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Universal Product Code

The Universal Product Code (UPC or UPC code) is a barcode symbology that is used worldwide for tracking trade items in stores.

The chosen symbology has bars (or spaces) of exactly 1, 2, 3, or 4 units wide each; each decimal digit to be encoded consists of two bars and two spaces chosen to have a total width of 7 units, in both an "even" and an "odd" parity form, which enables being scanned in either direction. Special "guard patterns" (3 or 5 units wide, not encoding a digit) are intermixed to help decoding.

A UPC (technically, a UPC-A) consists of 12 digits that are uniquely assigned to each trade item. The international GS1 organisation assigns the digits used for both the UPC and the related International Article Number (EAN) barcode. UPC data structures are a component of Global Trade Item Numbers (GTINs) and follow the global GS1 specification, which is based on international standards. Some retailers, such as clothing and furniture, do not use the GS1 system, instead using other barcode symbologies or article number systems. Some retailers use the EAN/UPC barcode symbology, but do not use a GTIN for products sold only in their own stores.

Research indicates that the adoption and diffusion of the UPC stimulated innovation and contributed to the growth of international retail supply chains.

History
Wallace Flint proposed an automated checkout system in 1932 using punched cards. Bernard Silver and Norman Joseph Woodland, a graduate student from Drexel Institute of Technology, developed a bull's-eye-style code and applied for the patent in 1949.

In the 1960s and early 1970s, railroads in North America experimented with multicolor bar codes for tracking railcars, but this system was eventually abandoned and replaced with a radio-based system called Automatic Equipment Identification (AEI).

In 1973, a group of trade associations from the grocery industry formed the Uniform Product Code Council (UPCC) which, with the help of consultants Larry Russell and Tom Wilson of McKinsey & Company, defined the numerical format that formed the basis of the Uniform Product Code. Technology firms including Charegon, IBM, Litton-Zellweger, Pitney Bowes-Alpex, Plessey-Anker, RCA, Scanner Inc., Singer, and Dymo Industries/Data General, put forward alternative proposals for symbol representations to the council. The Symbol Selection Committee finally chose to implement the IBM proposal designed by George J. Laurer, but with a slight modification to the font in the human readable area.

The first UPC-marked item ever to be scanned at a retail checkout was a 10-pack (50 sticks) of Wrigley's Juicy Fruit chewing gum, purchased at the Marsh supermarket in Troy, Ohio, at 8:01 a.m. on 26 June 1974. The NCR cash register rang up 67 cents. The shopping cart also contained other barcoded items but the gum was the first one picked up at the checkout. A facsimile of the gum packet went on display at the Smithsonian Institution's American history museum in Washington, D.C.

Murray Eden was a consultant on the team that created the Universal Product Code barcode. As Chairman of a committee of scientists at the Massachusetts Institute of Technology, he helped "select a symbol that would endure the inevitable rush of technology that lay ahead." He chose the font, and he came up with the idea to add numbers to the bottom, which is a fail-safe system, in case the barcode reader is not working correctly.

IBM proposal
Around late 1969, IBM at Research Triangle Park (RTP) in North Carolina assigned George Laurer to determine how to make a supermarket scanner and label. In late 1970, Heard Baumeister provided equations to calculate characters-per-inch achievable by two IBM bar codes, Delta A and Delta B. In February 1971, Baumeister joined Laurer.

Delta B compared bar widths to space width to code bits. This was extremely sensitive to ink spread, where improper levels of ink or pressure would cause both edges of a bar to spread outward or shrink in.

In mid 1971, William "Bill" Crouse invented a new bar code called Delta C. It achieved four times the characters per inch as Delta B.

Delta C achieved its higher performance by only using leading to leading or trailing to trailing edges which was unaffected by uniform ink spread. The code provided best performance when it had a defined character set with a fixed reference distance that spanned most or preferably all the character.

In August 1971, Crouse joined the scanner effort. After several months they had made no progress. They were aware of the RCA bull's eye label that could be scanned with a simple straight line laser scanner, but a readable label was far too large.

Although Litton Industries proposed a bull's eye symbol cut in half to reduce the area, it was still too large and presented the same ink smear printing problems as the RCA symbol. The redundancy and checking ability were removed completely. They were also aware of the many proposals from around the world, none of which were feasible.

In the spring of 1972, Baumeister announced a breakthrough. He proposed a label with bars that were slightly longer than the distance across all bars that needed to be read in a single pass. This label could be scanned with a simple "X" scanner only slightly more complex than the straight line laser scanner. The next day Baumeister suggested if the label were split into two halves the bar lengths could be cut nearly in half.

These two proposals reduced the area from the bull's eye by one third and then one sixth. The image to the right shows the label proposed by Baumeister. He did not specify any specific bar code as that was well understood. Except for the bar coding and ten digits the UPC label today is his proposal. Shortly after that Baumeister transferred to another area of RTP.

Laurer proceeded to define the details of the label and write a proposal. N.J. Woodland was assigned as planner for the project and aided Laurer with writing his proposal.

Laurer's first attempt with a bar code used Delta B. The resulting label size was about six inches by three inches which was too large. Crouse suggested that Laurer use his Delta C bar code and provided a copy of his patent that had a sample alphanumeric character set and rules to generate other size alphabets. This reduced the label size to about 1.5 x.

Later Laurer asked Crouse for assistance in how the scanner could detect a label. Together they defined guard bars and a definition of how to detect the label. The guard bars also provided identification for half label discrimination and training bars for the scanner threshold circuits. Laurer had a complete label definition and proceeded to write his proposal.

Previously Crouse had an idea for a simple wand worn like a ring and bracelet. He decided to develop that wand to provide a demonstration of the label.

On 1 December 1972, IBM presented Laurer's proposal to the Super Market Committee in Rochester, Minnesota, the location where IBM would develop the scanner. During the presentation, Crouse gave a lab demonstration where he read UPC-like labels with his ring wand. In addition to reading regular labels, he read the large two-page centerfold label in the proposal booklet. He then turned to a page showing a photo of labeled items sitting on a table. The labels were small and flawed due to the resolution of the printed photo but the wand read many of them. This demonstration showed the robustness of the pure Delta C code. The proposal was accepted.

One month later, 1 January 1973 Crouse transferred back to IBM's Advanced Technology group, and Laurer remained with the full responsibility for the label.

Dymo Industries, makers of handheld printing devices insisted that the code be character independent, so that handheld printing devices could produce the bar code in store if the items were not bar-coded by the manufacturers. Dymo's proposal was accepted by IBM and incorporated in IBM's latest proposal.

It was decided that the two halves of the label should have a different set of numeric characters. The character set Laurer derived from the Delta C patent used seven printable increments or units where two bars and two spaces would be printed. This yielded twenty combinations of characters, but there were two pairs that when read by Delta C rules yielded the same code for the pair.

Since eighteen characters were not enough Laurer tried adding one unit to the character set. This yielded twenty-six Delta C characters which could provide the two sets of decimal characters but it also added fourteen percent to the width of the label and thereby the height. This would be a thirty percent increase in area or a label of 1.7 x. Laurer felt this was not acceptable.

Laurer returned to the original character set with twenty characters but four of those were two pairs with the same Delta C reading. He decided to use them all. To distinguish between the pairs he would measure one bar width in each of the pairs to distinguish them from each other. For each pair those bars would be one or two units wide.

Laurer did not apply Baumeister's equations to this set. He felt just one bar width measurement would not be too serious. As it turned out it would have required over fifty percent increase in width and height for an area increase of more than double. Laurer later admitted these four characters in each set were responsible for most of the scanner read errors.

David Savir, a mathematician, was given the task of proving the symbol could be printed and would meet the reliability requirements, and was most likely unaware of Baumeister's equations. He and Laurer added two more digits to the ten for error detection and correction.

Then they decided to add odd/even parity to the number of units filled with bars in each side. Odd/even parity is a technique used to detect any odd number of bit errors in a bit stream. They decided to use odd on one half and even on the other. This would provide additional indication of which half ticket was being read. This meant that every bar width had to be read accurately to provide a good reading. It also meant every space would also be known.

Requiring every bit width to be read precisely basically nullified the Delta C advantage except for the Delta C reference measurement. Only the strange character set and the size of the label remains as a shadow of the Delta C code. The size was still that calculated for pure Delta C. If the label size had been properly recalculated, taking into account the required bar width measurements the label would have been far too large to be acceptable.

Mechanical engineering and electronic circuit design commonly require worst case designs using known tolerances. Many engineers working with bar codes had little experience with such things and used somewhat intuitive methods. This was the cause of the poor performance of the Delta B code and quite likely the failure of RCA's bull's eye scanner.

The following table shows the workable labels, available in the early 1970s, with their sizes.

This is assuming a bull's eye with the same information and reliable readability.

Composition
Each UPC-A barcode consists of a scannable strip of black bars and white spaces above a sequence of 12 numerical digits. No letters, characters or other content of any kind may appear on a UPC-A barcode. There is a one-to-one correspondence between 12-digit number and strip of black bars and white spaces, i.e. there is only one way to represent each 12-digit number visually and there is only one way to represent each strip of black bars and white spaces numerically.

The scannable area of every UPC-A barcode follows the pattern S L LLLLLMRRRRR R E, where S (start), M (middle), and E (end) guard patterns are represented the same way on every UPC-A barcode and the L (left) and R (right) sections collectively represent the 12 numerical digits that make each UPC-A unique. The first digit L indicates a particular number system to be used by the following digits. The last digit R is an error detecting check digit, that allows some errors to be detected in scanning or manual entry. The guard patterns separate the two groups of six numerical digits and establish the timing.

UPC-A 042100005264 is equivalent to UPC-E 425261 with the "EOEEOO" parity pattern, which is defined by UPC-A number system 0 and UPC-A check digit 4.

Formatting
UPC-A barcodes can be printed at various densities to accommodate a variety of printing and scanning processes. The significant dimensional parameter is called x-dimension (width of single module element). The width of each bar (space) is determined by multiplying the x-dimension and the module width (1, 2, 3, or 4 units) of each bar (space). Since the guard patterns each include two bars, and each of the 12 digits of the UPC-A barcode consists of two bars and two spaces, all UPC-A barcodes consist of exactly (3 × 2) + (12 × 2) = 30 bars, of which 6 represent guard patterns and 24 represent numerical digits.

The x-dimension for the UPC-A at the nominal size is 0.33 mm (0.013"). Nominal symbol height for UPC-A is 25.9 mm (1.02"). The bars forming the S (start), M (middle), and E (end) guard patterns, are extended downwards by 5 times x-dimension, with a resulting nominal symbol height of 27.55 mm (1.08"). This also applies to the bars of the first and last numerical digit of UPC-A barcode. UPC-A can be reduced or magnified anywhere from 80% to 200%.

A quiet zone, with a width of at least 9 times the x-dimension, must be present on each side of the scannable area of the UPC-A barcode. For a GTIN-12 number encoded in a UPC-A barcode, the first and last digits of the human-readable interpretation are always placed outside the symbol in order to indicate the quiet zones that are necessary for UPC barcode scanners to work properly.

Encoding
The UPC-A barcode is visually represented by strips of bars and spaces that encode the UPC-A 12-digit number. Each digit is represented by a unique pattern of 2 bars and 2 spaces. The bars and spaces are variable width, i.e. 1, 2, 3, or 4 modules wide. The total width for a digit is always 7 modules; consequently, UPC-A 12-digit number requires a total of 7×12 = 84 modules.

A complete UPC-A is 95 modules wide: 84 modules for the digits (L and R sections) combined with 11 modules for the S (start), M (middle), and E (end) guard patterns. The S (start) and E (end) guard patterns are 3 modules wide and use the pattern bar-space-bar, where each bar and space is one module wide. The M (middle) guard pattern is 5 modules wide and uses the pattern space-bar-space-bar-space, where each bar and space is also one module wide. In addition, a UPC-A symbol requires a quiet zone (extra space of 9 modules wide) before the S (start) and after the E (end) guard patterns.

The UPC-A's left-hand side digits (the digits to the left of the M (middle) guard pattern) have odd parity, which means the total width of the black bars is an odd number of modules. On the contrary, the right-hand side digits have even parity. Consequently, a UPC scanner can determine whether it is scanning a symbol from left-to-right or from right-to-left (the symbol is upside-down). After seeing a S (start) or E (end) guard pattern (they are the same, bar-space-bar, whichever direction they are read), the scanner will first see odd parity digits, if scanning left-to-right, or even parity digits, if scanning right-to-left. With the parity/direction information, an upside-down symbol will not confuse the scanner. When confronted with an upside-down symbol, the scanner may simply ignore it (many scanners alternate left-to-right and right-to-left scans, so they will read the symbol on a subsequent pass) or recognize the digits and put them in the right order. There is another property in the digit encoding. The right-hand side digits are the optical inverse of the left-hand side digits, i.e. black bars are turned into white spaces and vice versa. For example, the left-hand side "4" is space×1 - bar×1 - space×3 - bar×2, meanwhile the right-hand side "4" is bar×1 - space×1 - bar×3 - space×2.

Numbering
The number of UPC-A and UPC-E barcodes are limited by the standards used to create them.

\text{(possible values per left digit)} ^ \text{(left digits)} &\times \text{(possible values per right digit)} ^ \text{(5 right digits)}\\ = 10^6 &\times 10^5 = 100,000,000,000. \end{align}$$ \text{(possible values per digit)} ^ \text{(digits)} &\times \text{(possible parity patterns per UPC-E number)}\\ = 10^6 &\times 2 = 2,000,000.\end{align}$$
 * UPC-A: $$\begin{align}
 * UPC-E: $$\begin{align}

Number system digit
Below is description of all possible number systems with corresponding 12-digit UPC-A numbering schema L LLLLLRRRRR R, where L denotes number system digit and R check digit.
 * 0–1, 6–9 : For most products. The LLLLL digits are the manufacturer code (assigned by local GS1 organization), and the RRRRR digits are the product code.
 * 2 : Reserved for local use (store/warehouse), for items sold by variable weight. Variable-weight items, such as meats, fresh fruits, or vegetables, are assigned an item number by the store, if they are packaged there. In this case, the LLLLL is the item number, and the RRRRR is either the weight or the price, with the first R determining which (0 for weight).
 * 3 : Drugs by National Drug Code (NDC) number. Pharmaceuticals in the U.S. use the middle 10 digits of the UPC as their NDC number. Though usually only over-the-counter drugs are scanned at point of sale, NDC-based UPCs are used on prescription drug packages and surgical products and, in this case, are commonly called UPN Codes.
 * 4 : Reserved for local use (store/warehouse), often for loyalty cards or store coupons.
 * 5 : Coupons. The LLLLL digits are digits 2-6 of the product's UPC prefix, the next three RRR are a family code (set by manufacturer or supplied by the coupon clearing house), and the next two RR are a value code (according to the GS1 value code table), which determines the amount of the discount. These coupons can be doubled or tripled.

Check digit calculation
The UPC includes a check digit to detect common data entry errors. For example, UPC-A codes choose the check digit $$x_{12}$$ to satisfy the check digit equation:
 * $$(3x_1 + x_2 + 3x_3 + x_4 + 3x_5 + x_6 + 3x_7 + x_8 + 3x_9 + x_{10} + 3x_{11} + x_{12}) \equiv 0 \pmod{10}.$$

If an entered code does not satisfy the equation, then it is not a valid UPC-A.

The UPC-A check digit may be calculated as follows:

 * 1) Sum the digits at odd-numbered positions (first, third, fifth,..., eleventh).
 * 2) Multiply the result by 3.
 * 3) Add the digit sum at even-numbered positions (second, fourth, sixth,..., tenth) to the result.
 * 4) Find the result modulo 10 (i.e. the remainder, when divided by 10) and call it $M$.
 * 5) If $M$ is zero, then the check digit is 0; otherwise the check digit is $10 − M$.

For example, in a UPC-A barcode "03600029145x12", where $x_{12}$ is the unknown check digit, $x_{12}$ may be calculated by: Thus, the check digit $10 − M = 10 − 8 = 2$ is 2.
 * 1) Sum the odd-numbered digits (0 + 6 + 0 + 2 + 1 + 5 = 14).
 * 2) Multiply the result by 3 (14 × 3 = 42).
 * 3) Add the even-numbered digits (42 + (3 + 0 + 0 + 9 + 4) = 58).
 * 4) Find the result modulo 10 (58 mod 10 = 8 = M).
 * 5) If $M$ is not 0, subtract $M$ from 10 ($x_{12}$).

The check digit equation is selected to have reasonable error detection properties (see Luhn algorithm).
 * UPC-A can detect 100% of single digit errors.
 * A single digit error means exactly one digit is wrong. Let the difference modulo 10 of the erroneous digit and the correct digit be $d$. The value of $d$ cannot be zero because that means the digits are the same, but $d$ can be any other value in {1, 2, 3, 4, 5, 6, 7, 8, 9}. If the error digit is in an odd position (weight 1), the left hand side of check digit equation changes by $d$ and the equivalence is no longer zero. If the error digit is in an even position (weight 3), then the left hand side changes by $3d$, but that change is also nonzero modulo 10, so the check digit equation is not satisfied.
 * UPC-A can detect about 89% of transposition errors. Specifically, if and only if the difference between two adjacent digits is 5, the UPC-A can't detect their transposition.
 * If 2 neighboring digits are transposed, then one of the digits $a$ will be weighted by 1, and the other digit $b = a + d$ will be weighted by 3, where $d$ is the difference between the two digits. If the digits were in their correct order, they would contribute
 * $$1a + 3b = 1a + 3(a+d) = 4a + 3d$$
 * to the left hand side of the check digit equation. In the transposed order, they contribute
 * $$1b + 3a = 3a + 1(a+d) = 4a + d$$.
 * to the LHS. Subtracting the two contributions gives how much they change the LHS:
 * $$(4a + 3d) - (4a + d) = 2d$$
 * An error will be detected as long as the modular change is nonzero; if $2d ≡ 0$ modulo 10, then the change will not be detected. Consequently, only when the character difference $d ≡ 5$ will an error be undetected (when $d ≡ 0$ the degenerate "transposition" is not an error).
 * Next consider how often a transposition has a distance $d$ of 5.
 * Here is the Table of d-transpositions for UPC-A barcodes, where $$ d \in \{0, 1, 2, \ldots, 9\}:$$
 * {|class="wikitable"

! ! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 ! 1 ! 2 ! 3 ! 4 ! 5 ! 6 ! 7 ! 8 ! 9 ! 10 ! Sum
 * + Table of d-transpositions for UPC-A barcodes
 * 0 0 || 0 1 || 0 2 || 0 3 || 0 4 || 0 5 || 0 6 || 0 7 || 0 8 || 0 9
 * 1 1 || 1 2 || 1 3 || 1 4 || 1 5 || 1 6 || 1 7 || 1 8 || 1 9
 * 2 2 || 2 3 || 2 4 || 2 5 || 2 6 || 2 7 || 2 8 || 2 9
 * 3 3 || 3 4 || 3 5 || 3 6 || 3 7 || 3 8 || 3 9
 * 4 4 || 4 5 || 4 6 || 4 7 || 4 8 || 4 9
 * 5 5 || 5 6 || 5 7 || 5 8 || 5 9
 * 6 6 || 6 7 || 6 8 || 6 9
 * 7 7 || 7 8 || 7 9
 * 8 8 || 8 9
 * 9 9
 * 10 || 18 || 16 || 14 || 12 || 10 || 8 ||  6 ||  4 ||  2
 * }
 * Row Sum contains the number of d-transpositions, therefore the proportion of non-detectable transposition errors is (ignoring the transpositions where $d = 0$):
 * $$\frac{10}{18 + 16 + 14 + 12 + 10 + 8 + 6 + 4 + 2}=\frac{10}{90}=11.111\ldots\%.$$

Variations
UPC in its most common usage technically refers to UPC-A.

Other variants of the UPC exist:
 * UPC-B is a 12-digit version of UPC with no check digit, developed for the National Drug Code (NDC) and National Health Related Items Code.   It has 11 digits plus a 1-digit product code, and is not in common use.
 * UPC-C is a 12-digit code with a product code and a check digit; not in common use.
 * UPC-D is a variable length code (12 digits or more) with the 12th digit being the check digit. These versions are not in common use.
 * UPC-E is a 6-digit code, that has its equivalent in UPC-A 12-digit code with number system 0 or 1.
 * UPC-2 is a 2-digit supplement to the UPC used to indicate the edition of a magazine or periodical.
 * UPC-5 is a 5-digit supplement to the UPC used to indicate suggested retail price for books.

UPC-E
To allow the use of UPC barcodes on smaller packages, where a full 12-digit barcode may not fit, a zero-suppressed version of UPC was developed, called UPC-E, in which the number system digit, all trailing zeros in the manufacturer code, and all leading zeros in the product code, are suppressed (omitted). This symbology differs from UPC-A in that it only uses a 6-digit code, does not use M (middle) guard pattern, and the E (end) guard pattern is formed as space-bar-space-bar-space-bar, i.e. UPC-E barcode follows the pattern SDDDDDDE. The way in which a 6-digit UPC-E relates to a 12-digit UPC-A, is determined by UPC-E numerical pattern and UPC-E parity pattern. It can only correspond to UPC-A number system 0 or 1, the value of which, along with the UPC-A check digit, determines the UPC-E parity pattern of the encoding. With the manufacturer code digits represented by M's, and product code digits by P's, then:

For example, a UPC-E 654321 may correspond to the UPC-A 065100004327 or 165100004324, depending on the UPC-E parity pattern of the encoded digits, as described next:

UPC-E 654321 with "EOEOEO" parity pattern (UPC-A 065100004327) would be encoded as

 * 1-1-1 4-1-1-1  1-2-3-1  2-3-1-1  1-4-1-1  2-2-1-2  2-2-2-1  1-1-1-1-1-1.

The barcode would look like this:

EAN-13
The EAN-13 was developed as a superset of UPC-A, adding an extra digit to the beginning of every UPC-A number. This expanded the number of unique values theoretically possible by ten times to 1 trillion. EAN-13 barcodes also indicate the country in which the company that sells the product is based (which may or may not be the same as the country in which the good is manufactured). The three leading digits of the code determine this, according to the GS1 country codes. Every UPC-A code can be easily converted to the equivalent EAN-13 code by prepending 0 digit to the UPC-A code. This does not change the check digit. All point-of-sale systems can now understand both equally.

EAN-8 is an 8-digit variation of the EAN barcode.

UPC usage notes:
 * All products marked with an EAN will be accepted in North America currently, in addition to those already marked with a UPC.
 * Products with an existing UPC do not have to be re-marked with an EAN.
 * In North America, the EAN adds 30% more codes, mainly by adding digits 10 through 12 to the UPC digits 00 through 09. This is a powerful incentive to phase out the UPC.

title: Universal Product Code


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Boltzmann constant

The Boltzmann constant ($k_{B}$ or $1.381 J.K-1$) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy and heat capacity. It is named after the Austrian scientist Ludwig Boltzmann.

As part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven "defining constants" that have been given exact definitions. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly $8.617 eV.K-1$ joules per kelvin.

Roles of the Boltzmann constant
Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure $k$ and volume $1.381$ is proportional to the product of amount of substance $p$ and absolute temperature $V$:

$$pV = nRT ,$$

where $n$ is the molar gas constant ($T$). Introducing the Boltzmann constant as the gas constant per molecule $k = R/NA$ (being NA the Avogadro constant) transforms the ideal gas law into an alternative form:

$$p V = N k T ,$$

where $R$ is the number of molecules of gas.

Role in the equipartition of energy
Given a thermodynamic system at an absolute temperature $8.314 J⋅K^{−1}⋅mol^{−1}$, the average thermal energy carried by each microscopic degree of freedom in the system is $1⁄2 kT$ (i.e., about $N$, or $T$, at room temperature). This is generally true only for classical systems with a large number of particles, and in which quantum effects are negligible.

In classical statistical mechanics, this average is predicted to hold exactly for homogeneous ideal gases. Monatomic ideal gases (the six noble gases) possess three degrees of freedom per atom, corresponding to the three spatial directions. According to the equipartition of energy this means that there is a thermal energy of $3⁄2 kT$ per atom. This corresponds very well with experimental data. The thermal energy can be used to calculate the root-mean-square speed of the atoms, which turns out to be inversely proportional to the square root of the atomic mass. The root mean square speeds found at room temperature accurately reflect this, ranging from $2.07 J$ for helium, down to $0.013 eV$ for xenon.

Kinetic theory gives the average pressure $1,370 m/s$ for an ideal gas as

$$ p = \frac{1}{3}\frac{N}{V} m \overline{v^2}.$$

Combination with the ideal gas law

$$p V = N k T$$

shows that the average translational kinetic energy is

$$ \tfrac{1}{2}m \overline{v^2} = \tfrac{3}{2} k T.$$

Considering that the translational motion velocity vector $v$ has three degrees of freedom (one for each dimension) gives the average energy per degree of freedom equal to one third of that, i.e. $1⁄2 kT$.

The ideal gas equation is also obeyed closely by molecular gases; but the form for the heat capacity is more complicated, because the molecules possess additional internal degrees of freedom, as well as the three degrees of freedom for movement of the molecule as a whole. Diatomic gases, for example, possess a total of six degrees of simple freedom per molecule that are related to atomic motion (three translational, two rotational, and one vibrational). At lower temperatures, not all these degrees of freedom may fully participate in the gas heat capacity, due to quantum mechanical limits on the availability of excited states at the relevant thermal energy per molecule.

Role in Boltzmann factors
More generally, systems in equilibrium at temperature $240 m/s$ have probability $Pi$ of occupying a state $p$ with energy $T$ weighted by the corresponding Boltzmann factor:

$$P_i \propto \frac{\exp\left(-\frac{E}{k T}\right)}{Z},$$

where $i$ is the partition function. Again, it is the energy-like quantity $kT$ that takes central importance.

Consequences of this include (in addition to the results for ideal gases above) the Arrhenius equation in chemical kinetics.

Role in the statistical definition of entropy
In statistical mechanics, the entropy $E$ of an isolated system at thermodynamic equilibrium is defined as the natural logarithm of $Z$, the number of distinct microscopic states available to the system given the macroscopic constraints (such as a fixed total energy $S$):

$$S = k \,\ln W.$$

This equation, which relates the microscopic details, or microstates, of the system (via $W$) to its macroscopic state (via the entropy $E$), is the central idea of statistical mechanics. Such is its importance that it is inscribed on Boltzmann's tombstone.

The constant of proportionality $W$ serves to make the statistical mechanical entropy equal to the classical thermodynamic entropy of Clausius:

$$\Delta S = \int \frac{{\rm d}Q}{T}.$$

One could choose instead a rescaled dimensionless entropy in microscopic terms such that

$${S' = \ln W}, \quad \Delta S' = \int \frac{\mathrm{d}Q}{k T}.$$

This is a more natural form and this rescaled entropy exactly corresponds to Shannon's subsequent information entropy.

The characteristic energy $S$ is thus the energy required to increase the rescaled entropy by one nat.

The thermal voltage
In semiconductors, the Shockley diode equation—the relationship between the flow of electric current and the electrostatic potential across a p–n junction—depends on a characteristic voltage called the thermal voltage, denoted by $VT$. The thermal voltage depends on absolute temperature $k$ as

$$ V_\mathrm{T} =  { k T \over q } = { R T \over F },$$

where $kT$ is the magnitude of the electrical charge on the electron with a value Equivalently, $$ { V_\mathrm{T} \over T } = { k \over q } \approx 8.617333262 \times 10^{-5}\ \mathrm{V/K}.$$

At room temperature 300 K, $VT$ is approximately $T$ which can be derived by plugging in the values as follows:

$$V_\mathrm{T}={kT \over q} =\frac{1.38\times 10^{-23}\ \mathrm{J{\cdot}K^{-1}} \times 300\ \mathrm{K}}{1.6 \times 10^{-19}\ \mathrm{C}} \simeq 25.85\ \mathrm{mV}$$

At the standard state temperature of 298.15 K, it is approximately $q$. The thermal voltage is also important in plasmas and electrolyte solutions (e.g. the Nernst equation); in both cases it provides a measure of how much the spatial distribution of electrons or ions is affected by a boundary held at a fixed voltage.

History
The Boltzmann constant is named after its 19th century Austrian discoverer, Ludwig Boltzmann. Although Boltzmann first linked entropy and probability in 1877, the relation was never expressed with a specific constant until Max Planck first introduced $25.85 mV$, and gave a more precise value for it ($25.69 mV$, about 2.5% lower than today's figure), in his derivation of the law of black-body radiation in 1900–1901. Before 1900, equations involving Boltzmann factors were not written using the energies per molecule and the Boltzmann constant, but rather using a form of the gas constant $k$, and macroscopic energies for macroscopic quantities of the substance. The iconic terse form of the equation $S = k ln W$ on Boltzmann's tombstone is in fact due to Planck, not Boltzmann. Planck actually introduced it in the same work as his eponymous $1.346 J/K$.

In 1920, Planck wrote in his Nobel Prize lecture:

This "peculiar state of affairs" is illustrated by reference to one of the great scientific debates of the time. There was considerable disagreement in the second half of the nineteenth century as to whether atoms and molecules were real or whether they were simply a heuristic tool for solving problems. There was no agreement whether chemical molecules, as measured by atomic weights, were the same as physical molecules, as measured by kinetic theory. Planck's 1920 lecture continued:

In versions of SI prior to the 2019 redefinition of the SI base units, the Boltzmann constant was a measured quantity rather than a fixed value. Its exact definition also varied over the years due to redefinitions of the kelvin (see ) and other SI base units (see ).

In 2017, the most accurate measures of the Boltzmann constant were obtained by acoustic gas thermometry, which determines the speed of sound of a monatomic gas in a triaxial ellipsoid chamber using microwave and acoustic resonances. This decade-long effort was undertaken with different techniques by several laboratories; it is one of the cornerstones of the 2019 redefinition of SI base units. Based on these measurements, the CODATA recommended $R$ to be the final fixed value of the Boltzmann constant to be used for the International System of Units.

Value in different units
†The value is exact but not expressible as a finite decimal; approximated to 9 decimal places only.

Since $h$ is a proportionality factor between temperature and energy, its numerical value depends on the choice of units for energy and temperature. The small numerical value of the Boltzmann constant in SI units means a change in temperature by 1 K only changes a particle's energy by a small amount. A change of $1.381 J/K$ is defined to be the same as a change of $k$. The characteristic energy $1.381$ is a term encountered in many physical relationships.

The Boltzmann constant sets up a relationship between wavelength and temperature (dividing hc/k by a wavelength gives a temperature) with one micrometer being related to $8.617$, and also a relationship between voltage and temperature (kT in units of eV corresponds to a voltage) with one volt being related to $2.084$. The ratio of these two temperatures, $1.381$ / $1 J$ ≈ 1.239842, is the numerical value of hc in units of eV⋅μm.

Natural units
The Boltzmann constant provides a mapping from the characteristic microscopic energy $3.298$ to the macroscopic temperature scale $k/h$. In fundamental physics, this mapping is often simplified by using the natural units of setting $4.187 J$ to unity. This convention means that temperature and energy quantities have the same dimensions. In particular, the SI unit kelvin becomes superfluous, being defined in terms of joules as $k/(hc)$. With this convention, temperature is always given in units of energy, and the Boltzmann constant is not explicitly needed in formulas.

This convention simplifies many physical relationships and formulas. For example, the equipartition formula for the energy associated with each classical degree of freedom ($$\tfrac{1}{2} k T$$ above) becomes

$$E_{\mathrm{dof}} = \tfrac{1}{2} T $$

As another example, the definition of thermodynamic entropy coincides with the form of information entropy:

$$ S = - \sum_i P_i \ln P_i.$$

where $kN_{A}$ is the probability of each microstate.

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

title: Boltzmann constant


text:
Wilhelm Keitel

Wilhelm Bodewin Johann Gustav Keitel (22 September 1882 –16 October 1946) was a German field marshal who held office as chief of the Oberkommando der Wehrmacht (OKW), the high command of Nazi Germany's armed forces, during World War II. He signed a number of criminal orders and directives that led to numerous war crimes.

Keitel's rise to the Wehrmacht high command began with his appointment as the head of the Armed Forces Office at the Reich Ministry of War in 1935. Having taken command of the Wehrmacht in 1938, Adolf Hitler replaced the ministry with the OKW and Keitel became its chief. He was reviled among his military colleagues as Hitler's habitual "yes-man".

After the war, Keitel was indicted by the International Military Tribunal in Nuremberg as one of the "major war criminals". He was found guilty on all counts of the indictment: crimes against humanity, crimes against peace, criminal conspiracy, and war crimes. He was sentenced to death and executed by hanging in 1946.

Early life and career
Wilhelm Keitel was born in the village of Helmscherode near Gandersheim in the Duchy of Brunswick, Germany. He was the eldest son of Carl Keitel (1854–1934), a middle-class landowner, and his wife Apollonia Vissering (1855–1888). At the beginning he wanted to take over his family's estates after completing his education at a gymnasium. This plan failed as his father did not want to retire. Instead, he embarked on a military career in 1901, becoming an officer cadet of the Prussian Army. As a commoner, he did not join the cavalry, but a field artillery regiment in Wolfenbüttel, serving as adjutant from 1908. On 18 April 1909, Keitel married Lisa Fontaine, a wealthy landowner's daughter at Wülfel near Hanover.

Keitel was 1.85 m tall, later described as a solidly built and square-jawed Prussian.

During World War I, Keitel served on the Western Front and took part in the fighting in Flanders, where he was severely wounded. After being promoted to captain, Keitel was posted to the staff of an infantry division in 1915. After the war, Keitel was retained in the newly created Reichswehr of the Weimar Republic and played a part in organizing the paramilitary Freikorps units on the Polish border. In 1924, Keitel was transferred to the Ministry of the Reichswehr in Berlin, serving with the Truppenamt ('Troop Office'), the post-Versailles disguised German General Staff. Three years later, he returned to field command.

Now a lieutenant-colonel, Keitel was again assigned to the war ministry in 1929 and was soon promoted to Head of the Organizational Department ("T-2"), a post he held until Adolf Hitler took power in 1933. Playing a vital role in the German rearmament, he traveled at least once to the Soviet Union to inspect secret Reichswehr training camps. In the autumn of 1932, he suffered a heart attack and double pneumonia. Shortly after his recovery, in October 1933, Keitel was appointed as deputy commander of the 3rd Infantry Division; in 1934, he was given command of the 22nd Infantry Division at Bremen.

Rise to the Wehrmacht High Command

In 1935, at the recommendation of General Werner von Fritsch, Keitel was promoted to the rank of major general and appointed chief of the Reich Ministry of War's Armed Forces Office (Wehrmachtsamt), which oversaw the army, navy, and air force. After assuming office, Keitel was promoted to lieutenant general on 1 January 1936.

On 21 January 1938, Keitel received evidence revealing that the wife of his superior, War Minister Werner von Blomberg, was a former prostitute. Upon reviewing this information, Keitel suggested that the dossier be forwarded to Hitler's deputy, Hermann Göring, who used it to bring about Blomberg's resignation.

Hitler took command of the Wehrmacht in 1938 and replaced the war ministry with the Supreme Command of the Armed Forces (Oberkommando der Wehrmacht), with Keitel as its chief. As a result of his appointment, Keitel assumed the responsibilities of Germany's war minister. Although not officially appointed a Reichsminister, Keitel was granted cabinet-level rank. When von Blomberg was asked by Hitler (out of respect for him, after his dismissal in 1938) who he would recommend to replace him, he had said that Hitler himself should take over the job. He told Hitler that Keitel (who was his son-in-law's father) "is just the man who runs my office". Hitler snapped his fingers and exclaimed "That's exactly the man I'm looking for". So on 4 February 1938 when Hitler became Commander-in-Chief of the Wehrmacht, Keitel (to the astonishment of the General Staff, including himself) became chief of staff.

Soon after his promotion, Keitel convinced Hitler to appoint Walther von Brauchitsch as Commander-in-Chief of the Army, replacing von Fritsch. Keitel was promoted to Generaloberst (Colonel General) in November 1938, and in April 1939 he was awarded the Golden Party Badge by Hitler.

Criticism of capabilities
Field Marshal Ewald von Kleist labelled Keitel nothing more than a "stupid follower of Hitler" because of his servile "yes man" attitude toward Hitler. His sycophancy was well known in the army, and he acquired the nickname 'Lakeitel', a pun derived from Lakai ("lackey") and his surname. Hermann Göring's description of Keitel as having "a sergeant's mind inside a field marshal's body" was a feeling often expressed by his peers. He had been promoted because of his willingness to function as Hitler's mouthpiece. He was known by his peers as a "blindingly loyal toady" of Hitler, nicknamed "Nickgeselle", after a popular metal toy nodding donkey, the "Nickesel". During the war he was subject to verbal abuse from Hitler, who said to other officers (according to Gerd von Rundstedt) that "you know he has the brains of a movie usher ... (but he was made the highest ranking officer in the Army) ... because the man's as loyal as a dog" (said by Hitler with a sly smile).

Keitel was predisposed to manipulation because of his limited intellect and nervous disposition; Hitler valued his diligence and obedience. On one occasion, Generalleutnant Burkhart Müller-Hillebrand asked who Keitel was: upon finding out he became horrified at his own failure to salute his superior. Franz Halder, however, told him: "Don't worry, it's only Keitel". German officers consistently bypassed him and went directly to Hitler.

World War II
On 30 August 1939, immediately prior to the outbreak of the Second World War, Keitel was appointed by Hitler to the six-person Council of Ministers for the Defense of the Reich which was set up to operate as a "war cabinet". After Germany defeated France in the Battle of France in six weeks, Keitel described Hitler as "the greatest warlord of all time". Keitel conducted the negotiations of the French armistice, and on 19 July 1940 was promoted to Generalfeldmarschall (field marshal).

The planning for Operation Barbarossa, the 1941 invasion of the Soviet Union, was begun tentatively by Halder with the redeployment of the 18th Army into an offensive position against the Soviet Union. On 31 July 1940, Hitler held a major conference that included Keitel, Halder, Alfred Jodl, Erich Raeder, Brauchitsch, and Hans Jeschonnek which further discussed the invasion. The participants did not object to the invasion. Hitler asked for war studies to be completed and Georg Thomas was given the task of completing two studies on economic matters. The first study by Thomas detailed serious problems with fuel and rubber supplies. Keitel bluntly dismissed the problems, telling Thomas that Hitler would not want to see it. This influenced Thomas' second study which offered a glowing recommendation for the invasion based upon fabricated economic benefits.

In January 1943, just before the final surrender at Stalingrad, Hitler agreed to the creation of a three-man committee with representatives of the State, the Armed Forces High Command, and the Party in an attempt to centralize control of the war economy and over the home front. The committee members were Keitel, (Chief of OKW) Hans Lammers (Chief of the Reich Chancellery), and Martin Bormann (Chief of the Party Chancellery). The committee, soon known as the Dreierausschuß (Committee of Three), met eleven times between January and August 1943. However, it had little autonomy, with Hitler reserving most of the final decisions to himself. In addition, it ran up against resistance from cabinet ministers, who headed deeply entrenched spheres of influence and, seeing it as a threat to their power, worked together to undermine it. The result was that nothing changed, and the Committee declined into irrelevance.

Keitel played an important role after the failed 20 July plot in 1944. He sat on the army "court of honour" that handed over many officers who were involved, including Field Marshal Erwin von Witzleben, to Roland Freisler's notorious People's Court. Around 7,000 people were arrested, many of whom were tortured by the Gestapo, and around 5,000 were executed.

In April and May 1945, during the Battle of Berlin, Keitel called for counterattacks to drive back the Soviet forces and relieve Berlin. However, there were insufficient German forces to carry out such counterattacks. After Hitler's suicide on 30 April, Keitel stayed on as a member of the short-lived Flensburg Government under Grand Admiral Karl Dönitz. Upon arriving in Flensburg, Albert Speer, the Minister of Armaments and War Production, said that Keitel grovelled to Dönitz in the same way as he had done to Hitler. On 7 May 1945, Alfred Jodl, on behalf of Dönitz, signed Germany's unconditional surrender on all fronts. Joseph Stalin considered this an affront, so a second signing was arranged at the Berlin suburb of Karlshorst on 8 May. There, Keitel signed the German Instrument of Surrender on 8 May 1945. Five days later on 13 May, he was arrested at the request of the United States and interned at Camp Ashcan in Mondorf-les-Bains. Jodl succeeded him as Chief of OKW until the final dissolution of the Flensburg Government on 23 May.

Role in crimes of the Wehrmacht and the Holocaust
Keitel had full knowledge of the criminal nature of the planning and the subsequent invasion of Poland, agreeing to its aims in principle. The Nazi plans included mass arrests, population transfers, and mass murder. Keitel did not contest the regime's assault upon basic human rights or counter the role of the Einsatzgruppen in the murders. The criminal nature of the invasion was now obvious; local commanders continued to express shock and protest over the events they were witnessing. Keitel continued to ignore the protests among the officer corps while they became morally numbed to the atrocities.

Keitel issued a series of criminal orders from April 1941. The orders went beyond established codes of conduct for the military and broadly allowed the execution of Jews, civilians, and non-combatants for any reason. Those carrying out the murders were exempted from court-martial or later being tried for war crimes. The orders were signed by Keitel; however, other members of the OKW and the OKH, including Halder, wrote or changed the wording of his orders. Commanders in the field interpreted and carried out the orders.

In the summer and autumn of 1941, German military lawyers unsuccessfully argued that Soviet prisoners of war should be treated in accordance with the Geneva Conventions. Keitel rebuffed them, writing: "These doubts correspond to military ideas about wars of chivalry. Our job is to suppress a way of life." In September 1941, concerned that some field commanders on the Eastern Front did not exhibit sufficient harshness in implementing the May 1941 order on the "Guidelines for the Conduct of the Troops in Russia", Keitel issued a new order, writing: "[The] struggle against Bolshevism demands ruthless and energetic action especially also against the Jews, the main carriers of Bolshevism". Also in September, Keitel issued an order to all commanders, not just those in the occupied Soviet Union, instructing them to use "unusual severity" to stamp out resistance. In this context, the guideline stated that execution of 50 to 100 "Communists" was an appropriate response to a loss of a German soldier. Such orders and directives further radicalised the army's occupational policies and enmeshed it in the genocide of the Jews.

In December 1941, Hitler instructed the OKW to subject, with the exception of Denmark, Western Europe (which was under military occupation) to the Night and Fog Decree. Signed by Keitel, the decree made it possible for foreign nationals to be transferred to Germany for trial by special courts, or simply handed to the Gestapo for deportation to concentration camps. The OKW further imposed a blackout on any information concerning the fate of the accused. At the same time, Keitel increased pressure on Otto von Stülpnagel, the military commander in France, for a more ruthless reprisal policy in the country. In October 1942, Keitel signed the Commando Order that authorized the killing of enemy special operations troops even when captured in uniform.

In the spring and summer of 1942, as the deportations of the Jews to extermination camps progressed, the military initially protested when it came to the Jews that laboured for the benefit of the Wehrmacht. The army lost control over the matter when the SS assumed command of all Jewish forced labour in July 1942. Keitel formally endorsed the state of affairs in September, reiterating for the armed forces that "evacuation of the Jews must be carried out thoroughly and its consequences endured, despite any trouble it may cause over the next three or four months".

Trial, conviction, and execution
After the war, Keitel faced the International Military Tribunal (IMT), which indicted him on all four counts before it: conspiracy to commit crimes against peace, planning, initiating and waging wars of aggression, war crimes, and crimes against humanity. Most of the case against him was based on his signature being present on dozens of orders that called for soldiers and political prisoners to be killed or 'disappeared'. In court, Keitel admitted that he knew many of Hitler's orders were illegal. His defence relied almost entirely on the argument he was merely following orders in conformity to "the leader principle" (Führerprinzip) and his personal oath of loyalty to Hitler.

The IMT rejected this defence and convicted him on all charges. Although the tribunal's charter allowed "superior orders" to be considered a mitigating factor, it found Keitel's crimes were so egregious that "there is nothing in mitigation". In its judgment against him, the IMT wrote, "Superior orders, even to a soldier, cannot be considered in mitigation where crimes as shocking and extensive have been committed consciously, ruthlessly and without military excuse or justification." It also noted several instances where he issued illegal orders on his own authority.

In his statement before the Tribunal, Keitel said: "As these atrocities developed, one from the other, step by step, and without any foreknowledge of the consequences, destiny took its tragic course, with its fateful consequences." To underscore the criminal rather than military nature of Keitel's acts, the Allies denied his request to be shot by firing squad. Instead, he was executed at Nuremberg Prison by hanging.

On the day of the execution, Keitel told prison chaplain Henry F. Gerecke "You have helped me more than you know. May Christ, my saviour, stand by me all the way. I shall need him so much." He then received Communion and was executed later that day. Keitel was executed by US Army Master Sergeant John C. Woods. His last words were: "I call on God Almighty to have mercy on the German people. More than two million German soldiers went to their death for the fatherland before me. I follow now my sons – all for Germany." The trap door was small, causing head injuries to Keitel and several other condemned men as they dropped. Many of the executed Nazis fell from the gallows with insufficient force to snap their necks, resulting in convulsions that in Keitel's case lasted 24 minutes. The corpses of Keitel and the other nine executed men were, like Hermann Göring's, cremated at Ostfriedhof (Munich) and the ashes were scattered in the river Isar.

Works
Before his execution, Keitel published his memoirs, which were titled in English as In the Service of the Reich. It was later re-edited by Walter Görlitz as The Memoirs of Field-Marshal Keitel (ISBN 978-0-8154-1072-0). Another work by Keitel later published in English was Questionnaire on the Ardennes Offensive.

Family
Keitel was the uncle of Katherine "Kitty" Oppenheimer, wife of the physicist J. Robert Oppenheimer, the director of the Manhattan Project's Los Alamos Laboratory, where the first atomic bombs were developed.

Legacy
Keitel was frequently depicted in World War II films, such as by Dieter Mann in Downfall (2004). Notably, East German actor Gerd Michael Henneberg repeatedly reprised his role as Keitel in several Soviet-East German co-productions directed by Yuri Ozerov in the 1970s and 1980s, such as Soldiers of Freedom (1977), Battle of Moscow (1985) and Stalingrad (1990).

title: Wilhelm Keitel


text:
Treaty on European Union

The Treaty on European Union (2007) is one of the primary Treaties of the European Union, alongside the Treaty on the Functioning of the European Union (TFEU). The TEU forms the basis of EU law, by setting out general principles of the EU's purpose, the governance of its central institutions (such as the Commission, Parliament, and Council), as well as the rules on external, foreign and security policy.

History
While the current version of the TEU entered into force in 2009, following the Treaty of Lisbon (2007), the older form of the same document was implemented by the Maastricht Treaty (1992).

Provisions
After the preamble the consolidated treaty text is divided into six parts.

Title I: Common Provisions
The first deals with common provisions. Article 1 establishes the European Union, formally replacing the European Community, declares a "process of creating an ever closer union among the peoples of Europe", and lays out the legal value of the treaties.

Article 2 states that the EU is "founded on the values of respect for human dignity, freedom, democracy, equality, the rule of law and respect for human rights, including the rights of persons belonging to minorities". The member states share a "society in which pluralism, non-discrimination, tolerance, justice, solidarity and equality between women and men prevail".

Article 3 then states the aims of the EU in six points. The first is simply to promote peace, European values and its citizens' well-being. The second relates to free movement with external border controls in place. Point 3 deals with the internal market. Point 4 establishes the euro. Point 5 states the EU shall promote its values, contribute to eradicating poverty, observe human rights and respect the charter of the United Nations. The final sixth point states that the EU shall pursue these objectives by "appropriate means" according with its competences given in the treaties.

Article 4 relates to member states' sovereignty and obligations. Article 5 sets out the principles of conferral, subsidiarity and proportionality with respect to the limits of its powers. Article 6 binds the EU to the Charter of Fundamental Rights of the European Union and the European Convention on Human Rights. Article 7 deals with the suspension of a member state and article 8 deals with establishing close relations with neighbouring states.

Title II: Provisions on democratic principles
Article 9 establishes the equality of national citizens and citizenship of the European Union. Article 10 declares that the EU is founded in representative democracy and that decisions must be taken as closely as possible to citizens. It makes reference to European political parties and how citizens are represented: directly in the Parliament and by their governments in the Council and European Council – accountable to national parliaments. Article 11 establishes government transparency, declares that broad consultations must be made and introduces provision for a petition where at least 1 million citizens may petition the Commission to legislate on a matter. Article 12 gives national parliaments limited involvement in the legislative process.

Title III: Provisions on the institutions
Article 13 establishes the institutions in the following order and under the following names: the European Parliament, the European Council, the Council, the European Commission, the Court of Justice of the European Union, the European Central Bank and the Court of Auditors. It obliges co-operation between these and limits their competencies to the powers within the treaties.

Article 14 deals with the workings of Parliament and its election, article 15 with the European Council and its president, article 16 with the Council and its configurations and article 17 with the Commission and its appointment. Article 18 establishes the High Representative of the Union for Foreign Affairs and Security Policy and article 19 establishes the Court of Justice.

Title IV: Provisions on enhanced co-operation
Title 4 has only one article which allows a limited number of member states to co-operate within the EU if others are blocking integration in that field.

Title V: General provisions on the Union's external action
Chapter 1 of this title includes articles 21 and 22. Article 21 deals with the principles that outline EU foreign policy; including compliance with the UN charter, promoting global trade, humanitarian support and global governance. Article 22 gives the European Council, acting unanimously, control over defining the EU's foreign policy.

Chapter 2 is further divided into sections. The first, common provisions, details the guidelines and functioning of the EU's foreign policy, including establishment of the European External Action Service and member state's responsibilities. Section 2, articles 42 to 46, deal with military co-operation (including mutual defence).

On 17 November 2015, France called other member states for military assistance, on the basis of the Article 42. This was the first time the article had ever been applied and all of the member states were reported to respond in agreement. However at least one member state (Finland) made a conclusion that due to conflicting national law, military assistance was excluded.

Title VI: Final provisions
Article 47 establishes a legal personality for the EU. Article 48 deals with the method of treaty amendment; specifically the ordinary and simplified revision procedures. Article 49 deals with applications to join the EU and Article 50 with withdrawal. In the aftermath of the Brexit vote in the UK on 23 June 2016, the United Kingdom formally invoked Article 50 in March 2017, giving notice that it would leave the EU within two years. Article 51 deals with the protocols attached to the treaties and article 52 with the geographic application of the treaty. Article 53 states the treaty is in force for an unlimited period, article 54 deals with ratification and 55 with the different language versions of the treaties.

title: Treaty on European Union


text:
Oulipo

Oulipo (, short for Ouvroir de littérature potentielle; roughly translated: "workshop of potential literature", stylized OuLiPo) is a loose gathering of (mainly) French-speaking writers and mathematicians who seek to create works using constrained writing techniques. It was founded in 1960 by Raymond Queneau and François Le Lionnais. Other notable members have included novelists Georges Perec and Italo Calvino, poets Oskar Pastior and Jean Lescure, and poet/mathematician Jacques Roubaud.

The group defines the term littérature potentielle as (rough translation): "the seeking of new structures and patterns which may be used by writers in any way they enjoy". Queneau described Oulipians as "rats who construct the labyrinth from which they plan to escape."

Constraints are used as a means of triggering ideas and inspiration, most notably Perec's "story-making machine", which he used in the construction of Life: A User's Manual. As well as established techniques, such as lipograms (Perec's novel A Void) and palindromes, the group devises new methods, often based on mathematical problems, such as the knight's tour of the chess-board and permutations.

History
Oulipo was founded on November 24, 1960, as a subcommittee of the Collège de 'Pataphysique and titled Séminaire de littérature expérimentale. At their second meeting, the group changed its name to Ouvroir de littérature potentielle, or Oulipo, at Albert-Marie Schmidt's suggestion. The idea had arisen two months earlier, when a small group met in September at Cerisy-la-Salle for a colloquium on Queneau's work. During this seminar, Queneau and François Le Lionnais conceived the society.

During the subsequent decade, Oulipo (as it was commonly known) was only rarely visible as a group. As a subcommittee, they reported their work to the full Collège de 'Pataphysique in 1961. In addition, Temps Mêlés devoted an issue to Oulipo in 1964, and Belgian radio broadcast one Oulipo meeting. Its members were individually active during these years and published works which were created within their constraints. The group as a whole began to emerge from obscurity in 1973 with the publication of La Littérature Potentielle, a collection of representative pieces. Martin Gardner helped to popularize the group in America when he featured Oulipo in his February 1977 Mathematical Games column in Scientific American. In 2012 Harvard University Press published a history of the movement, Many Subtle Channels: In Praise of Potential Literature, by Oulipo member Daniel Levin Becker.

Oulipo was founded by a group of men in 1960 and it took 15 years before the first woman was allowed to join; this was Michèle Métail who became a member in 1975 and has since distanced herself from the group. Since 1960 only six women have joined Oulipo, with Clémentine Mélois last to join in June 2017.

Oulipian works

Some examples of Oulipian writing:
 * Queneau's Exercices de Style is the recounting ninety-nine times of the same inconsequential episode, in which a man witnesses a minor altercation on a bus trip; each account is unique in terms of tone and style.
 * Queneau's Cent Mille Milliards de Poèmes is inspired by children's picture books in which each page is cut into horizontal strips that can be turned independently, allowing different pictures (usually of people: heads, torsos, waists, legs, etc.) to be combined in many ways. Queneau applies this technique to poetry: the book contains 10 sonnets, each on a page. Each page is split into 14 strips, one for each line. The author estimates in the introductory explanation that it would take approximately 200 million years to read all possible combinations.
 * Perec's novel La disparition, translated into English by Gilbert Adair and published under the title A Void, is a 300-page novel written without the letter "e", an example of a lipogram. The English translation, A Void, is also a lipogram.  The novel is remarkable not only for the absence of "e", but it is a mystery in which the absence of that letter is a central theme. Perec would go on to write with the inverse constraint in Les Revenents, with only the vowel “e” present in the work. Ian Monk would later translate Les Revenents into English under the title The Exeter Text.
 * Singular Pleasures by Harry Mathews describes 61 different scenes, each told in a different style (generally poetic, elaborate, or circumlocutory) in which 61 different people (all of different ages, nationalities, and walks of life) masturbate.

Constraints
Some Oulipian constraints:

 * S+7, sometimes called N+7 : Replace every noun in a text with the seventh noun after it in a dictionary. For example, "Call me Ishmael. Some years ago..." becomes "Call me Ishmael. Some yes-men ago...". Results will vary depending upon the dictionary used. This technique can also be performed on other lexical classes, such as verbs.

 * Snowball, or a Rhopalism : A poem in which each line is a single word, and each successive word is one letter longer.

 * Stile: A method wherein each “new” sentence in a paragraph stems from the last word or phrase in the previous sentence (e.g. “I descend the long ladder brings me to the ground floor is spacious…”). In this technique the sentences in a narrative continually overlap, often turning the grammatical object in a previous sentence into the grammatical subject of the next. The author may also pivot on an adverb, prepositional phrase, or other transitory moment.

 * Lipogram : Writing that excludes one or more letters. The previous sentence is a lipogram in B, F, J, K, Q, V, Y, and Z (it does not contain any of those letters).

 * Prisoner's constraint, also called Macao constraint : A type of lipogram that omits letters with ascenders and descenders (b, d, f, g, h, j, k, l, p, q, t, and y).

 * Palindromes: Sonnets and other poems constructed using palindromic techniques.

 * Univocalism: A poem using only one vowel letter. In English and some other languages the same vowel letter can represent different sounds, which means that, for example, "born" and "cot" could both be used in a univocalism. (Words with the same American English vowel sound but represented by different 'vowel' letters could not be used – e.g. "blue" and "stew".)

 * Pilish: A method of writing wherein one matches the length of words (or amount of words in a sentence) to the digits of pi.

 * Mathews' Algorithm: Elements in a text are moved around by a set of predetermined rules

Founding members
The founding members of Oulipo represented a range of intellectual pursuits, including writers, university professors, mathematicians, engineers, and "pataphysicians":

 * Noël Arnaud
 * Jacques Bens
 * Claude Berge
 * Marcel Duchamp
 * Jacques Duchateau
 * Emmanuel Peillet ("Latis")
 * François Le Lionnais
 * Jean Lescure
 * Raymond Queneau
 * Jean Queval
 * Albert-Marie Schmidt

Living members

 * Michèle Audin
 * Valérie Beaudouin
 * Marcel Bénabou
 * Eduardo Berti
 * Bernard Cerquiglini
 * Frédéric Forte
 * Paul Fournel
 * Anne F. Garréta
 * Jacques Jouet
 * Hervé Le Tellier
 * Étienne Lécroart
 * Daniel Levin Becker
 * Clémentine Mélois
 * Michèle Métail
 * Ian Monk
 * Jacques Roubaud
 * Olivier Salon
 * Pablo Martín Sánchez

Deceased members

 * Noël Arnaud
 * Jacques Bens
 * Claude Berge
 * André Blavier
 * Paul Braffort
 * Italo Calvino
 * François Caradec
 * Ross Chambers
 * Stanley Chapman
 * Jacques Duchateau
 * Luc Etienne
 * Michelle Grangaud
 * Emmanuel Peillet ("Latis")
 * François Le Lionnais
 * Jean Lescure
 * Harry Mathews
 * Oskar Pastior
 * Georges Perec
 * Raymond Queneau
 * Jean Queval
 * Pierre Rosenstiehl
 * Albert-Marie Schmidt

title: Oulipo