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Perceptron

In machine learning, the perceptron (or McCulloch–Pitts neuron) is an algorithm for supervised learning of binary classifiers. A binary classifier is a function which can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector.

History

The perceptron was invented in 1943 by Warren McCulloch and Walter Pitts. The first hardware implementation was Mark I Perceptron machine built in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt, funded by the Information Systems Branch of the United States Office of Naval Research and the Rome Air Development Center. It was first publicly demonstrated on 23 June 1960. The machine was "part of a previously secret four-year NPIC [the US' National Photographic Interpretation Center] effort from 1963 through 1966 to develop this algorithm into a useful tool for photo-interpreters".

Rosenblatt described the details of the perceptron in a 1958 paper. His organization of a perceptron is constructed of three kinds of cells ("units"): AI, AII, R, which stand for "projection", "association" and "response".

Rosenblatt's project was funded under Contract Nonr-401(40) "Cognitive Systems Research Program", which lasted from 1959 to 1970, and Contract Nonr-2381(00) "Project PARA" ("PARA" means "Perceiving and Recognition Automata"), which lasted from 1957 to 1963.

Mark I Perceptron machine
The perceptron was intended to be a machine, rather than a program, and while its first implementation was in software for the IBM 704, it was subsequently implemented in custom-built hardware as the "Mark I perceptron" with the project name "Project PARA", designed for image recognition. The machine is currently in Smithsonian National Museum of American History.

The Mark I Perceptron has 3 layers.

Rosenblatt called this three-layered perceptron network the alpha-perceptron, to distinguish it from other perceptron models he experimented with.
 * An array of 400 photocells arranged in a 20x20 grid, named "sensory units" (S-units), or "input retina". Each S-unit can connect to up to 40 A-units.
 * A hidden layer of 512 perceptrons, named "association units" (A-units).
 * An output layer of 8 perceptrons, named "response units" (R-units).

The S-units are connected to the A-units randomly (according to a table of random numbers) via a plugboard (see photo), to "eliminate any particular intentional bias in the perceptron". The connection weights are fixed, not learned. Rosenblatt was adamant about the random connections, as he believed the retina was randomly connected to the visual cortex, and he wanted his perceptron machine to resemble human visual perception.

The A-units are connected to the R-units, with adjustable weights encoded in potentiometers, and weight updates during learning were performed by electric motors. The hardware details are in an operators' manual.

In a 1958 press conference organized by the US Navy, Rosenblatt made statements about the perceptron that caused a heated controversy among the fledgling AI community; based on Rosenblatt's statements, The New York Times reported the perceptron to be "the embryo of an electronic computer that [the Navy] expects will be able to walk, talk, see, write, reproduce itself and be conscious of its existence."

Principles of Neurodynamics (1962)
Rosenblatt described his experiments with many variants of the Perceptron machine in a book Principles of Neurodynamics (1962). The book is a published version of the 1961 report.

Among the variants are:

The machine was shipped from Cornell to Smithsonian in 1967, under a government transfer administered by the Office of Naval Research.
 * "cross-coupling" (connections between units within the same layer) with possibly closed loops,
 * "back-coupling" (connections from units in a later layer to units in a previous layer),
 * four-layer perceptrons where the last two layers have adjustible weights (and thus a proper multilayer perceptron),
 * incorporating time-delays to perceptron units, to allow for processing sequential data,
 * analyzing audio (instead of images).

Perceptrons (1969)
Although the perceptron initially seemed promising, it was quickly proved that perceptrons could not be trained to recognise many classes of patterns. This caused the field of neural network research to stagnate for many years, before it was recognised that a feedforward neural network with two or more layers (also called a multilayer perceptron) had greater processing power than perceptrons with one layer (also called a single-layer perceptron).

Single-layer perceptrons are only capable of learning linearly separable patterns. For a classification task with some step activation function, a single node will have a single line dividing the data points forming the patterns. More nodes can create more dividing lines, but those lines must somehow be combined to form more complex classifications. A second layer of perceptrons, or even linear nodes, are sufficient to solve many otherwise non-separable problems.

In 1969, a famous book entitled Perceptrons by Marvin Minsky and Seymour Papert showed that it was impossible for these classes of network to learn an XOR function. It is often believed (incorrectly) that they also conjectured that a similar result would hold for a multi-layer perceptron network. However, this is not true, as both Minsky and Papert already knew that multi-layer perceptrons were capable of producing an XOR function. (See the page on Perceptrons (book) for more information.) Nevertheless, the often-miscited Minsky/Papert text caused a significant decline in interest and funding of neural network research. It took ten more years until neural network research experienced a resurgence in the 1980s. This text was reprinted in 1987 as "Perceptrons - Expanded Edition" where some errors in the original text are shown and corrected.

Subsequent work
Rosenblatt continued working on perceptrons despite diminishing funding. The last attempt was Tobermory, built between 1961 and 1967, built for speech recognition. It occupied an entire room. It had 4 layers with 12,000 weights implemented by toroidal magnetic cores. By the time of its completion, simulation on digital computers had become faster than purpose-built perceptron machines. He died in a boating accident in 1971. The kernel perceptron algorithm was already introduced in 1964 by Aizerman et al. Margin bounds guarantees were given for the Perceptron algorithm in the general non-separable case first by Freund and Schapire (1998), and more recently by Mohri and Rostamizadeh (2013) who extend previous results and give new and more favorable L1 bounds.

The perceptron is a simplified model of a biological neuron. While the complexity of biological neuron models is often required to fully understand neural behavior, research suggests a perceptron-like linear model can produce some behavior seen in real neurons.

The solution spaces of decision boundaries for all binary functions and learning behaviors are studied in.

Definition
In the modern sense, the perceptron is an algorithm for learning a binary classifier called a threshold function: a function that maps its input $$\mathbf{x}$$ (a real-valued vector) to an output value $$f(\mathbf{x})$$ (a single binary value):

f(\mathbf{x}) = \theta(\mathbf{w} \cdot \mathbf{x} + b) $$

where $$\theta$$ is the Heaviside step-function, $$\mathbf{w}$$ is a vector of real-valued weights, $$\mathbf{w} \cdot \mathbf{x}$$ is the dot product $$\sum_{i=1}^m w_i x_i$$, where $m$ is the number of inputs to the perceptron, and $b$ is the bias. The bias shifts the decision boundary away from the origin and does not depend on any input value.

Equivalently, since $$\mathbf{w}\cdot \mathbf{x} + b = (\mathbf{w}, b) \cdot (\mathbf{x}, 1)$$, we can add the bias term $$b$$ as another weight $$\mathbf{w}_{m+1}$$ and add a coordinate $$1$$ to each input $$\mathbf{x}$$, and then write it as a linear classifier that passes the origin:$$ f(\mathbf{x}) = \theta(\mathbf{w} \cdot \mathbf{x}) $$

The binary value of $$f(\mathbf{x})$$ (0 or 1) is used to perform binary classification on $$\mathbf{x}$$ as either a positive or a negative instance. Spatially, the bias shifts the position (though not the orientation) of the planar decision boundary.

In the context of neural networks, a perceptron is an artificial neuron using the Heaviside step function as the activation function. The perceptron algorithm is also termed the single-layer perceptron, to distinguish it from a multilayer perceptron, which is a misnomer for a more complicated neural network. As a linear classifier, the single-layer perceptron is the simplest feedforward neural network.

Information theory
From an information theory point of view, a single perceptron with K inputs has a capacity of 2K bits of information. This result is due to Thomas Cover.

Specifically let $$T(N, K)$$ be the number of ways to linearly separate N points in K dimensions, then$$T(N, K)=\left\{\begin{array}{cc} 2^N & K \geq N \\ 2 \sum_{k=0}^{K-1}\left(\begin{array}{c} N-1 \\ k \end{array}\right) & K 2K$$. In words, one perceptron unit can almost certainly memorize a random assignment of binary labels on N points when $$N \leq 2K$$, but almost certainly not when $$N> 2K$$.

Boolean function
When operating on only binary inputs, a perceptron is called a linearly separable Boolean function, or threshold Boolean function. The sequence of numbers of threshold Boolean functions on n inputs is OEIS A000609. The value is only known exactly up to $$n=9$$ case, but the order of magnitude is known quite exactly: it has upper bound $$2^{n^2 - n \log_2 n + O(n)}$$ and lower bound $$2^{n^2 - n \log_2 n - O(n)}$$.

Any Boolean linear threshold function can be implemented with only integer weights. Furthermore, the number of bits necessary and sufficient for representing a single integer weight parameter is $$\Theta(n \ln n)$$.

Universal approximation theorem
A single perceptron can learn to classify any half-space. It cannot solve any linearly nonseparable vectors, such as the Boolean exclusive-or problem (the famous "XOR problem").

A perceptron network with one hidden layer can learn to classify any compact subset arbitrarily closely. Similarly, it can also approximate any compactly-supported continuous function arbitrarily closely. This is essentially a special case of the theorems by George Cybenko and Kurt Hornik.

Conjunctively local perceptron
Perceptrons (Minsky and Papert, 1969) studied the kind of perceptron networks necessary to learn various Boolean functions.

Consider a perceptron network with $$n$$ input units, one hidden layer, and one output, similar to the Mark I Perceptron machine. It computes a Boolean function of type $$f: 2^n \to 2 $$. They call a function conjuctively local of order $$k$$, iff there exists a perceptron network such that each unit in the hidden layer connects to at most $$k$$ input units.

Theorem. (Theorem 3.1.1): The parity function is conjuctively local of order $$n$$.

Theorem. (Section 5.5): The connectedness function is conjuctively local of order $$\Omega(n^{1/2})$$.

Learning algorithm for a single-layer perceptron
Below is an example of a learning algorithm for a single-layer perceptron with a single output unit. For a single-layer perceptron with multiple output units, since the weights of one output unit are completely separate from all the others', the same algorithm can be run for each output unit.

For multilayer perceptrons, where a hidden layer exists, more sophisticated algorithms such as backpropagation must be used. If the activation function or the underlying process being modeled by the perceptron is nonlinear, alternative learning algorithms such as the delta rule can be used as long as the activation function is differentiable. Nonetheless, the learning algorithm described in the steps below will often work, even for multilayer perceptrons with nonlinear activation functions.

When multiple perceptrons are combined in an artificial neural network, each output neuron operates independently of all the others; thus, learning each output can be considered in isolation.

Definitions
We first define some variables: We show the values of the features as follows: To represent the weights: To show the time-dependence of $$\mathbf{w}$$, we use:
 * $$r$$ is the learning rate of the perceptron. Learning rate is a positive number usually chosen to be less than 1. The larger the value, the greater the chance for volatility in the weight changes.
 * $$y = f(\mathbf{z}) $$ denotes the output from the perceptron for an input vector $$\mathbf{z}$$.
 * $$D = \{(\mathbf{x}_1,d_1),\dots,(\mathbf{x}_s,d_s)\} $$ is the training set of $$s$$ samples, where:
 * $$\mathbf{x}_j$$ is the $$n$$-dimensional input vector.
 * $$d_j $$ is the desired output value of the perceptron for that input.
 * $$x_{j,i} $$ is the value of the $$i$$th feature of the $$j$$th training input vector.
 * $$x_{j,0} = 1 $$.
 * $$w_i $$ is the $$i$$th value in the weight vector, to be multiplied by the value of the $$i$$th input feature.
 * Because $$x_{j,0} = 1 $$, the $$w_0 $$ is effectively a bias that we use instead of the bias constant $$b$$.
 * $$w_i(t) $$ is the weight $$i$$ at time $$t$$.

Steps
1. Initialize the weights. Weights may be initialized to 0 or to a small random value. In the example below, we use 0.

2. For each example $j$ in our training set $D$, perform the following steps over the input $\mathbf{x}_j $ and desired output $d_j $: 1. Calculate the actual output:
 * $\begin{align}

y_j(t) &= f[\mathbf{w}(t)\cdot\mathbf{x}_j] \\ &= f[w_0(t)x_{j,0} + w_1(t)x_{j,1} + w_2(t)x_{j,2} + \dotsb + w_n(t)x_{j,n}] \end{align}$

2. Update the weights:
 * $w_i(t+1) = w_i(t) \; \boldsymbol{+} \; r\cdot(d_j - y_j(t)) x_{j,i} $, for all features $0 \leq i \leq n$, $r$ is the learning rate.

3. For offline learning, the second step may be repeated until the iteration error $\frac{1}{s} \sum_{j=1}^s

4. d_j - y_j(t)

5. $ is less than a user-specified error threshold $\gamma $, or a predetermined number of iterations have been completed, where s is again the size of the sample set. The algorithm updates the weights after every training sample in step 2b.

Convergence of one perceptron on a linearly separable dataset
A single perceptron is a linear classifier. It can only reach a stable state if all input vectors are classified correctly. In case the training set $D$ is not linearly separable, i.e. if the positive examples cannot be separated from the negative examples by a hyperplane, then the algorithm would not converge since there is no solution. Hence, if linear separability of the training set is not known a priori, one of the training variants below should be used. Detailed analysis and extensions to the convergence theorem are in Chapter 11 of Perceptrons (1969).

Linear separability is testable in time $$\min(O(n^{d/2}), O(d^{2n}), O(n^{d-1} \ln n)) $$, where $$n$$ is the number of data points, and $$d$$ is the dimension of each point.

If the training set is linearly separable, then the perceptron is guaranteed to converge after making finitely many mistakes. The theorem is proved by Rosenblatt et al.

$$The following simple proof is due to Novikoff (1962). The idea of the proof is that the weight vector is always adjusted by a bounded amount in a direction with which it has a negative dot product, and thus can be bounded above by $O(√t)$, where $t$ is the number of changes to the weight vector. However, it can also be bounded below by $O(t)$ because if there exists an (unknown) satisfactory weight vector, then every change makes progress in this (unknown) direction by a positive amount that depends only on the input vector.$$

While the perceptron algorithm is guaranteed to converge on some solution in the case of a linearly separable training set, it may still pick any solution and problems may admit many solutions of varying quality. The perceptron of optimal stability, nowadays better known as the linear support-vector machine, was designed to solve this problem (Krauth and Mezard, 1987).

Perceptron cycling theorem
When the dataset is not linearly separable, then there is no way for a single perceptron to converge. However, we still have This is proved first by Bradley Efron.

Learning a Boolean function
Consider a dataset where the $$x$$ are from $$\{-1, +1\}^n$$, that is, the vertices of an n-dimensional hypercube centered at origin, and $$y = \theta(x_i)$$. That is, all data points with positive $$x_i$$ have $$y=1$$, and vice versa. By the perceptron convergence theorem, a perceptron would converge after making at most $$n$$ mistakes.

If we were to write a logical program to perform the same task, each positive example shows that one of the coordinates is the right one, and each negative example shows that its complement is a positive example. By collecting all the known positive examples, we eventually eliminate all but one coordinate, at which point the dataset is learned.

This bound is asymptotically tight in terms of the worst-case. In the worst-case, the first presented example is entirely new, and gives $$n$$ bits of information, but each subsequent example would differ minimally from previous examples, and gives 1 bit each. After $$n+1$$ examples, there are $$2n$$ bits of information, which is sufficient for the perceptron (with $$2n$$ bits of information).

However, it is not tight in terms of expectation if the examples are presented uniformly at random, since the first would give $$n$$ bits, the second $$n/2$$ bits, and so on, taking $$O(\ln n)$$ examples in total.

Variants
The pocket algorithm with ratchet (Gallant, 1990) solves the stability problem of perceptron learning by keeping the best solution seen so far "in its pocket". The pocket algorithm then returns the solution in the pocket, rather than the last solution. It can be used also for non-separable data sets, where the aim is to find a perceptron with a small number of misclassifications. However, these solutions appear purely stochastically and hence the pocket algorithm neither approaches them gradually in the course of learning, nor are they guaranteed to show up within a given number of learning steps.

The Maxover algorithm (Wendemuth, 1995) is "robust" in the sense that it will converge regardless of (prior) knowledge of linear separability of the data set. In the linearly separable case, it will solve the training problem – if desired, even with optimal stability (maximum margin between the classes). For non-separable data sets, it will return a solution with a small number of misclassifications. In all cases, the algorithm gradually approaches the solution in the course of learning, without memorizing previous states and without stochastic jumps. Convergence is to global optimality for separable data sets and to local optimality for non-separable data sets.

The Voted Perceptron (Freund and Schapire, 1999), is a variant using multiple weighted perceptrons. The algorithm starts a new perceptron every time an example is wrongly classified, initializing the weights vector with the final weights of the last perceptron. Each perceptron will also be given another weight corresponding to how many examples do they correctly classify before wrongly classifying one, and at the end the output will be a weighted vote on all perceptrons.

In separable problems, perceptron training can also aim at finding the largest separating margin between the classes. The so-called perceptron of optimal stability can be determined by means of iterative training and optimization schemes, such as the Min-Over algorithm (Krauth and Mezard, 1987) or the AdaTron (Anlauf and Biehl, 1989)). AdaTron uses the fact that the corresponding quadratic optimization problem is convex. The perceptron of optimal stability, together with the kernel trick, are the conceptual foundations of the support-vector machine.

The $$\alpha$$-perceptron further used a pre-processing layer of fixed random weights, with thresholded output units. This enabled the perceptron to classify analogue patterns, by projecting them into a binary space. In fact, for a projection space of sufficiently high dimension, patterns can become linearly separable.

Another way to solve nonlinear problems without using multiple layers is to use higher order networks (sigma-pi unit). In this type of network, each element in the input vector is extended with each pairwise combination of multiplied inputs (second order). This can be extended to an n-order network.

It should be kept in mind, however, that the best classifier is not necessarily that which classifies all the training data perfectly. Indeed, if we had the prior constraint that the data come from equi-variant Gaussian distributions, the linear separation in the input space is optimal, and the nonlinear solution is overfitted.

Other linear classification algorithms include Winnow, support-vector machine, and logistic regression.

Multiclass perceptron
Like most other techniques for training linear classifiers, the perceptron generalizes naturally to multiclass classification. Here, the input $$x$$ and the output $$y$$ are drawn from arbitrary sets. A feature representation function $$f(x,y)$$ maps each possible input/output pair to a finite-dimensional real-valued feature vector. As before, the feature vector is multiplied by a weight vector $$w$$, but now the resulting score is used to choose among many possible outputs:

 * $$\hat y = \operatorname{argmax}_y f(x,y) \cdot w.$$

Learning again iterates over the examples, predicting an output for each, leaving the weights unchanged when the predicted output matches the target, and changing them when it does not. The update becomes:

 * $$ w_{t+1} = w_t + f(x, y) - f(x,\hat y).$$

This multiclass feedback formulation reduces to the original perceptron when $$x$$ is a real-valued vector, $$y$$ is chosen from $$\{0,1\}$$, and $$f(x,y) = y x$$.

For certain problems, input/output representations and features can be chosen so that $$\mathrm{argmax}_y f(x,y) \cdot w$$ can be found efficiently even though $$y$$ is chosen from a very large or even infinite set.

Since 2002, perceptron training has become popular in the field of natural language processing for such tasks as part-of-speech tagging and syntactic parsing (Collins, 2002). It has also been applied to large-scale machine learning problems in a distributed computing setting.

title: Perceptron


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Belize District

Belize District is a district of the nation of Belize. Its capital is Belize City.

Geography
Most of the Belize District is in the east central mainland of Belize; the Belize District also includes various offshore islands, including Ambergris Caye, Caye Caulker, St. George's Caye, Caye Chapel, English Caye, Goff's Caye, and Turneffe Atoll. Ambergris Caye and Caye Caulker are considered two of the country's primary tourism areas. The longest river in the country, the Belize River, passes through the district and joins the Caribbean Sea along its coast. The Northern River, Sibun River, and Manatee River are also in this District.

Settlements
San Pedro Town, which is situated on the island of Ambergris Caye, is also in the Belize District. Caye Caulker and St. George's Caye are the island villages in this district. Maskall, Bomba, Corozalito, Santana, Lucky Strike, Rockstone Pond, Boston, Crooked Tree, Biscayne, May Pen, Gardenia, Grace Bank, Sand Hill, Lord's Bank, Ladyville, Burrel Boom, Buttercup, Scotland Halfmoon, Flowers Bank, Bermudian Landing, Isabella Bank, Double Head Cabbage, Willows Bank, Saint Paul's Bank, Big Falls, Rancho Dolores, Hattieville, Freetown Sibun, Gracie Rock, La Democracia, and Gales Point are all mainland villages in the Belize District. The Crooked Tree and Monkey Bay Wildlife Sanctuaries, the Belize Zoo (30 miles west of Belize City), as well as the ancient Maya ruins of Altun Ha are all in this district.

History
The Belize District was the area first settled by Europeans. They developed estates along the rivers and creeks; because these waterways were their transportation highways. Many of the estates were referred to as the owner's 'bank'(as in the banks of a river). Therefore, Mr. Lord's estate on the bank of the Belize River became Lord's Bank and Mr. Flowers' home place on this same river became Flowers Bank. Many of these old estates have grown into villages; while other places on our map such as Baker, Bob Eiley, Bocotora, Butcher Burns, Lime Walk, More Force, Nago Bank, Washing Tree, Cedar Bank, Churchyard, Egypt, Watters Bank, and White Hill are old estates which did not become villages. Some places like Davis Bank and Tropical Park have now become parts of larger communities.

Demographics
In 2005 mid-year population estimate to the Belize District was 87,000 with an estimated number of 69,200 of these living in the two urban areas. Belize City is by far the large of the two with an estimated population of 60,800. San Pedro Town has a population of about 8,900. The population of all the villages and outlying communities combined is about 17,800 people.

Population and housing
2010 Population and Housing Census has Belize district's total population as 89,247 residents, of this 43,980 are males and 45,267 are females. The total number of households is 27,161 and the average household size is 3.3.

Political divisions
Politically, Belize District contains 13 constituencies according to the Elections and Boundaries Department. 10 of these are in Belize City proper; the remainder are classified as rural.

Belize City constituencies
The 10 constituencies that fall within the city limits of Belize City are: Albert, Caribbean Shores, Collet, Fort George, Freetown, Lake Independence, Mesopotamia, Pickstock, Port Loyola, and Queen's Square. Both Leader of the Opposition Shyne Barrow (Mesopotamia) and former Leader of the Opposition Francis Fonseca (Freetown) represent Belize City constituencies.

Belize Rural North
Belize Rural North contains the northern half of mainland Belize District, including Maskall, Lucky Strike and villages in the Belize River Valley and along the Northern Highway, except for Ladyville and Lord's Bank. Its current representative is Marconi Leal of the People's United Party.

Belize Rural Central
Belize Rural Central is limited to the southern half of mainland Belize District and containing the important villages of Ladyville, Lord's Bank, Western Paradise, Hattieville, and Gales Point. As of 2012, the PUP's Dolores Balderamos is area representative.

Belize Rural South
Belize Rural South contains the offshore islands of the Belize District including Ambergris Caye, Caye Caulker, Caye Chapel, St. George's Caye, and the Turneffe Islands. Its main town is San Pedro on Ambergris Caye. The current representative is the UDP's Manuel Heredia. Ambergris Caye is also a pene-exclave, and it is the land that is completely separated through the rest of the district and in the country.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Belize District


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Talk:Linear operator

shouldn't redirect to "Linear transformation", links to this are about Del and derivatives. -- Tarquin 18:25 Jan 22, 2003 (UTC)

Maybe we should explain on Linear transformation how the terms are used: linear map when talking abstractly, linear transformation often in geometric applications, and linear operator when the space consists of functions. I don't think it makes sense to explain the concept of linearity in more than one article though, it's really the same thing in all three settings. AxelBoldt 03:03 Jan 23, 2003 (UTC)

title: Talk:Linear operator


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Talk:Knitting needle

There seems to be a dispute about whether knitting needles are used in pairs. I say yes. 203.202.5.75 says no. This is really a matter of usage. All knitters understand circular knitting needle to refer to two needles joined by flexible wire or length of nylon. So while it's true that you need only buy one thing, that thing has a pair of needles on it.

The Principles of Knitting, by June Hemmons Hiatt (considered the most authoritative book on knitting in the last 50 years) says, "A circular needle will have two pointed needle shafts." It then goes on to say that, "These needles [note the plural] are connected to one another by a length of fine-diameter, flexible nylon cord."

Mary Thomas's Knitting Book, continuously in print since 1938, is less direct, but implies the same thing. Mary Thomas says--even of the old fashioned single wire form of circular knitting needle, that the wire is "developed either end into a pointed knitting needle." So, once again, a knitting needle is on both ends of the circular needle. Thus, a pair.

So at least one world-famous knitter ( me and seemingly two) might agree with the way i last edited Knitting needle.

Can 203.202.5.75 find an authoritative source that says that a circular knitting needle is not made of two needles? For now, I'll assume that he or she can, and will provide it soon, But i'd be much happier if we used standard terminology.

Noted. Busy, so will have to delay full reply; noting to avoid appearance of avoidance. Basically, we should minimise technical usages and so anything that is "a needle" is singular. The needle is not the pointy bit. Experts speaking to experts are not what this is about. PML.

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Hey PML, if you're still around, I tried to give you your voice back on Knitting needle. I don't know why I was so adamant about excluding your view. If my rudeness hasn't driven you away, I wish you'd see if your view is adequately represented now.

Okay :) I think yours is the final "rudeness apology" I had to do. (I had to do four. shame on me.) I'm new here, and it took me a short while to understand how to function properly. I'm lucky it wasn't more.

By the way, did you see that Rutt might agree with you?

Arthur 04:26 Jan 28, 2003 (UTC)

Still busy. (And have to revisit Irish potato famine.)

But it may help to tell you that I came to this with some knowledge of the Tudor era single implement, and I quite see that the twin implement is twofold; it would have been better described with a phrasing like "pair of handcuffs/trousers" etc. But all that is necessary is some phrasing that acknowledges all this and does not make the absolute and general statement "they are used in pairs", which happens, historically, to have exceptions. PML.

I agree, in part. Sometimes needles are even used in sets of four, five, and even 8 (some american Indian knitters).

Pictures
Not that I'm against having pictures, but Johntex's photo does nothing to illustrate an article on knitting needles, as opposed to, say, knitting, where I notice he's already added it also. I'm not sure it's really needed there either, but as inclusivism is generally the rule I left it. But here? What is it illustrating, exactly? /blahedo (t) 07:08, 14 February 2006 (UTC)
 * I thought that it might be nice to have a photo of knitting here, to help illustrate the concept of knitting needles actually being used for knitting. In a similar fashion, our article on gun includes an image of a gun firing a projectile, and our swimsuit article includes the item of clothing on actual people instead of just items of clothing laying against a neutral background.
 * To me, it is usually worthwhile to show an object in the context of its use. It is certainly true that the reader is one-click away from knitting, but it seemed to me that this photo would provide some modest benefit here, and that it did no harm, especially since a large amount of white space was completely unused in the location where the image was placed.  Just an idea - I'm happy with whatever consensus arises. Best, Johntex\talk 07:26, 14 February 2006 (UTC)

Well, the whitespace thing depends very much on the size, shape, and font of your browser; on mine, there was no whitespace there and the introduced picture actually adds clutter. Making the other picture smaller (as I just did) helps a little. I don't think the gun and swimsuit comparisons are particularly relevant, since we do not have a corresponding "Firing a gun" article, and in the swimsuit article, nobody is swimming, they're just modelling the swimsuits. Even in the gun article, the fact that there's a guy holding the gun is secondary to the gun itself; in a sense, he is also "modelling" the gun. In your picture, the knitting needles are barely even visible, and the clear focus of the photo is on the knitting process and on the knit product, not on the implements. /blahedo (t) 23:11, 14 February 2006 (UTC)

Question on Needle Size Conversions, European to US
I recently purchased some lovely yarn, produced in Germany. The closest thing I can find to suggested needle size is a box that says, "2,5-3". I am deducing that this indicates us to use size 2-mm needles, but then what does the remaining "5-3" stand for? I haven't, as yet, found any conversion charts that help clarify this for me. Thank you for your help. Prrlgrrl 01:17, 19 April 2007 (UTC)

 * I have answered this question on your talk page, Prrlgrrl. --Edna H. 07:21, 21 April 2007 (UTC)

Gauges lower than zero
I'm no expert, but I know that needles come in much smaller sizes than the 2mm size 0. The smallest I've heard of is 00000000 (8x0), which is 0.5mm. Should we include all the <0 sizes, or just note that they exist?
 * If you could add a citation for that, it would be wonderful. Durova Charge! 02:33, 14 February 2008 (UTC)
 * I'm also not really familiar with wiki standards and such. I'm not sure I could find a great citation, but I've seen such needles for sale online.  I can't imagine that'd be sufficient as reference material, though.  What about the page at http://world.std.com/~kcl/kneedlesizecomparison.html ?  Would that be suitable?

In the states pretty much any JoAnn fabric store will sell a boxed set of needles from 1 down to 000. Being a sock knitter primarily I may come into contact with below zero sizes more often, but I feel them to be rather common. (At least, 00 and 000). Loggie (talk) 07:29, 14 February 2008 (UTC)

US Sizes
Originally, sizes in the US were based on inches. As a standard, the size 10 needle was one quarter inch in diameter. Sizes above size 10 were successively one sixteenth inch larger. Sizes smaller than 10 were successively one thirty-second smaller. For example, size 11 was 5/16ths in diameter and size 12 was 3/8ths inch. Size 9 was one thirty-second inch smaller at 7/32nds. Et cetera. My Flatley (talk) 15:43, 17 March 2013 (UTC)

title: Talk:Knitting needle


text:
Corozal District

Corozal District is the northernmost district of the nation of Belize. The population was 33,894 in 2000. The district capital is Corozal Town.

Pre-Columbian Maya ruins are found in Corozal at Santa Rita near Corozal Town, and at Cerros.

Towns and Villages
Corozal District includes Corozal Town and the villages of Buena Vista, Calcutta, Caledonia, Carolina, Chan Chen, Chunox, Concepcion, Consejo, Copper Bank, Cristo Rey, Estrella, Libertad, Little Belize, Louisville, Paraiso, Patchacan, Progresso, Ranchito, San Andres, San Antonio, San Joaquin, San Narciso, San Roman, San Victor, San Pedro, Santa Clara, Sarteneja, Xaibe, and Yo Chen.

In addition, the island of Ambergris Caye is geographically closer to Corozal District than the district in which it is administrated, Belize District.

Political divisions
There are four political divisions in the Corozal District.

 * Corozal Bay is represented by the Peoples United Party's David "Dido" Vega, in his first term. The division includes most of Corozal Town proper.
 * Corozal North covers the villages immediately north and west of Corozal Town and is held by three-term representative Hugo Patt of the UDP.
 * Corozal South East has long been a PUP stronghold under father and son Florencio Marin Sr. (who stepped down in 2008 after seven terms) and Florencio Marin Jr., who is now in his fourth term.
 * Corozal South West is represented by the PUP representative Ramiro Ramirez, who beat incumbent Dr. Angel Campos of the UDP in 2020.

Economy
While Corozal District depended for many years on the sugar industry, at one time having its own sugar factory in Libertad Village, today the economy is more diversified. Sugar production and other agricultural crops such as papaya are still central to the way of life of many rural Corozalenos, but occupations in the tourism industry are slowly becoming more prominent. Now almost 65% of Corozalenos depend on the Commercial Free Zone for employment. The Zone is located on the border of Belize and Mexico.

Contraband is the biggest source of growing income in Corozal since it is adjacent to Mexico, and includes such things as vegetables, fruits, liquors, cigarettes, and gasoline.

Languages
English is the most spoken language in Corozal, followed by Spanish. 80% speak English very well and 60% speak Spanish very well.

Corozal's villages are divided by colour and language:

Corozal Town, the main centre of the District, is peopled by a mix of Belize's races and cultures, most notably the Maya Mestizos. Spanish and English are the major languages spoken.

Calcutta, Estrella Village, Libertad, Ranchito, and San Antonio are populated by East Indian people and speak English and Spanish very well.

Chan Chen, Chunox, Cristo Rey, Louisville, Patchakan, San Pedro, San Victor Village, Xaibe, and Yo Chen are populated by Maya people and speak Spanish and Yucatec Maya language very well, along with some English.

Buena Vista, Caledonia, Conception, San Narciso, San Roman, and Santa Clara are populated by Maya-Mestizo people who speak Spanish, some English and elders speaking Yucatec Maya. They are not obliged to learn English, because school teachers teach in Spanish but write in English and because at work the primary language is Spanish, so villagers are not exposed to English on a daily basis.

Progresso, San Andres, and Sarteneja Village are populated by Creole and Hispanic people, who share their cultures and languages in English and Spanish.

Little Belize is populated by Mennonites, who speak German.

Education
Belize Adventist College and Belize Adventist Junior College are located in the village of Calcutta in the Corozal District. Corozal Community College and Corozal Junior College are found in the village of San Andres and also near San Antonio in Corozal District.

St. Viator Vocational High School is located just outside Chunox in the Corozal District.

Centro Escolar Mexico Junior College(CEMJC) and Escuela Secundaria Tecnica Mexico or E.S.T.M. is located in the village of San Roman in the Corozal District.

title: Corozal District


text:
User talk:Whazzy

Hello, welcome to wikipedia! Thanks for your upload of the map of India, but do you have permission to reuse it here? I notice that it has a copyright notice printed at the bottom of the image. Best wishes, Koyaanis Qatsi

India project
=Nichalp  «Talk»=  09:11, 25 November 2006 (UTC)

title: User talk:Whazzy


text:
Talk:B-tree

Untitled
'''This article needs a complete rewrite from an expert. It's completely useless in many ways. I will erase now the Access concurrency section; the reference links to a non-public site!, WTF?!'''

In response to the user Wolfkeeper: Thanks for explaining the Wikipedia policy about external links, however I still think this section is wrong, because in order to understand what it means, you must check the link. If it is not removed, at least I expect a more serious explanation. —Preceding unsigned comment added by 190.18.107.147 (talk) 04:39, 17 May 2009 (UTC)

—Preceding unsigned comment added by 190.18.107.147 (talk) 10:58, 15 May 2009 (UTC)

Shouldn't the majority of this be under (a,b)-tree? B-trees are a variant of (a,b) trees, so the (a,b) tree article should contain pretty much everything except stuff like the fact that a = B/4 and b = B/2 in a B-tree.

Moved this text to the discussion section from the main definition. Chadloder 18:34 Jan 22, 2003 (UTC)

''The original author interchanged between B+-tree and B-tree. If I remember correctly the only difference is that one only stores values in leaf nodes.''

''Also, should this article be titled B-tree instead of B tree? And does any know what the B stands for? I think it is balanced.''
 * German Wikipedia states that it is unclear what the B stands for and that the inventors didn't gave an explanation for it. It could be Balanced, Bayer, Broad, Bushy, or Boeing. (One of the inventors of the B-Tree is Rudolf Bayer, who worked for the Boeing Scientific Research Labs.)
 * Bayer tree is a common name for them, at least in German. This is the name by which I was taught about them as a computer science student.  A balanced tree is a tree that is balanced in general.  I'm not familiar with any of the terms broad tree, bushy tree, or Boeing tree.  So my vote is for Bayer. Rp (talk) 17:51, 8 July 2008 (UTC)

 * I moved the article from B tree to B-tree . The old title might have been that way because the author was trying to write about B+tree s and the '+' got gobbled up. --Mrwojo 15:32 Feb 15, 2003 (UTC)
 * Sometimes B+Trees are also named B*Trees.

There is some disagreement on what the B stands for. Some people think it stands for 'balanced', 'bushy', or even 'Bayer' after one of the authors. Chadloder 18:35 Jan 22, 2003 (UTC)
 * also Boeing, where it was developed.

132.160.49.90 (talk) 02:30, 26 March 2016 (UTC)

Deletion from an internal node is NOT clear
In the first case, joining will lead to disaster if the left and right subtrees are not leafs. Example: for a B-Tree of max size of 2, insert values of 1 to 11 and then delete 4. —Preceding unsigned comment added by 190.18.107.147 (talk) 04:52, 15 May 2009 (UTC)

Intro to Algorithms
I deleted the sentence about the psuedo-code for deletion being in intro to algorithms because I have the newest edition of the book and there is no psuedocode in the deletion section. --Anon —Preceding unsigned comment added by 70.226.19.144 (talk) 03:44, 21 July 2008 (UTC)

duplicates
B-trees can have duplicates, right? This could be added to the article. Meonkeys 19:16, May 16, 2005 (UTC)

''Yes. The B-tree representing the "name index" in a phone book database probably has lots of identical duplicate "John Smith" names.''

Also, is a B-tree the same as an n-ary tree? Meonkeys 19:16, May 16, 2005 (UTC)

''A B-tree can be seen as a very specialized form of n-ary tree, one that adds a pile of special restrictions. The restrictions make insertion and deletion a little more complicated -- but, in return, the B-tree can guarantee very fast searches.''

 * Some nodes in some n-ary trees have only 1 or 2 children. B-trees are constructed so every internal node has at least L children.

 * Some n-ary trees do not have all the leaves on the same level. (For example, it's impossible for a binary tree with 5 leaf nodes to put them all on the same level). B-trees are constructed so that every leaf is at the same level.

--DavidCary 20:52, 30 July 2005 (UTC)
 * REALLY?
 * Then, how can the left subtree of a key be "less than" and the right "greater than" if there can be duplicates?
 * 68.183.92.186 (talk) — Preceding undated comment added 22:56, 13 May 2014 (UTC)

 * Really. It is just a matter of choosing less-than-or-equal in place of less-than relation. That of course complicates the search algorithm, because when we find an item 'equal' to the given key, we need to check also its siblings for equality, and corresponding subtrees as well. In a degenerate case of a tree of N 'equal' nodes we need to find and return all nodes as a result of a single search. That's difficult, so we usually would rather keep a single instance of every key in the tree, and link duplicates in some additional piece of storage, say a kind of linked list. --CiaPan (talk) 19:47, 14 May 2014 (UTC)

Nodes structure
I 'm wondering if the U (maximum of elements) in the article is not an 2L (minimum of elements).

 * There may be a terminology problem here. The usage of L and U appears inconsistent below. For a simple definition, the number of elements (aka keys) should vary by a factor of 2 to allow splitting an merging to work. Comer uses $$d$$ as the minimum number of keys in node, and $$2d$$ as the maximum number of keys. The number of children will vary from $$d+1$$ to $$2d+1$$. Some use $$U$$ to be the maximum branching factor (max children) and other use it as the maximum number of keys in a node.Glrx (talk) 20:53, 18 August 2009 (UTC)

Other sources from goole tell U =2L (minimization factor): http://www.bluerwhite.org/btree/ (the structure of B-tree), http://www.semaphorecorp.com/btp/algo.html (3 paragraph). --Loading 07:29, 18 Jun 2005 (UTC)

''Certainly a programmer *could* pick U=2L. That type of B-tree is the simplest kind for a teacher to try to explain.'' But often programmers pick some maximum number of elements U that is is an odd number, such as 2-3 trees, L=2, U=3. Donald Knuth seems to like U = L * 3/2, in the form of a B*-tree. --DavidCary 20:52, 30 July 2005 (UTC)

I am teaching B-trees at San Jose State University. I have three sources (other than the Wikipedia article) that pairwise disagree on this L-U issue. Here are what they say:

(1) The well-known algorithms textbook, Introduction to Algorithms, by Corment, Leiserson, Rivest, and Stein (CLRS), defines B-trees in terms of one parameter t, the "minimal degree" (p. 439). Thus L = t and U = 2t. It is required that t be an integer, so in particular U has to be even.

 * Do L and U refer to limits on keys or the limits on branching? If they refer to keys, then setting t=1 would create a 1-key/2-key B-tree which would be the ordinary 2-3 B-tree. It depends on the definition of "minimal degree".  CLRS may be using t in the same sense as Comer's d.Glrx (talk) 20:53, 18 August 2009 (UTC)

(2) The B-tree animation applet of slady (linked from the article) also uses a single parameter, which he calls the "order". He doesn't explain it, but experiments with the applet give, for order 1,  L=2 and U = 3, and for order 2,  L=3 and U = 5. In particular you always get U odd, so  the animation applet can't duplicate any of the trees discussed in CLRS. (Do you suppose this confuses my students?!)

 * This would fit if Slady's "order" of a B-tree is Comer's $$d$$ -- the minimum number of keys in a node. Then L=d+1 and U=2d+1. U will always be odd. Here L and U are refering to number of children/subnodes and not number of keys.Glrx (talk) 20:53, 18 August 2009 (UTC)

(3) Knuth's "Art of Computer Programming", vol. 3, p. 473, defines B-trees in terms of the "order" m.   Comparing it to the Wikipedia articla, we see U=m and L = ceiling(m/2);  we need ceiling since m is not required to be even. So CLRS covers the case when m is even, m = 2t; but Knuth also allows the case L=t and U = 2t-1; this seems to be the case the applet covers,  where the "order" you enter in the applet is t-1.

Some restriction on the relation between L and U has to be made; when we split a full node (containing U-1 elements) upon inserting a new key, we will get two new nodes containing U/2 elements each (for even U) or one with  floor(U/2) and one with ceiling(U/2) elements, for odd U. We must require that L be at most floor(U/2) so that these nodes are legal. Moreover, L can't be too small either, or deletion won't work right. On 1 April 2006 I edited the article to correct this point, and also to correct the description of the deletion algorithm. --User and date unknown

 * The above description is incorrect because a key must be promoted to the parent level during the split. We split a full node (with U-1 elements) only when inserting a new element (for a total of U elements). The result of the split will keep U-1 elements at the current level and promote one element to the parent level. If U is even, then one sibling has (U-2)/2 and the other (U)/2 elements. If U is odd, then both siblings have (U-1)/2 elements.Glrx (talk) 20:53, 18 August 2009 (UTC)

In the following I'll try to explain the definition tought at Technical University of Munich where Bayer used to work. This definition seems to make sense, and is consistent with the 3 definitions above. Only the terms used differ slightly. As above, I'll use the letters L and U for the minimum and maximum number of children of a node, though the letters a and b are commonly used at TUM.

Any search-tree that works the way explained in the article needs to comply to U >= 2L-1. Otherwise splitting up a node upon insertion will not work. A balanced search tree complying this rule is called (a,b)-tree. An (a,b)-tree where U = 2L-1 is called a B-tree.

These definitions have the following implications:
 * The above definitions 2 and 3 comply to this definition of a B-tree. (In the second edition of Knuth's "Art of Computer Programming", vol. 3 it's on page 483, and it's a bit vague: does m/2 mean integer division here?)
 * The above definition 1 is not valid for a B-tree in this strict sense, but for another specialization of an (a,b)-tree.
 * The values U = L * 3/2 for B*-trees do not comply to this definition of a B-tree or an (a,b)-tree. Therefore a B*-tree is not a specialization of a B-tree, but a different though related datastructure.
 * The term (a,b)-tree gives another possible explaination for the meaning of the B in B-tree. For a B-tree, only the b needs to be known, and it's always odd. The a can be calculated as ceiling(b/2).

I don't know if the above nomenclature is common outside of TUM. I'm not an expert on the topic. The only references I can provide are two lecture notes in German: ead_ws9697.ps.gz and ead_ws9798.ps.gz.

Maybe someone should check the original publications! However, this node structure issue needs to be clarified in the article. In particular the rule U >= 2L-1 should be mentioned, even if it turns out that all (a,b)-trees are commonly called B-trees.

Michael R. 22:55, 16 August 2006 (UTC)

Order
I removed "order 2" from the caption because the citation there does not define order, but only calls it parameter k. Knuth does define order, while describing Two-Three B Trees. Some later textbook authors and web resources have since published different numbers, typically 2. To be less ambiguous, the value could perhaps be referred to as "Knuth's order" (see Knuth,TAOCP)

--132.160.49.90 (talk), 26 March 2016

variants
Should *this* article B-tree have a section that explains variants such as B*-tree, B+ tree, etc.? Then I want a section that explains pros and cons -- why would someone use one variant instead of another, or instead of a simple binary tree ? Some people find that preferable to having a bunch of very short stub articles that say "just like a B-tree except that ..." -- or, worse, a bunch of fully-fleshed out articles that repeat the preliminary explanation over and over. --DavidCary 20:52, 30 July 2005 (UTC)

-

Are 2-3-4 trees a kind of B-tree with L=2, U=4 ?

Error in illustration of B+ tree
It appears that there is an error in the illustration. According to the text, all values in the leftmost subtree should be less than a1. In the illustration, however, the leftmost subtree contains the value 3, which is equal to a1.

I agree, from "Database Systems: The Complete Book" -- if j pointers are used then there will be j - 1 keys, e.g. K_1, K_2, ..., K_j-1 so the first pointer points to a part of the B tree where some of the records with values < K_1 will be found; the second pointer points to  where records with values >= K_1 and < K_2 will be found and so on. 132.205.155.150

---

This ordering is also used in 'Silberschatz, Korth, Sudarshan: Database System Concepts, 4th Edition'. Schmid 12:39, 13 August 2006 (UTC)

---

Concurrent access
The paragraph at the end of the insertion section suggests that an improvement involves splitting nodes that might fill on a leaf node split on the way down the tree. This buys nothing. It only reduces the effective node size by one.

Unless the nodes are locked there is no guarantee the nodes will remain non-full on the way back up during a split. To allow maximal concurrency, you don't want to lock nodes on the insert descent.

--Karl Malbrain 20:52, 18 May 2006 (UTC)

Second that, please stop restoring that section because is completely off. —Preceding unsigned comment added by 190.18.107.147 (talk) 21:26, 15 May 2009 (UTC)

---

What is "completely off" about this section? I have a copy of the reference material and summarized it for this section. N.b. there is no requirement that reference materials be available on the web for free.

--karl m {{User electrical engineer}} (talk) 21:58, 15 May 2009 (UTC)

If I publish an online paper (free or not) about "B-Tree Programming" is not enough to reference it, unless we call this advertising. If this is not the case, the least I expect from a summary is what are the alternatives, in which cases is better (not the -why-, I can check the reference if I am interested enough) and optionally which vendor implements it. —Preceding unsigned comment added by 201.231.39.110 (talk) 14:59, 20 May 2009 (UTC)

The paper was published by the Association for Computing Machinery, it is not an on-line paper. Are you challenging this source in specific? I added the section in an attempt to flesh out the material from the perspective of a high-school understanding of computer science. I don't know which vendors use the forward pointers in their B-tree structures. Again, what is "completely off" about this section?

-- karl m {{User electrical engineer}} (talk) 15:58, 20 May 2009 (UTC) --

Thanks for the response. The "off" I meant, is that it sounds like summarizing JFK as a president assassinated with a reference to a book about his life. What are the different strategies? (the current summary sounds like there are not other alternatives. If this is the case, then at least it must say that there are not other). In which cases this specific strategy is convinient?. Are there any known engines that implement this? (MyISAM maybe?). —Preceding unsigned comment added by 201.231.39.110 (talk) 00:52, 21 May 2009 (UTC)

Repeated info
A lot of information is repeated redundantly throughout the article. Please consider rewriting it to make it a bit more concise. --221.134.26.57 17:37, 21 May 2006 (UTC)
 * I like the use of "repeated redundancy" - Yogi Berra would be proud. The article is basically a joke, full of too many ambiguities and self-contradictions.    One problem that seems to occur in every Wikepedia article about trees is the failure to distinguish between "keys" and "values" - or state that the two terms are synonymous.   Here, that's just one factor that makes this article useless.  — Preceding unsigned comment added by 68.183.37.170 (talk) 18:32, 21 May 2014 (UTC)

Picture
I think the picture should be removed. Why would you put a picture of a B+tree on the B-tree page. It would be like looking up the US capital and finding a picture of the Eiffel tower. Not to mention the B+tree picture is incorrect. 3 should be in the middle node and 5 in the last. The pictures are great but people look at the picture instead of reading and the info in the picture is wrong. I would recommend removing the pictures unless they can be corrected. —The preceding unsigned comment was added by 216.239.10.103 (talk • contribs).

weight-balancing scheme
Could someone explain the weight-balancing schema invented by Arge and Vitter? It seems to have better performance than the 2-3 B-trees. — Preceding unsigned comment added by 62.195.5.235 (talk • contribs) 15 September 2006 (UTC)

Relaxed Balance
There has been quite a bit of work by Kim S Larsen and Rolf Fagerberg (e.g. http://citeseer.ist.psu.edu/51205.html ) showing how the balance of a btree can be maintained lazily with several benefits. For the purposes of elucidation relaxed balance is particularly good because you can describe insertion or deletion and separate the basic steps of the algorithm and the steps for the maintenance of balance. Another benefit is that all modifications to the structure of the tree are local, so concurrency is more easily exploited.

It'd be nice for the text to include a description of this work. Dr Tom Conway (talk) 01:20, 3 January 2008 (UTC)

Minor Quibble
I could be missing something obvious, but I don't see why tuning a B-tree to disk block sizes would result in a 257-513 B-tree. Shouldn't it be a 257-512 B-tree? —Preceding unsigned comment added by 128.221.197.21 (talk) 12:47, 31 July 2008 (UTC)

hop?
This depth will increase slowly as elements are added to the tree, but an increase in the overall depth is infrequent, and results in all leaf nodes being one more hop further removed from the root.

Is that "hop" just the writer's voice, or do people frequently use the word "hop" to describe that? I know there are a lot of terms used in computer science that don't sound nearly as technical as they are, but on the other hand, "hop" only occurs once in the entire page. (Not saying it's a problem and needs to be fixed, just wondering.) --146.187.184.231 (talk) 19:45, 6 November 2008 (UTC)
 * It's a term borrowed from networking, apparently. I would use "one node," and have modified it accordingly. Dcoetzee 21:16, 6 November 2008 (UTC)

Boeing citation
There is a "citation needed" marked beside the word Boeing.

The citation is in the external link mentioned below, named NIST's Dictionary of Algorithms and Data Structures: B-tree at http://www.nist.gov/dads/HTML/btree.html written as this:

Note:
 *  The origin of "B-tree" has never been explained by the authors. ... "balanced," "broad," or "bushy" might apply. Others suggest that the "B" stands for Boeing. [Bayer and McCreight were at Boeing Scientific Research Labs in 1972.] Because of his contributions, however, it seems appropriate to think of B-trees as "Bayer"-trees.
 *        -   Douglas Comer, The Ubiquitous B-Tree, Computing Surveys, 11(2):123, June 1979.

I am just not sure, how to edit links on the page... ~ —Preceding unsigned comment added by 195.146.109.168 (talk) 15:46, 13 November 2008 (UTC)

Leaves "carry no information"?
All leaves appear in the same level, and carry no information.

That's not how the pictures look.

Big Oh notation
"can be done in O(log2N) comparisons. If the table had 1,000,000 records, then a specific record could be located with about 20 comparisons: log21,000,000 = 19.931". It's a detail, but that's not the meaning of the Big-Oh notation. Depending on the implementation it may need a million comparisons or even more. The big Oh notation only says something about how the performance scales as N increases. I understand, though, that this may be harder to explain in Layman's terms and that it might confuse readers who don't know about complexity analysis, but what is written now is just plain wrong. 84.194.88.199 (talk) 15:44, 8 May 2010 (UTC)

I fixed some things; more improvements needed
I'll get right down to it.

Problem with definition
First, in the list of five Definition rules, the second rule is:

"2. Every node (except root) has at least $m/2$ children."

But, leaf nodes have no children. In defining the number of elements by the number of children, the article later leaves ambiguous the number of elements in leaf nodes.

Furthermore, the section decribing bulkloading uses a different set of rules where the leaf nodes and internal nodes have different maximum sizes, and seems to imply an expectation of the disconnection of the number of elements in leaf nodes from the number of elements in internal nodes. However, the rest of the article above this section assumes leaf nodes have the same maximum number of elements as internal nodes (as I understand it).

Near the top of the article, some inconsistencies in terminology in the literature about B-trees are raised. Perhaps this is at least part of the origin of some of these problems. The article would be better if after expositing the variations in terminology, it would choose and assert definitions for a system of terms to be used at within the remainder of this article. That would make the article clearer both in the minds of editors and to the reader, and would provide a framework on which judgements of correctness (by editors) and building of understanding (by interested end-user readers) could be based.

B-trees in filesystems and FAT filesystem
I have corrected an incorrect application of the terms "logical block" and "physical block" in the section of B-trees in file systems. Almost nothing in modern file systems refers to physical blocks, as disks present an interface in terms of Logical Block Addresses (LBAs) or logical, not physical, CHS addresses. (Floppy disks still use physical CHS addresses, but are becoming rarer and rarer.) Furthermore, even DOS file systems like FAT12 and FAT16, considered primitive by most today, use logical addresses in the FAT which are relative to the data area of the file system volume and are not the physical addresses of the disk nor addresses relative to the start of the partition.

Therefore, I have changed this section of the article to use the terms "file block" and "disk block". I think it is clearly enough implied that a file block is a block addressed relative to a file, and it is obvious that such a block address is logical, not physical, so I have not used the word "logical" with "file block", and I have not explicitly defined what a file block address is. As for disk blocks, it is not really pertinent to the B-tree discussion whether they are physical or logical, so long as it is clear that disk block addresses address actual blocks on the disk, not abstract blocks in an abstract file, using an address scheme that is global over at least the part of the disk used by the file system. Again, I think implication suffices to expose this; anyone who has a basic understanding of the purpose, nature, and rudimentary fucntion of a file system should understand this, and anyone who does not will not understand, or probably be interested in, the discussion of B-trees in file systems anyway. The point is that file systems map file blocks--parts of a file--to disk blocks--units of storage on a disk--and that this is what B-trees (and File Allocation Tables, and other alternative concepts and structures) are used for in file systems. The physical/logical dichotomy here is both incorrect and overly narrow so as to confuse or at least complicate the essential concepts about B-trees in file systems.

 * I think that the term "Disk Block" is still very problematic for a number of reasons, starting with the fact that in most OS environments and jargon it has a very specific meaning that is different from how it is used here. "File Block" is confusing because it is unfamiliar and unclear what it means.  The term actually used by almost all implementers, practitioners and analysts of extant B-Tree indexing is "Bucket".  This is the term that I would suggest be used in this article.  RBarryYoung (talk) 15:24, 28 February 2013 (UTC)

Algorithms - deletion of a node
I had made more improvements in this section, but all my work was unceremoniously reverted. I've reinstated the parts I think actually weren't in dispute. The other parts, in this section, really need improvements, as I think others above have said. Anyway, my suggested edits are in the history, if someone wants to revive them.

–Stephen 141.158.233.114 (talk) 12:15, 23 July 2010 (UTC)

Comment
I have many issues with these edits, and that is why I reverted all of them.

While there are some improvements (such as FAT12 being 4080-2), there are many inaccuracies. In the B-tree, entries are rotated. Entries are not duplicated. There are unwarranted claims about the size of a file. There are extraneous comments about disk utilities.

I have reverted one of the reinstatements. I am considering reverting the FAT edits again.

Glrx (talk) 16:08, 23 July 2010 (UTC)

Where is the complexity?
There is a nice table at the top for complexity reference in big O notation but...nothing there.66.14.187.7 (talk) 18:10, 1 October 2010 (UTC)

English
"The seek time may be 0 to 20 or more milliseconds..." Everything takes 0 to 20 or more milliseconds. Leegee23 (talk) 11:33, 12 December 2011 (UTC)

Recent edit to Knuth's description of a B-tree
I'm tempted to revert/modify this edit]. The edit uses another reference to overrule what is ostensibly Knuth's definition. The literature is troubled with differing terminology. See B-tree. Knuth's terminology has an unusual bottom level of the tree -- leaves are below lowest keys. "Carry information" is also troubling; in some variations, the associated information is present above the leaves; in others, only key information is above the leaf; in still others, key information is copied above but retained below. Ordinary leaves, however, would have either the associated data or a pointer to that data and carry information. In Knuth's definition, the leaves appear to be the records -- and therefore carry information. Glrx (talk) 18:54, 28 December 2011 (UTC)

Your analysis is correct and the edit should be reverted. karl m {{User electrical engineer}} (talk) 19:58, 28 December 2011 (UTC)

Request revision on the Rebalancing after deletion
Under section 5.3.3 Rebalancing after deletion there are

3. Append the first child of the right sibling as the last child of the deficient node

under

1. If the right sibling has more than the minimum number of elements

and

3. Insert the last child of the left sibling as the first child of the deficient node

under

2. Otherwise, if the left sibling has more than the minimum number of elements

From my understanding of B-Tree, these two steps make no sense as after you execute the first two steps described in that section. The separator and the first/last child of the sibling have been rotated. There should be no extra step to append or insert. I have no idea where this step comes from. But maybe I am wrong. I hope someone could further explain this.

Thank you. — Preceding unsigned comment added by Johnmave126 (talk • contribs) 10:47, 6 May 2013 (UTC)

 * The section appears to describe the operation for a B+-tree rather than a B-tree. In the former, the parent only has a copy of the separator; there is not a full rotation in the B-tree sense. I've changed the section to use the B-tree rotation (and suggest that a left or right sibling may not exist). Glrx (talk) 16:20, 6 May 2013 (UTC)

Is 2-3 tree a B-tree?
By the definition in the book Introduction to Algorithms, a B-tree of order t is such that its every non-root node contains at least t children, and every node contains at most 2t children. The reason for this is that splitting a node into two nodes is possible only if it contains at least 2t nodes. This is a fundamental requirement for the data-structure algorithms on B-tree to work. In particular then, a 2-3 tree is not a B-tree; it's algorithms are different than those of B-trees. The text currently uses 2-3 trees as a recurring example; those examples should be changed to refer to the 2-3-4-tree, the smallest example of a B-tree. What do you think? --Kaba3 (talk) 18:15, 26 September 2013 (UTC)

 * A 2–3 tree is a B-tree; it fits Knuth's definition. There are many definitions of order and many variations of the B-tree, but the basic algorithms are similar. If I take your definition literally, a 2–3 tree is B-tree of order 2 because non-root nodes contain at least 2 children and every node contains at most 3 children (which is less than 2t but does not violate 2t). Your second sentence is not the driving force behind balancing the tree; if a node may have nmax children, then there is no reason to split that node. The node is happy as it stands. There is also a subtle issue about keys/separators and children; a node has one more child than it has keys. A 2–3 tree has either one or two keys in each internal node. If an internal node of a 2–3 tree has 2 keys (3 children) already and I need to add a third key (a 4th child), then I can split the node into two nodes with one key each (total of 4 children) and the remaining key to the parent. Glrx (talk) 22:48, 27 September 2013 (UTC)

Animation
Hi. I am trying to develop a B-tree toy at. This article already has a link to an animation applet. Since applets are becoming unfashionable, I hope to replace this applet some day. I would appreciate it a lot if you would try out the toy and tell me how it can be improved. Maybe we could replace the applet linked then. --Ysangkok (talk) 13:41, 3 March 2014 (UTC)

key - copies contradiction
"In the B+-tree, copies of the keys are stored in the internal nodes; the keys and records are stored in leaves" vs. " The keys act as separation values which divide its subtrees"

Since a B+-tree is a B-tree, one must be incorrect. The "copies" can't be in the internal nodes when the original keys are. — Preceding unsigned comment added by 68.183.92.186 (talk) 22:38, 13 May 2014 (UTC)

The B-tree uses all those
"The B-tree uses all of the ideas described above." (What ideas?) "In particular, a B-tree:" . . . "keeps the index balanced with an elegant recursive algorithm" (where is balancing mentioned above?)

-- the above unsigned note was added on 14 May 2014 by 68.183.92.186 (talk)

 * Balancing is not mentioned because there is no balancing. The tree is balanced when it gets created and it remains balanced during insertion and during deletion of data – the tree is inherently balanced. Just as it is said: the algorithm 'keeps it balanced', not '(re)balances it after the operation destroys the balance' (like in other balanced trees, e.g. AVL trees). --CiaPan (talk) 17:06, 4 January 2016 (UTC)

2014-11-21 BS Comments
"Overview":

"In B-trees, internal (non-leaf)" - 'non-leaf' is not mentioned in the referred to article. Could you please choose a different term than 'non-leaf', or define 'non-leaf' in the referred to article. i.e. In referring to something to explain something else, that something does not exist to be able to follow what is trying to be explained.

"within some pre-defined range." - range of what?

There is a basic problem here of a lack of definition of what a node is. There is also a problem that "A node is a structure which may contain a value or condition, or represent a separate data structure (which could be a tree of its own)." is too vague or intangible to be meaningful. In particular, 'condition' above is gibberish (to the reader at this point in their reading). Better, a node [which has an address, i.e. a path (address) by which it can be found <- this 'address' is the missing piece or attribute of the explanation), contains a piece of data. That data could be a value (such as the number 4, or the word 'red'), or a pointer (address) of (i.e. to) another node. [Missing, or, unless, a btree node can (must?) contain at least a value, AND zero or more pointers - at most one to the left (by definition, decreasing?), AND (at most) one to the right (by definition, increasing?)]. So, more succinctly, a node (with/having an address) contains a piece of data. Which is to say, a node is an address/(data and/or left and right pointing) pair.

- now this (above) paragraph may be completely wrong, and that's fine, but in being wrong demonstrates that my (the reader's) purpose in coming to this article is not getting satisfied. Either the above is correct and the article does not so explain 'simplistically' (too conceptual / intangible too fast), or does not well explain soon and simplistically enough what is actually meant (is true / actually is).

"When data is inserted or removed from a node, its number of child nodes changes." is baffling. Probably because it is self-referencing. (It is becoming apparent to me that I don't understand the lingo, or at least the established/recognized lingo, and if I don't, then that says the lingo is not being well explained.) So this bit ("When data is inserted or removed from a node, its number of child nodes changes.") says to me that what should be said is a node is a address/data+pointer 'pair', and nodes (and this is the problem with the use of the same term 'node' twice) contain SETS of nodes (or node sets). Thus the referred to diagram does not make sense (node-wise) as written. However, if one says nodes contain sets of nodes, it starts to come together. (That one does not understand how a node could contain a set of nodes, being a circular description, is ok - one can suspend understanding, expecting such to be explained in subsequent text.) The basic problem with the diagram is that it does not show lines between the .#. pairs. Saying that differently - the 'problem' is either that the diagram is 'wrong' OR the explanation thus far is, since I don't understand / haven't followed.

- by the diagram, the above node = address/data+pointer pairs is wrong. By the diagram, it would appear more correct to say that nodes contain (ordered) sequences of data, WITH POINTERS BETWEEN EACH PAIR OF DATA TO NODES THAT DESCRIBE (COVER) the data/value space between those adjacent values.

So, said differently, one assumes, or soon comes to assume b-tree = binary-tree, which is to say, a node could have at most left and right pointers. By this diagram, a node could have many pointers, and this is not made clear enough early on. So, perhaps earlier in the article it can say a b-tree is not (necessarily) a tree of binary nodes, but a tree of nodes, period. Binary or otherwise. Saying (noting), although possibly considered as redundant, noting that being a tree, nodes have descendants, and by its address knows its ascendant (if the latter is true - does a node's address tell the node where its parent is?).

Summarizing all of the above - the article, within only a few sentences, is as clear as mud. Since the purpose of writing an article is to clear up the mud, perhaps some reworking could be done? [I came here to learn / read / understand, so I'm not the guy to do the rework. i.e. If I understood the material I could contribute to the material, but because I came here to learn the material I can't. I can say, having come here to learn the material - I don't understand. [Therefore purpose in being written hasn't been satisfied. (?)]

"but may waste some space, since nodes are not entirely full" - does not yet follow / make sense. One would assume that a node size is dynamic, therefore only as big as the data contained, and so can waste no space. For the statement to be true, nodes are of a pre-defined size - something that should be stated beforehand. That this is true in the diagram is only now apparent to me. Adding to the diagram, or it's description, '4-element nodes' would make grasping what's being said much more clear much more readily. (Assuming 'element' is the correct term, there.)

The '2–3_tree' diagram illustrates what I say above - there is a diagram depicting a node (to my mind). The diagram depicted within this (b-tree) article shows something (node) that I can't understand as being a node (as I can in the 2-3 article's diagram) - they appear different. Thus I have a mental image of two different things being called 'nodes', and I don't understand (it hasn't been explained in this article) how the term 'node' is accurate for both diagrams. ('One of these things is not like the other' - so, i.e., understanding is not present [same name for two obviously different things]).

Bs27975 (talk) 18:39, 21 November 2014 (UTC)
 * Will be glad if someone takes care of these problems. 120.59.185.182 (talk) 07:32, 3 January 2016 (UTC)

The "The Database Problem" section needs cleanup
It currently reads very informally and feels out of place with the rest of the article. I'd suggest it be condensed and then split into a pro/con type section. Possibly moved down the page. I'm going to try to formalize the language where I can, but I'm not familiar enough with B-trees to do the rest myself. TheWisestOfFools (talk) 17:03, 29 October 2015 (UTC)

Undefined terms used in Overview
Some examples --

pre-defined range,

From the image it looks as if a single node can host a lot of data, a concept which the the article assumes that the reader knows about.

Joining or splitting of nodes is not defined. 120.59.185.182 (talk) 07:31, 3 January 2016 (UTC)

Generalization?
I think it is not correct to call B-tree the generalization of a binary search tree, as the B-tree requires all the leafs to be at the same depth, and BST does not. So in this way the BST is the generalization of B-tree???

Skrew (talk) 07:38, 24 May 2016 (UTC)

Nodes can have multiple keys, not just >2 children
The introduction mentions that, unlike a binary search tree, a B-Tree's nodes can have multiple children. But surely it should also mention that each node can have multiple keys. The B-Tree chapter in CLRS doesn't mention that until its third paragraph, but it seems to be important. The wikipedia page for 2-3 Trees does mention this. I wonder if the 2-3 Tree page should be combined with the B-Tree page, or if they should at least reference each other more. — Preceding unsigned comment added by Murraycu (talk • contribs) 12:02, 7 July 2016 (UTC)

Disadvantages entry is humbug, remove?
I don't have the time to verify this, only got one's confirmation that i'm correct on this one -

"maximum key length cannot be changed without completely rebuilding the database. This led to many database systems truncating full human names to 70 characters.", that is humbug!? Remove= — Preceding unsigned comment added by 14.199.34.215 (talk) 09:04, 7 April 2017 (UTC)

Initial construction by bulkloading
(Referring the version .)

The whole section #Initial construction, originating from revisions Special:Diff/174287958 in November 2007 and Special:Diff/260712701 in December 2008, is unsourced. Even worse, it is useless: even though it is a subsection to Algorithms, it actually presents no algorithm! It just describes a specific case, but it does not explain why the case is handled this way or how other cases would be handled.

For an example let's take twenty FIVE items instead of 24. Then we CAN'T add the key 25 to the fifth leaf node in the initial step, because the fifth key from each leaf is later detached to be used as a separating key in some ancestor node – and there is no sixth leaf node to be separated from the fifth one, so the key 25 would remain unused. We also CAN'T avoid adding the 25 key to the fifth leaf node and make a sixth node of it instead, because then the fifth node has no fifth key to be used as a separator between leafs No 5 and 6. Possibly we could detach the key 24 from the fifth node for this purpose, but the 'algorithm' does not provide such option. Actually, it doesn't provide any options, just one, pre-determined case...

Anyway, the sixth node would break the requirements, because a single key 25 in a 4-slots node would be using only 1/4 of the node's capacity, while it is required that each node is at least half-filled! An actual algorithm should calculate an optimum distribution of keys between leaf nodes while keeping enough spare keys to fulfill the filling requirements in internal nodes, too. And keeping internal nodes and leaf nodes of different size complicates things even further.

Should we rescue that bulksh*t somehow or just delete it from the article? --CiaPan (talk) 18:08, 30 December 2017 (UTC)

 * Yes, the section has severe problems. It does suggest an algorithm, but the suggestion is poor/flawed. The text before he revision had a better toplevel viewpoint.
 * From an algorithmic standpoint, doing single record insertions is sufficient to load a database. Sequentially inserting sorted data will leave a B-tree sparsely populated because the rightmost node is continually split leaving lots of half-filled left siblings behind.
 * Before BTrees, it was common practice to reload/reorg a database to make it more efficient (get rid of overflow blocks).
 * Bulkloading often does not want to maximally fill each page. If each page is full at loading, then most subsequent insertion will cause a split. Usually some compromise is chosen so an insertion won't cause a split and a deletion won't cause a merge. The issues are complicated.
 * I'd keep the section and hope it gets improved.
 * Glrx (talk) 18:52, 28 January 2018 (UTC)

 * StackOverflow has several threads about B-trees, and some of them about bulkloading. The most complete I found is this answer by didierc to the question Is there any algorithm for bulk loading in B-Tree? by nbbk. However, it contains detailed hints only, not a fully specified algorithm. It also does not reference any outside sources, so from Wikipedia's point of view it should be considered original research, not appropriate as a source for us. [[file:sad.png]] --CiaPan (talk) 20:44, 29 January 2018 (UTC)

 * I looked at the cited QA, and it seems wrong. WP:NOR is good policy. There's little difference between the B-Tree versions, and wrt loading one promotes the key and deletes the leaf if an ordinary B-Tree. Glrx (talk) 19:59, 26 February 2018 (UTC)

 * I rewrote the section de novo. It still needs references ( my bad ), but it's shorter, simpler, and correct now.  Is it at least an improvement?  23.83.37.241 (talk) 07:15, 4 April 2018 (UTC)

Etymology
User:EEng has cutdown a long-standing section on Etymology. I'll agree that the original section buried the lead (the DB world has long wondered what the "B" stands for; I wondered, but I never had the courage to ask McCreight in the summer of 1979). But EEng's version cuts it down to nothing and is contradictory. The first sentence says Bayer and McCreight "did not explain what, if anything, the B stands for"; the second sentence then states, "McCreight has said that ..." (referring to a 2013 quotation that describes Bayer and McCreight debating B for Boeing, Bayer, and balanced). The original should be restored and eventually improved; it is better than the contradiction. Glrx (talk) 02:02, 4 May 2018 (UTC)
 * Here's what the section says:
 * Rudolf Bayer and Ed McCreight invented the B-tree while working at Boeing Research Labs in 1971 (Bayer & McCreight 1972), but did not explain what, if anything, the B stands for: Boeing, balanced, broad, bushy, and Bayer have been suggested.(Comer 1979, p. 123 footnote 1)[1][2] McCreight has said that "the more you think about what the B in B-trees means, the better you understand B-trees."[1]
 * There's nothing contradictory about this, and it faithfully reflects the sources. For contrast, here's the prior, bloated version:
 * Rudolf Bayer and Ed McCreight invented the B-tree while working at Boeing Research Labs in 1971 (Bayer & McCreight 1972), but they did not explain what, if anything, the B stands for. Douglas Comer explains:
 * The origin of "B-tree" has never been explained by the authors. As we shall see, "balanced," "broad," or "bushy" might apply. Others suggest that the "B" stands for Boeing. Because of his contributions, however, it seems appropriate to think of B-trees as "Bayer"-trees. (Comer 1979, p. 123 footnote 1)
 * Donald Knuth speculates on the etymology of B-trees in his May, 1980 lecture on the topic "CS144C classroom lecture about disk storage and B-trees", suggesting the "B" may have originated from Boeing or from Bayer's name.[4]
 * Ed McCreight answered a question on B-tree's name in 2013:
 * Bayer and I were in a lunchtime where we get to think [of] a name. And ... B is, you know ... We were working for Boeing at the time, we couldn't use the name without talking to lawyers. So, there is a B. [The B-tree] has to do with balance, another B. Bayer was the senior author, who [was] several years older than I am and had many more publications than I did. So there is another B. And so, at the lunch table we never did resolve whether there was one of those that made more sense than the rest. What really lives to say is: the more you think about what the B in B-trees means, the better you understand B-trees."[5]
 * Now then... what information enlightening to the reader is present in that rambling trip to nowhere that isn't in the pithy version? EEng 02:27, 4 May 2018 (UTC)

Floor and ceiling symbols
The article uses what seems to be floor and ceiling symbols/brackets eg: ˥ ˩. But I don't see how you can have a floor or ceiling when there is only one value between these symbols. Do these symbols have another meaning? Or have I missed something? FreeFlow99 (talk) 11:08, 27 January 2024 (UTC)
 * But why would you need more than one argument to Floor and ceiling functions??? --CiaPan (talk) 18:22, 27 January 2024 (UTC)

title: Talk:B-tree


text:
Talk:Live Aid

O'Reilly sourcing
The O'Reilly quote references Charity Navigator, the same group responsible for the (discredited) BBC claims about Live Aid funds. Seems either the quote should go, or the countered information should follow... 50.55.147.176 (talk) 16:13, 11 August 2011 (UTC)

Neil Mallard/Visnews
There's an awful lot of waffle about Neil Mallard and Visnews in the opening 'Origins' section that is superfluous information in my opinion. As it appears to be the sole Wikipedia contribution by the anonymous editor, I think it is highly likely that it was written as promotional puff by Mallard/Visnews himself. I think most of it should be struck out – we don't really need to know all the details of how the TV deals were set up. Richard3120 (talk) 09:35, 24 September 2014 (UTC)
 * Forgot to mention, it's all unreferenced too. I can certainly find mention of Hal Uplinger's role in the set-up, but nothing about Mallard, which makes me even more suspicious that somebody is trying to inflate the importance of his role in the proceedings. Richard3120 (talk) 09:42, 24 September 2014 (UTC)

Criticisms and controversies
Seems to me this could use expanding, as the event was widely and pointedly satirized after the fact by the likes of Living Colour ("Go Away"), Faith No More ("We Care a Lot"), Chumbawamba (Pictures of Starving Children Sell Records), P.J. O'Rourke ("Fiddling While Africa Starves"), and Cracked.com ("5 Embarrassing Failures History Class Turned Into Victories"). Worth mentioning? Calbaer (talk) 18:54, 13 December 2014 (UTC)

 * This is one of the most moronic Wiki sections I have ever read. Adam Ant is cited as saying the performances were "boring." Really? Anybody look at the Freddie Mercury performance?" We need more context and nuance. I understand that's a lot to ask of Wikipedia. — Preceding unsigned comment added by 2601:240:cb81:3770:b1a7:6b84:9dad:83a4 (talk • contribs) 21:40, 13 May 2020 (UTC)
 * It was Andy Kershaw who called the performancees boring, not Adam Ant. And what's your point? Whether Mercury's performance is good or bad is personal opinion, not fact. And nuance is exactly what is being provided here, by adding a section on criticism of the event. Richard3120 (talk) 21:56, 13 May 2020 (UTC)

External links modified
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B.B. King?
Seems to have played, at least according to my ears (and mp3s). But no mention of him. What's that about? — Preceding unsigned comment added by 116.228.6.74 (talk) 21:47, 16 January 2016 (UTC)
 * Whereabouts do you think he played? Between which other artists in the running order? Richard3120 (talk) 00:58, 17 January 2016 (UTC)
 * I just checked the DVD's out from the library and I see no mention of him and nothing in the notes saying that he played and the video was not included in the DVD's. Ckruschke (talk) 18:02, 21 January 2016 (UTC)Ckruschke
 * He certainly didn't play the UK leg - I didn't watch all the US leg at the time but the only acts I think that could possibly have been mistaken for him were George Thorogood and Santana. Richard3120 (talk) 19:20, 21 January 2016 (UTC)
 * Good point - he might be mistaking Bo Diddley or Albert Collins, who both played with George Thorogood during The Destroyers set, for King. Ckruschke (talk) 18:50, 25 January 2016 (UTC)Ckruschke
 * He didn't play live on stage in London or Philadelphia, but the BBC showed him performing a couple of songs in The Netherlands during the day.Swaddon1903 (talk) 16:21, 24 June 2020 (UTC)

Repeated reverts by Ajax1995
Over the past week I have been reverting vandalism by Ajax1995, who has taken to gutting reliably cited text on WP:JDLI grounds. I'm kicking off this section to make sure we avoid any potential "He's-an-IP-so-revert-him" silliness.

According to journalist and author Dylan Jones in his book The Eighties: One Day, One Decade, Simon LeBon's off-key note at JFK was widely described in the media as "The Bum Note Heard Round the World". Jones is very much a reliable source, and the ubiquity of this phrase following Live Aid makes it notable for the article. This material is also supported by Digital Spy (a news site published by Hearst that has been in existence since 1999), which is used elsewhere to support Freddie Mercury's Wembley high note being described as "The Note Heard Round the World". The publication also states that the descriptions of the Mercury and LeBon notes were used as contrasting phrases. All relevant, all reliable. 2A02:C7D:6A44:4600:6897:461E:6828:4B3D (talk) 21:08, 22 July 2016 (UTC)

 * Inappropriate WP:TONE with this stuff. Binksternet (talk) 17:30, 23 July 2016 (UTC)
 * Point to specific examples of where WP:TONE is violated. If a description is widely used, then it's widely used and should be in the encyclopedia, regardless of user opinion on that description. In the meantime I'll revert to the extant version per not only WP:STATUSQUO, but WP:NEIPIAV. 2A02:C7D:6A44:4600:64D5:1068:1FC6:9E77 (talk) 20:02, 23 July 2016 (UTC)
 * You go off on a tangent! nothing to do with WP:STATUSQUO or WP:NEIPIAV, your point is only CHIT CHAT, irrelevant POV by some British tabloids, and those ridiculous "The Bum Note Heard Round the World" and "The Note Heard Round the World" is pure gossip by some pseudo-journalist and nobody cares this, two stupid phrases which nothing brings to an ENCYCLOPEDIC article.Ajax1995 (talk) 15:13, 26 July 2016 (UTC)

I am now dealing with harassment from Binksternet for using "multiple IP addresses" to "vandalize" this page (um, who's removing fully cited text with no argument whatsoever, again?), even though I previously made clear that I am "on a dynamic Sky IP that changes regularly". All the while, he still cannot provide a single shred of reasoning for reverting my edits – anti-IP editor agenda seems likely. 2A02:C7D:6A44:4600:95C7:5E02:1840:6A58 (talk) 00:38, 24 July 2016 (UTC)
 * "fully cited"?, everybody can add sourced stuff and ridiculous phrases, the question is which of those "sourced" information is appropiate to add, discern between valuable and pure chit-chat, silly info which is already available on blogs and trivia sites. Salutes, I hope (as a civilized person I think you are) you understand this point, Binksternet tries to maintain order and a neutral-"encyclopedic" language on Wikipedia.Ajax1995 (talk) 15:46, 26 July 2016 (UTC)

I've semi-protected the article this time as the IP seems to have no support for their changes. IP, please stop reverting multiple editors and start a WP:RFC if you want wider input. --Neil N  talk to me 09:39, 3 August 2016 (UTC)
 * Lolzer, "seems to have no support"? If you actually looked at what's going on (rather than driving the "revert-all-IPs!" agenda plaguing this site) you'd see I'm restoring fully supported material being removed with no rationale other than "I don't like it!" So yes, I'll continue to de-rig the article in the face of WP:OWN antics from "established"/agenda-driven editors. 94.1.67.27 (talk) 15:40, 3 August 2016 (UTC)
 * I'm neutral here, but I think the argument is more whether such content has a place in an encyclopedia or not, rather than editors "liking" it or not. It would be better to open this up as an RfC, as NeilN suggests. Richard3120 (talk) 16:39, 3 August 2016 (UTC)
 * Well, that makes you and I for the neutral team. I've already been falsely accused of "sockpuppetry", "vandalism" and adding "unsourced" information – all utterly bollocks claims that I've shot down and which hint strongly at an anti-IP agenda (not like that hasn't plagued Wikipedia for years). What's really going on is restoration of cited material that's being repeatedly removed by an editor who will simply offer no reasoning; other "established" editors see this and jump on back of the IP, who must be a vandal. 2A02:C7D:6A44:4600:24D2:7F93:E176:1BD5 (talk) 05:07, 5 August 2016 (UTC)
 * Are you going to add an RFC? Also, please read wp:BOLD, revert, discuss cycle (WP:BRD) and wp:edit warring. Thank you Jim1138 (talk) 07:26, 5 August 2016 (UTC)

External links modified
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Cliff Richard
Cliff Richard is included both in the section of notable absences and also in the performers under 'other', introduced by Andy Kershaw. This requires clarification.Martin Turner (talk) 23:25, 1 May 2019 (UTC)
 * What happened was that he didn't play the concert, he turned up unannounced to the BBC studio after the London leg had finished (but they were continuing to broadcast the rest of the Philadelphia leg), and he proceeded to sing and play the song on an acoustic guitar in the BBC studio. But it wasn't a planned part of the concert. Richard3120 (talk) 23:38, 1 May 2019 (UTC)

Performances default collapse
Most of the content in the "Performances" section renders as default collapse in my user agent (presently a slightly dated Firefox).

When I click on a section title within this section, such as "Notable absences", my click takes me nowhere, because the content is default collapse. This is a bad thing.

See WP:COLLAPSE.

Collapsible templates should not conceal article content by default upon page loading.

Reasons are given there. — MaxEnt 05:05, 16 November 2020 (UTC)

 * Hi - this is not a "bad thing". This section is a 4+ page wall of words. The decision was made to allow for better reading of the overall page while still having this information available for readers who are interested. I was able to open up the entire section at one click. Not sure why you are seeing an issue. Ckruschke (talk) 18:16, 16 November 2020 (UTC)Ckruschke

logo
Steve Maher should get a shout-out for his logo. my man put out a logo which still resonates four decades on. Electricmaster (talk) 21:02, 5 July 2023 (UTC)

FEED THE WORLD
What does the FEED THE WORLD sign at Wembly Stadium mean?Sleigh (talk) 01:06, 28 January 2024 (UTC)
 * You're asking what is the meaning of the words that are repeated at the end of the Band Aid single that inspired this event, which was to raise money to provide food to starving people in Africa? Richard3120 (talk) 22:38, 25 March 2024 (UTC)

title: Talk:Live Aid