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NaN

In computing, NaN, standing for Not a Number, is a particular value of a numeric data type (often a floating-point number) which is undefined as a number, such as the result of 0/0. Systematic use of NaNs was introduced by the IEEE 754 floating-point standard in 1985, along with the representation of other non-finite quantities such as infinities.

In mathematics, the result of 0/0 is typically not defined as a number and may therefore be represented by NaN in computing systems.

The square root of a negative number is not a real number, and is therefore also represented by NaN in compliant computing systems. NaNs may also be used to represent missing values in computations.

Two separate kinds of NaNs are provided, termed quiet NaNs and signaling NaNs. Quiet NaNs are used to propagate errors resulting from invalid operations or values. Signaling NaNs can support advanced features such as mixing numerical and symbolic computation or other extensions to basic floating-point arithmetic.

Floating point
In floating-point calculations, NaN is not the same as infinity, although both are typically handled as special cases in floating-point representations of real numbers as well as in floating-point operations. An invalid operation is also not the same as an arithmetic overflow (which would return an infinity or the largest finite number in magnitude) or an arithmetic underflow (which would return the smallest normal number in magnitude, a subnormal number, or zero).

IEEE 754 NaNs are encoded with the exponent field filled with ones (like infinity values), and some non-zero number in the significand field (to make them distinct from infinity values); this allows the definition of multiple distinct NaN values, depending on which bits are set in the significand field, but also on the value of the leading sign bit (but applications are not required to provide distinct semantics for those distinct NaN values).

For example, an IEEE 754 single precision (32-bit) NaN would be encoded as

where s is the sign (most often ignored in applications) and the x sequence represents a non-zero number (the value zero encodes infinities). In practice, the most significant bit from x is used to determine the type of NaN: "quiet NaN" or "signaling NaN" (see details in Encoding). The remaining bits encode a payload (most often ignored in applications).

Floating-point operations other than ordered comparisons normally propagate a quiet NaN (qNaN). Most floating-point operations on a signaling NaN (sNaN) signal the invalid-operation exception; the default exception action is then the same as for qNaN operands and they produce a qNaN if producing a floating-point result.

The propagation of quiet NaNs through arithmetic operations allows errors to be detected at the end of a sequence of operations without extensive testing during intermediate stages. For example, if one starts with a NaN and adds 1 five times in a row, each addition results in a NaN, but there is no need to check each calculation because one can just note that the final result is NaN. However, depending on the language and the function, NaNs can silently be removed from a chain of calculations where one calculation in the chain would give a constant result for all other floating-point values. For example, the calculation x0 may produce the result 1, even where x is NaN, so checking only the final result would obscure the fact that a calculation before the x0 resulted in a NaN. In general, then, a later test for a set invalid flag is needed to detect all cases where NaNs are introduced (see Function definition below for further details).

In section 6.2 of the old IEEE 754-2008 standard, there are two anomalous functions (the maxNum and minNum functions, which return the maximum and the minimum, respectively, of two operands that are expected to be numbers) that favor numbers — if just one of the operands is a NaN then the value of the other operand is returned. The IEEE 754-2019 revision has replaced these functions as they are not associative (when a signaling NaN appears in an operand).

Comparison with NaN
Comparisons are specified by the IEEE 754 standard to take into account possible NaN operands. When comparing two real numbers, or extended real numbers (as in the IEEE 754 floating-point formats), the first number may be either less than, equal to, or greater than the second number. This gives three possible relations. But when at least one operand of a comparison is NaN, this trichotomy does not apply, and a fourth relation is needed: unordered. In particular, two NaN values compare as unordered, not as equal.

As specified, the predicates associated with the <, ≤, =, ≥, > mathematical symbols (or equivalent notation in programming languages) return false on an unordered relation. So, for instance, NOT(x < y) is not logically equivalent to x ≥ y: on unordered, i.e. when x or y is NaN, the former returns true while the latter returns false. However, ≠ is defined as the negation of =, thus it returns true on unordered.

From these rules, comparing x with itself, x ≠ x or x = x, can be used to test whether x is NaN or non-NaN.

The comparison predicates are either signaling or non-signaling on quiet NaN operands; the signaling versions signal the invalid-operation exception for such comparisons (i.e., by default, this just sets the corresponding status flag in addition to the behavior of the non-signaling versions). The equality and inequality predicates are non-signaling. The other standard comparison predicates associated with the above mathematical symbols are all signaling if they receive a NaN operand. The standard also provides non-signaling versions of these other predicates. The predicate  determines whether a value is a NaN and never signals an exception, even if x is a signaling NaN.

The IEEE floating-point standard requires that NaN ≠ NaN hold. In contrast, the 2022 private standard of posit arithmetic has a similar concept, NaR (Not a Real), where NaR = NaR holds.

Operations generating NaN
There are three kinds of operations that can return NaN:

 * Most operations with at least one NaN operand.
 * Indeterminate forms:
 * The divisions $(±0) / (±0)$ and $(±∞) / (±∞)$.
 * The multiplications $(±0) × (±∞)$ and $(±∞) × (±0)$.
 * Remainder $x % y$ when $x$ is an infinity or $y$ is zero.
 * The additions $(+∞) + (−∞)$, $(−∞) + (+∞)$ and equivalent subtractions $(+∞) − (+∞)$ and $(−∞) − (−∞)$.
 * The standard has alternative functions for powers:
 * The standard pow function and the integer exponent pown function define $0^{0}$, $1^{∞}$, and $∞^{0}$ as $1$.
 * The powr function defines all three indeterminate forms as invalid operations and so returns NaN.
 * Real operations with complex results, for example:
 * The square root of a negative number.
 * The logarithm of a negative number.
 * The inverse sine or inverse cosine of a number that is less than −1 or greater than 1.

NaNs may also be explicitly assigned to variables, typically as a representation for missing values. Prior to the IEEE standard, programmers often used a special value (such as −99999999) to represent undefined or missing values, but there was no guarantee that they would be handled consistently or correctly.

NaNs are not necessarily generated in all the above cases. If an operation can produce an exception condition and traps are not masked then the operation will cause a trap instead. If an operand is a quiet NaN, and there is also no signaling NaN operand, then there is no exception condition and the result is a quiet NaN. Explicit assignments will not cause an exception even for signaling NaNs.

Quiet NaN
In general, quiet NaNs, or qNaNs, do not raise any additional exceptions, as they propagate through most operations. But the invalid-operation exception is signaled by some operations that do not return a floating-point value, such as format conversions or certain comparison operations.

Signaling NaN
Signaling NaNs, or sNaNs, are special forms of a NaN that, when consumed by most operations, should raise the invalid operation exception and then, if appropriate, be "quieted" into a qNaN that may then propagate. They were introduced in IEEE 754. There have been several ideas for how these might be used:

When encountered, a trap handler could decode the sNaN and return an index to the computed result. In practice, this approach is faced with many complications. The treatment of the sign bit of NaNs for some simple operations (such as absolute value) is different from that for arithmetic operations. Traps are not required by the standard. There are other approaches to this sort of problem that would be more portable.
 * Filling uninitialized memory with signaling NaNs would produce the invalid operation exception if the data is used before it is initialized
 * Using an sNaN as a placeholder for a more complicated object, such as:
 * A representation of a number that has underflowed
 * A representation of a number that has overflowed
 * Number in a higher precision format
 * A complex number

Payload operations
IEEE 754-2019 recommends the operations getPayload, setPayload, and setPayloadSignaling be implemented, standardizing the access to payloads to streamline application use. According to the IEEE 754-2019 background document, this recommendation should be interpreted as "required for new implementations, with reservation for backward compatibility".

Encoding
In IEEE 754 interchange formats, NaNs are identified by specific, pre-defined bit patterns unique to NaNs. The sign bit does not matter. Binary format NaNs are represented with the exponential field filled with ones (like infinity values), and some non-zero number in the significand field (to make them distinct from infinity values). The original IEEE 754 standard from 1985 (IEEE 754-1985) only described binary floating-point formats, and did not specify how the signaling/quiet state was to be tagged. In practice, the most significant bit of the significand field determined whether a NaN is signaling or quiet. Two different implementations, with reversed meanings, resulted: The former choice has been preferred as it allows the implementation to quiet a signaling NaN by just setting the signaling/quiet bit to 1. The reverse is not possible with the latter choice because setting the signaling/quiet bit to 0 could yield an infinity.
 * most processors (including those of the Intel and AMD's x86 family, the Motorola 68000 family, the AIM PowerPC family, the ARM family, the Sun SPARC family, and optionally new MIPS processors) set the signaling/quiet bit to non-zero if the NaN is quiet, and to zero if the NaN is signaling. Thus, on these processors, the bit represents an is_quiet flag;
 * in NaNs generated by the PA-RISC and old MIPS processors, the signaling/quiet bit is zero if the NaN is quiet, and non-zero if the NaN is signaling. Thus, on these processors, the bit represents an is_signaling flag.

The 2008 and 2019 revisions of the IEEE 754 standard make formal requirements and recommendations for the encoding of the signaling/quiet state.
 * For binary interchange formats, the most significant bit of the significand field is exclusively used to distinguish between quiet and signaling NaNs. (This requirement has been added in the 2019 revision.) Moreover, it should be an is_quiet flag. That is, this bit is non-zero if the NaN is quiet, and zero if the NaN is signaling.
 * For decimal interchange formats, whether binary or decimal encoded, a NaN is identified by having the top five bits of the combination field after the sign bit set to ones. The sixth bit of the field is the is_signaling flag. That is, this bit is zero if the NaN is quiet, and non-zero if the NaN is signaling.

For IEEE 754-2008 conformance, the meaning of the signaling/quiet bit in recent MIPS processors is now configurable via the NAN2008 field of the FCSR register. This support is optional in MIPS Release 3 and required in Release 5.

The state/value of the remaining bits of the significand field are not defined by the standard. This value is called the 'payload' of the NaN. If an operation has a single NaN input and propagates it to the output, the result NaN's payload should be that of the input NaN (this is not always possible for binary formats when the signaling/quiet state is encoded by an is_signaling flag, as explained above). If there are multiple NaN inputs, the result NaN's payload should be from one of the input NaNs; the standard does not specify which.

Canonical NaN
A number of systems have the concept of a "canonical NaN", where one specific NaN value is chosen to be the only possible qNaN generated by floating-point operations not having a NaN input. The value is usually chosen to be a quiet NaN with an all-zero payload and an arbitrarily-defined sign bit.
 * On RISC-V, floating-point operations only ever generate the canonical NaN, even if a NaN is given as the operand (the payload is not propagated). ARM can enable a "default NaN" mode for this behavior. WebAssembly has the same behavior, though it allows two canonical values.
 * A number of languages do not distinguish among different NaN values, without requiring their implementations to force a certain NaN value. ECMAScript (JavaScript) treats all NaN as if they are the same value. Java has the same treatment "for the most part".

Using a limited amount of NaN representations allows the system to use other possible NaN values for non-arithmetic purposes, the most important being "NaN-boxing", i.e. using the payload for arbitrary data. (This concept of "canonical NaN" is not the same as the concept of a "canonical encoding" in IEEE 754.)

Function definition
There are differences of opinion about the proper definition for the result of a numeric function that receives a quiet NaN as input. One view is that the NaN should propagate to the output of the function in all cases to propagate the indication of an error. Another view, and the one taken by the ISO C99 and IEEE 754-2008 standards in general, is that if the function has multiple arguments and the output is uniquely determined by all the non-NaN inputs (including infinity), then that value should be the result. Thus for example the value returned by hypot(±∞, qNaN) and hypot(qNaN, ±∞) is +∞.

The problem is particularly acute for the exponentiation function = xy. The expressions 00, ∞0 and 1∞ are considered indeterminate forms when they occur as limits (just like ∞ × 0), and the question of whether zero to the zero power should be defined as 1 has divided opinion.

If the output is considered as undefined when a parameter is undefined, then pow(1, qNaN) should produce a qNaN. However, math libraries have typically returned 1 for for any real number y, and even when y is an infinity. Similarly, they produce 1 for even when x is 0 or an infinity. The 2008 version of the IEEE 754 standard says that pow(1, qNaN) and pow(qNaN, 0) should both return 1 since they return 1 whatever else is used instead of quiet NaN. Moreover, ISO C99, and later IEEE 754-2008, chose to specify = 1 instead of qNaN; the reason of this choice is given in the C rationale: "Generally, C99 eschews a NaN result where a numerical value is useful. ... The result of pow(−2, ∞) is +∞, because all large positive floating-point values are even integers."

To satisfy those wishing a more strict interpretation of how the power function should act, the 2008 standard defines two additional power functions:, where the exponent must be an integer, and , which returns a NaN whenever a parameter is a NaN or the exponentiation would give an indeterminate form.

Integer NaN
Most fixed-size integer formats cannot explicitly indicate invalid data. In such a case, when converting NaN to an integer type, the IEEE 754 standard requires that the invalid-operation exception be signaled. For example in Java, such operations throw instances of java.lang.ArithmeticException. In C, they lead to undefined behavior, but if annex F is supported, the operation yields an "invalid" floating-point exception (as required by the IEEE standard) and an unspecified value.

Perl's Math::BigInt package uses "NaN" for the result of strings that do not represent valid integers.

Display
Different operating systems and programming languages may have different string representations of NaN.

nan (C, C++, Python) NaN (ECMAScript, Rust, C#, Julia). Julia may show alternative NaN, depending on precision, NaN32, and NaN16; NaN is for Float64 type. NaN% NAN (C, C++, Rust) NaNQ (IBM XL and AIX: Fortran, C++ proposal n2290) NaNS (ditto) qNaN sNaN 1.#SNAN (Excel) 1.#QNAN (Excel) -1.#IND (Excel) +nan.0 (Scheme)

Since, in practice, encoded NaNs have a sign, a quiet/signaling bit and optional 'diagnostic information' (sometimes called a payload), these will occasionally be found in string representations of NaNs, too. Some examples are:

 * For the C and C++ languages, the sign bit is always shown by the standard-library functions (e.g. -nan) when present. There is no standard display of the payload nor of the signaling status, but a quiet NaN value of a specific payload may either be constructed by providing the string  to a number-parsing function (e.g. strtod) or by providing the char-sequence string to nan (or nans for sNaN), both interpreted in an implementation-defined manner.
 * GCC and LLVM provides built-in implementations of nan and nans. They parse the char-sequence as an integer for strtoull (or a differently-sized equivalent) with its detection of integer bases.
 * The GNU C Library's float-parser uses the char-sequence string in "some unspecified fashion". In practice, this parsing has been equivalent to GCC/LLVM's for up to 64 bits of payload.
 * Newlib does not implement nan parsing, but strtod accepts a hexadecimal format without prefix.
 * musl does not implement any payload parsing.

Not all languages admit the existence of multiple NaNs. For example, ECMAScript only uses one NaN value throughout.


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Talk:Sociobiology

Confusing paragraph
5th graph, under Sociobiological theory, reads:

"Anthropologist Colin Turnbull found another supporting example (described in The Mountain People, 1972) about an African tribe, the "Ik," which he said so lacked altruism that the society lost battles with neighboring tribes. His controversial conclusions raised responses among anthropologists and journalists."

This paragraph needs a lot of explanation. Colin Turnbull's findings were "another supporting example" of what, exactly? Also, what is the connection between altruism and losing battles? Why would a society lacking in altruism lose battles with neighbours? Also, what exactly were his controversial conclusions?

--User:Pariah 05:56, 24 Mar 2005 (UTC)

Memetics
I hope everyone is fine with my minor editing of the last paragraph contasting sociobiology and memetics. Aside from that, doesn't it seem a little odd finishing an article about one thing by denying its connection with another? It seems like memetics steals the scene a bit here, but I could be wrong.Maprovonsha172 29 June 2005 02:49 (UTC)

Branch of Social Evolutionism
I removed the following line (sic), because I believe it needs clarification.
 * It is one of the more modern branches of the Social evolutionism theory.

Apart from s/more/most, is Sociobiology really a branch of Social evolutionism? The article on Social Evolutionism doesnt seems to make it clear. And more so, what does it means to be one of the most moderns branches of something? --Abu Badali 13:55, July 14, 2005 (UTC)

Spelling
This article has mixed AE and BE spellings, contrary to Wikipedia policy. This version using "behavior" was early in the article's creation, so AE spelling should be used throughout, except of course in direct quotations. JamesMLane t c 06:17, 12 April 2024 (UTC)

 * WP:SOFIXIT? Chiswick Chap (talk) 08:38, 12 April 2024 (UTC)

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

title: Talk:Sociobiology


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Biological determinism

Biological determinism, also known as genetic determinism, is the belief that human behaviour is directly controlled by an individual's genes or some component of their physiology, generally at the expense of the role of the environment, whether in embryonic development or in learning. Genetic reductionism is a similar concept, but it is distinct from genetic determinism in that the former refers to the level of understanding, while the latter refers to the supposed causal role of genes. Biological determinism has been associated with movements in science and society including eugenics, scientific racism, and the debates around the heritability of IQ, the basis of sexual orientation, and evolutionary foundations of cooperation in sociobiology.

In 1892, the German evolutionary biologist August Weismann proposed in his germ plasm theory that heritable information is transmitted only via germ cells, which he thought contained determinants (genes). The English polymath Francis Galton, supposing that undesirable traits such as club foot and criminality were inherited, advocated eugenics, aiming to prevent supposedly defective people from breeding. The American physician Samuel George Morton and the French physician Paul Broca attempted to relate the cranial capacity (internal skull volume) to skin colour, intending to show that white people were superior. Other workers such as the American psychologists H. H. Goddard and Robert Yerkes attempted to measure people's intelligence and to show that the resulting scores were heritable, again to demonstrate the supposed superiority of people with white skin.

Galton popularized the phrase nature and nurture, later often used to characterize the heated debate over whether genes or the environment determined human behaviour. Scientists such as behavioural geneticists now see it as obvious that both factors are essential, and that they are intertwined, especially through the mechanisms of epigenetics. The American biologist E. O. Wilson, who founded the discipline of sociobiology based on observations of animals such as social insects, controversially suggested that its explanations of social behaviour might apply to humans.

Germ plasm
In 1892, the Austrian biologist August Weismann proposed that multicellular organisms consist of two separate types of cell: somatic cells, which carry out the body's ordinary functions, and germ cells, which transmit heritable information. He called the material that carried the information, now identified as DNA, the germ plasm, and individual components of it, now called genes, determinants which controlled the organism. Weismann argued that there is a one-way transfer of information from the germ cells to somatic cells, so that nothing acquired by the body during an organism's life can affect the germ plasm and the next generation. This effectively denied that Lamarckism (inheritance of acquired characteristics) was a possible mechanism of evolution. The modern equivalent of the theory, expressed at molecular rather than cellular level, is the central dogma of molecular biology.

Eugenics

Early ideas of biological determinism centred on the inheritance of undesirable traits, whether physical such as club foot or cleft palate, or psychological such as alcoholism, bipolar disorder and criminality. The belief that such traits were inherited led to an attempt to solve the problem with the eugenics movement. This was led by a follower of Darwin, Francis Galton (1822–1911), who advocated forcibly reducing breeding among people with those traits. By the 1920s, many U.S. states enacted laws permitting the compulsory sterilization of people considered genetically unfit, including inmates of prisons and psychiatric hospitals. This was followed by similar laws in Germany, and throughout the Western world, in the 1930s.

Scientific racism
Under the influence of determinist beliefs, the American craniologist Samuel George Morton (1799–1851), and later the French anthropologist Paul Broca (1824–1880), attempted to measure the cranial capacities (internal skull volumes) of people of different skin colours, intending to show that whites were superior to the rest, with larger brains. All the supposed proofs from such studies were invalidated by methodological flaws. The results were used to justify slavery, and to oppose women's suffrage.

Heritability of IQ
Alfred Binet (1857–1911) designed tests specifically to measure performance, not innate ability. From the late 19th century, the American school, led by researchers such as H. H. Goddard (1866–1957), Lewis Terman (1877–1956), and Robert Yerkes (1876–1956), transformed these tests into tools for measuring inherited mental ability. They attempted to measure people's intelligence with IQ tests, to demonstrate that the resulting scores were heritable, and so to conclude that people with white skin were superior to the rest. It proved impossible to design culture-independent tests and to carry out testing in a fair way given that people came from different backgrounds, or were newly arrived immigrants, or were illiterate. The results were used to oppose immigration of people from southern and eastern Europe to the USA.

Human sexual orientation
Human sexual orientation, which ranges over a continuum from exclusive attraction to the opposite sex to exclusive attraction to the same sex, is caused by the interplay of genetic and environmental influences. There is considerably more evidence for biological causes of sexual orientation than social factors, especially for males.

Sociobiology

Sociobiology emerged with E. O. Wilson's 1975 book Sociobiology: The New Synthesis. The existence of a putative altruism gene has been debated; the evolutionary biologist W. D. Hamilton proposed "genes underlying altruism" in 1964, while the biologist Graham J. Thompson and colleagues identified the genes OXTR, CD38, COMT, DRD4, DRD5, IGF2, GABRB2 as candidates "affecting altruism". The geneticist Steve Jones argues that altruistic behaviour like "loving our neighbour" is built into the human genome, with the proviso that neighbour means member of "our tribe", someone who shares many genes with the altruist, and that the behaviour can thus be explained by kin selection. Evolutionary biologists such as Jones have argued that genes that did not lead to selfish behaviour would die out compared to genes that did, because the selfish genes would favour themselves. However, the mathematician George Constable and colleagues have argued that altruism can be an evolutionarily stable strategy, making organisms better able to survive random catastrophes.

Nature versus nurture debate
The belief in biological determinism was matched in the 20th century by a blank slate denial of any possible influence of genes on human behaviour, leading to a long and heated debate about "nature and nurture". By the 21st century, many scientists had come to feel that the dichotomy made no sense. They noted that genes are expressed within an environment, in particular that of prenatal development, and that gene expression is continuously influenced by the environment through mechanisms such as epigenetics. Epigenetics provides evidence that human behaviours or physiology can be decided by interactions between genes and environments. For example, monozygotic twins usually have exactly identical genomes. Scientists have focused on comparison studies of such twins for evaluating the heritability of genes and the roles of epigenetics in divergences and similarities between monozygotic twins, and have found that epigenetics plays an important part in human behaviours, including the stress response.

title: Biological determinism


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User:Martin Pool

http://sourcefrog.net/mbp/

Welcome
Hi and welcome to Wikipedia. I saw you over on the Talk:Puzzle_Bobble page and thought you might appreciate a small list of useful Wikipedia links. Also you can sign your name on talk pages and vote pages with three tildes like this, and your name with a time stamp with four like this ~. --Daev
 * Welcome
 * How to edit a page
 * Editing, policy, conduct, and structure tutorial
 * Picture tutorial
 * How to write a great article
 * Naming conventions
 * Manual of Style
 * Help pages
 * Village pump
 * help desk
 * Wiquette

title: User:Martin Pool


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Byron White

Byron Raymond "Whizzer" White (June 8, 1917 – April 15, 2002) was an American lawyer, jurist, and professional football player who served as an associate justice of the Supreme Court of the United States from 1962 until 1993. By his retirement, he was its only sitting Democrat and the last-living member of the progressive Warren Court.

Born and raised in a small homestead in Wellington, Colorado, White distinguished himself as a student athlete who came from a background of poor farmhands to become a consensus All-American halfback for the Colorado Buffaloes. After being the runner-up for the Heisman Trophy in 1937, he was selected in the 1938 NFL Draft by the Pittsburgh Pirates for the National Football League (NFL). He led the league in rushing yards during his rookie season. White graduated from the University of Colorado Boulder as class valedictorian, attaining a Rhodes Scholarship to study at Oxford University. After World War II forced him to return to the United States, he matriculated at Yale Law School, played for the Detroit Lions in the 1940 and 1941 seasons while still enrolled, and served as an officer for the United States Navy in the Pacific Theatre.

White graduated from law school with honors in 1946 and clerked for Chief Justice Fred M. Vinson. He eschewed work for a white-shoe firm and returned to Colorado in order to enter private practice in Denver as a transactional attorney. Minor work as the Colorado state chair of John F. Kennedy's 1960 presidential campaign led to him being unexpectedly tapped in 1961 for a position as U.S. Deputy Attorney General. He was successfully nominated by Kennedy to the Supreme Court the next year, becoming the Court's first justice from Colorado.

White espoused a pragmatic and non-doctrinaire judicial approach which strengthened the powers of the federal government, advocated for the desegregation of public schools, and upheld the use of affirmative action. Though expected to be a reliably liberal justice, he was by contrast a vociferous opponent of substantive due process, penning dissents in both Miranda v. Arizona and Roe v. Wade. White wrote the majority opinion in Bowers v. Hardwick (upholding the ability for states to restrict homosexual conduct) and dissented in Runyon v. McCrary (against the ability for the government to restrict racial discrimination in private schools) and Planned Parenthood v. Casey. Due to his unwillingness to align with either the liberal or conservative blocs, White was largely oriented with the Court's center.

Early life and education
White was born in Fort Collins, Colorado, on June 8, 1917. He was the younger son of Maude Elizabeth (née Burger) and Alpha Albert White. Despite being poor German settlers that never attended high school, White's parents instilled a heavy emphasis on his education and took active roles in the local community. Both White and his brother, Clayton "Sam" Samuel White, were raised in the nearby town of Wellington where they attended the local high school. As a young student, White worked odd jobs to support his family during the town's decline in the 1920s; these included roles in harvesting beets, shoveling coal, and hard construction work among other forms of manual labor. In his junior year, he and his brother rented out land and spent long hours in the fields, during which time White adopted a nearly lifelong habit of smoking.

Sam, four years White's senior, became an accomplished student and athlete that graduated as valedictorian, earning a scholarship to study at the University of Colorado, where he was later elected by the university to become a Rhodes Scholar. Whereas Sam was a gregarious and socially active child, White was described as a taciturn boy who "was very quiet, measuring every single word, showing no emotion, and revealing nothing."

White excelled academically in high school, graduating in 1934 as the class valedictorian with the highest grades in the school's history. He studied diligently in order to attain a scholarship to attend college, later describing his philosophy in Wellington as "do your work and don't be late for dinner." White followed his brother's footsteps in attending the University of Colorado Boulder on the scholarship offered to all Colorado high school valedictorians, intending to go to medical school and major in chemistry. Though he joined the Phi Gamma Delta fraternity on campus, he stuck to a strict routine of working and studying with little to no social life. However, he would become a star athlete after playing as an All-American halfback for the Colorado Buffaloes football team, winning a series of victories to become among the most acclaimed players in the country.

In 1935, Sam White was awarded a Rhodes Scholarship to study at Oxford University. After news of his brother's success became a local sensation, White saw his brother as an inspiration and felt pressured to achieve the scholarship himself. He served as student body president his senior year, switched his major to the humanities, and graduated Phi Beta Kappa and valedictorian from the University of Colorado in 1938 with a Bachelor of Arts degree in economics. In his last year, the Colorado Buffaloes went undefeated, and White's status as a football star earned him the moniker "Whizzer White" by the student newspaper. After months of study, White also attained the Rhodes Scholarship, deferring it for a year to play professional football before attending Hertford College.

Oxford
On January 3, 1939, White departed to England aboard the SS Europa, arriving in Southampton on January 9 harassed by reporters wishing to see a "Yank at Oxford." Upon moving into Hertford College with the intent of studying law, he befriended the future mathematician George Piranian and was assigned with C. H. S. Fifoot as a tutor. White spent his days at Oxford tirelessly studying from day until night, becoming "the only Rhodes scholar who ever worked fourteen hours a day on his studies." During one Easter vacation, he became acquainted with Joseph P. Kennedy and future U.S. president John F. Kennedy as their father, Joseph Kennedy, was the U.S. ambassador to London. In the period of political upheaval just before the Second World War, Oxford students—Rhodes scholars especially—took an active role in international politics, with many American Rhodes scholars beckoning President Roosevelt to take action against Spanish nationalists. White, however, remained closed in the affairs of politics, rarely speaking out and becoming estranged from other students; he prioritized his studies and physique above all else.

Following the end of a term, White spent a summer vacation touring France and Germany, settling down in Munich in order to study the German language and Roman law. He unexpectedly reunited with John F. Kennedy, who was on his own tour of Europe with Torbert Macdonald, and on one occasion the three were heckled by a mob who recognized their English license plates. As the oncoming war made it impossible for students to continue studying abroad, White left the country to return to Oxford in late August 1939, choosing to leave the university in order to continue his legal education at Yale Law School.

Law school and the NFL
Upon enrolling at Yale, White continued his previous routine of studying fourteen hours a day, taking breaks only to exercise in the gymnasium where he would frequent the basketball courts, often clashing against Yale halfback Clint Frank in pick-up games. Despite attempts by the New York Giants and other NFL teams to get him to sign back into football, White publicly repudiated his football career, telling a local newspaper that "my football playing days are over. I'm started on a law career."

At the time, Yale was home to a number of legal realists who rebuked Lochner and substantive due process, and were generally scholars with an expertise in legal fields outside of constitutional law. Two of such realists—Myres S. McDougal and Arthur Corbin—had a significant influence on White early in law school. Future justice Potter Stewart, one year ahead of him at the university, remembered White as "a serious-minded, scholarly, and rather taciturn (except when he found himself engaged in lively colloquy with J. W. Moore in his class on Procedure), and extremely likable young man with steel-rimmed eyeglasses."

White earned the highest grades in his first-year class and was subsequently awarded the Edgar M. Cullen Prize, an award given to the highest-achieving first-year student. During the summer, he returned to Colorado and attended summer school at the University of Colorado Law School, got an appendectomy, and became a waiter at his old fraternity. White would turn down an offer to join the editorship of the Yale Law Journal, instead taking a leave of absence to promptly return to professional football as a member of the Detroit Lions, again leading the league in rushing in 1940. In three NFL seasons, he played in 33 games and led the NFL in rushing yards in 1938 and 1940. With an offer of $15,800, he was the National Football League's highest-paid player, and ultimately ended the season with the highest number of yards in the NFL at 514. Despite White's performance, the Lions had a largely mediocre season, finishing in third-place with a 5–5–1 record. At the end of the season in December 1941, he returned to Yale to await a call to serve in the U.S. Navy after the Attack on Pearl Harbor; in May 1942, he was assigned to naval intelligence and spent weeks training at Dartmouth College and in New York City. His original intention was to join the Marine Corps, but was kept out due to being colorblind.

World War II
In July 1943, White was stationed at Nouméa, New Caledonia, tasked with protecting Guadalcanal and Tulagi; he narrowly missed being assigned with John F. Kennedy, his former acquaintance who had also been stationed at Tulagi before being reassigned to the Russell Islands. During World War II, White served as an intelligence officer in the Navy, and was stationed in the Pacific Theatre. He wrote the intelligence report on the sinking of future President John F. Kennedy's PT-109. For his service, White was awarded two Bronze Star medals, and was honorably discharged as a lieutenant commander in 1945.

Legal career
After his military service, White returned to Yale Law School, graduating in 1946 ranked first in his class with a Bachelor of Laws degree, magna cum laude, and membership in the Order of the Coif. White served as a law clerk to Chief Justice Fred M. Vinson of the U.S. Supreme Court from 1946 to 1947, then returned to Colorado and entered private practice in Denver with the law firm now known as Davis Graham & Stubbs. This was a time in which the Denver economy flourished, and White rendered legal service to the business community. White was for the most part a transactional attorney; he drafted contracts and advised insolvent companies, and he argued the occasional case in court.

During the 1960 presidential election, White used his status as a football star to aid him as chair of John F. Kennedy's campaign in Colorado. White had first met the candidate when White was a Rhodes scholar and Kennedy's father, Joseph Kennedy, was Ambassador to the Court of St. James's. During the Kennedy administration, White served as United States Deputy Attorney General, the number two man in the Justice Department, under Robert F. Kennedy. He took the lead in protecting the Freedom Riders in 1961, negotiating with Alabama Governor John Malcolm Patterson.

Supreme Court
On April 3, 1962, President Kennedy nominated White to be an associate justice of the Supreme Court, succeeding Charles Evans Whittaker. The president said of White—a longtime friend of his—that "he has excelled at everything. And I know that he will excel on the highest court in the land." White was confirmed on April 11, 1962, by a voice vote. He took the judicial oath of office on April 16, 1962, and served until June 28, 1993. His Supreme Court tenure was the fourth-longest of the 20th century.

Upon the request of Vice President-Elect Al Gore, White administered the oath of office on January 20, 1993, to Gore. It was the only time White administered an oath of office to a vice president. During his service on the high court, White wrote 994 opinions. He was fierce in questioning attorneys in court, and his votes and opinions on the bench reflect an ideology that has been notoriously difficult for popular journalists and legal scholars alike to pin down. He was seen as a disappointment by some Kennedy supporters who wished he had joined the more liberal wing of the court in its opinions on Miranda v. Arizona and Roe v. Wade.

White often took a narrow, fact-specific view of cases before the Court and generally refused to make broad pronouncements on constitutional doctrine or adhere to a specific judicial philosophy, preferring what he viewed as a practical approach to the law. In the tradition of the New Deal, White frequently supported a broad view and expansion of governmental powers. He consistently voted against creating constitutional restrictions on the police, dissenting in the landmark 1966 case Miranda v. Arizona. In that dissent, he said that aggressive police practices enhance the individual rights of law-abiding citizens. His jurisprudence has sometimes been praised for adhering to the doctrine of judicial restraint.

Substantive due process doctrine
Frequently a critic of the doctrine of "substantive due process", which involves the judiciary reading substantive content into the term "liberty" in the Due Process Clause of the Fifth Amendment and Fourteenth Amendment, White's first published opinion as a Supreme Court Justice was a joint dissent with Justice Clark in Robinson v. California (1962), foreshadowing his career-long distaste for the doctrine. In Robinson, he criticized the remainder of the Court's unprecedented expansion of the Eighth Amendment's prohibition of "cruel and unusual punishment" to strike down a California law providing for civil commitment of drug addicts. He argued that the Court was "imposing its own philosophical predilections" on the state in this exercise of judicial power, although its historic "allergy to substantive due process" would never permit it to strike down a state's economic regulatory law in such a manner.

In the same vein, he dissented in the controversial 1973 case Roe v. Wade. White voted to strike down a state ban on contraceptives in the 1965 case of Griswold v. Connecticut, although he did not join the majority opinion, which famously asserted a "right of privacy" on the basis of the "penumbras" of the Bill of Rights. White and Justice William Rehnquist were the only dissenters from the Court's decision in Roe, though White's dissent used stronger language, suggesting that Roe was "an exercise in raw judicial power" and criticizing the decision for "interposing a constitutional barrier to state efforts to protect human life." White, who usually adhered firmly to the doctrine of stare decisis, remained a critic of Roe throughout his term on the bench and frequently voted to uphold laws restricting abortion, including in Planned Parenthood v. Casey in 1992.

White explained his general views on the validity of substantive due process at length in his dissent in Moore v. City of East Cleveland (1977):

"The Judiciary, including this Court, is the most vulnerable and comes nearest to illegitimacy when it deals with judge-made constitutional law having little or no cognizable roots in the language or even the design of the Constitution. Realizing that the present construction of the Due Process Clause represents a major judicial gloss on its terms, as well as on the anticipation of the Framers, and that much of the underpinning for the broad, substantive application of the Clause disappeared in the conflict between the Executive and the Judiciary in the 1930s and 1940s, the Court should be extremely reluctant to breathe still further substantive content into the Due Process clause so as to strike down legislation adopted by a State or city to promote its welfare. Whenever the Judiciary does so, it unavoidably pre-empts for itself another part of the governance of the country without express constitutional authority."

White parted company with Rehnquist in strongly supporting the Supreme Court decisions striking down laws that discriminated on the basis of sex, agreeing with Justice William J. Brennan in 1973's Frontiero v. Richardson that such laws should be subject to strict scrutiny. Only three justices joined Brennan's plurality opinion in Frontiero; later gender discrimination cases would be subjected to intermediate scrutiny (see Craig v. Boren). In Rostker v. Goldberg, White joined Brennan and Marshall in dissent arguing that male-only Selective Service registration was unconstitutional.

White wrote the majority opinion in Bowers v. Hardwick (1986), which upheld Georgia's anti-sodomy law against a substantive due process attack:

"The Court is most vulnerable and comes nearest to illegitimacy when it deals with judge-made constitutional law having little or no cognizable roots in the language or design of the Constitution.... There should be, therefore, great resistance to ... redefining the category of rights deemed to be fundamental. Otherwise, the Judiciary necessarily takes to itself further authority to govern the country without express constitutional authority."

White's opinion in Bowers typified his fact-specific, deferential style, treating the issue in that case as presenting only the question of whether homosexuals had a fundamental right to privacy, even though the statute in Bowers potentially applied to heterosexual sodomy. Georgia, however, conceded during oral argument that the law would be inapplicable to married couples under the precedent set forth in Griswold v. Connecticut. A year after White's death, Bowers was overruled in Lawrence v. Texas (2003).

Death penalty
White took a middle course on the issue of the death penalty: he was one of five justices who voted in Furman v. Georgia (1972) to strike down several state capital punishment statutes, voicing concern over the arbitrary way in which the death penalty was administered. The Furman decision ended capital punishment in the U.S. until the court's ruling in Gregg v. Georgia (1976). In that case, White voted to uphold Georgia's new capital punishment law.

White accepted the position that the Eighth Amendment to the United States Constitution required that all punishments be "proportional" to the crime; thus, in Coker v. Georgia (1977), he wrote the opinion that invalidated the death penalty for rape of a 16-year-old married girl. His first reported Supreme Court decision was a dissent in Robinson v. California (1962), in which he criticized the Court for extending the reach of the Eighth Amendment. In Robinson the Court for the first time expanded the constitutional prohibition of "cruel and unusual punishments" from examining the nature of the punishment imposed and whether it was an uncommon punishment − as, for example, in the cases of flogging, branding, banishment, or electrocution − to deciding whether any punishment at all was appropriate for the defendant's conduct. White said: "If this case involved economic regulation, the present Court's allergy to substantive due process would surely save the statute and prevent the Court from imposing its own philosophical predilections upon state legislatures or Congress." Consistent with his view in Robinson, White thought that imposing the death penalty on minors was constitutional, and he was one of the three dissenters in Thompson v. Oklahoma (1988), a decision that declared that the death penalty as applied to offenders below 16 years of age was unconstitutional as a cruel and unusual punishment.

Abortion
Along with Justice William Rehnquist, White dissented in Roe v. Wade (the dissenting decision was in the companion case, Doe v. Bolton), castigating the majority for holding that the U.S. Constitution "values the convenience, whim or caprice of the putative mother more than the life or potential life of the fetus."

Civil rights
White consistently supported the Court's post-Brown v. Board of Education attempts to fully desegregate public schools, even through the controversial line of forced busing cases. He voted to uphold affirmative action remedies to racial inequality in an education setting in the famous Regents of the University of California v. Bakke case of 1978. Though White voted to uphold federal affirmative action programs in cases such as Metro Broadcasting, Inc. v. FCC, 497 U.S. 547 (1990) (later overruled by Adarand Constructors v. Peña, 515 U.S. 200 (1995)), he voted to strike down an affirmative action plan regarding state contracts in Richmond v. J.A. Croson Co. (1989).

White dissented in Runyon v. McCrary (1976), which held that federal law prohibited private schools from discriminating on the basis of race. He argued that the legislative history of 42 U.S.C. § 1981 (popularly known as the "Ku Klux Klan Act") indicated that the Act was not designed to prohibit private racial discrimination but only state-sponsored racial discrimination (as had been held in the Civil Rights Cases of 1883). White was concerned about the potential far-reaching impact of holding private racial discrimination illegal, which if taken to its logical conclusion might ban many varied forms of voluntary self-segregation, including social and advocacy groups that limited their membership to blacks: "Whether such conduct should be condoned or not, whites and blacks will undoubtedly choose to form a variety of associational relationships pursuant to contracts which exclude members of the other race. Social clubs, black and white, and associations designed to further the interests of blacks or whites are but two examples". Runyon was essentially overruled by 1989's Patterson v. McLean Credit Union, which itself was superseded by the Civil Rights Act of 1991.

Relationships with other justices
White said he was most comfortable on Rehnquist's court. He once said of Earl Warren, "I wasn't exactly in his circle." On the Burger Court, the chief justice often assigned important criminal procedure and individual rights opinions to White because of his frequently conservative views on these questions.

Court operations and retirement
White frequently urged the Supreme Court to consider cases when federal appeals courts were in conflict on issues of federal law, believing that resolving such was a primary role of the Supreme Court. Thus, White voted to grant certiorari more often than many of his colleagues; he also wrote numerous opinions dissenting from denials of certiorari. After White (along with fellow Justice Harry Blackmun, who also often voted for liberal grants of certiorari) retired, the number of cases heard each session of the Court declined steeply.

White disliked the politics of Supreme Court appointments, but had great faith in representative democracy, responding to complaints about politicians and mediocrity in government with exhortations to "get more involved and help fix it." He retired in 1993, during Bill Clinton's presidency, saying that "someone else should be permitted to have a like experience." When he retired, White had been the only Democrat on the Court. Clinton nominated (and the Senate approved) Justice Ruth Bader Ginsburg, a judge from the U.S. Court of Appeals for the D.C. Circuit and a former Columbia University law professor, to succeed him.

Later years and death
After retiring from the Supreme Court, White occasionally sat with lower federal courts. He maintained chambers in the federal courthouse in Denver until shortly before his death. He also served for the Commission on Structural Alternatives for the Federal Courts of Appeals.

White died of pneumonia on April 15, 2002, at the age of 84. He was the last living Justice to have served on the Warren Court, and the last justice appointed by Kennedy; he died the day before the fortieth anniversary of his swearing in as a Justice. From his death until the retirement of Sandra Day O'Connor in 2006, there were no living former justices.

His remains are interred at All Souls Walk at St. John's Cathedral in Denver.

Then-Chief Justice Rehnquist said White "came as close as anyone I have known to meriting Matthew Arnold's description of Sophocles: 'He saw life steadily and he saw it whole.' All of us who served with him will miss him."

Personal life
White first met his wife Marion Stearns (1921–2009), the daughter of the president of the University of Colorado, when she was in high school and he was a college football player. During World War II, Marion served in the WAVES while her future husband was a Navy intelligence officer. They married in 1946 and had two children: a son named Charles Byron (Barney) and a daughter named Nancy.

His older brother Clayton Samuel "Sam" White (1912–2004) was also a high school valedictorian and Rhodes Scholar. He later became a physician and medical researcher, particularly on the effects of atomic bomb blasts.

Awards and honors
The NFL Players Association gives the Byron "Whizzer" White NFL Man of the Year Award to one player each year for his charity work. Michael McCrary, who was involved in Runyon v. McCrary, grew up to be a professional football player and won the award in 2000.

The federal courthouse in Denver that houses the Tenth Circuit is named after White.

White was elected to the College Football Hall of Fame in 1952.

White was made an honorary fellow of Hertford College, Oxford.

White was posthumously awarded the Presidential Medal of Freedom in 2003 by President George W. Bush.

White was inducted into the Rocky Mountain Athletic Conference Hall of Fame on July 14, 2007, in addition to being a member of the College Football Hall of Fame and the University of Colorado's Athletic Hall of Fame, where he is enshrined as "The Greatest Buff Ever".

title: Byron White