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Kanga

Kanga may refer to:

Places

 * Kanga, Tanzania, a ward of Chunya District
 * Kangavar, a city in Kermanshah Province, Iran

People

 * Guélor Kanga, Gabonese footballer
 * Hormasji Kanga (1880–1945), Indian cricketer
 * Kanga Cricket League, Indian cricket league named after Hormasji Kanga
 * Wilfried Kanga, French footballer
 * John Kennedy Sr. (nicknamed Kanga) (1928–2020), Australian rules footballer
 * Dale Tryon, Baroness Tryon (nicknamed Kanga) (1948–1997), British businesswoman

Other

 * Kangaroo, the Australian animal and icon
 * Kanga people, an ethnic minority in Sudan
 * Kanga language, spoken by the Kanga people
 * Kanga (garment), a sheet of fabric worn by women in East Africa
 * Kanga (comics), a fictional species of kangaroos in DC Comics
 * Kangha, a small wooden comb that is supposed to be kept with the hair at all times
 * "Kanga" (song), a 2018 song by 6ix9ine from the album Dummy Boy
 * Kanga (Winnie-the-Pooh), a character in the children's book Winnie the Pooh
 * Kanga Loaders, an Australian brand of compact utility loaders
 * Kanga, nickname of Dale Tryon, Baroness Tryon (1948–1997), and the name of her clothing line
 * KANGA, the callsign for V Australia Airlines

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

title: Kanga


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Regularization (mathematics)

In mathematics, statistics, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting.

Although regularization procedures can be divided in many ways, the following delineation is particularly helpful:
 * Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem. These terms could be priors, penalties, or constraints. Explicit regularization is commonly employed with ill-posed optimization problems. The regularization term, or penalty, imposes a cost on the optimization function to make the optimal solution unique.
 * Implicit regularization is all other forms of regularization. This includes, for example, early stopping, using a robust loss function, and discarding outliers. Implicit regularization is essentially ubiquitous in modern machine learning approaches, including stochastic gradient descent for training deep neural networks, and ensemble methods (such as random forests and gradient boosted trees).

In explicit regularization, independent of the problem or model, there is always a data term, that corresponds to a likelihood of the measurement and a regularization term that corresponds to a prior. By combining both using Bayesian statistics, one can compute a posterior, that includes both information sources and therefore stabilizes the estimation process. By trading off both objectives, one chooses to be more addictive to the data or to enforce generalization (to prevent overfitting). There is a whole research branch dealing with all possible regularizations. In practice, one usually tries a specific regularization and then figures out the probability density that corresponds to that regularization to justify the choice. It can also be physically motivated by common sense or intuition.

In machine learning, the data term corresponds to the training data and the regularization is either the choice of the model or modifications to the algorithm. It is always intended to reduce the generalization error, i.e. the error score with the trained model on the evaluation set and not the training data.

One of the earliest uses of regularization is Tikhonov regularization (ridge regression), related to the method of least squares.

Regularization in machine learning
In machine learning, a key challenge is enabling models to accurately predict outcomes on unseen data, not just on familiar training data. Regularization is crucial for addressing overfitting—where a model memorizes training data details but can't generalize to new data—and underfitting, where the model is too simple to capture the training data's complexity. This concept mirrors teaching students to apply learned concepts to new problems rather than just recalling memorized answers. The goal of regularization is to encourage models to learn the broader patterns within the data rather than memorizing it. Techniques like Early Stopping, L1 and L2 regularization, and Dropout are designed to prevent overfitting and underfitting, thereby enhancing the model's ability to adapt to and perform well with new data, thus improving model generalization.

Early Stopping
Stops training when validation performance deteriorates, preventing overfitting by halting before the model memorizes training data.

L1 and L2 Regularization
Adds penalty terms to the cost function to discourage complex models:

 * L1 regularization (also called LASSO) leads to sparse models by adding a penalty based on the absolute value of coefficients.
 * L2 regularization (also called ridge regression) encourages smaller, more evenly distributed weights by adding a penalty based on the square of the coefficients.

Dropout
Randomly ignores a subset of neurons during training, simulating training multiple neural network architectures to improve generalization.

Classification
Empirical learning of classifiers (from a finite data set) is always an underdetermined problem, because it attempts to infer a function of any $$x$$ given only examples $$x_1, x_2, \dots, x_n$$.

A regularization term (or regularizer) $$R(f)$$ is added to a loss function: $$\min_f \sum_{i=1}^{n} V(f(x_i), y_i) + \lambda R(f)$$ where $$V$$ is an underlying loss function that describes the cost of predicting $$f(x)$$ when the label is $$y$$, such as the square loss or hinge loss; and $$\lambda$$ is a parameter which controls the importance of the regularization term. $$R(f)$$ is typically chosen to impose a penalty on the complexity of $$f$$. Concrete notions of complexity used include restrictions for smoothness and bounds on the vector space norm.

A theoretical justification for regularization is that it attempts to impose Occam's razor on the solution (as depicted in the figure above, where the green function, the simpler one, may be preferred). From a Bayesian point of view, many regularization techniques correspond to imposing certain prior distributions on model parameters.

Regularization can serve multiple purposes, including learning simpler models, inducing models to be sparse and introducing group structure into the learning problem.

The same idea arose in many fields of science. A simple form of regularization applied to integral equations (Tikhonov regularization) is essentially a trade-off between fitting the data and reducing a norm of the solution. More recently, non-linear regularization methods, including total variation regularization, have become popular.

Generalization
Regularization can be motivated as a technique to improve the generalizability of a learned model.

The goal of this learning problem is to find a function that fits or predicts the outcome (label) that minimizes the expected error over all possible inputs and labels. The expected error of a function $$f_n$$ is: $$ I[f_n] = \int_{X \times Y} V(f_n(x),y) \rho(x,y) \, dx \, dy $$ where $$X$$ and $$Y$$ are the domains of input data $$x$$ and their labels $$y$$ respectively.

Typically in learning problems, only a subset of input data and labels are available, measured with some noise. Therefore, the expected error is unmeasurable, and the best surrogate available is the empirical error over the $$ N $$ available samples: $$ I_S[f_n] = \frac{1}{n} \sum_{i=1}^N V(f_n(\hat x_i), \hat y_i) $$ Without bounds on the complexity of the function space (formally, the reproducing kernel Hilbert space) available, a model will be learned that incurs zero loss on the surrogate empirical error. If measurements (e.g. of $$x_i$$) were made with noise, this model may suffer from overfitting and display poor expected error. Regularization introduces a penalty for exploring certain regions of the function space used to build the model, which can improve generalization.

Tikhonov regularization (ridge regression)
These techniques are named for Andrey Nikolayevich Tikhonov, who applied regularization to integral equations and made important contributions in many other areas.

When learning a linear function $$f$$, characterized by an unknown vector $$w$$ such that $$f(x) = w \cdot x$$, one can add the $$L_2$$-norm of the vector $$w$$ to the loss expression in order to prefer solutions with smaller norms. Tikhonov regularization is one of the most common forms. It is also known as ridge regression. It is expressed as: $$\min_w \sum_{i=1}^{n} V(\hat x_i \cdot w, \hat y_i) + \lambda \left\|w\right\|_2^2,$$ where $$(\hat x_i, \hat y_i), \, 1 \leq i \leq n,$$ would represent samples used for training.

In the case of a general function, the norm of the function in its reproducing kernel Hilbert space is: $$\min_f \sum_{i=1}^{n} V(f(\hat x_i), \hat y_i) + \lambda \left\|f\right\|_{\mathcal{H}}^2$$

As the $$L_2$$ norm is differentiable, learning can be advanced by gradient descent.

Tikhonov-regularized least squares
The learning problem with the least squares loss function and Tikhonov regularization can be solved analytically. Written in matrix form, the optimal $$w$$ is the one for which the gradient of the loss function with respect to $$w$$ is 0. $$\min_w \frac{1}{n} \left(\hat X w - Y\right)^\mathsf{T} \left(\hat X w - Y\right) + \lambda \left\|w\right\|_2^2$$ $$\nabla_w = \frac{2}{n} \hat X^\mathsf{T} \left(\hat X w - Y\right) + 2 \lambda w$$ $$0 = \hat X^\mathsf{T} \left(\hat X w - Y\right) + n \lambda w$$$$w = \left(\hat X^\mathsf{T} \hat X + \lambda n I\right)^{-1} \left(\hat X^\mathsf{T} Y\right)$$ where the third statement is a first-order condition.

By construction of the optimization problem, other values of $$w$$ give larger values for the loss function. This can be verified by examining the second derivative $$\nabla_{ww}$$.

During training, this algorithm takes $$O(d^3 + n d^2)$$ time. The terms correspond to the matrix inversion and calculating $$X^\mathsf{T} X$$, respectively. Testing takes $$O(nd)$$ time.

Early stopping
Early stopping can be viewed as regularization in time. Intuitively, a training procedure such as gradient descent tends to learn more and more complex functions with increasing iterations. By regularizing for time, model complexity can be controlled, improving generalization.

Early stopping is implemented using one data set for training, one statistically independent data set for validation and another for testing. The model is trained until performance on the validation set no longer improves and then applied to the test set.

Theoretical motivation in least squares
Consider the finite approximation of Neumann series for an invertible matrix $A$ where $$\left\| I - A \right\| < 1$$: $$\sum_{i=0}^{T-1} \left(I - A\right)^i \approx A^{-1}$$

This can be used to approximate the analytical solution of unregularized least squares, if $γ$ is introduced to ensure the norm is less than one. $$w_T = \frac{\gamma}{n} \sum_{i=0}^{T-1} \left( I - \frac{\gamma}{n} \hat X^\mathsf{T} \hat X \right)^i \hat X^\mathsf{T} \hat Y$$

The exact solution to the unregularized least squares learning problem minimizes the empirical error, but may fail. By limiting $T$, the only free parameter in the algorithm above, the problem is regularized for time, which may improve its generalization.

The algorithm above is equivalent to restricting the number of gradient descent iterations for the empirical risk $$I_s[w] = \frac{1}{2n} \left\| \hat X w - \hat Y \right\|^{2}_{\mathbb{R}^n}$$ with the gradient descent update: $$\begin{align} w_0 &= 0 \\[1ex] w_{t+1} &= \left(I - \frac{\gamma}{n} \hat X^\mathsf{T} \hat X\right) w_t + \frac{\gamma}{n} \hat X^\mathsf{T} \hat Y \end{align}$$

The base case is trivial. The inductive case is proved as follows: $$\begin{align} w_{T} &= \left(I - \frac{\gamma}{n} \hat X^\mathsf{T} \hat X\right) \frac{\gamma}{n} \sum_{i=0}^{T-2} \left(I - \frac{\gamma}{n} \hat X^\mathsf{T} \hat X \right)^i \hat X^\mathsf{T} \hat Y + \frac{\gamma}{n}\hat X^\mathsf{T} \hat Y \\[1ex] &= \frac{\gamma}{n} \sum_{i=1}^{T-1} \left(I - \frac{\gamma}{n} \hat X^\mathsf{T} \hat X \right)^i \hat X^\mathsf{T} \hat Y + \frac{\gamma}{n}\hat X^\mathsf{T} \hat Y \\[1ex] &= \frac{\gamma}{n} \sum_{i=0}^{T-1} \left(I - \frac{\gamma}{n} \hat X^\mathsf{T} \hat X \right)^i \hat X^\mathsf{T} \hat Y \end{align}$$

Regularizers for sparsity
Assume that a dictionary $$\phi_j$$ with dimension $$p$$ is given such that a function in the function space can be expressed as: $$f(x) = \sum_{j=1}^{p} \phi_j(x) w_j$$

Enforcing a sparsity constraint on $$w$$ can lead to simpler and more interpretable models. This is useful in many real-life applications such as computational biology. An example is developing a simple predictive test for a disease in order to minimize the cost of performing medical tests while maximizing predictive power.

A sensible sparsity constraint is the $L_0$ norm $$\|w\|_0$$, defined as the number of non-zero elements in $$w$$. Solving a $$L_0$$ regularized learning problem, however, has been demonstrated to be NP-hard.

The $L_1$ norm (see also Norms) can be used to approximate the optimal $L_0$ norm via convex relaxation. It can be shown that the $L_1$ norm induces sparsity. In the case of least squares, this problem is known as LASSO in statistics and basis pursuit in signal processing. $$\min_{w \in \mathbb{R}^p} \frac{1}{n} \left\|\hat X w - \hat Y \right\|^2 + \lambda \left\|w\right\|_{1}$$

$L_1$ regularization can occasionally produce non-unique solutions. A simple example is provided in the figure when the space of possible solutions lies on a 45 degree line. This can be problematic for certain applications, and is overcome by combining $L_1$ with $L_2$ regularization in elastic net regularization, which takes the following form: $$\min_{w \in \mathbb{R}^p} \frac{1}{n} \left\|\hat X w - \hat Y \right\|^2 + \lambda \left(\alpha \left\|w\right\|_1 + (1 - \alpha)\left\|w\right\|_2^2\right), \alpha \in [0, 1]$$

Elastic net regularization tends to have a grouping effect, where correlated input features are assigned equal weights.

Elastic net regularization is commonly used in practice and is implemented in many machine learning libraries.

Proximal methods
While the $L_1$ norm does not result in an NP-hard problem, the $L_1$ norm is convex but is not strictly differentiable due to the kink at x = 0. Subgradient methods which rely on the subderivative can be used to solve $L_1$ regularized learning problems. However, faster convergence can be achieved through proximal methods.

For a problem $$\min_{w \in H} F(w) + R(w)$$ such that $$F$$ is convex, continuous, differentiable, with Lipschitz continuous gradient (such as the least squares loss function), and $$R$$ is convex, continuous, and proper, then the proximal method to solve the problem is as follows. First define the proximal operator $$\operatorname{prox}_R(v) = \mathop\operatorname{argmin}_{w \in \mathbb{R}^D} \left\{ R(w) + \frac{1}{2} \left\|w - v\right\|^2 \right\}, $$ and then iterate $$w_{k+1} = \mathop\operatorname{prox}_{\gamma, R} \left(w_k - \gamma \nabla F(w_k)\right)$$

The proximal method iteratively performs gradient descent and then projects the result back into the space permitted by $$R$$.

When $$R$$ is the $L_{1}$ regularizer, the proximal operator is equivalent to the soft-thresholding operator, $$S_\lambda(v)f(n) = \begin{cases} v_i - \lambda, & \text{if }v_i > \lambda \\ 0, & \text{if } v_i \in [-\lambda, \lambda] \\ v_i + \lambda, & \text{if }v_i < - \lambda \end{cases}$$

This allows for efficient computation.

Group sparsity without overlaps
Groups of features can be regularized by a sparsity constraint, which can be useful for expressing certain prior knowledge into an optimization problem.

In the case of a linear model with non-overlapping known groups, a regularizer can be defined: $$R(w) = \sum_{g=1}^G \left\|w_g\right\|_2,$$ where $$\|w_g\|_2 = \sqrt{\sum_{j=1}^{|G_g|} \left(w_g^j\right)^2}$$

This can be viewed as inducing a regularizer over the $$L_2$$ norm over members of each group followed by an $$L_1$$ norm over groups.

This can be solved by the proximal method, where the proximal operator is a block-wise soft-thresholding function:

$$\operatorname{prox}\limits_{\lambda, R, g}(w_g) = \begin{cases} \left(1 - \dfrac{\lambda}{\left\|w_g\right\|_2}\right) w_g, & \text{if } \left\|w_g\right\|_2 > \lambda \\[1ex] 0, & \text{if } \|w_g\|_2 \leq \lambda \end{cases}$$

Group sparsity with overlaps
The algorithm described for group sparsity without overlaps can be applied to the case where groups do overlap, in certain situations. This will likely result in some groups with all zero elements, and other groups with some non-zero and some zero elements.

If it is desired to preserve the group structure, a new regularizer can be defined: $$R(w) = \inf \left\{ \sum_{g=1}^G \|w_g\|_2 : w = \sum_{g=1}^G \bar w_g \right\}$$

For each $$w_g$$, $$\bar w_g$$ is defined as the vector such that the restriction of $$\bar w_g$$ to the group $$g$$ equals $$w_g$$ and all other entries of $$\bar w_g$$ are zero. The regularizer finds the optimal disintegration of $$w$$ into parts. It can be viewed as duplicating all elements that exist in multiple groups. Learning problems with this regularizer can also be solved with the proximal method with a complication. The proximal operator cannot be computed in closed form, but can be effectively solved iteratively, inducing an inner iteration within the proximal method iteration.

Regularizers for semi-supervised learning
When labels are more expensive to gather than input examples, semi-supervised learning can be useful. Regularizers have been designed to guide learning algorithms to learn models that respect the structure of unsupervised training samples. If a symmetric weight matrix $$W$$ is given, a regularizer can be defined: $$R(f) = \sum_{i,j} w_{ij} \left(f(x_i) - f(x_j)\right)^2$$

If $$W_{ij}$$ encodes the result of some distance metric for points $$x_i$$ and $$x_j$$, it is desirable that $$f(x_i) \approx f(x_j)$$. This regularizer captures this intuition, and is equivalent to: $$R(f) = \bar f^\mathsf{T} L \bar f$$ where $$L = D- W$$ is the Laplacian matrix of the graph induced by $$W$$.

The optimization problem $$\min_{f \in \mathbb{R}^m} R(f), m = u + l$$ can be solved analytically if the constraint $$f(x_i) = y_i$$ is applied for all supervised samples. The labeled part of the vector $$f$$ is therefore obvious. The unlabeled part of $$f$$ is solved for by: $$\min_{f_u \in \mathbb{R}^u} f^\mathsf{T} L f = \min_{f_u \in \mathbb{R}^u} \left\{ f^\mathsf{T}_u L_{uu} f_u + f^\mathsf{T}_l L_{lu} f_u + f^\mathsf{T}_u L_{ul} f_l \right\}$$ $$\nabla_{f_u} = 2L_{uu}f_u + 2L_{ul}Y$$ $$f_u = L_{uu}^\dagger \left(L_{ul} Y\right)$$ The pseudo-inverse can be taken because $$L_{ul}$$ has the same range as $$L_{uu}$$.

Regularizers for multitask learning
In the case of multitask learning, $$T$$ problems are considered simultaneously, each related in some way. The goal is to learn $$T$$ functions, ideally borrowing strength from the relatedness of tasks, that have predictive power. This is equivalent to learning the matrix $$W: T \times D$$.

Sparse regularizer on columns
$$R(w) = \sum_{i=1}^D \left\|W\right\|_{2,1}$$

This regularizer defines an L2 norm on each column and an L1 norm over all columns. It can be solved by proximal methods.

Nuclear norm regularization
$$R(w) = \left\|\sigma(W)\right\|_1$$ where $$\sigma(W)$$ is the eigenvalues in the singular value decomposition of $$W$$.

Mean-constrained regularization
$$R(f_1 \cdots f_T) = \sum_{t=1}^T \left\|f_t - \frac{1}{T} \sum_{s=1}^T f_s \right\|_{H_k}^2$$

This regularizer constrains the functions learned for each task to be similar to the overall average of the functions across all tasks. This is useful for expressing prior information that each task is expected to share with each other task. An example is predicting blood iron levels measured at different times of the day, where each task represents an individual.

Clustered mean-constrained regularization
$$R(f_1 \cdots f_T) = \sum_{r=1}^C \sum_{t \in I(r)} \left\|f_t - \frac{1}{I(r)} \sum_{s \in I(r)} f_s\right\|_{H_k}^2$$ where $$I(r)$$ is a cluster of tasks.

This regularizer is similar to the mean-constrained regularizer, but instead enforces similarity between tasks within the same cluster. This can capture more complex prior information. This technique has been used to predict Netflix recommendations. A cluster would correspond to a group of people who share similar preferences.

Graph-based similarity
More generally than above, similarity between tasks can be defined by a function. The regularizer encourages the model to learn similar functions for similar tasks. $$R(f_1 \cdots f_T) = \sum_{t,s=1, t \neq s}^\mathsf{T} \left\| f_t - f_s \right\|^2 M_{ts} $$ for a given symmetric similarity matrix $$M$$.

Other uses of regularization in statistics and machine learning
Bayesian learning methods make use of a prior probability that (usually) gives lower probability to more complex models. Well-known model selection techniques include the Akaike information criterion (AIC), minimum description length (MDL), and the Bayesian information criterion (BIC). Alternative methods of controlling overfitting not involving regularization include cross-validation.

Examples of applications of different methods of regularization to the linear model are:

title: Regularization (mathematics)


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Regularization (physics)

In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a "cutoff", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for (and requires) the possibility of separation of scales that "new physics" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an "effective theory" within its intended scale of use.

It is distinct from renormalization, another technique to control infinities without assuming new physics, by adjusting for self-interaction feedback.

Regularization was for many decades controversial even amongst its inventors, as it combines physical and epistemological claims into the same equations. However, it is now well understood and has proven to yield useful, accurate predictions.

Overview
Regularization procedures deal with infinite, divergent, and nonsensical expressions by introducing an auxiliary concept of a regulator (for example, the minimal distance $$\epsilon$$ in space which is useful, in case the divergences arise from short-distance physical effects). The correct physical result is obtained in the limit in which the regulator goes away (in our example, $$\epsilon\to 0$$), but the virtue of the regulator is that for its finite value, the result is finite.

However, the result usually includes terms proportional to expressions like $$1/ \epsilon$$ which are not well-defined in the limit $$\epsilon\to 0$$. Regularization is the first step towards obtaining a completely finite and meaningful result; in quantum field theory it must be usually followed by a related, but independent technique called renormalization. Renormalization is based on the requirement that some physical quantities — expressed by seemingly divergent expressions such as $$1/ \epsilon$$ — are equal to the observed values. Such a constraint allows one to calculate a finite value for many other quantities that looked divergent.

The existence of a limit as ε goes to zero and the independence of the final result from the regulator are nontrivial facts. The underlying reason for them lies in universality as shown by Kenneth Wilson and Leo Kadanoff and the existence of a second order phase transition. Sometimes, taking the limit as ε goes to zero is not possible. This is the case when we have a Landau pole and for nonrenormalizable couplings like the Fermi interaction. However, even for these two examples, if the regulator only gives reasonable results for $$\epsilon \gg \hbar c/\Lambda$$ (where $$\Lambda$$ is a superior energy cuttoff) and we are working with scales of the order of $$\hbar c/\Lambda'$$, regulators with $$\hbar c/\Lambda \ll \epsilon \ll \hbar c/\Lambda'$$ still give pretty accurate approximations. The physical reason why we can't take the limit of ε going to zero is the existence of new physics below Λ.

It is not always possible to define a regularization such that the limit of ε going to zero is independent of the regularization. In this case, one says that the theory contains an anomaly. Anomalous theories have been studied in great detail and are often founded on the celebrated Atiyah–Singer index theorem or variations thereof (see, for example, the chiral anomaly).

Classical physics example
The problem of infinities first arose in the classical electrodynamics of point particles in the 19th and early 20th century.

The mass of a charged particle should include the mass–energy in its electrostatic field (electromagnetic mass). Assume that the particle is a charged spherical shell of radius $r_{e}$. The mass–energy in the field is

 * $$m_\mathrm{em} = \int {1\over 2}E^2 \, dV = \int_{r_e}^{\infty} \frac{1}{2} \left( {q\over 4\pi r^2} \right)^2 4\pi r^2 \, dr = {q^2 \over 8\pi r_e},$$

which becomes infinite as $r_{e} → 0$. This implies that the point particle would have infinite inertia, making it unable to be accelerated. Incidentally, the value of $r_{e}$ that makes $$m_{\mathrm{em}}$$ equal to the electron mass is called the classical electron radius, which (setting $$q = e$$ and restoring factors of $c$ and $$\varepsilon_0$$) turns out to be

 * $$r_e = {e^2 \over 4\pi\varepsilon_0 m_{\mathrm{e}} c^2} = \alpha {\hbar\over m_{\mathrm{e}} c} \approx 2.8 \times 10^{-15}\ \mathrm{m}.$$

where $$\alpha \approx 1/137.040$$ is the fine-structure constant, and $$\hbar/m_{\mathrm{e}} c$$ is the Compton wavelength of the electron.

Regularization: Classical physics theory breaks down at small scales, e.g., the difference between an electron and a point particle shown above. Addressing this problem requires new kinds of additional physical constraints. For instance, in this case, assuming a finite electron radius (i.e., regularizing the electron mass-energy) suffices to explain the system below a certain size. Similar regularization arguments work in other renormalization problems. For example, a theory may hold under one narrow set of conditions, but due to calculations involving infinities or singularities, it may breakdown under other conditions or scales. In the case of the electron, another way to avoid infinite mass-energy while retaining the point nature of the particle is to postulate tiny additional dimensions over which the particle could 'spread out' rather than restrict its motion solely over 3D space. This is precisely the motivation behind string theory and other multi-dimensional models including multiple time dimensions. Rather than the existence of unknown new physics, assuming the existence of particle interactions with other surrounding particles in the environment, renormalization offers an alternative strategy to resolve infinities in such classical problems.

Specific types
Specific types of regularization procedures include
 * Dimensional regularization
 * Pauli–Villars regularization
 * Lattice regularization
 * Zeta function regularization
 * Causal regularization
 * Hadamard regularization

Conceptual problem
Perturbative predictions by quantum field theory about quantum scattering of elementary particles, implied by a corresponding Lagrangian density, are computed using the Feynman rules, a regularization method to circumvent ultraviolet divergences so as to obtain finite results for Feynman diagrams containing loops, and a renormalization scheme. Regularization method results in regularized n-point Green's functions (propagators), and a suitable limiting procedure (a renormalization scheme) then leads to perturbative S-matrix elements. These are independent of the particular regularization method used, and enable one to model perturbatively the measurable physical processes (cross sections, probability amplitudes, decay widths and lifetimes of excited states). However, so far no known regularized n-point Green's functions can be regarded as being based on a physically realistic theory of quantum-scattering since the derivation of each disregards some of the basic tenets of conventional physics (e.g., by not being Lorentz-invariant, by introducing either unphysical particles with a negative metric or wrong statistics, or discrete space-time, or lowering the dimensionality of space-time, or some combination thereof). So the available regularization methods are understood as formalistic technical devices, devoid of any direct physical meaning. In addition, there are qualms about renormalization. For a history and comments on this more than half-a-century old open conceptual problem, see e.g.

Pauli's conjecture
As it seems that the vertices of non-regularized Feynman series adequately describe interactions in quantum scattering, it is taken that their ultraviolet divergences are due to the asymptotic, high-energy behavior of the Feynman propagators. So it is a prudent, conservative approach to retain the vertices in Feynman series, and modify only the Feynman propagators to create a regularized Feynman series. This is the reasoning behind the formal Pauli–Villars covariant regularization by modification of Feynman propagators through auxiliary unphysical particles, cf. and representation of physical reality by Feynman diagrams.

In 1949 Pauli conjectured there is a realistic regularization, which is implied by a theory that respects all the established principles of contemporary physics. So its propagators (i) do not need to be regularized, and (ii) can be regarded as such a regularization of the propagators used in quantum field theories that might reflect the underlying physics. The additional parameters of such a theory do not need to be removed (i.e. the theory needs no renormalization) and may provide some new information about the physics of quantum scattering, though they may turn out experimentally to be negligible. By contrast, any present regularization method introduces formal coefficients that must eventually be disposed of by renormalization.

Opinions
Paul Dirac was persistently, extremely critical about procedures of renormalization. In 1963, he wrote, "… in the renormalization theory we have a theory that has defied all the attempts of the mathematician to make it sound. I am inclined to suspect that the renormalization theory is something that will not survive in the future,…" He further observed that "One can distinguish between two main procedures for a theoretical physicist. One of them is to work from the experimental basis ... The other procedure is to work from the mathematical basis. One examines and criticizes the existing theory. One tries to pin-point the faults in it and then tries to remove them. The difficulty here is to remove the faults without destroying the very great successes of the existing theory."

Abdus Salam remarked in 1972, "Field-theoretic infinities first encountered in Lorentz's computation of electron have persisted in classical electrodynamics for seventy and in quantum electrodynamics for some thirty-five years. These long years of frustration have left in the subject a curious affection for the infinities and a passionate belief that they are an inevitable part of nature; so much so that even the suggestion of a hope that they may after all be circumvented - and finite values for the renormalization constants computed - is considered irrational."

However, in Gerard ’t Hooft’s opinion, "History tells us that if we hit upon some obstacle, even if it looks like a pure formality or just a technical complication, it should be carefully scrutinized. Nature might be telling us something, and we should find out what it is."

The difficulty with a realistic regularization is that so far there is none, although nothing could be destroyed by its bottom-up approach; and there is no experimental basis for it.

Minimal realistic regularization
Considering distinct theoretical problems, Dirac in 1963 suggested: "I believe separate ideas will be needed to solve these distinct problems and that they will be solved one at a time through successive stages in the future evolution of physics. At this point I find myself in disagreement with most physicists. They are inclined to think one master idea will be discovered that will solve all these problems together. I think it is asking too much to hope that anyone will be able to solve all these problems together. One should separate them one from another as much as possible and try to tackle them separately. And I believe the future development of physics will consist of solving them one at a time, and that after any one of them has been solved there will still be a great mystery about how to attack further ones."

According to Dirac, "Quantum electrodynamics is the domain of physics that we know most about, and presumably it will have to be put in order before we can hope to make any fundamental progress with other field theories, although these will continue to develop on the experimental basis."

Dirac’s two preceding remarks suggest that we should start searching for a realistic regularization in the case of quantum electrodynamics (QED) in the four-dimensional Minkowski spacetime, starting with the original QED Lagrangian density.

The path-integral formulation provides the most direct way from the Lagrangian density to the corresponding Feynman series in its Lorentz-invariant form. The free-field part of the Lagrangian density determines the Feynman propagators, whereas the rest determines the vertices. As the QED vertices are considered to adequately describe interactions in QED scattering, it makes sense to modify only the free-field part of the Lagrangian density so as to obtain such regularized Feynman series that the Lehmann–Symanzik–Zimmermann reduction formula provides a perturbative S-matrix that: (i) is Lorentz-invariant and unitary; (ii) involves only the QED particles; (iii) depends solely on QED parameters and those introduced by the modification of the Feynman propagators—for particular values of these parameters it is equal to the QED perturbative S-matrix; and (iv) exhibits the same symmetries as the QED perturbative S-matrix. Let us refer to such a regularization as the minimal realistic regularization, and start searching for the corresponding, modified free-field parts of the QED Lagrangian density.

Transport theoretic approach
According to Bjorken and Drell, it would make physical sense to sidestep ultraviolet divergences by using more detailed description than can be provided by differential field equations. And Feynman noted about the use of differential equations: "... for neutron diffusion it is only an approximation that is good when the distance over which we are looking is large compared with the mean free path. If we looked more closely, we would see individual neutrons running around." And then he wondered, "Could it be that the real world consists of little X-ons which can be seen only at very tiny distances? And that in our measurements we are always observing on such a large scale that we can’t see these little X-ons, and that is why we get the differential equations? ... Are they [therefore] also correct only as a smoothed-out imitation of a really much more complicated microscopic world?"

Already in 1938, Heisenberg proposed that a quantum field theory can provide only an idealized, large-scale description of quantum dynamics, valid for distances larger than some fundamental length, expected also by Bjorken and Drell in 1965. Feynman's preceding remark provides a possible physical reason for its existence; either that or it is just another way of saying the same thing (there is a fundamental unit of distance) but having no new information.

Hints at new physics
The need for regularization terms in any quantum field theory of quantum gravity is a major motivation for physics beyond the standard model. Infinities of the non-gravitational forces in QFT can be controlled via renormalization only but additional regularization - and hence new physics—is required uniquely for gravity. The regularizers model, and work around, the breakdown of QFT at small scales and thus show clearly the need for some other theory to come into play beyond QFT at these scales. A. Zee (Quantum Field Theory in a Nutshell, 2003) considers this to be a benefit of the regularization framework—theories can work well in their intended domains but also contain information about their own limitations and point clearly to where new physics is needed.

title: Regularization (physics)


text:
Comitatenses

The comitatenses and later the palatini were the units of the field armies of the late Roman Empire. They were the soldiers that replaced the legionaries, who had formed the backbone of the Roman military since the late republic.

Organization
Units such as the Joviani and Herculiani had 5,000 soldiers and 726–800 cavalrymen. Many units' sizes would vary. There were three types of units, the heavy infantry, medium infantry, and light infantry. The comitatenses were the heavy infantry. The auxiliaries, auxilia palatina, and the peltasts were the medium infantry, and the psiloi were the light infantry. Comitatenses regiments consisted of 1,024 soldiers. Comitatenses legions could consist of 6,000 to 7,000 soldiers. Some of these soldiers would be lightly armed, while others would be heavily armed. During a battle the army would divide into 3-4 divisions. The army might use a double phalanx to protect its rear. Reserves would be located behind or between each division.

Command structure

 * Comes
 * Primicerius (Commander of the first cohort)
 * Ducenarius (Commander of 200 soldiers)
 * Centenarius (Commander of 100 soldiers)
 * Centenarius Protector
 * Centenarius Ordinarius
 * Centenarius Ordinatus
 * Biarchus (former Optio)
 * Semisallis

Tactics and usage
In the Late Roman Empire the army was divided into two major units, the limitanei border guards and mobile armies consisting of comitatenses. The limitanei would deal with smaller raids, or, in the case of larger invasions, try to defend or stall long enough for the comitatenses legions to arrive. These comitatenses would be grouped into field armies. This strategy has been described as "defense in depth." To conserve manpower, the general would do his best to avoid a pitched battle. Rather than attack the enemy, the legions would form a shield wall and wait for the enemy to attack the Romans. The Romans would use their superior coordination to defeat the enemy. The Emperor would command a comitatenses field army to put down rebellions.

Terminology
Comitatenses is the Latin nominative plural of comitatensis, an adjective derived from comitatus ('company, party, suite'; in this military context it came to the novel meaning of 'the field army'), itself derived from comes ('companion', but hence specific historical meanings, military and civilian).

However, historically it became the accepted (substantiated) name for those Roman imperial troops (legions and auxiliary) which were not merely garrisoned at a limes (fortified border, on the Rhine and Danube in Europe and near Persia and the desert tribes elsewhere)—the limitanei or ripenses, i.e. "along the shores"—but more mobile line troops; furthermore there were second line troops, named pseudocomitatenses, former limitanei attached to the comitatus; palatini, elite ("palace") units typically assigned to the magister militum; and the scholae palatinae of actual palace guards, usually under the magister officiorum, a senior court official of the Late Empire.

List of comitatenses units
Among the comitatenses units listed by Notitia Dignitatum are:

Under the Western magister peditum

 * 1) Undecimani (originally formed from the Legio XI Claudia pia fidelis, Moesia);
 * 2) Secundani Italiciani (originally formed from the Legio II Italica, Africa);
 * 3) Tertiani Italica (originally formed from the Legio III Italica, Illyricum);
 * 4) Tertia Herculea, Illyricum;
 * 5) Secunda Britannica, Gallias;
 * 6) Tertia Iulia Alpina, Italia;
 * 7) Prima Flavia Pacis, Africa;
 * 8) Secunda Flavia Virtutis, Africa;
 * 9) Tertia Flavia Salutis, Africa;
 * 10) Secunda Flavia Constantiniana, Africa Tingitania;
 * 11) Tertioaugustani (Legio III Augusta);

Under the Magister Militum per Orientem

 * 1) Quinta Macedonica (Legio V Macedonica);
 * 2) Septima gemina (Legio VII Gemina);
 * 3) Decima gemina (Legio X Gemina);
 * 4) Prima Flavia Constantia;
 * 5) Secunda Flavia Virtuti, Africa;
 * 6) Secunda Felix Valentis Thebaeorum;
 * 7) Prima Flavia Theodosiana;

Under the Magister Militum per Thracias

 * 1) Prima Maximiana Thebaeorum;
 * 2) Tertia Diocletiana Thebaeorum;
 * 3) Tertiodecimani (Legio XIII Gemina?);
 * 4) Quartodecimani (Legio XIV Gemina Martia Victrix?);
 * 5) Prima Flavia gemina;
 * 6) Secunda Flavia gemina.

title: Comitatenses


text:
Wikipedia:Articles for deletion/Manpon

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was delete. Sjakkalle (Check!)  14:09, 17 Jun 2005 (UTC)

Manpon
neologism from the Man Show, delete --nixie 12:00, 8 Jun 2005 (UTC)
 * Delete neologism Tobycat 04:07, 9 Jun 2005 (UTC)
 * Delete neologism. carmeld1 04:55, 9 Jun 2005 (UTC)
 * Delete neologism. JamesBurns 07:14, 9 Jun 2005 (UTC)
 * This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages.  Please do not edit this page .

title: Wikipedia:Articles for deletion/Manpon


text:
Talk:Kermit Roosevelt

Model "T" Ford Not "Ancient" during WWI
the Ford Model T wasn't "ancient" during WWI... It was a current high production vehicle at the zenith of its model run. [unsigned]

Expanded Article and Added Photos
So towering was Theodore Roosevelt that his children, and their accomplishments, trials and tribulations have often been overlooked in the popular mind. I've expanded on the articles on Kermit as well as as "Archie" to show what unique and gifted individuals they were.SimonATL 13:42, 28 February 2006 (UTC)

Kermit's Fight with Depression
Added info on family history of depression that seems to be traceable to his grandmother, Martha Bulloch's side of the family. SimonATL 13:42, 28 February 2006 (UTC)

Problem
This page is difficult to read; there are too many pictures clumped together. I don't have the wikifu to fix it myself, so if someone could possibly do some rearranging...? 64.211.50.218roguesparks

Request for further information on circumstances of decline.
The article lacks specifics regarding his plunge into depression that I think would be of great interest.

Specifically, what were the "problems" referred to that drove him further to alcoholism upon his medical discharge? That he had dishonored his family name by not being able to complete his duties in war? After a career that reads like a success story including accomplishments achieved while still on military active duty, the reader is left to speculate.

Also, who and to what extent were these 'acquaintances' referred to as being such a negative influence on his life that FDR felt compelled enough to send him off to Alaska? This seems to be such an extreme measure of forced isolation that requires some explanation. Ydef 08:37, 3 April 2007 (UTC)

 * Here was Kermit's basic problem. He was highly emotional and extremely dependent on his father, Theodore Roosevelt and when he died, he wrote that he felt like he had lost an island in a sea or uncertainty or something to that idea. As long as his dad was alive, he felt secure in life. He was his mother's favorite.  When you study the Roosevelts you learn that TR's mother's family, the Bullochs seemed to really carry the "depression gene."  All of TR's children had it to some extent. TR, himself had it - especially in periods of inactivity. This is why he wrote that "black care (depression or the blues in modern terms) seldom sits (on a horse) behind a rider whose pace (in life) is fast enough.  TR's daughter, Alice Roosevelt Longworth in her interviews that eventually became the basis of the book, "Conversations with Mrs. L" also said clearly, "my father had this tendency toward depression too. I've spoken personally to several modern-day Roosevelt family members and one of them, who is quite well known, said to me, "Well, I think people make TOO much of this depression business, personally. I just don't see it."  Well he doesn't see it because he doesn't WANT to see it, frankly.  TR's mother [Martha Bulloch Roosevelt]] used to be so overcome by bouts of depression that she would lock herself in her room for a week and the maids would just shove her meals under her door. She was either up or down.  When you combine this natural tendency toward depression with the circumstances of Kermit's loss of both his beloved father and his closest sibling, Quentin Roosevelt and then add in the fact that he soon became totally estranged from his wife, Belle, but in deference to the Roosevelt family traditions, could simply NOT divorce her, all those things were commulative and mutually supportive. I think he turned to drink as a form of deadening the pain of being unable to live up to his father's high standards. He carried on an affair with the "real love" of his life for over 20 years being unable to divorce Belle.  He would disappear literally for weeks and months at a time with his mistress. His wife and his brothers would then put out a dragnet even bringing in the FBI to locate him. By the time WWII came around, they had to send those agents looking for him. He went back into service in the British Army, but they soon had to discharge him for ill health. He was overweight and was having recurring bouts of  malaria and self-medicating the pain with alcohol. His wife then intervened with the US President, FDR to get him a commission in the US Army. Not knowing what to do with him, they sent him off to Alaska with no really useful job description. Isolation + depression + inactivity = a deadly combination. Shortly before committing suicide, he spoke of a poem that discussed suicidal thoughts and the "peace" that a gun would bring to personal suffering.  His mother, [Edith Kermit Roosevelt]] was never told of the suicide. Instead she was told that he died of a heart attack.  A tragic life really. In modern times, he might have found some professional help.  In his day, it simply didn't exist. He really was an amazing person. Incredible courage. Native intellect, sensitive. A gifted linguist. So sad he was unable to overcome those personal demons. SimonATL (talk) 02:18, 7 August 2008 (UTC)

 * Thank you SimonATL for providing the insight to my question and more depth to this article that it had previously lacked.  You explanation is very much appreciated. eYeDEF (talk) 15:39, 2 January 2009 (UTC)

 * Yes, all very interesting, and in scholarly quality, on par with the rest of the article—which is comparably unsourced, editorial WP:Original Research, and therefore (last I checked) disallowed as encyclopedic content. Perhaps come back with sources, or quotes from sources, so there is material usable for advancing the article. Le Prof 71.201.62.200 (talk) 03:59, 17 June 2015 (UTC)
 * I don't know how to place this correctly, but I just read this on pg. 249 of Yoram Hazony's "The Jewish State" from 2000: "...Committee for Justice and Peace in the Holy Land, whose executive director Kermit Roosevelt was one of the architects of the anti-Zionist policies of the State Department and the CIA."
 * FWIW. 93.173.55.129 (talk) 16:56, 8 May 2023 (UTC)

"Template:DEFAUTSORT:Roosevelt, Kermit"
I noticed that when this is categorized, it gets put under the K section instead of the R (see here). I'm guessing this has something to do with the "Template:DEFAUTSORT:Roosevelt, Kermit" link near the bottom of this page. I won't try to fix this because I don't know how, but someone who does know should. 66.234.32.20 19:35, 19 April 2007 (UTC)

"River of Doubt?"
What is this crap posted under his death? It's unsourced and sounds like some odd inspirational email or church tract more than it does a wikipedia entry. I've no wikifu of my own, somebody fix it. --Bluedeanie (talk) 05:21, 21 April 2010 (UTC)
 * Consistent with this opinion/assessment, I have marked it as possibly plagiarised. Le Prof 71.201.62.200 (talk) 04:03, 17 June 2015 (UTC)

Removed Information about wrong Kermit Roosevelt
The following information is about his son, Kermit Roosevelt Jr., [and so was r]emoved from page.""Roosevelt's role in the 1953 CIA coup to overthrow the government of Mohammed Mossadegh in Iran becomes part of the plot of Nick & Jake, a novel by Tad Richards and Jonathan Richards, published in 2012 by Arcade Publishing. In the novel, The Roosevelt character becomes Larry Darrell, the hero of Somerset Maugham's The Razor's Edge.""

— Preceding unsigned comment added by Bill.budington (talk • contribs) 21:45, 25 June 2012 (UTC)

Moving material inappropriate to this article here
...for transfer to another article. It was inappropriate for a single child of the title person to have a long paragraph, and the sources for that inappropriate volume of content were poor, and incomplete. This information can be moved to the article on his son, if the sources are completed and verified:""Kermit Roosevelt, Jr. (1916–2000) was the mastermind of the Central Intelligence Agency's (CIA) Operation Ajax, which orchestrated the coup against Iran's democratically-elected Mohammed Mossadegh administration, and returned Mohammad Reza Pahlavi, the Shah of Iran, to Iran's Peacock Throne in August 1953 for the purpose of returning Western control of Middle Eastern oil supplies. ""

Please do not reintroduce the text unless similar amounts of explanatory information is added for each child, and good sources are provided for all material. Le Prof 71.201.62.200 (talk) 03:49, 17 June 2015 (UTC)

title: Talk:Kermit Roosevelt


text:
Talk:A Contract with God

Publication date
Indicia of copies indicate the work was first copyrighted in 1978, and Eisner's webpage also lists that as year of publication. However, some web sources indicate a publication date of 1976, and Eddie Campbell's Alec: How To Be An Artist gave the date as October of 1977. Hiding 09:16, 8 Jun 2005 (UTC)

Move
I moved this page again to bring into line with the naming convention, since the work's full title is A Contract with God: And Other Tenement Stories. A Contract with God and A Contract With God both redirect here. Hiding 09:06, 8 Jun 2005 (UTC)

And I've put it back where Wikipedia naming conventions actually recommend it belongs. Tverbeek 12:01, 8 Jun 2005 (UTC)

Jewish perspective content
Although I ain't really a scholar on Judaism myself, but I saw the comments on the WikiProject Judaism talk page, and as someone kind of interested in comics, decided to have a little look-see.

The content is basically sound, and I personally have no reservations whatsoever about having individuals with mainstream literary credentials included in such articles. Having said that, I have some reservations about the exact content added. I am not myself sure, for instance, that the phrase "not a recognizably Jewish story" really adds much, because, honestly, I'm not sure that anyone ever said it was necessarily a "Jewish story," but maybe just a story about American Jews of a particular era, which isn't quite the same thing. A lot of the other content added also seems to deal primarily if not exclusively with the idea of Jewishness as well, and the same reservations more or less apply there - that they seem to be criticizing the story on its apparent lack of understanding of Judaism. Maybe I'm wrong, but I think maybe a lot of the possibly real people Eisner used as the basis for his characters might have been comparatively "devoid of Jewish learning or insight," and on that basis the material might accuraately represent them, even if Klingenstein finds it a disappointment.

The idea that Hersh unrealistically struggles with basic Jewish teaching does seem to me to be potentially the most encyclopedic material included, because it is talking about the story itself as a story, rather than as a story from the Jewish perspective. I might revise the paragraph to start with that material, and then maybe edit down the other material to maybe saying something to the effect that the characters are presented as being what a possibly Jewish scholar? said are "devoid of Jewish learning and insight," with perhaps a few examples. But, again, the story is allegedly more or less autobiographical, and it could well be that the real people used as bases for the characters might not have been particularly well informed Jews themselves for all I know. Just a few ideas, anyway. John Carter (talk) 15:24, 17 March 2013 (UTC)

 * Thanks for your feedback. I'll try rearranging the paragraph along those lines.
 * As to the last point you made, I think that'd be fair to apply to the other characters in the book, but Hersh is depicted as particularly pious, and I think the criticism might come from that—that someone who was that religious wouldn't have struggled with such an (allegedly) elementary point. "Cookalein" is an autobiographical story, but "A Contract with God" is autobiographical only in the base situation, where both Hersh and Eisner lost their teenaged daughters.  I think the idea is that Eisner channeled his feelings through Hersh, but the character of Hersh himself was not actually based on Eisner (who was born in the US, and, I get the feeling, was not devoutly Jewish(?) ).  Curly Turkey (gobble) 21:32, 17 March 2013 (UTC)
 * I don't know much about Eisner's religious life - I think the editors at the Comics project probably know more. I know he dealt with other Jewish issues in his other late work, but it could be possible that he might not have been particularly religiously Jewish. Alternately, it might be that the New Yorkers he grew up around might not have been, and I personally think that the latter might be the more likely. For all I know, this particular episode might be based on one or more real situation Eisner knew of as a child, which he in some way "edited down" to the story. John Carter (talk) 22:16, 17 March 2013 (UTC)
 * Right. Well, I guess this is why I was asking for help—I know little about the religious life, and much less about the religious lives of American Jews, so I wasn't confident if I was summing up the criticism adequately, or if I was giving it undue weight.  I'll post something at WikiProject Comics.  It looks like you've already posted there.  Curly Turkey (gobble) 22:54, 17 March 2013 (UTC)
 * I've rewritten refocused it, cutting it down to roughly half the length it was. Curly Turkey (gobble) 23:03, 17 March 2013 (UTC)
 * Schumacher, gives a lot of information about Eisner's relationship with Judaism. Neither he nor his parents seem to have been particularly religious. User:Maunus ·ʍaunus·snunɐw· 00:24, 28 January 2014 (UTC)

Tellement truc unusité
Je recherche une liscense pour mes photos. Mes la photo en particulier est une photo de moi avec la lumière venant du soleil.Ou l"on peux voir une main de lumière me toucher le front. Puis je tombe sur cette pages mettant en lumière Le livres Contrat avec Dieu...... Bref sa m"étonne plus mais je devais marqué ce monent Ednozel (talk) 01:46, 6 December 2015 (UTC)

First "modern" graphic novel
I'd like to improve some misleading descriptions in the Reception and legacy section. Namely, the first sentence: "A Contract with God has frequently, though erroneously, been cited as the first graphic novel;...." The statement is both right and wrong, however the "wrong" part is missing.

For example, W.W. Norton explains pretty clearly that it was, in fact, considered the first "modern graphic novel," which it contrasts with the then traditional "comic-book format." This fact is also noted in Paul Levitz's Will Eisner: Champion of the Graphic Novel (Abrams, 2015), where Levitz notes that Eisner's obituary in the NY Times described him as having "created ... the first modern graphic novel." So the key word missing is "modern," which makes it somewhat erroneous to say that the book was "erroneously" cited as being the "first graphic novel." Expanding that aspect would be useful. Thoughts? --Light show (talk) 21:29, 6 December 2015 (UTC)

BTW, this is how Schumacher, who is cited throughout the article, explains the difference: ""Using this knowledge of publishing, Eisner created a book that didn't look like a comic book. It was the size of a trade paperback, had lettering on its spine, boasted a cover design that didn't scream 'children's book' to bookstore owners and librarians, and provided an interior that eschewed the panel-by-panel artistry typical of comic books." (p. 204) --Light show (talk) 21:44, 6 December 2015 (UTC)"

 * I have to wonder what "modern" is supposed to mean in this context. There were books that were appearing in the few years before Contract that were advertised as graphic novels: aside from The First Kingdom in 1974, in 1976 there were Bloodstar, Chandler: Red Tide, and George Metzger's Beyond Time and Again.  How "modern" is "modern"?  Further muddying the waters is the fact the definition of the term "graphic novel" has never been set in stone, and in the 21st is getting closer and closer to be a synonym for "comics" in general.  What does "modern graphic novel" mean in that context? Curly Turkey 🍁 ¡gobble! 21:46, 6 December 2015 (UTC)

 * The meaning of "modern" has always been disputed, whether for modern art, architecture or furniture. All we can do is cite reliable sources if they use the term in the context of a subject. And we can cite other sources who dispute the use of the term in that context. It doesn't need to be set in stone to cite it. Comic writer and historian Michael Gilbert agreed that the issue "was one of definition." He noted that the older Classics Illustrated comic books could be described as being graphic novels. That's why describing the different physical format of Contract as more of a paperback book would be helpful.--Light show (talk) 22:06, 6 December 2015 (UTC)
 * Is that what the sources say they mean by "modern", or your interpretation of it? There are certainly plenty of precursors—a striking parallel being Harvey Kurtzman's Jungle Book (1959, a four-story paperback aimed at mature audiences by a contemporary and friend of Eisner's).  I think we'd need to demonstrate that there is a general consensus that Contract is "the first modern graphic novel", and I doubt there is such a consensus.  We also have to be careful what comics "scholarship" has to say, as comics "scholars" are notoriously sloppy researchers (witness how many sources continue to claim Eisner first used the term "graphic novel", or that claim comics is an American artform). Curly Turkey 🍁 ¡gobble! 23:14, 6 December 2015 (UTC)
 * It sounds like you're creating a new guideline, namely that a reliable source can only be cited after there is consensus. And I wasn't sure about your question. I didn't interpret anything; the Gilbert comment came from Schumacher. In any case, if source A says calls something "modern," "first" or a "graphic novel," and source B says it isn't, that's all fine, so long as their opinions are attributed. --Light show (talk) 23:43, 6 December 2015 (UTC)
 * When reliacle sources disagree about a fact it is an editorial decision how to describe it in the article, whether to privilege one view as a consensus view or take a neutral stance. I think in this case I would recommend something along the lines of "often considered the first modern graphic novel", to accomodate the fact that some disagree on technical arguments with the fact that it clearly is the first well known and broadly popular graphic novel, and that it is very commonly described as such.·maunus · snunɐɯ· 23:48, 6 December 2015 (UTC)
 * Light show: "Is sounds like you're creating a new guideline, namely that a reliable source can only be cited after there is consensus."—no, you misread my comment. "Consensus" refers to "scholarly consensus".
 * "if source A says calls something "modern," "first" or a "graphic novel," and source B says it isn't, that's all fine, so long as their opinions are attributed."—so we should create an exhaustive list of people's opinions and their refutations, as long as we can cite them? How does that serve the reader?
 * ·maunus: The article already states that it is the book that popularized the term and describes the background behind the term. Why is that not sufficient?  Is the article unclear on the book's place in comics history without loading up the article with disputed peacocky statements? Curly Turkey 🍁 ¡gobble! 00:11, 7 December 2015 (UTC)
 * I dont think clearly stating the significance of a topic is peacockery. Currently the lead says that "although the term graphic novel did not originate with will eisner the book is credited with popularizing its use". I would call that an understatement of the fact that it is widely considered the world's first significant graphic novel. It would not be peacockery to state "the work is often describe as the first graphic novel", and then put into a footnote that the term did not originate with Eisner and that two relatively obscure works had previously used it. We discussed this in the GA review and I still think you are letting your own distaste for the work overshadow the way that the general public views it.·maunus · snunɐɯ· 00:19, 7 December 2015 (UTC)
 * "the world's first significant graphic novel"—uh, no, maunus. Surely you are aware that book-length comics were well established in Europe and Japan decades before Anglo comics managed to get in on the game.
 * "two relatively obscure works had previously used it"—two? You might want to check your facts.  At least one in 1974 and three in 1976 (just off the top of my head) use the term "graphic novel".  Plenty of others had the form without using the term, such as Blackmark in 1971.  Contract was an important watermark, but it's hard to argue it was the "first" anything, as Tenebrae agreed at the GAN.
 * "letting your own distaste for the work": I think it's Eisner's best graphic novel and put in the time bringing it up to FA. This is "distaste"? Curly Turkey 🍁 ¡gobble! 00:33, 7 December 2015 (UTC)
 * I may have misremembered when I seemed to have a memory of you saying something to the effect that it wasnt particularly good or important and that mostly the reason it has come to be known as the worlds first significant graphic novel (I dont think any of the previous ones, regardless of their number are remotely comparable in significance) was that Eisner used it as a marketing ploy.·maunus · snunɐɯ· 00:45, 7 December 2015 (UTC)
 * Also the fact that "it is hard to argue that Contract was the first anything" is not relevant, what is relevant is that many people consider it to be so, and know it as such. And note that noone is argueing that the article should say that it IS the first graphic novel, but only that it is often considered to be so. ·maunus · snunɐɯ· 00:48, 7 December 2015 (UTC)
 * "what is relevant is that many people consider it to be so": which is dealt with in the article, so what's the problem? Curly Turkey 🍁 ¡gobble! 01:12, 7 December 2015 (UTC)
 * Curly Turkey states the facts accurately and succinctly. I would also note that it's a very serious thing when any editor tries to make major, substantive changes to a Featured Article, which has been peer-reviewed throughly and considered among Wikipedia's best. --Tenebrae (talk) 00:39, 7 December 2015 (UTC)
 * FAs are not immune to editing, and the FA status is not a valid reason to stifle discussion on how to improve the article. I am not going to press the point further, but simply wanted to acknowledge that I think Light show has a valid point that merits discussion.·maunus · snunɐɯ· 00:46, 7 December 2015 (UTC)
 * I in no way said "immune" or "immutable", and the fact we're discussing it shows no one's stifling discussion. And do you really not believe that major, substantive changes to an FA is not something that should be undertaken with great seriousness? --Tenebrae (talk) 01:05, 7 December 2015 (UTC)
 * Who is being less than serious here?·maunus · snunɐɯ· 01:26, 7 December 2015 (UTC)
 * I don't understand: If we all agree with my reiteration that we should take this seriously, then what's the issue? --Tenebrae (talk) 01:35, 7 December 2015 (UTC)
 * Simply that you seemed to use an appeal to seriousness to imply that the discussion proposed by Light show was somehow not sufficiently serious to merit attention. If that is not what you meant then there is no problem.·maunus · snunɐɯ· 01:47, 7 December 2015 (UTC)
 * No one suggested FAs were untouchable, so let's put an end to this tangent. Curly Turkey 🍁 ¡gobble! 02:02, 7 December 2015 (UTC)

Most of the first paragraph of the Legacy section could be considered a synthesis conclusion, stating that reliable sourced opinions are "erroneous," and trying to prove it with the sentences following. And even without the OR, why any Legacy section would start with proving cited descriptions are not true is beyond me. --Light show (talk) 00:59, 7 December 2015 (UTC)

 * There's no SYNTH whatsoever. It's a verifiable fact that A Contract with God is not the first graphic novel. That said, we may not need the whole litany of history that follows the statement, since the statement is cited and anyone can go to Graphic novel to learn more of the form's history. --Tenebrae (talk) 01:09, 7 December 2015 (UTC)
 * I don't think it's a "litany": there's the first use of the term, the earliest known use of the term on a work, and a well-known early instance of the form. I'd consider that minimum context. Curly Turkey 🍁 ¡gobble! 02:00, 7 December 2015 (UTC)
 * : Now you've gone off the deep end. Demonstrate the synthesis from this quote from the actual cited source:
 * "It has become common in histories of the medium to cite Will Eisner and his 1978 A Contract with God as the first graphic novel and the first use of that term to promote an extended-length comics narrative."
 * However, as comics studies has come into its own as a discipline, scholars have taken pains to document that Contract was not the first graphic novel. ... [long list of precursors] ... In 1978, alongside Contract, there were at least five other long-form comics that, by virtue of content and format, had a better claim to the designation graphic novel
 * Now do your magic and show how what's in the article is WP:SYNTH or WP:OR! Curly Turkey 🍁 ¡gobble! 01:10, 7 December 2015 (UTC)
 * Now do your magic and show how what's in the article is WP:SYNTH or WP:OR! Curly Turkey 🍁 ¡gobble! 01:10, 7 December 2015 (UTC)

 * The problem is that you're juggling the time element. The Legacy now states, "A Contract with God has frequently, though erroneously, been cited as the first graphic novel." To be accurate, it could state, "At the time of its publication, 'A Contract with God was widely considered to be the first 'modern graphic novel.' However, as comics studies came into its own as a discipline, scholars have documented that Contract was not the first 'graphic novel,' although various sources (Norton, NYT, etc.) still consider it the first 'modern' graphic novel." I would follow that with the reasons and who gave them, as noted above by Schumacher and others.  As primary editor, your're no doubt aware that even Duncan & Smith, the two most used sources in the article, wrote a number of details that would expand on the subject:
 * ""It has become common in histories of the medium to cite Will Eisner and his 1978 A Contract with God as the first graphic novel and first instance of that term used to promote an extended-length comics narrative.(citing Williams and Lyons, 2010) In fact, in 1998 the University of Massachusetts hosted a three-day symposium, "The Graphic Novel: A Twentieth Anniversary Conference on an Emerging Literary and Artistic Medium," which was clearly honoring the 1978 publication of Contract as the beginning of the graphic novel. In 2003, Time's "The Graphic Novel Silver Anniversary" article marked those 25 years as beginning in 1978 with Contract."(Duncan, p. 148)"

 * Duncan goes into much more detail, as you know, about what made his graphic novel distinct from previous ones. --Light show (talk) 02:00, 7 December 2015 (UTC)
 * "At the time of its publication, 'A Contract with God was widely considered to be the first "modern graphic novel.": and your citation for that is? Find me a source from 1978–79 that considered Contract "the first graphic novel".  My understanding is that it gained that status retroactively, after the "graphic novel boom" of the mid-1980s and the publication of Comics and Sequential Art.  The quote you cite above gives no date earlier than 1998 that Contract may have been considered the "first".  That the book is often considered the first is actually handled in the article, by the way, as you're aware. Curly Turkey 🍁 ¡gobble! 02:09, 7 December 2015 (UTC)
 * It states in the Background section, "He marketed it as a 'graphic novel'—a term which had been in use since the 1960s, but was little known until Eisner popularized it with Contract.[31]" That implies that at the time, "it was considered to be the first." In any case, the first sentence in the Legacy section is based on today's knowledge, so the unstated time gap in the sentence could be explained to be clear. Was it therefore "erroneous" at the time to think the book was the first? Apparently not.--Light show (talk) 02:34, 7 December 2015 (UTC)
 * Wow, that's quite the limb you've gone out on! Nothing in that statement coems anywhere in the vicinity of anything resembling "it was considered to be the first".  You've WP:ORed yourself out of credibility, I'm afraid.  Good luck building a consensus on that fantasy. Curly Turkey 🍁 ¡gobble! 03:14, 7 December 2015 (UTC)

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