title: Binomial coefficient

text: Another occurrence of this number is in combinatorics, where it gives the number of ways, disregarding order, that "k" objects can be chosen from among "n" objects; more formally, the number of "k"-element subsets (or "k"-combinations) of an "n"-element set. This number can be seen as equal to the one of the first definition, independently of any of the formulas below to compute it: if in each of the "n" factors of the power one temporarily labels the term "X" with an index "i" (running from 1 to "n"), then each subset of "k" indices gives after expansion a contribution "X", and the coefficient of that monomial in the result will be the number of such subsets. This shows in particular that formula_16 is a natural number for any natural numbers "n" and "k". There are many other combinatorial interpretations of binomial coefficients (counting problems for which the answer is given by a binomial coefficient expression), for instance the number of words formed of "n" bits (digits 0 or 1) whose sum is "k" is given by formula_16, while the number of ways to write formula_20 where every "a" is a nonnegative integer is given by formula_21. Most of these interpretations are easily seen to be equivalent to counting "k"-combinations.


title: Binomial coefficient

text: Several methods exist to compute the value of formula_9 without actually expanding a binomial power or counting "k"-combinations.


title: Binomial coefficient

text: The formula follows from considering the set and counting separately (a) the "k"-element groupings that include a particular set element, say ""i"", in every group (since ""i"" is already chosen to fill one spot in every group, we need only choose from the remaining ) and (b) all the "k"-groupings that don't include ""i""; this enumerates all the possible "k"-combinations of "n" elements. It also follows from tracing the contributions to "X" in . As there is zero or in , one might extend the definition beyond the above boundaries to include formula_28 when either or . This recursive formula then allows the construction of Pascal's triangle, surrounded by white spaces where the zeros, or the trivial coefficients, would be.


title: Binomial coefficient

text: The numerator gives the number of ways to select a sequence of "k" distinct objects, retaining the order of selection, from a set of "n" objects. The denominator counts the number of distinct sequences that define the same "k"-combination when order is disregarded.


title: Binomial coefficient

text: Due to the symmetry of the binomial coefficient with regard to "k" and , calculation may be optimised by setting the upper limit of the product above to the smaller of "k" and .


title: Binomial coefficient

text: Finally, though computationally unsuitable, there is the compact form, often used in proofs and derivations, which makes repeated use of the familiar factorial function:


title: Binomial coefficient

text: where "n"! denotes the factorial of "n". This formula follows from the multiplicative formula above by multiplying numerator and denominator by ; as a consequence it involves many factors common to numerator and denominator. It is less practical for explicit computation (in the case that "k" is small and "n" is large) unless common factors are first cancelled (in particular since factorial values grow very rapidly). The formula does exhibit a symmetry that is less evident from the multiplicative formula (though it is from the definitions)


title: Binomial coefficient

text: which leads to a more efficient multiplicative computational routine. Using the falling factorial notation,


title: Binomial coefficient

text: The multiplicative formula allows the definition of binomial coefficients to be extended by replacing "n" by an arbitrary number "α" (negative, real, complex) or even an element of any commutative ring in which all positive integers are invertible:


title: Binomial coefficient

text: With this definition one has a generalization of the binomial formula (with one of the variables set to 1), which justifies still calling the formula_34 binomial coefficients:


title: Binomial coefficient

text: This formula is valid for all complex numbers "α" and "X" with |"X"| < 1. It can also be interpreted as an identity of formal power series in "X", where it actually can serve as definition of arbitrary powers of power series with constant coefficient equal to 1; the point is that with this definition all identities hold that one expects for exponentiation, notably


title: Binomial coefficient

text: If "α" is a nonnegative integer "n", then all terms with are zero, and the infinite series becomes a finite sum, thereby recovering the binomial formula. However, for other values of "α", including negative integers and rational numbers, the series is really infinite.


title: Binomial coefficient

text: which can be used to prove by mathematical induction that formula_36 is a natural number for all integer "n" ≥ 0 and all integer "k", a fact that is not immediately obvious from formula (1). To the left and right of Pascal's triangle, the entries (shown as blanks) are all zero.


title: Binomial coefficient

text: Row number contains the numbers formula_9 for . It is constructed by first placing 1s in the outermost positions, and then filling each inner position with the sum of the two numbers directly above. This method allows the quick calculation of binomial coefficients without the need for fractions or multiplications. For instance, by looking at row number 5 of the triangle, one can quickly read off that


title: Binomial coefficient

text: Binomial coefficients are of importance in combinatorics, because they provide ready formulas for certain frequent counting problems:


title: Binomial coefficient

text: For any nonnegative integer "k", the expression formula_45 can be simplified and defined as a polynomial divided by :


title: Binomial coefficient

text: As such, it can be evaluated at any real or complex number "t" to define binomial coefficients with such first arguments. These "generalized binomial coefficients" appear in Newton's generalized binomial theorem.


title: Binomial coefficient

text: For each "k", the polynomial formula_47 can be characterized as the unique degree "k" polynomial satisfying and .


title: Binomial coefficient

text: This can cause a problem when evaluated at integers from formula_51 to formula_52, but using identities below we can compute the derivative as:


title: Binomial coefficient

text: Over any field of characteristic 0 (that is, any field that contains the rational numbers), each polynomial "p"("t") of degree at most "d" is uniquely expressible as a linear combination formula_54 of binomial coefficients. The coefficient "a" is the "k"th difference of the sequence "p"(0), "p"(1), ..., "p"("k"). Explicitly,


title: Binomial coefficient

text: Each polynomial formula_47 is integer-valued: it has an integer value at all integer inputs formula_56. (One way to prove this is by induction on "k", using Pascal's identity.) Therefore, any integer linear combination of binomial coefficient polynomials is integer-valued too. Conversely, () shows that any integer-valued polynomial is an integer linear combination of these binomial coefficient polynomials. More generally, for any subring "R" of a characteristic 0 field "K", a polynomial in "K"["t"] takes values in "R" at all integers if and only if it is an "R"-linear combination of binomial coefficient polynomials.


title: Binomial coefficient

text: The factorial formula facilitates relating nearby binomial coefficients. For instance, if "k" is a positive integer and "n" is arbitrary, then


title: Binomial coefficient

text: says the elements in the th row of Pascal's triangle always add up to 2 raised to the th power. This is obtained from the binomial theorem () by setting "x" = 1 and "y" = 1. The formula also has a natural combinatorial interpretation: the left side sums the number of subsets of {1, ..., "n"} of sizes "k" = 0, 1, ..., "n", giving the total number of subsets. (That is, the left side counts the power set of {1, ..., "n"}.) However, these subsets can also be generated by successively choosing or excluding each element 1, ..., "n"; the "n" independent binary choices (bit-strings) allow a total of formula_63 choices. The left and right sides are two ways to count the same collection of subsets, so they are equal.


title: Binomial coefficient

text: follow from the binomial theorem after differentiating with respect to (twice for the latter) and then substituting .


title: Binomial coefficient

text: The Chu–Vandermonde identity, which holds for any complex values "m" and "n" and any non-negative integer "k", is


title: Binomial coefficient

text: and can be found by examination of the coefficient of formula_65 in the expansion of using equation (). When , equation () reduces to equation (). In the special case , using (), the expansion () becomes (as seen in Pascal's triangle at right)


title: Binomial coefficient

text: Another form of the Chu–Vandermonde identity, which applies for any integers "j", "k", and "n" satisfying , is


title: Binomial coefficient

text: This can be proved by induction using () or by Zeckendorf's representation. A combinatorial proof is given below.


title: Binomial coefficient

text: For integers "s" and "t" such that formula_69 series multisection gives the following identity for the sum of binomial coefficients:


title: Binomial coefficient

text: for "n" > 0. This latter result is also a special case of the result from the theory of finite differences that for any polynomial "P"("x") of degree less than "n",


title: Binomial coefficient

text: where "m" and "d" are complex numbers. This follows immediately applying () to the polynomial instead of , and observing that still has degree less than or equal to "n", and that its coefficient of degree "n" is "da".


title: Binomial coefficient

text: The series formula_85 is convergent for "k" ≥ 2. This formula is used in the analysis of the German tank problem. It follows from formula_86 which is proved by induction on "M".


title: Binomial coefficient

text: Many identities involving binomial coefficients can be proved by combinatorial means. For example, for nonnegative integers formula_87, the identity


title: Binomial coefficient

text: (which reduces to () when "q" = 1) can be given a double counting proof, as follows. The left side counts the number of ways of selecting a subset of ["n"] = {1, 2, ..., "n"} with at least "q" elements, and marking "q" elements among those selected. The right side counts the same thing, because there are formula_89 ways of choosing a set of "q" elements to mark, and formula_90 to choose which of the remaining elements of ["n"] also belong to the subset.


title: Binomial coefficient

text: both sides count the number of "k"-element subsets of ["n"]: the two terms on the right side group them into those that contain element "n" and those that do not.


title: Binomial coefficient

text: Suppose you have formula_93 empty squares arranged in a row and you want to mark (select) "n" of them. There are formula_94 ways to do this. On the other hand, you may select your "n" squares by selecting "k" squares from among the first "n" and formula_95 squares from the remaining "n" squares; any "k" from 0 to "n" will work. This gives


title: Binomial coefficient

text: has the following combinatorial proof. One may show by induction that counts the number of ways that a strip of squares may be covered by and tiles. On the other hand, if such a tiling uses exactly of the tiles, then it uses of the tiles, and so uses tiles total. There are formula_98 ways to order these tiles, and so summing this coefficient over all possible values of gives the identity.


title: Binomial coefficient

text: The number of "k"-combinations for all "k", formula_99, is the sum of the "n"th row (counting from 0) of the binomial coefficients. These combinations are enumerated by the 1 digits of the set of base 2 numbers counting from 0 to formula_100, where each digit position is an item from the set of "n".


title: Binomial coefficient

text: Certain trigonometric integrals have values expressible in terms of binomial coefficients: For any formula_103


title: Binomial coefficient

text: These can be proved by using Euler's formula to convert trigonometric functions to complex exponentials, expanding using the binomial theorem, and integrating term by term.


title: Binomial coefficient

text: More generally, this remains true if "n" is any number and "k" is such that all the numbers between 1 and "k" are coprime to "n".


title: Binomial coefficient

text: In 1852, Kummer proved that if "m" and "n" are nonnegative integers and "p" is a prime number, then the largest power of "p" dividing formula_118 equals "p", where "c" is the number of carries when "m" and "n" are added in base "p".


title: Binomial coefficient

text: equals the number of nonnegative integers "j" such that the fractional part of "k"/"p" is greater than the fractional part of "n"/"p". It can be deduced from this that formula_39 is divisible by "n"/gcd("n","k"). In particular therefore it follows that "p" divides formula_121 for all positive integers "r" and "s" such that . However this is not true of higher powers of "p": for example 9 does not divide formula_122.


title: Binomial coefficient

text: A somewhat surprising result by David Singmaster (1974) is that any integer divides almost all binomial coefficients. More precisely, fix an integer "d" and let "f"("N") denote the number of binomial coefficients formula_39 with "n" < "N" such that "d" divides formula_39. Then


title: Binomial coefficient

text: Since the number of binomial coefficients formula_39 with "n" < "N" is "N"("N" + 1) / 2, this implies that the density of binomial coefficients divisible by "d" goes to 1.


title: Binomial coefficient

text: Binomial coefficients have divisibility properties related to least common multiples of consecutive integers. For example:


title: Binomial coefficient

text: otherwise the numerator has to be divisible by , this can only be the case when is divisible by "p". But "n" is divisible by "p", so "p" does not divide and because "p" is prime, we know that "p" does not divide and so the numerator cannot be divisible by "n".


title: Binomial coefficient

text: and each of these formula_138 terms in this product is formula_139. A similar argument can be made to show the second inequality. The final strict inequality is equivalent to formula_140, that is clear since the RHS is a term of the exponential series formula_141.


title: Binomial coefficient

text: Stirling's approximation yields the following approximation, valid when formula_24 both tend to infinity:


title: Binomial coefficient

text: Because the inequality forms of Stirling's formula also bound the factorials, slight variants on the above asymptotic approximation give exact bounds.


title: Binomial coefficient

text: If "n" is large and "k" is linear in "n", various precise asymptotic estimates exist for the binomial coefficient formula_153. For example, if formula_154 then


title: Binomial coefficient

text: A simple and rough upper bound for the sum of binomial coefficients can be obtained using the binomial theorem:


title: Binomial coefficient

text: The infinite product formula for the gamma function also gives an expression for binomial coefficients


title: Binomial coefficient

text: as well. (Here formula_165 is the "k"-th harmonic number and formula_166 is the Euler–Mascheroni constant.)


title: Binomial coefficient

text: While the binomial coefficients represent the coefficients of ("x"+"y"), the multinomial coefficients


title: Binomial coefficient

text: The combinatorial interpretation of multinomial coefficients is distribution of "n" distinguishable elements over "r" (distinguishable) containers, each containing exactly "k" elements, where "i" is the index of the container.


title: Binomial coefficient

text: Multinomial coefficients have many properties similar to those of binomial coefficients, for example the recurrence relation:


title: Binomial coefficient

text: Using Stirling numbers of the first kind the series expansion around any arbitrarily chosen point formula_178 is


title: Binomial coefficient

text: The definition of the binomial coefficients can be extended to the case where formula_149 is real and formula_181 is integer.


title: Binomial coefficient

text: One can express the product of two binomial coefficients as a linear combination of binomial coefficients:


title: Binomial coefficient

text: where the connection coefficients are multinomial coefficients. In terms of labelled combinatorial objects, the connection coefficients represent the number of ways to assign labels to a pair of labelled combinatorial objects—of weight "m" and "n" respectively—that have had their first "k" labels identified, or glued together to get a new labelled combinatorial object of weight . (That is, to separate the labels into three portions to apply to the glued part, the unglued part of the first object, and the unglued part of the second object.) In this regard, binomial coefficients are to exponential generating series what falling factorials are to ordinary generating series.


title: Binomial coefficient

text: The product of all binomial coefficients in the "n"th row of the Pascal triangle is given by the formula:


title: Binomial coefficient

text: Newton's binomial series, named after Sir Isaac Newton, is a generalization of the binomial theorem to infinite series:


title: Binomial coefficient

text: Binomial coefficients count subsets of prescribed size from a given set. A related combinatorial problem is to count multisets of prescribed size with elements drawn from a given set, that is, to count the number of ways to select a certain number of elements from a given set with the possibility of selecting the same element repeatedly. The resulting numbers are called "multiset coefficients"; the number of ways to "multichoose" (i.e., choose with replacement) "k" items from an "n" element set is denoted formula_192.


title: Binomial coefficient

text: while the corresponding multiset coefficient is defined by replacing the falling with the rising factorial:


title: Binomial coefficient

text: In particular, binomial coefficients evaluated at negative integers "n" are given by signed multiset coefficients. In the special case formula_200, this reduces to formula_201


title: Binomial coefficient

text: The binomial coefficient is generalized to two real or complex valued arguments using the gamma function or beta function via


title: Binomial coefficient

text: The resulting function has been little-studied, apparently first being graphed in . Notably, many binomial identities fail: formula_207 but formula_208 for "n" positive (so formula_209 negative). The behavior is quite complex, and markedly different in various octants (that is, with respect to the "x" and "y" axes and the line formula_210), with the behavior for negative "x" having singularities at negative integer values and a checkerboard of positive and negative regions:


title: Binomial coefficient

text: where A is some set with cardinality formula_219. One can show that the generalized binomial coefficient is well-defined, in the sense that no matter what set we choose to represent the cardinal number formula_219, formula_221 will remain the same. For finite cardinals, this definition coincides with the standard definition of the binomial coefficient.


title: Binomial coefficient

text: The notation formula_224 is convenient in handwriting but inconvenient for typewriters and computer terminals. Many programming languages do not offer a standard subroutine for computing the binomial coefficient, but for example both the APL programming language and the (related) J programming language use the exclamation mark: codice_1. The binomial coefficient is implemented in SciPy as "scipy.special.comb".


title: Binomial coefficient

text: are very slow and are useless for calculating factorials of very high numbers (in languages such as C or Java they suffer from overflow errors because of this reason). A direct implementation of the multiplicative formula works well:


title: Binomial coefficient

text: Pascal's rule provides a recursive definition which can also be implemented in Python, although it is less efficient:


title: Binomial coefficient

text: The example mentioned above can be also written in functional style. The following Scheme example uses the recursive definition


title: Binomial coefficient

text: When computing formula_227 in a language with fixed-length integers, the multiplication by formula_228 may overflow even when the result would fit. The overflow can be avoided by dividing first and fixing the result using the remainder:


title: Binomial coefficient

text: where formula_231 denotes the natural logarithm of the gamma function at formula_149. It is a special function that is easily computed and is standard in some programming languages such as using "log_gamma" in Maxima, "LogGamma" in Mathematica, "gammaln" in MATLAB and Python's SciPy module, "lngamma" in PARI/GP or "lgamma" in C, R, and Julia. Roundoff error may cause the returned value to not be an integer.


title: Future of Earth

text: The biological and geological future of Earth can be extrapolated based on the estimated effects of several long-term influences. These include the chemistry at Earth's surface, the cooling rate of the planet's interior, the gravitational interactions with other objects in the Solar System, and a steady increase in the Sun's luminosity. An uncertain factor is the pervasive influence of technology introduced by humans, such as climate engineering, which could cause significant changes to the planet. For example, the current Holocene extinction is being caused by technology, and the effects may last for up to five million years. In turn, technology may result in the extinction of humanity, leaving the planet to gradually return to a slower evolutionary pace resulting solely from long-term natural processes.


title: Future of Earth

text: Over time intervals of hundreds of millions of years, random celestial events pose a global risk to the biosphere, which can result in mass extinctions. These include impacts by comets or asteroids and the possibility of a near-Earth supernova—a massive stellar explosion within a radius of the Sun. Other large-scale geological events are more predictable. Milankovitch's theory predicts that the planet will continue to undergo glacial periods at least until the Quaternary glaciation comes to an end. These periods are caused by the variations in eccentricity, axial tilt, and precession of Earth's orbit. As part of the ongoing supercontinent cycle, plate tectonics will probably result in a supercontinent in 250–350 million years. Sometime in the next 1.5–4.5 billion years, Earth's axial tilt may begin to undergo chaotic variations, with changes in the axial tilt of up to 90°.


title: Future of Earth

text: The luminosity of the Sun will steadily increase, resulting in a rise in the solar radiation reaching Earth, resulting in a higher rate of weathering of silicate minerals, affecting the carbonate–silicate cycle, which will cause a decrease in the level of carbon dioxide in the atmosphere. In about 600 million years from now, the level of carbon dioxide will fall below the level needed to sustain C carbon fixation photosynthesis used by trees. Some plants use the C carbon fixation method to persist at carbon dioxide concentrations as low as ten parts per million. However, the long-term trend is for plant life to die off altogether. The extinction of plants will be the demise of almost all animal life since plants are the base of the food chain on Earth.


title: Future of Earth

text: In about one billion years, the solar luminosity will be 10% higher, causing the atmosphere to become a "moist greenhouse", resulting in a runaway evaporation of the oceans. As a likely consequence, plate tectonics and the entire carbon cycle will end. Following this event, in about 2–3 billion years, the planet's magnetic dynamo may cease, causing the magnetosphere to decay and leading to an accelerated loss of volatiles from the outer atmosphere. Four billion years from now, the increase in Earth's surface temperature will cause a runaway greenhouse effect, creating conditions more extreme than present-day Venus and heating Earth's surface enough to melt it. By that point, all life on Earth will be extinct. Finally, the most probable fate of the planet is absorption by the Sun in about 7.5 billion years, after the star has entered the red giant phase and expanded beyond the planet's current orbit.


title: Future of Earth

text: Humans play a key role in the biosphere, with the large human population dominating many of Earth's ecosystems. This has resulted in a widespread, ongoing mass extinction of other species during the present geological epoch, now known as the Holocene extinction. The large-scale loss of species caused by human influence since the 1950s has been called a biotic crisis, with an estimated 10% of the total species lost as of 2007. At current rates, about 30% of species are at risk of extinction in the next hundred years. The Holocene extinction event is the result of habitat destruction, the widespread distribution of invasive species, poaching, and climate change. In the present day, human activity has had a significant impact on the surface of the planet. More than a third of the land surface has been modified by human actions, and humans use about 20% of global primary production. The concentration of carbon dioxide in the atmosphere has increased by close to 50% since the start of the Industrial Revolution.


title: Future of Earth

text: The consequences of a persistent biotic crisis have been predicted to last for at least five million years. It could result in a decline in biodiversity and homogenization of biotas, accompanied by a proliferation of species that are opportunistic, such as pests and weeds. Novel species may emerge; in particular taxa that prosper in human-dominated ecosystems may rapidly diversify into many new species. Microbes are likely to benefit from the increase in nutrient-enriched environmental niches. No new species of existing large vertebrates are likely to arise and food chains will probably be shortened.


title: Future of Earth

text: There are multiple scenarios for known risks that can have a global impact on the planet. From the perspective of humanity, these can be subdivided into survivable risks and terminal risks. Risks that humans pose to themselves include climate change, the misuse of nanotechnology, a nuclear holocaust, warfare with a programmed superintelligence, a genetically engineered disease, or a disaster caused by a physics experiment. Similarly, several natural events may pose a doomsday threat, including a highly virulent disease, the impact of an asteroid or comet, runaway greenhouse effect, and resource depletion. There may be the possibility of an infestation by an extraterrestrial lifeform. The actual odds of these scenarios occurring are difficult if not impossible to deduce.


title: Future of Earth

text: Should the human species become extinct, then the various features assembled by humanity will begin to decay. The largest structures have an estimated decay half-life of about 1,000 years. The last surviving structures would most likely be open-pit mines, large landfills, major highways, wide canal cuts, and earth-fill flank dams. A few massive stone monuments like the pyramids at the Giza Necropolis or the sculptures at Mount Rushmore may still survive in some form after a million years.


title: Future of Earth

text: As the Sun orbits the Milky Way, wandering stars may approach close enough to have a disruptive influence on the Solar System. A close stellar encounter may cause a significant reduction in the perihelion distances of comets in the Oort cloud—a spherical region of icy bodies orbiting within half a light-year of the Sun. Such an encounter can trigger a 40-fold increase in the number of comets reaching the inner Solar System. Impacts from these comets can trigger a mass extinction of life on Earth. These disruptive encounters occur an average of once every 45 million years. The mean time for the Sun to collide with another star in the solar neighborhood is approximately 30 trillion () years, which is much longer than the estimated age of the Universe, at approximately 13.8 billion years. This can be taken as an indication of the low likelihood of such an event occurring during the lifetime of the Earth.


title: Future of Earth

text: The energy released from the impact of an asteroid or comet with a diameter of or larger is sufficient to create a global environmental disaster and cause a statistically significant increase in the number of species extinctions. Among the deleterious effects resulting from a major impact event is a cloud of fine dust ejecta blanketing the planet, blocking some direct sunlight from reaching the Earth's surface thus lowering land temperatures by about within a week and halting photosynthesis for several months (similar to a nuclear winter). The mean time between major impacts is estimated to be at least 100 million years. During the last 540 million years, simulations demonstrated that such an impact rate is sufficient to cause five or six mass extinctions and 20 to 30 lower severity events. This matches the geologic record of significant extinctions during the Phanerozoic Eon. Such events can be expected to continue.


title: Future of Earth

text: A supernova is a cataclysmic explosion of a star. Within the Milky Way galaxy, supernova explosions occur on average once every 40 years. During the history of Earth, multiple such events have likely occurred within a distance of 100 light-years; known as a near-Earth supernova. Explosions inside this distance can contaminate the planet with radioisotopes and possibly impact the biosphere. Gamma rays emitted by a supernova react with nitrogen in the atmosphere, producing nitrous oxides. These molecules cause a depletion of the ozone layer that protects the surface from ultraviolet (UV) radiation from the Sun. An increase in UV-B radiation of only 10–30% is sufficient to cause a significant impact on life; particularly to the phytoplankton that form the base of the oceanic food chain. A supernova explosion at a distance of 26 light-years will reduce the ozone column density by half. On average, a supernova explosion occurs within 32 light-years once every few hundred million years, resulting in a depletion of the ozone layer lasting several centuries. Over the next two billion years, there will be about 20 supernova explosions and one gamma ray burst that will have a significant impact on the planet's biosphere.


title: Future of Earth

text: The incremental effect of gravitational perturbations between the planets causes the inner Solar System as a whole to behave chaotically over long time periods. This does not significantly affect the stability of the Solar System over intervals of a few million years or less, but over billions of years, the orbits of the planets become unpredictable. Computer simulations of the Solar System's evolution over the next five billion years suggest that there is a small (less than 1%) chance that a collision could occur between Earth and either Mercury, Venus, or Mars. During the same interval, the odds that Earth will be scattered out of the Solar System by a passing star are on the order of 1 in 100,000 (0.001%). In such a scenario, the oceans would freeze solid within several million years, leaving only a few pockets of liquid water about underground. There is a remote chance that Earth will instead be captured by a passing binary star system, allowing the planet's biosphere to remain intact. The odds of this happening are about 1 in 3 million.


title: Future of Earth

text: The gravitational perturbations of the other planets in the Solar System combine to modify the orbit of Earth and the orientation of its rotation axis. These changes can influence the planetary climate. Despite such interactions, highly accurate simulations show that overall, Earth's orbit is likely to remain dynamically stable for billions of years into the future. In all 1,600 simulations, the planet's semimajor axis, eccentricity, and inclination remained nearly constant.


title: Future of Earth

text: Historically, there have been cyclical ice ages in which glacial sheets periodically covered the higher latitudes of the continents. Ice ages may occur because of changes in ocean circulation and continentality induced by plate tectonics. The Milankovitch theory predicts that glacial periods occur during ice ages because of astronomical factors in combination with climate feedback mechanisms. The primary astronomical drivers are a higher than normal orbital eccentricity, a low axial tilt (or obliquity), and the alignment of the northern hemisphere's summer solstice with the aphelion. Each of these effects occur cyclically. For example, the eccentricity changes over time cycles of about 100,000 and 400,000 years, with the value ranging from less than 0.01 up to 0.05. This is equivalent to a change of the semiminor axis of the planet's orbit from 99.95% of the semimajor axis to 99.88%, respectively.


title: Future of Earth

text: Earth is passing through an ice age known as the quaternary glaciation, and is presently in the Holocene interglacial period. This period would normally be expected to end in about 25,000 years. However, the increased rate of carbon dioxide released into the atmosphere by humans may delay the onset of the next glacial period until at least 50,000–130,000 years from now. On the other hand, a global warming period of finite duration (based on the assumption that fossil fuel use will cease by the year 2200) will probably only impact the glacial period for about 5,000 years. Thus, a brief period of global warming-induced through a few centuries' worth of greenhouse gas emission would only have a limited impact in the long term.


title: Future of Earth

text: The tidal acceleration of the Moon slows the rotation rate of the Earth and increases the Earth-Moon distance. Friction effects—between the core and mantle and between the atmosphere and surface—can dissipate the Earth's rotational energy. These combined effects are expected to increase the length of the day by more than 1.5 hours over the next 250 million years, and to increase the obliquity by about a half degree. The distance to the Moon will increase by about 1.5 Earth radii during the same period.


title: Future of Earth

text: Based on computer models, the presence of the Moon appears to stabilize the obliquity of the Earth, which may help the planet to avoid dramatic climate changes. This stability is achieved because the Moon increases the precession rate of the Earth's rotation axis, thereby avoiding resonances between the precession of the rotation and precession of the planet's orbital plane (that is, the precession motion of the ecliptic). However, as the semimajor axis of the Moon's orbit continues to increase, this stabilizing effect will diminish. At some point, perturbation effects will probably cause chaotic variations in the obliquity of the Earth, and the axial tilt may change by angles as high as 90° from the plane of the orbit. This is expected to occur between 1.5 and 4.5 billion years from now.


title: Future of Earth

text: A high obliquity would probably result in dramatic changes in the climate and may destroy the planet's habitability. When the axial tilt of the Earth exceeds 54°, the yearly insolation at the equator is less than that at the poles. The planet could remain at an obliquity of 60° to 90° for periods as long as 10 million years.


title: Future of Earth

text: Tectonics-based events will continue to occur well into the future and the surface will be steadily reshaped by tectonic uplift, extrusions, and erosion. Mount Vesuvius can be expected to erupt about 40 times over the next 1,000 years. During the same period, about five to seven earthquakes of magnitude 8 or greater should occur along the San Andreas Fault, while about 50 magnitudes of 9 events may be expected worldwide. Mauna Loa should experience about 200 eruptions over the next 1,000 years, and the Old Faithful Geyser will likely cease to operate. The Niagara Falls will continue to retreat upstream, reaching Buffalo in about 30,000–50,000 years.


title: Future of Earth

text: In 10,000 years, the post-glacial rebound of the Baltic Sea will have reduced the depth by about . The Hudson Bay will decrease in depth by 100 m over the same period. After 100,000 years, the island of Hawaii will have shifted about to the northwest. The planet may be entering another glacial period by this time.


title: Future of Earth

text: The theory of plate tectonics demonstrates that the continents of the Earth are moving across the surface at the rate of a few centimeters per year. This is expected to continue, causing the plates to relocate and collide. Continental drift is facilitated by two factors: the energy generated within the planet and the presence of a hydrosphere. With the loss of either of these, continental drift will come to a halt. The production of heat through radiogenic processes is sufficient to maintain mantle convection and plate subduction for at least the next 1.1 billion years.


title: Future of Earth

text: At present, the continents of North and South America are moving westward from Africa and Europe. Researchers have produced several scenarios about how this will continue in the future. These geodynamic models can be distinguished by the subduction flux, whereby the oceanic crust moves under a continent. In the introversion model, the younger, interior, Atlantic Ocean becomes preferentially subducted and the current migration of North and South America is reversed. In the extroversion model, the older, exterior, Pacific Ocean remains preferentially subducted and North and South America migrate toward eastern Asia.


title: Future of Earth

text: As the understanding of geodynamics improves, these models will be subject to revision. In 2008, for example, a computer simulation was used to predict that a reorganization of the mantle convection will occur over the next 100 million years, creating a new supercontinent composed of Africa, Eurasia, Australia, Antarctica and South America to form around Antarctica.


title: Future of Earth

text: Regardless of the outcome of the continental migration, the continued subduction process causes water to be transported to the mantle. After a billion years from the present, a geophysical model gives an estimate that 27% of the current ocean mass will have been subducted. If this process were to continue unmodified into the future, the subduction and release would reach an equilibrium after 65% of the current ocean mass has been subducted.


title: Future of Earth

text: Christopher Scotese and his colleagues have mapped out the predicted motions several hundred million years into the future as part of the Paleomap Project. In their scenario, 50 million years from now the Mediterranean Sea may vanish, and the collision between Europe and Africa will create a long mountain range extending to the current location of the Persian Gulf. Australia will merge with Indonesia, and Baja California will slide northward along the coast. New subduction zones may appear off the eastern coast of North and South America, and mountain chains will form along those coastlines. The migration of Antarctica to the north will cause all of its ice sheets to melt. This, along with the melting of the Greenland ice sheets, will raise the average ocean level by . The inland flooding of the continents will result in climate changes.


title: Future of Earth

text: As this scenario continues, by 100 million years from the present, the continental spreading will have reached its maximum extent and the continents will then begin to coalesce. In 250 million years, North America will collide with Africa. South America will wrap around the southern tip of Africa. The result will be the formation of a new supercontinent (sometimes called Pangaea Ultima), with the Pacific Ocean stretching across half the planet. Antarctica will reverse direction and return to the South Pole, building up a new ice cap.


title: Future of Earth

text: The first scientist to extrapolate the current motions of the continents was Canadian geologist Paul F. Hoffman of Harvard University. In 1992, Hoffman predicted that the continents of North and South America would continue to advance across the Pacific Ocean, pivoting about Siberia until they begin to merge with Asia. He dubbed the resulting supercontinent, Amasia. Later, in the 1990s, Roy Livermore calculated a similar scenario. He predicted that Antarctica would start to migrate northward, and East Africa and Madagascar would move across the Indian Ocean to collide with Asia.


title: Future of Earth

text: In an extroversion model, the closure of the Pacific Ocean would be complete in about 350 million years. This marks the completion of the current supercontinent cycle, wherein the continents split apart and then rejoin each other about every 400–500 million years. Once the supercontinent is built, plate tectonics may enter a period of inactivity as the rate of subduction drops by an order of magnitude. This period of stability could cause an increase in the mantle temperature at the rate of every 100 million years, which is the minimum lifetime of past supercontinents. As a consequence, volcanic activity may increase.


title: Future of Earth

text: The formation of a supercontinent can dramatically affect the environment. The collision of plates will result in mountain building, thereby shifting weather patterns. Sea levels may fall because of increased glaciation. The rate of the surface weathering can rise, increasing the rate that organic material is buried. Supercontinents can cause a drop in global temperatures and an increase in atmospheric oxygen. This, in turn, can affect the climate, further lowering temperatures. All of these changes can result in more rapid biological evolution as new niches emerge.


title: Future of Earth

text: The formation of a supercontinent insulates the mantle. The flow of heat will be concentrated, resulting in volcanism and the flooding of large areas with basalt. Rifts will form and the supercontinent will split up once more. The planet may then experience a warming period as occurred during the Cretaceous period, which marked the split-up of the previous Pangaea supercontinent.


title: Future of Earth

text: The iron-rich core region of the Earth is divided into a diameter solid inner core and a diameter liquid outer core. The rotation of the Earth creates convective eddies in the outer core region that cause it to function as a dynamo. This generates a magnetosphere about the Earth that deflects particles from the solar wind, which prevents significant erosion of the atmosphere from sputtering. As heat from the core is transferred outward toward the mantle, the net trend is for the inner boundary of the liquid outer core region to freeze, thereby releasing thermal energy and causing the solid inner core to grow. This iron crystallization process has been ongoing for about a billion years. In the modern era, the radius of the inner core is expanding at an average rate of roughly per year, at the expense of the outer core. Nearly all of the energy needed to power the dynamo is being supplied by this process of inner core formation.


title: Future of Earth

text: The inner core is expected to consume most or all of the outer core 3–4 billion years from now, resulting in an almost completely solidified core composed of iron and other heavy elements. The surviving liquid envelope will mainly consist of lighter elements that will undergo less mixing. Alternatively, if at some point plate tectonics cease, the interior will cool less efficiently, which would slow down or even stop the inner core's growth. In either case, this can result in the loss of the magnetic dynamo. Without a functioning dynamo, the magnetic field of the Earth will decay in a geologically short time period of roughly 10,000 years. The loss of the magnetosphere will cause an increase in erosion of light elements, particularly hydrogen, from the Earth's outer atmosphere into space, resulting in less favorable conditions for life.


title: Future of Earth

text: The energy generation of the Sun is based upon thermonuclear fusion of hydrogen into helium. This occurs in the core region of the star using the proton–proton chain reaction process. Because there is no convection in the solar core, the helium concentration builds up in that region without being distributed throughout the star. The temperature at the core of the Sun is too low for nuclear fusion of helium atoms through the triple-alpha process, so these atoms do not contribute to the net energy generation that is needed to maintain hydrostatic equilibrium of the Sun.


title: Future of Earth

text: At present, nearly half the hydrogen at the core has been consumed, with the remainder of the atoms consisting primarily of helium. As the number of hydrogen atoms per unit mass decreases, so too does their energy output provided through nuclear fusion. This results in a decrease in pressure support, which causes the core to contract until the increased density and temperature bring the core pressure into equilibrium with the layers above. The higher temperature causes the remaining hydrogen to undergo fusion at a more rapid rate, thereby generating the energy needed to maintain the equilibrium.


title: Future of Earth

text: The result of this process has been a steady increase in the energy output of the Sun. When the Sun first became a main sequence star, it radiated only 70% of the current luminosity. The luminosity has increased in a nearly linear fashion to the present, rising by 1% every 110 million years. Likewise, in three billion years the Sun is expected to be 33% more luminous. The hydrogen fuel at the core will finally be exhausted in five billion years when the Sun will be 67% more luminous than at present. Thereafter the Sun will continue to burn hydrogen in a shell surrounding its core until the luminosity reaches 121% above the present value. This marks the end of the Sun's main-sequence lifetime, and thereafter it will pass through the subgiant stage and evolve into a red giant.


title: Future of Earth

text: By this time, the collision of the Milky Way and Andromeda galaxies should be underway. Although this could result in the Solar System being ejected from the newly combined galaxy, it is considered unlikely to have any adverse effect on the Sun or its planets.


title: Future of Earth

text: The rate of weathering of silicate minerals will increase as rising temperatures speed up chemical processes. This in turn will decrease the level of carbon dioxide in the atmosphere, as reactions with silicate minerals convert carbon dioxide gas into solid carbonates. Within the next 600 million years from the present, the concentration of carbon dioxide will fall below the critical threshold needed to sustain C photosynthesis: about 50 parts per million. At this point, trees and forests in their current forms will no longer be able to survive. This decline in plant life is likely to be a long-term decline rather than a sharp drop. The C plant group will likely die one by one well before the 50 parts per million level are reached. The first plants to disappear will be C3 herbaceous plants, followed by deciduous forests, evergreen broad-leaf forests and finally evergreen conifers. However, C carbon fixation can continue at much lower concentrations, down to above 10 parts per million. Thus plants using photosynthesis may be able to survive for at least 0.8 billion years and possibly as long as 1.2 billion years from now, after which rising temperatures will make the biosphere unsustainable. Currently, plants represent about 5% of Earth's plant biomass and 1% of its known plant species. For example, about 50% of all grass species (Poaceae) use the photosynthetic pathway, as do many species in the herbaceous family Amaranthaceae.


title: Future of Earth

text: When the levels of carbon dioxide fall to the limit where photosynthesis is barely sustainable, the proportion of carbon dioxide in the atmosphere is expected to oscillate up and down. This will allow land vegetation to flourish each time the level of carbon dioxide rises due to tectonic activity and respiration from animal life. However, the long-term trend is for the plant life on land to die off altogether as most of the remaining carbon in the atmosphere becomes sequestered in the Earth.


title: Future of Earth

text: Plants—and, by extension, animals—could survive longer by evolving other strategies such as requiring less carbon dioxide for photosynthetic processes, becoming carnivorous, adapting to desiccation, or associating with fungi. These adaptations are likely to appear near the beginning of the moist greenhouse (see further).


title: Future of Earth

text: The loss of higher plant life will result in the eventual loss of oxygen as well as ozone due to the respiration of animals, chemical reactions in the atmosphere, volcanic eruptions, and people. This will result in less attenuation of DNA-damaging UV, as well as the death of animals; the first animals to disappear would be large mammals, followed by small mammals, birds, amphibians and large fish, reptiles and small fish, and finally invertebrates. Before this happens, it's expected that life would concentrate at refugia of lower temperature such as high elevations where less land surface area is available, thus restricting population sizes. Smaller animals would survive better than larger ones because of lesser oxygen requirements, while birds would fare better than mammals thanks to their ability to travel large distances looking for cooler temperatures. Based on oxygen half-life in the atmosphere, animal life would last at most 100 million years after the loss of higher plants. Some cyanobacteria and phytoplankton could outlive plants due to their tolerance for carbon dioxide levels as low as 1 ppm, and may survive for around the same time as animals before carbon dioxide becomes too depleted to support any form of photosynthesis.


title: Future of Earth

text: In their work "The Life and Death of Planet Earth", authors Peter D. Ward and Donald Brownlee have argued that some form of animal life may continue even after most of the Earth's plant life has disappeared. Ward and Brownlee use fossil evidence from the Burgess Shale in British Columbia, Canada, to determine the climate of the Cambrian Explosion, and use it to predict the climate of the future when rising global temperatures caused by a warming Sun and declining oxygen levels result in the final extinction of animal life. Initially, they expect that some insects, lizards, birds, and small mammals may persist, along with sea life. However, without oxygen replenishment by plant life, they believe that animals would probably die off from asphyxiation within a few million years. Even if sufficient oxygen were to remain in the atmosphere through the persistence of some form of photosynthesis, the steady rise in global temperature would result in a gradual loss of biodiversity.


title: Future of Earth

text: As temperatures continue to rise, the last of animal life will be driven toward the poles, and possibly underground. They would become primarily active during the polar night, aestivating during the polar day due to the intense heat. Much of the surface would become a barren desert and life would primarily be found in the oceans. However, due to a decrease in the amount of organic matter entering the oceans from land as well as a decrease in dissolved oxygen, sea life would disappear too following a similar path to that on Earth's surface. This process would start with the loss of freshwater species and conclude with invertebrates, particularly those that do not depend on living plants such as termites or those near hydrothermal vents such as worms of the genus "Riftia". As a result of these processes, multicellular life forms may be extinct in about 800 million years, and eukaryotes in 1.3 billion years, leaving only the prokaryotes.


title: Future of Earth

text: One billion years from now, about 27% of the modern ocean will have been subducted into the mantle. If this process were allowed to continue uninterrupted, it would reach an equilibrium state where 65% of the current surface reservoir would remain at the surface. Once the solar luminosity is 10% higher than its current value, the average global surface temperature will rise to . The atmosphere will become a "moist greenhouse" leading to a runaway evaporation of the oceans. At this point, models of the Earth's future environment demonstrate that the stratosphere would contain increasing levels of water. These water molecules will be broken down through photodissociation by solar UV, allowing hydrogen to escape the atmosphere. The net result would be a loss of the world's seawater by about 1.1 billion years from the present.


title: Future of Earth

text: There will be two variations of this future warming feedback: the "moist greenhouse" where water vapor dominates the troposphere while water vapor starts to accumulate in the stratosphere (if the oceans evaporate very quickly), and the "runaway greenhouse" where water vapor becomes a dominant component of the atmosphere (if the oceans evaporate too slowly). In this ocean-free era, there will continue to be surface reservoirs as water is steadily released from the deep crust and mantle, where it is estimated that there is an amount of water equivalent to several times that currently present in the Earth's oceans. Some water may be retained at the poles and there may be occasional rainstorms, but for the most part, the planet would be a desert with large dunefields covering its equator, and a few salt flats on what was once the ocean floor, similar to the ones in the Atacama Desert in Chile.


title: Future of Earth

text: With no water to serve as a lubricant, plate tectonics would very likely stop and the most visible signs of geological activity would be shield volcanoes located above mantle hotspots. In these arid conditions the planet may retain some microbial and possibly even multicellular life. Most of these microbes will be halophiles and life could find refuge in the atmosphere as has been proposed to have happened on Venus. However, the increasingly extreme conditions will likely lead to the extinction of the prokaryotes between 1.6 billion years and 2.8 billion years from now, with the last of them living in residual ponds of water at high latitudes and heights or in caverns with trapped ice. However, underground life could last longer. What proceeds after this depends on the level of tectonic activity. A steady release of carbon dioxide by volcanic eruption could cause the atmosphere to enter a "super-greenhouse" state like that of the planet Venus. But, as stated above, without surface water, plate tectonics would probably come to a halt and most of the carbonates would remain securely buried until the Sun becomes a red giant and its increased luminosity heats the rock to the point of releasing the carbon dioxide. However, as pointed out by Peter Ward and Donald Brownlee in their book "The Life and Death of Planet Earth", according to NASA Ames scientist Kevin Zahnle, it is highly possible that plate tectonics may stop long before the loss of the oceans, due to the gradual cooling of the Earth's core, which could happen in just 500 million years. This could potentially turn the Earth back into a waterworld, and even perhaps drowning all remaining land life.


title: Future of Earth

text: The loss of the oceans could be delayed until 2 billion years in the future if the atmospheric pressure were to decline. Lower atmospheric pressure would reduce the greenhouse effect, thereby lowering the surface temperature. This could occur if natural processes were to remove the nitrogen from the atmosphere. Studies of organic sediments have shown that at least of nitrogen has been removed from the atmosphere over the past four billion years; enough to effectively double the current atmospheric pressure if it were to be released. This rate of removal would be sufficient to counter the effects of increasing solar luminosity for the next two billion years.


title: Future of Earth

text: By 2.8 billion years from now, the surface temperature of the Earth will have reached , even at the poles. At this point, any remaining life will be extinguished due to extreme conditions. What happens beyond this depends on how much water is left on the surface. If all of the water on Earth has evaporated by this point already (via the "moist greenhouse" at ~1 Gyr from now), the planet will stay in the same conditions with a steady increase in the surface temperature until the Sun becomes a red giant. If not and there are still pockets of water left, and evaporates too slowly, then in about 3–4 billion years, once the amount of water vapor in the lower atmosphere rises to 40%, and the luminosity from the Sun reaches 35–40% more than its present-day value, a "runaway greenhouse" effect will ensue, causing the atmosphere to heat up and raising the surface temperature to around . This is sufficient to melt the surface of the planet. However, most of the atmosphere will be retained until the Sun has entered the red giant stage.


title: Future of Earth

text: With the extinction of life, 2.8 billion years from now it is expected that Earth's biosignatures will disappear, to be replaced by signatures caused by non-biological processes.


title: Future of Earth

text: Once the Sun changes from burning hydrogen within its core to burning hydrogen in a shell around its core, the core will start to contract, and the outer envelope will expand. The total luminosity will steadily increase over the following billion years until it reaches 2,730 times its current luminosity at the age of 12.167 billion years. Most of Earth's atmosphere will be lost to space. Its surface will consist of a lava ocean with floating continents of metals and metal oxides and icebergs of refractory materials, with its surface temperature reaching more than . The Sun will experience more rapid mass loss, with about 33% of its total mass shed with the solar wind. The loss of mass will mean that the orbits of the planets will expand. The orbital distance of Earth will increase to at most 150% of its current value (that is, ).


title: Future of Earth

text: The most rapid part of the Sun's expansion into a red giant will occur during the final stages, when the Sun will be about 12 billion years old. It is likely to expand to swallow both Mercury and Venus, reaching a maximum radius of . Earth will interact tidally with the Sun's outer atmosphere, which would decrease Earth's orbital radius. Drag from the chromosphere of the Sun would reduce Earth's orbit. These effects will counterbalance the impact of mass loss by the Sun, and the Sun will likely engulf Earth in about 7.59 billion years.


title: Future of Earth

text: The drag from the solar atmosphere may cause the orbit of the Moon to decay. Once the orbit of the Moon closes to a distance of , it will cross Earth's Roche limit, meaning that tidal interaction with Earth would break apart the Moon, turning it into a ring system. Most of the orbiting rings will begin to decay, and the debris will impact Earth. Hence, even if the Sun does not swallow up Earth, the planet may be left moonless. Furthermore, the ablation and vaporization caused by its fall on a decaying trajectory towards the Sun may remove Earth's mantle, leaving just its core, which will finally be destroyed after at most 200 years. Earth's sole legacy will be a very slight increase (0.01%) of the solar metallicity following this event.


title: Future of Earth

text: After fusing helium in its core to carbon, the Sun will begin to collapse again, evolving into a compact white dwarf star after ejecting its outer atmosphere as a planetary nebula. The predicted final mass is 54% of the present value, most likely consisting primarily of carbon and oxygen.


title: Future of Earth

text: Currently, the Moon is moving away from Earth at a rate of per year. In 50 billion years, if the Earth and Moon are not engulfed by the Sun, they will become tidelocked into a larger, stable orbit, with each showing only one face to the other. Thereafter, the tidal action of the Sun will extract angular momentum from the system, causing the orbit of the Moon to decay and the Earth's rotation to accelerate. In about 65 billion years, it is estimated that the Moon may end up colliding with the Earth, due to the remaining energy of the Earth–Moon system being sapped by the remnant Sun, causing the Moon to slowly move inwards toward the Earth.


title: Future of Earth

text: On a time scale of 10 (10 quintillion) years the remaining planets in the Solar System will be ejected from the system by violent relaxation. If Earth is not destroyed by the expanding red giant Sun and the Earth is not ejected from the Solar System by violent relaxation, the ultimate fate of the planet will be that it collides with the black dwarf Sun due to the decay of its orbit via gravitational radiation, in 10 (Short Scale: 100 quintillion, Long Scale: 100 trillion) years.


title: Impact factor

text: The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as indexed by Clarivate's Web of Science. As a journal-level metric, it is frequently used as a proxy for the relative importance of a journal within its field; journals with higher impact factor values are given the status of being more important, or carry more prestige in their respective fields, than those with lower values. While frequently used by universities and funding bodies to decide on promotion and research proposals, it has come under attack for distorting good scientific practices.


title: Impact factor

text: The impact factor was devised by Eugene Garfield, the founder of the Institute for Scientific Information (ISI) in Philadelphia. Impact factors began to be calculated yearly starting from 1975 for journals listed in the "Journal Citation Reports" (JCR). ISI was acquired by Thomson Scientific & Healthcare in 1992, and became known as Thomson ISI. In 2018, Thomson-Reuters spun off and sold ISI to Onex Corporation and Baring Private Equity Asia. They founded a new corporation, Clarivate, which is now the publisher of the JCR.


title: Impact factor

text: In any given year, the two-year journal impact factor is the ratio between the number of citations received in that year for publications in that journal that were published in the two preceding years and the total number of "citable items" published in that journal during the two preceding years:


title: Impact factor

text: This means that, on average, its papers published in 2015 and 2016 received roughly 42 citations each in 2017. Note that 2017 impact factors are reported in 2018; they cannot be calculated until all of the 2017 publications have been processed by the indexing agency.


title: Impact factor

text: The value of impact factor depends on how to define "citations" and "publications"; the latter are often referred to as "citable items". In current practice, both "citations" and "publications" are defined exclusively by ISI as follows. "Publications" are items that are classed as "article", "review" or "proceedings paper" in the Web of Science (WoS) database; other items like editorials, corrections, notes, retractions and discussions are excluded. WoS is accessible to all registered users, who can independently verify the number of citable items for a given journal. In contrast, the number of citations is extracted not from the WoS database, but from a dedicated JCR database, which is not accessible to general readers. Hence, the commonly used "JCR Impact Factor" is a proprietary value, which is defined and calculated by ISI and can not be verified by external users.


title: Impact factor

text: New journals, which are indexed from their first published issue, will receive an impact factor after two years of indexing; in this case, the citations to the year prior to volume 1, and the number of articles published in the year prior to volume 1, are known zero values. Journals that are indexed starting with a volume other than the first volume will not get an impact factor until they have been indexed for three years. Occasionally, "Journal Citation Reports" assigns an impact factor to new journals with less than two years of indexing, based on partial citation data. The calculation always uses two complete and known years of item counts, but for new titles one of the known counts is zero. Annuals and other irregular publications sometimes publish no items in a particular year, affecting the count. The impact factor relates to a specific time period; it is possible to calculate it for any desired period. For example, the JCR also includes a five-year impact factor, which is calculated by dividing the number of citations to the journal in a given year by the number of articles published in that journal in the previous five years.


title: Impact factor

text: While originally invented as a tool to help university librarians to decide which journals to purchase, the impact factor soon became used as a measure for judging academic success. This use of impact factors was summarised by Hoeffel in 1998:


title: Impact factor

text: Impact Factor is not a perfect tool to measure the quality of articles but there is nothing better and it has the advantage of already being in existence and is, therefore, a good technique for scientific evaluation. Experience has shown that in each specialty the best journals are those in which it is most difficult to have an article accepted, and these are the journals that have a high impact factor. Most of these journals existed long before the impact factor was devised. The use of impact factor as a measure of quality is widespread because it fits well with the opinion we have in each field of the best journals in our specialty...In conclusion, prestigious journals publish papers of high level. Therefore, their impact factor is high, and not the contrary.


title: Impact factor

text: As impact factors are a journal-level metric, rather than an article- or individual-level metric, this use is controversial. Eugene Garfield, the inventor of the JIF agreed with Hoeffel, but warned about the "misuse in evaluating individuals" because there is "a wide variation [of citations] from article to article within a single journal". Despite this warning, the use of the JIF has evolved, playing a key role in the process of assessing individual researchers, their job applications and their funding proposals. In 2005, "The Journal of Cell Biology" noted that:


title: Impact factor

text: Impact factor data ... have a strong influence on the scientific community, affecting decisions on where to publish, whom to promote or hire, the success of grant applications, and even salary bonuses.


title: Impact factor

text: More targeted research has begun to provide firm evidence of how deeply the impact factor is embedded within formal and informal research assessment processes. A review in 2019 studied how often the JIF featured in documents related to the review, promotion, and tenure of scientists in US and Canadian universities. It concluded that 40% of universities focussed on academic research specifically mentioned the JIF as part of such review, promotion, and tenure processes. And a 2017 study of how researchers in the life sciences behave concluded that "everyday decision-making practices as highly governed by pressures to publish in high-impact journals". The deeply embedded nature of such indicators not only effect research assessment, but the more fundamental issue of what research is actually undertaken: "Given the current ways of evaluation and valuing research, risky, lengthy, and unorthodox project rarely take center stage."


title: Impact factor

text: Numerous critiques have been made regarding the use of impact factors, both in terms of its statistical validity and also of its implications for how science is carried out and assessed. A 2007 study noted that the most fundamental flaw is that impact factors present the mean of data that are not normally distributed, and suggested that it would be more appropriate to present the median of these data. There is also a more general debate on the validity of the impact factor as a measure of journal importance and the effect of policies that editors may adopt to boost their impact factor (perhaps to the detriment of readers and writers). Other criticism focuses on the effect of the impact factor on behavior of scholars, editors and other stakeholders. Others have made more general criticisms, arguing that emphasis on impact factor results from the negative influence of neoliberal politics on academia. These more politicised arguments demand not just replacement of the impact factor with more sophisticated metrics but also discussion on the social value of research assessment and the growing precariousness of scientific careers in higher education.


title: Impact factor

text: It has been stated that impact factors in particular and citation analysis in general are affected by field-dependent factors which invalidate comparisons not only across disciplines but even within different fields of research of one discipline. The percentage of total citations occurring in the first two years after publication also varies highly among disciplines from 1–3% in the mathematical and physical sciences to 5–8% in the biological sciences. Thus impact factors cannot be used to compare journals across disciplines.


title: Impact factor

text: Impact factors are sometimes used to evaluate not only the journals but the papers therein, thereby devaluing papers in certain subjects. In 2004, the Higher Education Funding Council for England was urged by the House of Commons Science and Technology Select Committee to remind Research Assessment Exercise panels that they are obliged to assess the quality of the content of individual articles, not the reputation of the journal in which they are published. Other studies have repeatedly stated that impact factor is a metric for journals and should not be used to assess individual researchers or institutions.


title: Impact factor

text: Because impact factor is commonly accepted as a proxy for research quality, some journals adopt editorial policies and practices, some acceptable and some of dubious purpose, to increase its impact factor. For example, journals may publish a larger percentage of review articles which generally are cited more than research reports. Research undertaken in 2020 on dentistry journals concluded that the publication of "systematic reviews have significant effect on the Journal Impact Factor ... while papers publishing clinical trials bear no influence on this factor. Greater yearly average of published papers ... means a higher impact factor."


title: Impact factor

text: Journals may also attempt to limit the number of "citable items"—i.e., the denominator of the impact factor equation—either by declining to publish articles that are unlikely to be cited (such as case reports in medical journals) or by altering articles (e.g., by not allowing an abstract or bibliography in hopes that Journal Citation Reports will not deem it a "citable item"). As a result of negotiations over whether items are "citable", impact factor variations of more than 300% have been observed. Items considered to be uncitable—and thus are not incorporated in impact factor calculations—can, if cited, still enter into the numerator part of the equation despite the ease with which such citations could be excluded. This effect is hard to evaluate, for the distinction between editorial comment and short original articles is not always obvious. For example, letters to the editor may be part of either class.


title: Impact factor

text: Another less insidious tactic journals employ is to publish a large portion of its papers, or at least the papers expected to be highly cited, early in the calendar year. This gives those papers more time to gather citations. Several methods, not necessarily with nefarious intent, exist for a journal to cite articles in the same journal which will increase the journal's impact factor.


title: Impact factor

text: Beyond editorial policies that may skew the impact factor, journals can take overt steps to game the system. For example, in 2007, the specialist journal "Folia Phoniatrica et Logopaedica", with an impact factor of 0.66, published an editorial that cited all its articles from 2005 to 2006 in a protest against the "absurd scientific situation in some countries" related to use of the impact factor. The large number of citations meant that the impact factor for that journal increased to 1.44. As a result of the increase, the journal was not included in the 2008 and 2009 "Journal Citation Reports".


title: Impact factor

text: Coercive citation is a practice in which an editor forces an author to add extraneous citations to an article before the journal will agree to publish it, in order to inflate the journal's impact factor. A survey published in 2012 indicates that coercive citation has been experienced by one in five researchers working in economics, sociology, psychology, and multiple business disciplines, and it is more common in business and in journals with a lower impact factor. Editors of leading business journals banded together to disavow the practice. However, cases of coercive citation have occasionally been reported for other disciplines.


title: Impact factor

text: The journal impact factor was originally designed by Eugene Garfield as a metric to help librarians make decisions about which journals were worth indexing, as the JIF aggregates the number of citations to articles published in each journal. Since then, the JIF has become associated as a mark of journal "quality", and gained widespread use for evaluation of research and researchers instead, even at the institutional level. It thus has significant impact on steering research practices and behaviours.


title: Impact factor

text: By 2010, national and international research funding institutions were already starting to point out that numerical indicators such as the JIF should not be considered as a measure of quality. In fact, research was indicating that the JIF is a highly manipulated metric, and the justification for its continued widespread use beyond its original narrow purpose seems due to its simplicity (easily calculable and comparable number), rather than any actual relationship to research quality.


title: Impact factor

text: Empirical evidence shows that the misuse of the JIF—and journal ranking metrics in general—has a number of negative consequences for the scholarly communication system. These include gaps between the reach of a journal and the quality of its individual papers and insufficient coverage of social sciences and humanities as well as research outputs from across Latin America, Africa, and South-East Asia. Additional drawbacks include the marginalization of research in vernacular languages and on locally relevant topics and inducement to unethical authorship and citation practices. More generally, the impact factors fosters a reputation economy, where scientific success is based on publishing in prestigious journals ahead of actual research qualities such as rigorous methods, replicability and social impact. Using journal prestige and the JIF to cultivate a competition regime in academia has been shown to have deleterious effects on research quality.


title: Impact factor

text: A number of regional and international initiatives are now providing and suggesting alternative research assessment systems, including key documents such as the Leiden Manifesto and the San Francisco Declaration on Research Assessment (DORA). Plan S calls for a broader adoption and implementation of such initiatives alongside fundamental changes in the scholarly communication system. As appropriate measures of quality for authors and research, concepts of research excellence should be remodelled around transparent workflows and accessible research results.


title: Impact factor

text: JIFs are still regularly used to evaluate research in many countries which is a problem since a number of issues remain around the opacity of the metric and the fact that it is often negotiated by publishers.


title: Impact factor

text: Results of an impact factor can change dramatically depending on which items are considered as "citable" and therefore included in the denominator. One notorious example of this occurred in 1988 when it was decided that meeting abstracts published in "FASEB Journal" would no longer be included in the denominator. The journal's impact factor jumped from 0.24 in 1988 to 18.3 in 1989. Publishers routinely discuss with Clarivate how to improve the "accuracy" of their journals' impact factor and therefore get higher scores.


title: Impact factor

text: Such discussions routinely produce "negotiated values" which result in dramatic changes in the observed scores for dozens of journals, sometimes after unrelated events like the purchase by one of the larger publishers.


title: Impact factor

text: Because citation counts have highly skewed distributions, the mean number of citations is potentially misleading if used to gauge the typical impact of articles in the journal rather than the overall impact of the journal itself. For example, about 90% of "Nature"s 2004 impact factor was based on only a quarter of its publications. Thus the actual number of citations for a single article in the journal is in most cases much lower than the mean number of citations across articles. Furthermore, the strength of the relationship between impact factors of journals and the citation rates of the papers therein has been steadily decreasing since articles began to be available digitally.


title: Impact factor

text: The effect of outliers can be seen in the case of the article "A short history of SHELX", which included this sentence: "This paper could serve as a general literature citation when one or more of the open-source SHELX programs (and the Bruker AXS version SHELXTL) are employed in the course of a crystal-structure determination". This article received more than 6,600 citations. As a consequence, the impact factor of the journal "Acta Crystallographica Section A" rose from 2.051 in 2008 to 49.926 in 2009, more than "Nature" (at 31.434) and "Science" (at 28.103). The second-most cited article in "Acta Crystallographica Section A" in 2008 only had 28 citations.


title: Impact factor

text: Critics of the JIF state that use of the arithmetic mean in its calculation is problematic because the pattern of citation distribution is skewed and citation distributions metrics have been proposed as an alternative to impact factors.


title: Impact factor

text: However, there have also been pleas to take a more nuanced approach to judging the distribution skewness of the impact factor. Waltman and Traag, in their 2021 paper, ran numerous simulations and concluded that "statistical objections against the use of the IF at the level of individual articles are not convincing", and that "the IF may be a more accurate indicator of the value of an article than the number of citations of the article".


title: Impact factor

text: While the underlying mathematical model is publicly known, the dataset which is used to calculate the JIF is not publicly available. This prompted criticism: "Just as scientists would not accept the findings in a scientific paper without seeing the primary data, so should they not rely on Thomson Scientific's impact factor, which is based on hidden data". However, a 2019 article demonstrated that "with access to the data and careful cleaning, the JIF can be reproduced", although this required much labour to achieve. A 2020 research paper went further. It indicated that by querying open access or partly open-access databases, like Google Scholar, ResearchGate, and Scopus, it is possible to calculate approximate impact factors without the need to purchase Web of Science / JCR.


title: Impact factor

text: Just as the impact factor has attracted criticism for various immediate problems associated with its application, so has there also been criticism that its application undermines the broader process of science. Research has indicated that bibliometrics figures, particularly the impact factor, decrease the quality of peer review an article receiving, a reluctance to share data, decreasing quality of articles, and a reduced scope in terms of what they can research. "For many researchers the only research questions and projects that appear viable are those that can meet the demand of scoring well in terms of metric performance indicators - and chiefly the journal impact factor.". Furthermore, the process of publication and science is slowed down - authors automatically try and publish with the journals with the highest impact factor - "as editors and reviewers are tasked with reviewing papers that are not submitted to the most appropriate venues."


title: Impact factor

text: Given the growing criticism and its widespread usage as a means of research assessment, organisations and institutions have begun to take steps to move away from the journal impact factor. In November 2007 the European Association of Science Editors (EASE) issued an official statement recommending "that journal impact factors are used only—and cautiously—for measuring and comparing the influence of entire journals, but not for the assessment of single papers, and certainly not for the assessment of researchers or research programmes".


title: Impact factor

text: In July 2008, the International Council for Science Committee on Freedom and Responsibility in the Conduct of Science issued a "statement on publication practices and indices and the role of peer review in research assessment", suggesting many possible solutions—e.g., considering a limit number of publications per year to be taken into consideration for each scientist, or even penalising scientists for an excessive number of publications per year—e.g., more than 20.


title: Impact factor

text: In February 2010, the Deutsche Forschungsgemeinschaft (German Research Foundation) published new guidelines to reduce the number of publications could submit when applying for funding: "The focus has not been on what research someone has done but rather how many papers have been published and where." They noted that for decisions concerning "performance-based funding allocations, postdoctoral qualifications, appointments, or reviewing funding proposals, [where] increasing importance has been given to numerical indicators such as the h-index and the impact factor". The UK's Research Assessment Exercise for 2014 also banned the journal impact factor although evidence suggested that this ban was often ignored.


title: Impact factor

text: In response to growing concerns over the inappropriate use of journal impact factors in evaluating scientific outputs and scientists themselves, the American Society for Cell Biology together with a group of editors and publishers of scholarly journals created the San Francisco Declaration on Research Assessment (DORA). Released in May 2013, DORA has garnered support from thousands of individuals and hundreds of institutions, including in March 2015 the League of European Research Universities (a consortium of 21 of the most renowned research universities in Europe), who have endorsed the document on the DORA website.


title: Impact factor

text: Publishers, even those with high impact factors, also recognised the flaws. "Nature" magazine criticised the over reliance of JIF, pointing not just to its statistical but to negative effects on science: "The resulting pressures and disappointments are nothing but demoralizing, and in badly run labs can encourage sloppy research that, for example, fails to test assumptions thoroughly or to take all the data into account before submitting big claims." Various publishers now use a mixture of metrics on their website; the PLOS series of journals does not display the impact factor. Microsoft Academic took a similar view, stating that h-index, EI/SCI and journal impact factors are not shown because "the research literature has provided abundant evidence that these metrics are at best a rough approximation of research impact and scholarly influence."


title: Impact factor

text: In 2021, Utrecht University promised to abandon all quantitative bibliometrics, including the impact factor. The university stated that "it has become a very sick model that goes beyond what is really relevant for science and putting science forward." This followed a 2018 decision by the main Dutch funding body for research, NWO, to remove all references to journal impact factors and the h-index in all call texts and application forms. Utrecht's decision met with some resistance. An open letter signed by over 150 Dutch academics argued that while imperfect, the JIF is still useful, and that omitting it "will lead to randomness and a compromising of scientific quality."


title: Impact factor

text: As with the impact factor, there are some nuances to this: for example, Clarivate excludes certain article types (such as news items, correspondence, and errata) from the denominator.


title: Impact factor

text: Additional journal-level metrics are available from other organizations. For example, "CiteScore" is a metric for serial titles in Scopus launched in December 2016 by Elsevier. While these metrics apply only to journals, there are also author-level metrics, such as the h-index, that apply to individual researchers. In addition, article-level metrics measure impact at an article level instead of journal level.


title: Impact factor

text: Other more general alternative metrics, or "altmetrics", that include article views, downloads, or mentions in social media, offer a different perspective on research impact, concentrating more on immediate social impact in and outside academia.


title: Impact factor

text: Fake impact factors or bogus impact factors are produced by certain companies or individuals. According to an article published in the "Electronic Physician", these include Global Impact Factor, Citefactor, and Universal Impact Factor. Jeffrey Beall maintained a list of such misleading metrics. Another deceitful practice is reporting "alternative impact factors", calculated as the average number of citations per article using citation indices other than JCR, even if based on reputable sources such as Google Scholar (e.g., "Google-based Journal Impact Factor").


title: Impact factor

text: False impact factors are often used by predatory publishers. Consulting Journal Citation Reports' master journal list can confirm if a publication is indexed by the "Journal Citation Reports". The use of fake impact metrics is considered a red flag.


title: Assassination of William McKinley

text: William McKinley, the 25th president of the United States, was shot on the grounds of the Pan-American Exposition at the Temple of Music in Buffalo, New York, on September 6, 1901, six months into his second term. He was shaking hands with the public when anarchist Leon Czolgosz shot him twice in the abdomen. McKinley died on September 14 of gangrene caused by the wounds. He was the third American president to be assassinated, following Abraham Lincoln in 1865 and James A. Garfield in 1881.


title: Assassination of William McKinley

text: McKinley enjoyed meeting the public and was reluctant to accept the security available to his office. Secretary to the President George B. Cortelyou feared that an assassination attempt would take place during a visit to the Temple of Music and took it off the schedule twice, but McKinley restored it each time.


title: Assassination of William McKinley

text: Czolgosz had lost his job during the economic Panic of 1893 and turned to anarchism, a political philosophy adhered to by recent assassins of foreign leaders. He regarded McKinley as a symbol of oppression and was convinced that it was his duty as an anarchist to kill him. He was unable to get near the president during an earlier visit, but he shot him twice as McKinley reached to shake his hand in the reception line at the temple. One bullet grazed McKinley; the other entered his abdomen and was never found.


title: Assassination of William McKinley

text: McKinley initially appeared to be recovering, but he took a turn for the worse on September 13 as his wounds became gangrenous, and he died early the next morning; he was succeeded by his vice president, Theodore Roosevelt. Czolgosz was sentenced to death in the electric chair, and Congress passed legislation to officially charge the Secret Service with the responsibility for protecting the president.


title: Assassination of William McKinley

text: In September 1901, William McKinley was at the height of his power as president. Elected in 1896, during the serious economic depression resulting from the Panic of 1893, he had defeated his Democratic rival, William Jennings Bryan. McKinley led the nation both to a return to prosperity and to victory in the Spanish–American War in 1898, taking possession of such Spanish colonies as Puerto Rico and the Philippines. Re-elected handily in a rematch against Bryan in 1900, according to historical writer Eric Rauchway, "it looked as if the McKinley Administration would continue peaceably unbroken for another four years, a government devoted to prosperity".


title: Assassination of William McKinley

text: McKinley's original vice president, Garret Hobart, had died in 1899, and McKinley left the choice of a running mate to the 1900 Republican National Convention. In advance of the convention, New York's Republican political boss, Senator Thomas C. Platt, saw an opportunity to politically sideline his state's governor, former Assistant Secretary of the Navy Theodore Roosevelt, by pushing for his nomination as vice president. Roosevelt accepted the nomination and was elected on McKinley's ticket.


title: Assassination of William McKinley

text: Leon Czolgosz was born in Detroit, Michigan, in 1873, the son of Polish immigrants. The Czolgosz family moved several times as Paul Czolgosz, Leon's father, sought work throughout the Midwest. As an adult, Leon Czolgosz worked in a Cleveland factory until he lost his job in a labor dispute in 1893. Thereafter, he worked irregularly and attended political and religious meetings, trying to understand the reasons for the economic turmoil of the Panic of 1893. In doing so, he became interested in anarchism. By 1901, this movement was feared in the United States – New York's highest court had ruled that the act of identifying oneself as an anarchist in front of an audience was a breach of the peace. Anarchists had taken a toll in Europe by assassinating or attempting assassinations of a half-dozen officials and members of royal houses, and had been blamed for the 1886 Haymarket bombing in Chicago.


title: Assassination of William McKinley

text: Two American presidents had been assassinated in the 19th centuryAbraham Lincoln in 1865 and James A. Garfield in 1881. Even considering this history, McKinley did not like security personnel to come between him and the people. When in his hometown, Canton, Ohio, he often walked to church or the business district without protection, and in Washington went on drives with his wife without any guard in the carriage.


title: Assassination of William McKinley

text: McKinley gave a short speech at his second inauguration on March 4, 1901. Having long been an advocate of protective tariffs, and believing the Dingley Tariff, passed during his first year in office, had helped the nation reach prosperity, McKinley planned to negotiate reciprocal trade agreements with other countries. This would open foreign markets to United States manufacturers that had dominated the domestic market thanks to the tariff, and who sought to expand. During a long trip planned for the months after his inauguration, he intended to make major speeches promoting this plan, culminating in a visit and address at the Pan-American Exposition in Buffalo on June 13.


title: Assassination of William McKinley

text: McKinley, his wife Ida, and their official party left Washington on April 29 for a tour of the nation by train, scheduled to conclude in Buffalo for a speech on what had been designated as "President's Day". He met with rapturous receptions in the Far West, where many had never seen a president. In California, the First Lady became seriously ill, and for a time was thought to be dying. She recovered in San Francisco, but her husband canceled the remainder of the tour and the McKinleys returned to Washington. The speech at the Exposition was postponed until September 5, after McKinley spent some weeks in Washington and two months in Canton. He used his time in his Ohio home working on the Buffalo speech and in supervising improvements to his house. He intended to remain based in Canton until October.


title: Assassination of William McKinley

text: Czolgosz had lived on his parents' farm near Cleveland beginning in 1898, working littlehe may have suffered a nervous breakdown. He is known to have attended a speech by anarchist Emma Goldman in May 1901 in Cleveland: he approached her before the speech and asked her to recommend books on anarchism; she obliged. The talk, in which Goldman did not advocate violence but expressed understanding for those driven to it, was a great influence on Czolgosz; he later stated that her words burned in his head. He came to see her at her Chicago home in July as she was about to depart on a trip to Buffalo to see the fair, and the two anarchists rode together to the train station. Goldman expressed concern to another radical that Czolgosz (who was using the alias Fred Nieman) was following her around; soon after, he apparently departed Chicago. William Arntz, a worker at a park in Canton, stated that he had seen a man resembling Czolgosz in mid-1901, when the President was staying at home and sometimes visiting the park. The man was wearing two guns, and when Arntz reminded him that firearms were not permitted outside the park's shooting range, responded dismissively. Arntz sought the police, but the man was never found.


title: Assassination of William McKinley

text: Later in the summer, Czolgosz moved to Buffalo, though his reasons for doing so are not known. Author and journalist Scott Miller speculated that he may have chosen Buffalo because of its large Polish population. He boarded in the suburb of West Seneca and spent much of his time reading. Czolgosz then left for Cleveland, though what he did there is uncertain; he may have picked up anarchist literature or procured more money. After Cleveland, Czolgosz went to Chicago, where he saw a newspaper mention of President McKinley's impending visit to Buffalo. He returned to Buffalo, as yet uncertain of what he would do; at first, he only sought to be near the man who to him embodied injustice. On Tuesday, September 3, he made up his mind. Czolgosz later stated to the police:


title: Assassination of William McKinley

text: It was in my heart, there was no escape for me. I could not have conquered it had my life been at stake. There were thousands of people in town on Tuesday. I heard it was President's Day. All those people seemed bowing to the great ruler. I made up my mind to kill that ruler.


title: Assassination of William McKinley

text: On September 3, Czolgosz went to Walbridge's Hardware Store on Buffalo's Main Street and purchased a .32-caliber Iver Johnson revolver. He had as yet no clear plan for the assassination of the President. The following day, William and Ida McKinley arrived in Buffalo by train. The cannon that fired a salute to the President on his arrival in the city had been set too close to the track, and the explosions blew out several windows in the train, unnerving the First Lady. About a dozen people on the platform, believing the damage was caused by a bomb, shouted "Anarchists!" As William McKinley stepped down from the train to the official welcome, Czolgosz shoved his way forward in the crowd, but found the President too well guarded to make an attempt on his life.


title: Assassination of William McKinley

text: McKinley's trip to Buffalo was part of a planned ten-day absence from Canton, beginning on September 4, 1901, which was to include a visit in Cleveland to an encampment of the Grand Army of the Republic; he was a member as a Union veteran. The McKinleys stayed in Buffalo at the Milburn House, the large home of the Exposition's president, John G. Milburn. On Saturday, September 7, they were to travel to Cleveland and stay first at the home of businessman and future Ohio governor Myron Herrick, a friend of the President, and then with McKinley's close friend and adviser, Ohio Senator Mark Hanna. Upon arrival in Buffalo, the presidential party was driven through the fairgrounds on the way to the Milburn House, pausing for a moment at the Triumphal Bridge at the Exposition so the visitors could look upon the fair's attractions.