoming, with West later signing her to his GOOD Music imprint. She went on to feature on the songs "Ghost Town" and "Violent Crimes" from West's "Ye", as well as appearing on Pusha T's "Daytona" and Nas' "Nasir". Shake released her debut album, "Modus Vivendi", in 2020 and released her second album, "You Can't Kill Me", in 2022.


title: 070 Shake

text: 070 Shake was born in North Bergen, New Jersey, and is of Dominican descent. Balbuena attended North Bergen High School, where she played on the school's basketball team. Prior to her music career, Shake wrote poetry.


title: 070 Shake

text: Shake began her music career in late 2015, recording the songs "Proud" and "Swervin". Shake's stage name is derived from her affiliation with the 070 music collective; 070 coming from New Jersey's 070 ZIP Codes. By 2018, the 070 crew was noted to have 11 members including artists and producers.


title: 070 Shake

text: By 2016, Shake was earning hundreds of thousands of streams on SoundCloud. Soon after posting several songs on SoundCloud, Shake attracted the attention of Miami-based promoter and social media personality YesJulz. After hearing "Proud" specifically, YesJulz reached out to Shake on Twitter, quickly signing on to be her manager. Shake broke through with "Trust Nobody", released early in that year. In August, Shake collaborated with fellow 070 members Ralphy River, Hack, and Treee Safari on the single "Honey". The song featured production from frequent collaborators The Kompetition, a three-person production group. "Honey" simultaneously premiered on "Complex" and 1 AM Radio on Dash. "Vibe" commented that the track "[sounded] tailor made to rock on dance floors everywhere."


title: 070 Shake

text: Also in 2016, Shake signed with Kanye West's GOOD Music label. GOOD Music found out about Shake through Julz, as she played some of Shake's music at a Yeezy fitting, interesting the label's president, Pusha T. After signing Shake, the label picked up her "Trust Nobody" track and re-released it in September. Shake spent October and November opening up for English rock band The 1975 during the American leg of their 2016 tour. On December 8, 070 released their first mixtape, "The 070 Project: Chapter 1".


title: 070 Shake

text: Shake modeled for Gypsy Sport's Fall 2017 runway show. She also went on her first headlining tour in April. In a 2017 interview with "Paper", Shake mentioned her "Yellow Girl" EP would release later that year. However, the project was moved back to release after "Glitter", another collaboration with The Kompetition.


title: 070 Shake

text: Her solo debut, the 6-track "Glitter" EP was released on March 23, 2018, although it was originally slated for a January 26 release and to include 12 tracks. At the time of "Glitter"s release, media outlets noted that her lyrical content concentrated on her self-esteem issues, drug use, and sexuality. Shake described "Glitter" as "about being in a dark place and finding yourself and figuring it out. It's about being in the lowest of lows type of shit." Shortly prior to "Glitter"s release, Shake performed at the SXSW music festival.


title: 070 Shake

text: In May, Shake was featured on "Santeria", a track from Pusha T's album "Daytona". Shake also had featured vocals on "Ghost Town" and "Violent Crimes" from Kanye West's album "Ye".


title: 070 Shake

text: Michael Saponara praised the two tracks as "standout cuts" on the album, and ranked "Ghost Town" specifically as the album's best song. "HotNewHipHop" praised Shake's performance on "Ghost Town" as the highlight of the song, and called the track the climax of the album. Shake told "Pigeons & Planes" that "Ghost Town" was nearly left off "Ye", as the track was finished on the same day of the album's release. "Ghost Town" also featured vocals from Kid Cudi, another inspiration of Shake's; she shared with "Pigeons & Planes", "All my life I grew up listening to Kanye West and Kid Cudi. I've cried to their music. They've definitely changed my life, and saved me from a lot of stuff." Shake's recording experience with West in Wyoming for his "Ye" album impacted her thoughts about "Yellow Girl"; she stated "I don't know if it's going to be called "Yellow Girl". I know the songs are definitely changing. The experience I had in Wyoming makes me want to make music on a different level."


title: 070 Shake

text: In 2019, she featured on DJ Khaled's album "Father of Asahd" alongside Buju Banton, Sizzla and Mavado on the song "Holy Mountain".


title: 070 Shake

text: Shake released her debut album, "Modus Vivendi," on January 17, 2020. Her second studio album, "You Can't Kill Me" was released in June 2022. Its first single, "Lose My Cool" featuring NLE Choppa, was released on December 3, 2021.


title: 070 Shake

text: In the summer of 2022, Shake accompanied American musician Kid Cudi on his To the Moon World Tour as an opening act. In October 2022, Shake was featured on the song "Escapism" by Raye. After going viral on TikTok, the song charted internationally and became Shake's first song to chart on the Billboard Hot 100.


title: 070 Shake

text: Prominently referenced in her music, Shake uses she/her pronouns when describing lovers. A 2017 "Vogue" essay on rising queer stars in rap music mentioned Shake being in a relationship with Sophia Diana Lodato. In a 2018 "Pitchfork" article, Shake said she doesn't like to put labels on her sexuality. "I don't really identify myself as queer or gay or anything. I just like girls." As of April 2022, she is in a relationship with singer Kehlani.


title: 070 Shake

text: The song "Glitter" from "Glitter EP" is featured in the Netflix series "On My Block", season 2 episode 1.


title: 070 Shake

text: The song "The Pines" from "Modus Vivendi" (2020) is featured in the Netflix series "Inventing Anna" (2022).


title: Erotica

text: Erotica is literature or art that deals substantively with subject matter that is erotic, sexually stimulating or sexually arousing. Some critics regard pornography as a type of erotica, but many consider it to be different. Erotic art may use any artistic form to depict erotic content, including painting, sculpture, drama, film or music. Erotic literature and erotic photography have become genres in their own right. Erotica also exists in a number of subgenres including gay erotica, lesbian erotica, women's erotica, bondage erotica, monster erotica and tentacle erotica.


title: Erotica

text: Curiosa are curiosities or rarities, especially unusual or erotic books. In the antiquarian book trade, pornographic works are often listed under "curiosa", "erotica" or "facetiae".


title: Erotica

text: A distinction is often made between erotica and pornography (and the lesser-known genre of sexual entertainment, ribaldry), although some viewers may not distinguish between them. A key distinction, some have argued, is that pornography's objective is the graphic depiction of sexually explicit scenes. At the same time, erotica "seeks to tell a story that involves sexual themes" that include a more plausible depiction of human sexuality than in pornography. Additionally, works considered degrading or exploitative tend to be classified by those who see them as such, as "porn" rather than as "erotica" and consequently, pornography is often described as exploitative or degrading. Many countries have laws banning or at least regulating what is considered pornographic material, a situation that generally does not apply to erotica.


title: Erotica

text: For the anti-pornography activist Andrea Dworkin, "Erotica is simply high-class pornography; better produced, better conceived, better executed, better packaged, designed for a better class of consumer." Feminist writer Gloria Steinem distinguishes erotica from pornography, writing: "Erotica is as different from pornography as love is from rape, as dignity is from humiliation, as partnership is from slavery, as pleasure is from pain." Steinem's argument hinges on the distinction between reciprocity versus domination, as she writes: "Blatant or subtle, pornography involves no equal power or mutuality. In fact, much of the tension and drama comes from the clear idea that one person is dominating the other."


title: Númenor

text: Númenor, also called Elenna-nórë or Westernesse, is a fictional place in J. R. R. Tolkien's writings. It was the kingdom occupying a large island to the west of Middle-earth, the main setting of Tolkien's writings, and was the greatest civilization of Men. However, after centuries of prosperity many of the inhabitants ceased to worship the One God, Eru Ilúvatar, and rebelled against the Valar, resulting in the destruction of the island and the death of most of its people. Tolkien intended Númenor to allude to the legendary Atlantis. Commentators have noted that the destruction of Númenor echoes the Biblical stories of the fall of man and the destruction of Sodom and Gomorrah, and John Milton's "Paradise Lost".


title: Númenor

text: "A Description of the Island of Númenor", published in "Unfinished Tales", was supposedly derived from the archives of Gondor. The island of Númenor was in the Great Sea, closer to Aman in the West than to the continent of Middle-earth in the east. In shape it was a five-pointed star, with five peninsulas extending from the central region. The latter is stated to have been around across, and the promontories were nearly of the same length each. The island itself was "tilted southward and a little eastward". The largest river was the Siril. Karen Wynn Fonstad estimated the island to be 167,691 square miles [435,017 km²] in area.


title: Númenor

text: Mittalmar or "the Inlands" was the central region, high and land-locked except for a small coast around Rómenna, with the mountain of Meneltarma at its centre. Much of the region consisted of grasslands, pastures and low downs with few trees. Númenor's main rivers, Siril and Nunduinë, arose in Mittalmar, on or near Meneltarma. Mittalmar's eastern district, Arandor, was the most populated part of Númenor, with Armenelos, the capital, and Rómenna. In the south-west of Mittalmar lay the district of Emerië, Númenor's prime sheep-grazing area.


title: Númenor

text: Andustar or "the Westlands" was a fertile wooded region, rocky to the north, with high coastal cliffs to the west. Its bays held several harbours. The northern highlands were covered by fir-woods, while in the south the forests consisted mainly of birches and beeches upon the upper ground and of oaks and elms in vales.


title: Númenor

text: Hyarnustar or "the Southwestlands" had vineyards and fertile farmlands in the east, with wide beaches on that coast, and highlands and coastal cliffs to the west.


title: Númenor

text: Hyarrostar or "the Southeastlands" was the lowest-lying region, with long gentle shores, especially in the west, and plantations to supply timber for shipbuilding.


title: Númenor

text: Orrostar or "the Eastlands" was a cool but fertile region, with highlands in the north. In the south-west were vast plantations of grain.


title: Númenor

text: Forostar or "the Northlands" was rocky and the least fertile region, with heather moors rising in the north to rocky hills, and few trees. Its quarries provided the best building stone. The fifth king Tar-Meneldur built his tall tower here to watch the stars.


title: Númenor

text: The most populous towns were coastal, mostly connected by dirt roads. A paved highway ran across the island of Númenor from east to west, connecting Rómenna, Armenelos, the Valley of Tombs, Ondosto and Andúnië.


title: Númenor

text: Armenelos, "Royal citadel", was the capital and in later years the largest city of Númenor. It lay inland, near the centre of Arandor, about 20 miles from mount Meneltarma. The closest coast was some 50 miles to the east at Rómenna. It contained the royal palace, the King's House. A tall tower was constructed there by the first King Elros, son of the seafaring hero Earendil, and the White Tree Nimloth, living symbol of the Kingdom of Númenor, was planted in the days of the sixth King, the explorer Tar-Aldarion. During the reign of the 25th and last King, the proud Ar-Pharazôn, a giant circular temple to Morgoth was built in the city, over five hundred feet in diameter and as much in height to its cornice line, above which a silver dome rose. The dome had an oculus, from which the smoke of numerous burned sacrifices rose, tarnishing the silver soon after its completion.


title: Númenor

text: Andúnië, "Sunset", was a port on the west side of Númenor, which looked towards the Undying Lands; the Eldar used to land there. Valandil was the first Lord of Andúnië, and his successors were important in shaping Númenórean policies. As the Shadow fell over Númenor, Armenelos overtook Andúnië.


title: Númenor

text: Rómenna, "Eastwards" (for ships sailing to Middle-earth), was a harbour at the head of the long firth on the east of Númenor. It became important as shipbuilding and seafaring grew, especially from the reign of Tar-Aldarion.


title: Númenor

text: Eldalondë or "Elf-haven" was a seaport on the western coast where the Elves would arrive from Tol Eressëa, and the river Nunduinë emptied into the Bay of Eldanna. It was "the most beautiful of all the havens of Númenor", compared by the Elves to a town in Eressëa.


title: Númenor

text: The Númenóreans were descended from the Edain of Beleriand, with three clans: the people of Hador, the people of Bëor, and the Folk of Haleth. Most Númenóreans descended from the fair-haired and blue-eyed people of Hador. The settlers of the western regions, especially Andustar, came mostly from the people of Bëor, with darker hair and grey eyes. A few remnants of the Folk of Haleth and a few families of the Drúedain were also present. The average Númenórean was taller than two "rangar", or 6'4". Elendil was the tallest of Men who escaped the Downfall (almost 2.5 "rangar" tall, 7'11"). Tolkien originally suggested that Númenóreans not of the Line of Elros lived for 200 years, with royal kindred living 400 years. Later, royal Númenóreans were said to have "five times" the lifespan of normal men, or 300–350 years. Men of the House of Elros lived for some 400 years; this diminished due to their rebellion. Coming-of-age was at 25 years.


title: Númenor

text: The common language of the Númenóreans, Adûnaic, was derived from Taliska, the speech of the Hadorians. The descendants of the people of Bëor were sometimes said to have spoken an accented form of Adûnaic, while elsewhere it is stated that they had dropped their own tongue before coming to the island and used the Grey-elven Sindarin as daily speech in Númenor. All texts, however, agree that Sindarin was known to most Númenóreans and was widely used in noble families; the latter also knew the High-elven Quenya, employing it in works of lore and nomenclature. This changed when the friendship with the Elves was broken; usage of both Sindarin and Quenya lessened, until at last King Ar-Adûnakhôr forbade their teaching, and knowledge of the Elven-tongues was only preserved by the Faithful.


title: Númenor

text: Before the coming of the Shadow, the Númenóreans maintained several traditions connected with the worship of Ilúvatar and respect to the Valar. Among them are recorded the setting a bough of the fragrant "oiolairë" upon the prow of a departing ship, the ceremonies concerned with the passing of the Sceptre, and laying down one's life. The most famous traditions were the Three Prayers, during which a great concourse of people ascended to the holy summit of Meneltarma and the King praised Eru Ilúvatar. These were the spring prayer for a good year, "Erukyermë"; the midsummer prayer for a good harvest, "Erulaitalë"; and the autumn harvest thanksgiving, "Eruhantalë".


title: Númenor

text: The Númenórean calendar, the "King's Reckoning", is similar to the Gregorian, with a week of seven days, a year of 365 days except in leap years, and twelve months ("astar"): ten with 30 days and two with 31. However, King's Reckoning has some days outside the months, a feature borrowed from Elvish Calendars, which were generally holidays. Two of these were the pair which book-ends the year; thus the last month of the year was followed by "mettarë", the last day of the year; this was followed by "yestarë", New Year's Day, before the start of the first month. The other monthless day was "loëndë", mid-year day. In a leap year there were two mid-year days. In the Second and Third Ages, years were reckoned from the beginning of the age. Various irregularities occur in this calendar, especially following the Downfall. Mardil Voronwë revised the calendar, and the new version became the "Steward's Reckoning": all the months had 30 days, with two additional "extra" days at the equinoxes, "tuilérë" and "yáviérë". The five extra days (the equinoxes, midsummer and two at midwinter) were holidays.


title: Númenor

text: The Reunited Kingdom adopted a "New Reckoning", which began the year on March 25 (cf. Lady Day, the English new year between A.D. 1155 and 1752), the date of the downfall of Sauron. This made it correspond more closely to the spring beginning of the Elven calendar.


title: Númenor

text: This is similar in structure to the French Republican calendar. For example, the names of the third month of Winter, "Súlímë", "Gwaeron", and "Ventôse", all mean 'Windy', and so on for the other months.


title: Númenor

text: The island of Númenor was raised from the sea as a gift from the Valar to the Edain, the Fathers of Men who had stood with the Elves of Beleriand against Morgoth in the wars of the First Age. Númenor was offered as a reward, a "rest after the war" for the Edain. Early in the Second Age the greater part of those Edain who had survived the wars left Middle-earth and journeyed to the isle, sailing in ships provided and steered by the Elves. The migration took 50 years and brought 5,000 to 10,000 people to the island.


title: Númenor

text: The realm was established early in the Second Age, when Elros Half-elven, son of Eärendil, gave up his Elven immortality to become a Man and the first King of Númenor. Under his rule, and those of his descendants, the Númenóreans rose to become a powerful people, friendly with Elves, both of Eressëa and of Middle-earth. The Elves of Eressëa brought gifts including skills and plants. Elros brought a measure of Elvish blood and magical power to the kingdom. Among these gifts were seven "palantíri", magical orbs that could foresee the future, for the Lords of Andúnië.


title: Númenor

text: Númenor was surrounded by the Great Sea of Arda, and the sea had a profound influence on Númenor's culture and history. From the earliest times in its history, fish from the sea were a significant part of Númenórean diet; those providing this food were Númenor's first sea-farers. The Númenóreans swiftly became skilled shipbuilders and mariners, with a desire to explore and master the ocean. There was one limitation on this activity: the Ban of the Valar. When the island of Númenor had been gifted to the Edain, they were strictly prohibited from sailing west out of sight of the island. This was because the Undying Lands, forbidden to mortals, lay tantalizingly close to the west of Númenor.


title: Númenor

text: So the Númenóreans began exploring the seas to the north, east, and south. They reached Middle-earth to the east, and explored its coasts including the Eastern Sea on the far side of Middle-earth. The Númenóreans brought the gifts of their superior civilization to the Men of Middle-earth, who called the Númenóreans the Sea-kings. News of Númenórean seafarers spread far inland in Middle-earth; even the reclusive Ents heard of the coming of "the Great Ships".


title: Númenor

text: Númenóreans had established good relations with Gil-galad, the king of the High Elves of the northwest of Middle-earth, whose ships sailed from the Grey Havens.


title: Númenor

text: Aldarion founded the Uinendili, a guild of sea-farers, in honour of Uinen, goddess of the Sea. He succeeded to the throne and became known as the Mariner-king. He established Vinyalondë (later called Lond Daer), the first Númenórean settlement in Middle-earth. This port provided access to the great forests of Eriador, which the Númenóreans needed for ship-building.


title: Númenor

text: The Númenóreans assisted Gil-galad in Middle-earth's War of the Elves and Sauron, which broke out after the forging of the Rings of Power, in particular the One Ring. Tar-Minastir, later the eleventh King of Númenor, assembled an armada, and sent it to Gil-galad's aid. The forces of Númenor were without peer in war, and together with the Elves, they were able to temporarily defeat Sauron.


title: Númenor

text: The increasing power of the Númenóreans had a dark side; the exploitation of Middle-earth's forests had devastated large regions of Eriador. The Númenóreans established further settlements in Middle-earth, coming to rule a coastal empire with no rival. At first, they had engaged with the Men of Middle-earth in a friendly manner, but Minastir's successors, Tar-Ciryatan and Tar-Atanamir "the Great", became increasingly tyrannical, oppressing the Men of Middle-earth and exacting heavy tribute.


title: Númenor

text: The Númenóreans made Umbar, the harbour city in the south of Middle-earth, into a great fortress and greatly expanded Pelargir, a landing in Gondor near the Mouths of the Anduin.


title: Númenor

text: Increasing numbers of Númenóreans became jealous of Elves for their immortality, resenting the Ban of the Valar, and sought everlasting life. Those of this persuasion were the faction of "King's Men".


title: Númenor

text: Those who remained loyal to the Valar and friendly to the Elves (and using Elvish languages) were the "Faithful", also called the "Elf-friends" or "Elendili"; they were led by the Lords of Andúnië. In the reign of Tar-Ancalimon (S.A. 2221-2386), the King's Men became dominant, and the Faithful became a persecuted minority accused of being "spies of the Valar".


title: Númenor

text: Late in the Second Age, Ar-Pharazôn, the 25th monarch of Númenor, sailed to Middle-earth to challenge Sauron, known to the Númenóreans as "Zigûr", who had claimed to be the King of Men and overlord of Middle-earth. Ar-Pharazôn landed at Umbar to do battle, but seeing the might of Númenor, Sauron's armies fled, and Sauron surrendered without a fight. He was brought back to Númenor as a prisoner, but he soon seduced the king and many other Númenóreans, promising them eternal life if they worshipped his master Melkor. With Sauron as his advisor, Ar-Pharazôn had a tall temple erected in Armenelos, the capital. In this temple human sacrifices were offered to Melkor. During this time, the White Tree Nimloth, which stood before the King's House in Armenelos and whose fate was tied to the line of kings, was cut down and burned as a sacrifice to Melkor, at Sauron's direction. Isildur rescued a fruit of the tree which became an ancestor of the White Tree of Gondor.


title: Númenor

text: Prompted by Sauron and fearing old age and death, Ar-Pharazôn built a great armada and sailed into the West to make war upon the Valar, intending to seize the Undying Lands and achieve immortality. Sauron remained behind. Ar-Pharazôn landed on the shores of Aman. As the Valar were forbidden to take direct action against Men, Manwë, chief of the Valar, called upon Eru Ilúvatar, the One God.


title: Númenor

text: In response, Eru caused the Changing of the World: the hitherto flat Earth was transformed into a globe, Númenor sank beneath the ocean, and the Undying Lands were removed from the Earth forever. The whole population on the island was drowned. Most of Ar-Pharazôn's armada, too, met their doom in the cataclysm. This was the second fall of Men, the first being when Men first awoke and fell swiftly under the dominion of Melkor.


title: Númenor

text: Sauron himself was caught in the cataclysm he had helped bring about. His body was destroyed, and he could never again assume a fair form. He fled back to Middle-earth as a monstrous spirit of hatred that "passed as a shadow and a black wind over the sea", returning to Mordor.


title: Númenor

text: The Faithful, led by the nobleman Elendil, came to Middle-earth before the cataclysm. Elendil's sons, Isildur and Anárion, founded the two Kingdoms in Exile: Arnor in the north, and Gondor in the south. The two kingdoms attempted to maintain Númenórean culture. Gondor flourished, and "for a while its splendour grew, recalling somewhat of the might of Númenor". Sauron gathered strength in nearby Mordor, setting the scene for a struggle lasting thousands of years. Some of his servants, called the Black Númenóreans since they worshipped the Darkness and were "enamoured of evil knowledge", had left Númenor before its destruction. For over a millennium, their descendants lingered on and remained allied to Sauron in Middle-earth.


title: Númenor

text: The Kings of Arnor and of Gondor were directly descended from Isildur and Anárion, and therefore from the Lords of Andúnië; like their ancestors, they had prolonged lifespans. The kings of Arnor inherited the silver rod of the Lord of Andúnië; it was renamed the Sceptre of Annúminas, and was the chief symbol of Arnor's kingship. The "high men" of Gondor "married late, and their children were few"; eventually the line of kings died out, and Gondor was ruled by Stewards. Aragorn is the head of the Dúnedain ("Men of the West", Númenóreans) surviving in the North at the end of the Third Age and as a descendant of Isildur, has a claim on the kingship.


title: Númenor

text: The Princes of Dol Amroth were descended from a family of The Faithful who had ruled over the land of Belfalas since the Second Age. This family was kin to the Lords of Andúnië, and thus related to Elendil. Sam Gamgee notices Faramir's wizard-like air, to which Faramir replies "Maybe you discern from afar the air of Númenor".


title: Númenor

text: Initially and for many centuries after the downfall of Númenor, the Black Númenóreans retained control of Númenor's colonies and coastal outposts south of the River Anduin and east in Middle-earth. The nearest to Gondor was Umbar, where a Black Númenórean aristocracy survived for a thousand years, exerting strong influence over Harad; two of their number, Herumor and Fuinur, became lords among the Haradwaith. Tolkien writes that their race became mixed with lesser men and as a consequence, "quickly dwindled". Though Gondor fought frequently against Umbar and its allies, King Tarannon Falastur, who ruled during the 9th century of the Third Age, attempted a diplomatic alliance by marrying the Black Númenórean Queen Berúthiel. Theirs was a loveless match: she dabbled in the dark arts and kept ten cats which she used as spies, so Tarannon sent her southward on a ship that was last seen sailing past Umbar. Gondor eventually captured Umbar and held it for about 500 years, while the Black Númenóreans continued to stir up the Southrons against Umbar and Gondor. During the War of the Ring, a nameless Black Númenórean known as the Mouth of Sauron emerged from the Black Gate and spoke to the Captains of the West before the Battle of the Morannon.


title: Númenor

text: As time went on, Gondor became complacent and assumed of their antagonists of old that "some were given over wholly to idleness and ease, and some fought among themselves, until they became conquered in their weakness by the wild men." Gondor lost control of Umbar at the end of the Kin-strife, when rebels from Gondor led by descendants of the usurper Castamir seized the port, and later called themselves the Corsairs of Umbar. A monument at Umbar, which originally commemorated Ar-Pharazôn's defeat of Sauron, stood until an unspecified date late in the Third Age when it was finally torn down.


title: Númenor

text: Atlantis (, "island of Atlas") is a fictional island mentioned within an allegory on the hubris (excessive pride leading to a downfall) of nations in the ancient Greek philosopher Plato's works "Timaeus" and "Critias".


title: Númenor

text: The destruction of Númenor earned it the Quenya name "Atalantë" "the Downfallen"; Tolkien described his invention of this additional allusion to Atlantis as a happy accident when he realized that the Quenya root "talat-" "to fall" could be incorporated into a name for Númenor. Tolkien wrote of Númenor as Atlantis in several of his letters.


title: Númenor

text: The commentator Charles Delattre has noted that the tale of Númenor is a retelling of the myth of Atlantis, the only drowned island in surviving ancient literature, matching several details: it began as a perfect world, geometrically laid out to reflect its balance and harmony; it abounds in valuable minerals; and it has unmatched power, with a strong fleet able to project control far beyond its shores, like ancient Athens. Númenor's pride, too, writes Delattre, matches the hubris of Plato's Atlantis; and its downfall recalls the destruction of Atlantis, the divine Old Testament retribution on Sodom and Gomorrah, and Milton's "Paradise Lost".


title: Númenor

text: Númenor first appears in "The Lord of the Rings", as the vague land of "Westernesse", an advanced civilisation which had existed long ago, far to the west over the Sea, and the ancestral home of the Dúnedain. Tolkien chose the name for its resonance with "Lyonesse", a faraway land that sank into the sea in the Middle English romance "King Horn".


title: Númenor

text: Tolkien was a professional philologist. For him, the existence of ideas embodied in ancient words and names indicated that there must have been "some original conception", a once-living tradition, behind those ideas. The Tolkien scholar Tom Shippey notes that in Tolkien's "The Lost Road", the key names are from Germanic legend, and they speak of elves:


title: Númenor

text: Tolkien, a devout Roman Catholic, stated that "The Downfall of Númenor" ("Akallabêth") was effectively a second fall of man, with "its central theme .. (inevitably, I think, in a story of Men) a Ban, or Prohibition". Bradley J. Birzer, writing in the "J.R.R. Tolkien Encyclopedia", notes that Tolkien thought that every story was essentially about a fall, and accordingly his legendarium contains many "falls": that of Morgoth, of Fëanor and his relatives, and that of Númenor among them. Eric Schweicher, writing in "Mythlore", notes that the ban was "soon defied", as in the Biblical fall. The temptation for the Númenoreans was the desire for immortality, and the ban that they broke was not to sail towards the Undying Lands of Aman.


title: Númenor

text: The names connected by his philological studies formed for Tolkien the possibility of an inexorable downward progression, from the long-lost mythical world of Númenor in the Second Age, to his fantasy world of Middle-earth in the Third Age, also now lost, to the real ancient Germanic and Anglo-Saxon thousands of years later, and finally down to the modern world, where names like Edwin still survive, all (in the fiction) that is left of Middle-earth, carrying for the knowledgeable philologist a hint of a rich living English mythology. Shippey notes that in Númenor, the myth would have been still stronger, as being an Elf-friend, one of the hated "Elendili", marked a person out to the King's Men faction as a target for human sacrifice to Morgoth. Tolkien's "continuous playing with names" led to characters and situations, and sometimes to stories.


title: Númenor

text: Delattre notes that the position of Númenor in Tolkien's Middle-earth is curious, being "at once marginal and central", not least because in "The Lord of the Rings", the glory of Númenor is already ancient history, evoking a sense of loss and nostalgia. This, he writes, is just one of many losses and downfalls in Tolkien's legendarium, leading finally to the last remnants of Númenor in the North, the Dúnedain, and the last Númenorean kingdom, Gondor, which "keeps alive the illusion that Númenor still exists in the South".


title: Númenor

text: Marjorie Burns writes that the feeling of "inevitable disintegration" is borrowed from the Nordic world view which emphasises that all may be lost at any moment. She writes that in Norse mythology, this began during the creation: in the realm of fire, Muspell, the jötunn Surt was even then awaiting the end of the world. Burns comments that in that mythology, even the gods can die, everything has an end, and that, "though [the evil] Sauron may go, the elves will fade as well."


title: Númenor

text: Originally intended to be a part of a time-travel story in "The Notion Club Papers", Tolkien once saw the tale of the fall of Númenor as a conclusion to his "The Silmarillion" and the "last tale" about the Elder Days. Later, with the emergence of "The Lord of the Rings", it became the link back to his mythology of earlier ages.


title: Númenor

text: C. S. Lewis's 1945 novel "That Hideous Strength" makes reference to "Numinor and the True West", which Lewis credits as a then-unpublished creation of J. R. R. Tolkien; they were friends and colleagues at Oxford University, and members of The Inklings literary discussion group. The misspelling came from Lewis's only hearing Tolkien say the name in one of his readings.


title: Númenor

text: The television series "" is set mainly in the Second Age. It includes a port city in Númenor, its architecture designed to convey the character of its people. The set is described as "an entire seaside city" with buildings, alleyways, shrines, graffiti, and a ship docked at the harbour. The production designer Ramsey Avery based Númenor's "looming marble structures" on Ancient Greece and Venice, while he used the colour blue to reflect the culture's emphasis on water and sailing.


title: Sioux Falls, South Dakota

text: Sioux Falls () is the most populous city in the U.S. state of South Dakota and the 130th-most populous city in the United States. It is the county seat of Minnehaha County and also extends into Lincoln County to the south, which continues up to the Iowa state line. As of 2020, Sioux Falls had a population of 192,517, which was estimated in 2022 to have increased to 202,600. The Sioux Falls metro area accounts for more than 30% of the state's population. Chartered in 1856 on the banks of the Big Sioux River, the city is situated in the rolling hills at the junction of interstates 29 and 90.


title: Sioux Falls, South Dakota

text: The history of Sioux Falls revolves around the cascades of the Big Sioux River. The falls were created about 14,000 years ago during the last ice age. The lure of the falls has been a powerful influence. Ho-Chunk, Ioway, Otoe, Missouri, Omaha (and Ponca at the time), Quapaw, Kansa, Osage, Arikira, Dakota, and Cheyenne people inhabited and settled the region previous to Europeans and European descendants. Numerous burial mounds still exist on the high bluffs near the river and are spread throughout the general vicinity. Indigenous people maintained an agricultural society with fortified villages, and the later arrivals rebuilt on many of the same sites that were previously settled. Lakota populate urban and reservation communities in the contemporary state and many Lakota, Dakota, and numerous other Indigenous Americans reside in Sioux Falls today.


title: Sioux Falls, South Dakota

text: French voyagers/explorers visited the area in the early 18th century. The first documented visit by an American of European descent was by Philander Prescott, who camped overnight at the falls in December 1832. Captain James Allen led a military expedition out of Fort Des Moines in 1844. Jacob Ferris described the Falls in his 1856 book "The States and Territories of the Great West".


title: Sioux Falls, South Dakota

text: Two separate groups, the Dakota Land Company of St. Paul and the Western Town Company of Dubuque, Iowa organized in 1856 to claim the land around the falls, considered a promising townsite for its beauty and water power. Each laid out claims, but worked together for mutual protection. They built a temporary barricade of turf which they dubbed "Fort Sod", in response to native tribes attempting to defend their land from the settlers. Seventeen men then spent "the first winter" in Sioux Falls. The following year the population grew to near 40.


title: Sioux Falls, South Dakota

text: Although conflicts in Minnehaha County between Native Americans and white settlers were few, the Dakota War of 1862 engulfed nearby southwestern Minnesota. The town was evacuated in August of that year when two local settlers were killed as a result of the conflict. The settlers and soldiers stationed here traveled to Yankton in late August 1862. The abandoned townsite was pillaged and burned.


title: Sioux Falls, South Dakota

text: Fort Dakota, a military reservation established in present-day downtown, was established in May 1865. Many former settlers gradually returned and a new wave of settlers arrived in the following years. The population grew to 593 by 1873, and a building boom was underway in that year. The Village of Sioux Falls, consisting of , was incorporated in 1876 and was granted a city charter by the Dakota Territorial legislature on March 3, 1883.


title: Sioux Falls, South Dakota

text: The arrival of the railroads ushered in the great Dakota Boom decade of the 1880s. The population of Sioux Falls mushroomed from 2,164 in 1880 to 10,167 at the close of the decade. The growth transformed the city. A severe plague of grasshoppers and a national depression halted the boom by the early 1890s. The city grew by only 89 people from 1890 to 1900.


title: Sioux Falls, South Dakota

text: But prosperity eventually returned with the opening of the John Morrell meat packing plant in 1909, the establishment of an airbase and a military radio and communications training school in 1942, and the completion of the interstate highways in the early 1960s. Much of the growth in the first part of the 20th century was fueled by agriculturally based industry, such as the Morrell plant and the nearby stockyards (one of the largest in the nation).


title: Sioux Falls, South Dakota

text: In 1955 the city decided to consolidate the neighboring incorporated city of South Sioux Falls. At the time South Sioux Falls had a population of nearly 1,600 inhabitants, according to the 1950 census. It was the third largest city in the county after Sioux Falls and Dell Rapids. By October 18, 1955, South Sioux Falls residents voted 704 in favor and 227 against to consolidate with Sioux Falls. On the same issue, Sioux Falls residents voted on November 15 by the vote 2,714 in favor and 450 against.


title: Sioux Falls, South Dakota

text: In 1981, to take advantage of recently relaxed state usury laws, Citibank relocated its primary credit card center from New York City to Sioux Falls. Some claim that this event was the primary impetus for the increased population and job growth rates that Sioux Falls has experienced over the past quarter-century. Others point out that Citibank's relocation was only part of a more general transformation of the city's economy from an industrially based one to an economy centered on health care, finance, and retail trade.


title: Sioux Falls, South Dakota

text: Sioux Falls has grown at a rapid pace since the late 1970s, with the city's population increasing from 81,182 in 1980 to 192,517 in 2020.


title: Sioux Falls, South Dakota

text: On the night of September 10, 2019, the south side of Sioux Falls was hit by three strong EF2 tornadoes, severely damaging at least 37 buildings, including the Plaza 41 Shopping Center. One tornado hit the Avera Heart Hospital, damaging portions of the roof and windows, and causing seven injuries, including a man who fractured his skull as he was thrown into an exterior wall of the hospital. Another tornado hit the busy commercial district near the Empire Mall, injuring one woman inside her home. Another touched down on the far south side in a suburban residential area, tearing the roofs off homes. The total damage was more than $5 million.


title: Sioux Falls, South Dakota

text: According to the United States Census Bureau, the city has an area of , of which is land and is water. The city is in extreme eastern South Dakota, about west of the Minnesota border. Sioux Falls has been assigned the ZIP Codes 57101, 57103–57110, 57117–57118, 57188–57189, and 57192–57198, and the FIPS place code 59020.


title: Sioux Falls, South Dakota

text: The Sioux Falls Metropolitan Statistical Area consists of four South Dakota counties: Lincoln, McCook, Minnehaha, and Turner. The estimated population of this MSA in 2017 was 259,094, an increase of 13.51% from the 2010 census. According to recent estimates, Lincoln County is the 16th-fastest-growing county in the United States. In addition to Sioux Falls, the metropolitan area includes Canton, Brandon, Dell Rapids, Tea, Harrisburg, Worthing, Beresford, Lennox, Hartford, Crooks, Baltic, Montrose, Salem, Renner, Rowena, Chancellor, Colton, Humboldt, Parker, Hurley, Garretson, Sherman, Corson, Viborg, Irene, and Centerville.