Compton scattering

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https://en.wikipedia.org/wiki/Compton_scattering

 

Light–matter interaction

Compton scattering (or the Compton effect) is the quantum theory of scattering of a high-frequency photon through an interaction with a charged particle, usually an electron. Specifically, when the photon interacts with a loosely bound electron, it releases the electron from an outer valence shell of an atom or molecule.

The effect was discovered in 1923 by Arthur Holly Compton while researching the scattering of X-rays by light elements, which earned him the Nobel Prize in Physics in 1927. The Compton effect significantly deviated from dominating classical theories, using both special relativity and quantum mechanics to explain the interaction between high frequency photons and charged particles.

Photons can interact with matter at the atomic level (e.g. photoelectric effect and Rayleigh scattering), at the nucleus, or with only an electron. Pair production and the Compton effect occur at the level of the electron. When a high-frequency photon scatters due to an interaction with a charged particle, the photon's energy is reduced, and thus its wavelength is increased. This trade-off between wavelength and energy in response to the collision is the Compton effect. Because of conservation of energy, the energy that is lost by the photon is transferred to the recoiling particle (such an electron would be called a "Compton recoil electron").

This implies that if the recoiling particle initially carried more energy than the photon has, the reverse would occur. This is known as inverse Compton scattering, in which the scattered photon increases in energy.

Introduction

Fig. 1: Schematic diagram of Compton's experiment. Compton scattering occurs in the graphite target on the left. The slit passes X-ray photons scattered at the selected angle and their average energy rate is measured using Bragg scattering from the crystal on the right in conjunction with an ionization chamber.

Plot of photon energies calculated for a given element (atomic number Z) at which the cross section value for the process on the right becomes larger than the cross section for the process on the left. For calcium (Z = 20), Compton scattering starts to dominate at hυ = 0.08 MeV and ceases at 12 MeV.

In Compton's original experiment (see Fig. 1), the energy of the X-ray photon (≈ 17 keV) was significantly larger than the binding energy of the atomic electron, so the electrons could be treated as being free after scattering. The amount by which the light's wavelength changes is called the Compton shift. Although Compton scattering from a nucleus exists, Compton scattering usually refers to the interaction involving only the electrons of an atom. The Compton effect was observed by Arthur Holly Compton in 1923 at Washington University in St. Louis and further verified by his graduate student Y. H. Woo in the years following. Compton was awarded the 1927 Nobel Prize in Physics for the discovery.

The effect is significant because it demonstrates that light cannot be explained purely as a wave phenomenon. Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain shifts in wavelength at low intensity: classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light, but the effect would become arbitrarily small at sufficiently low light intensities regardless of wavelength. Thus, if we are to explain low-intensity Compton scattering, light must behave as if it consists of particles. Or the assumption that the electron can be treated as free is invalid resulting in the effectively infinite electron mass equal to the nuclear mass (see e.g. the comment below on elastic scattering of X-rays being from that effect). Compton's experiment convinced physicists that light can be treated as a stream of particle-like objects (quanta called photons), whose energy is proportional to the light wave's frequency.

As shown in Fig. 2, the interaction between an electron and a photon results in the electron being given part of the energy (making it recoil), and a photon of the remaining energy being emitted in a different direction from the original, so that the overall momentum of the system is also conserved. If the scattered photon still has enough energy, the process may be repeated. In this scenario, the electron is treated as free or loosely bound. Experimental verification of momentum conservation in individual Compton scattering processes by Bothe and Geiger as well as by Compton and Simon has been important in disproving the BKS theory.

Compton scattering is commonly described as inelastic scattering. This is because, unlike the more common Thomson scattering that happens at the low-energy limit, the energy in the scattered photon in Compton scattering is less than the energy of the incident photon. As the electron is typically weakly bound to the atom, the scattering can be viewed from either the perspective of an electron in a potential well, or as an atom with a small ionization energy. In the former perspective, energy of the incident photon is transferred to the recoil particle, but only as kinetic energy. The electron gains no internal energy, respective masses remain the same, the mark of an elastic collision. From this perspective, Compton scattering could be considered elastic because the internal state of the electron does not change during the scattering process. In the latter perspective, the atom's state is changed, constituting an inelastic collision. Whether Compton scattering is considered elastic or inelastic depends on which perspective is being used, as well as the context.

Compton scattering is one of four competing processes when photons interact with matter. At energies of a few eV to a few keV, corresponding to visible light through soft X-rays, a photon can be completely absorbed and its energy can eject an electron from its host atom, a process known as the photoelectric effect. High-energy photons of 1.022 MeV and above may bombard the nucleus and cause an electron and a positron to be formed, a process called pair production; even-higher-energy photons (beyond a threshold energy of at least 1.670 MeV, depending on the nuclei involved), can eject a nucleon or alpha particle from the nucleus in a process called photodisintegration. Compton scattering is the most important interaction in the intervening energy region, at photon energies greater than those typical of the photoelectric effect but less than the pair-production threshold.

Description of the phenomenon

Fig. 2: A photon of wavelength ${\displaystyle \lambda }$ comes in from the left, collides with a target at rest, and a new photon of wavelength ${\displaystyle {\lambda }^{\prime }}$ emerges at an angle ${\displaystyle \theta }$. The target recoils, carrying away an angle-dependent amount of the incident energy.

By the early 20th century, research into the interaction of X-rays with matter was well under way. It was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle ${\displaystyle \theta }$ and emerge at a different wavelength related to ${\displaystyle \theta }$. Although classical electromagnetism predicted that the wavelength of scattered rays should be equal to the initial wavelength, multiple experiments had found that the wavelength of the scattered rays was longer (corresponding to lower energy) than the initial wavelength.

In 1923, Compton published a paper that explained the X-ray shift by attributing particle-like momentum to light quanta (Albert Einstein had proposed light quanta in 1905 in explaining the photo-electric effect, but Compton did not build on Einstein's work). The energy of light quanta depends only on the frequency of the light. In his paper, Compton derived the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays by assuming that each scattered X-ray photon interacted with only one electron. His paper concludes by reporting on experiments which verified his derived relation: $${\displaystyle {\lambda }^{\prime }-\lambda =\frac{h}{m_{\text{e}}c}(1-\cos \theta ),}$$ where

• ${\displaystyle \lambda }$ is the initial wavelength,
• ${\displaystyle {\lambda }^{\prime }}$ is the wavelength after scattering,
• ${\displaystyle h}$ is the Planck constant,
• ${\displaystyle m_{\text{e}}}$ is the electron rest mass,
• ${\displaystyle c}$ is the speed of light, and
• ${\displaystyle \theta }$ is the scattering angle.

The quantity ⁠h/m_ec⁠ is known as the Compton wavelength of the electron; it is equal to 2.43×10⁻¹² m. The wavelength shift λ′ − λ is at least zero (for θ = 0°) and at most twice the Compton wavelength of the electron (for θ = 180°).

Compton found that some X-rays experienced no wavelength shift despite being scattered through large angles; in each of these cases the photon failed to eject an electron. Thus the magnitude of the shift is related not to the Compton wavelength of the electron, but to the Compton wavelength of the entire atom, which can be upwards of 10000 times smaller. This is known as "coherent" scattering off the entire atom since the atom remains intact, gaining no internal excitation.

In Compton's original experiments the wavelength shift given above was the directly measurable observable. In modern experiments it is conventional to measure the energies, not the wavelengths, of the scattered photons. For a given incident energy ${\displaystyle E_{\gamma }=hc/\lambda }$, the outgoing final-state photon energy, ${\displaystyle E_{{\gamma }^{\mathrm{\prime }}}}$, is given by $${\displaystyle E_{{\gamma }^{\mathrm{\prime }}}=\frac{E_{\gamma }}{1+(E_{\gamma }/m_{\text{e}}{c}^2)(1-\cos \theta )}.}$$

Derivation of the scattering formula

Feynman diagrams (time from left to right)
s channel
u channel

Fig. 3: Energies of a photon at 500 keV and an electron after Compton scattering.

A photon γ with wavelength λ collides with an electron e in an atom, which is treated as being at rest. The collision causes the electron to recoil, and a new photon γ′ with wavelength λ′ emerges at angle θ from the photon's incoming path. Let e′ denote the electron after the collision. Compton allowed for the possibility that the interaction would sometimes accelerate the electron to speeds sufficiently close to the velocity of light as to require the application of Einstein's special relativity theory to properly describe its energy and momentum.

At the conclusion of Compton's 1923 paper, he reported results of experiments confirming the predictions of his scattering formula, thus supporting the assumption that photons carry momentum as well as quantized energy. At the start of his derivation, he had postulated an expression for the momentum of a photon from equating Einstein's already established mass-energy relationship of E = mc² to the quantized photon energies of hf, which Einstein had separately postulated. If mc² = hf, the equivalent photon mass must be hf/c². The photon's momentum is then simply this effective mass times the photon's frame-invariant velocity c. For a photon, its momentum ${\displaystyle p=hf/c}$, and thus hf can be substituted for pc for all photon momentum terms which arise in course of the derivation below. The derivation which appears in Compton's paper is more terse, but follows the same logic in the same sequence as the following derivation.

The conservation of energy E merely equates the sum of energies before and after scattering.

${\displaystyle E_{\gamma }+E_{\text{e}}=E_{{\gamma }^{\prime }}+E_{{\text{e}}^{\prime }}.}$

Compton postulated that photons carry momentum; thus from the conservation of momentum, the momenta of the particles should be similarly related by

${\displaystyle {\mathbf{p}}_{\gamma }={\mathbf{p}}_{{\gamma }^{\prime }}+{\mathbf{p}}_{{\text{e}}^{\prime }},}$

in which p_e is omitted as being negligible.

The photon energies are related to the frequencies by

${\displaystyle E_{\gamma }=hf}$

${\displaystyle E_{{\gamma }^{\prime }}=h{f}^{\prime }}$

where h is the Planck constant.

Before the scattering event, the electron is treated as sufficiently close to being at rest that its total energy consists entirely of the mass–energy equivalence of its rest mass m_e,

${\displaystyle E_{\text{e}}=m_{\text{e}}{c}^2.}$

After scattering, the possibility that the electron might be accelerated to a significant fraction of the speed of light, requires that its total energy be represented using the relativistic energy–momentum relation

${\displaystyle E_{{\text{e}}^{\prime }}=\sqrt{(p_{{\text{e}}^{\prime }}c{)}^2+(m_{\text{e}}{c}^2{)}^2}.}$

Substituting these quantities into the expression for the conservation of energy gives

${\displaystyle hf+m_{\text{e}}{c}^2=h{f}^{\prime }+\sqrt{(p_{{\text{e}}^{\prime }}c{)}^2+(m_{\text{e}}{c}^2{)}^2}.}$

This expression can be used to find the magnitude of the momentum of the scattered electron,

$${\displaystyle p_{{\text{e}}^{\prime }}^2{c}^2=(hf-h{f}^{\prime }+m_{\text{e}}{c}^2{)}^2-m_{\text{e}}^2{c}^4.}$$

1

Note that this magnitude of the momentum gained by the electron (formerly zero) exceeds the energy/c lost by the photon,

${\displaystyle \frac{1}{c}\sqrt{(hf-h{f}^{\prime }+m_{\text{e}}{c}^2{)}^2-m_{\text{e}}^2{c}^4}>\frac{hf-h{f}^{\prime }}{c}.}$

Equation (1) relates the various energies associated with the collision. The electron's momentum change involves a relativistic change in the energy of the electron, so it is not simply related to the change in energy occurring in classical physics. The change of the magnitude of the momentum of the photon is not just related to the change of its energy; it also involves a change in direction.

Solving the conservation of momentum expression for the scattered electron's momentum gives

${\displaystyle {\mathbf{p}}_{{\text{e}}^{\prime }}={\mathbf{p}}_{\gamma }-{\mathbf{p}}_{{\gamma }^{\prime }}.}$

Making use of the scalar product yields the square of its magnitude,

${\displaystyle \begin{array}{rl}{p}_{{\text{e}}^{\prime }}^2& ={\mathbf{p}}_{{\text{e}}^{\prime }}\cdot {\mathbf{p}}_{{\text{e}}^{\prime }}=({\mathbf{p}}_{\gamma }-{\mathbf{p}}_{{\gamma }^{\prime }})\cdot ({\mathbf{p}}_{\gamma }-{\mathbf{p}}_{{\gamma }^{\prime }})\\ & =p_{\gamma }^2+p_{{\gamma }^{\prime }}^2-2p_{\gamma }{p}_{{\gamma }^{\prime }}\cos \theta .\end{array}}$

In anticipation of ${\displaystyle p_{\gamma }c}$ being replaced with hf, multiply both sides by c²,

${\displaystyle p_{{\text{e}}^{\prime }}^2{c}^2=p_{\gamma }^2{c}^2+p_{{\gamma }^{\prime }}^2{c}^2-2c^2{p}_{\gamma }{p}_{{\gamma }^{\prime }}\cos \theta .}$

After replacing the photon momentum terms with hf/c, we get a second expression for the magnitude of the momentum of the scattered electron,

$${\displaystyle p_{e^{\prime }}^2{c}^2=(hf{)}^2+(h{f}^{\prime }{)}^2-2(hf)(h{f}^{\prime })\cos \theta .}$$

2

Equating the alternate expressions for this momentum gives

${\displaystyle (hf-h{f}^{\prime }+m_{\text{e}}{c}^2{)}^2-m_{\text{e}}^2{c}^4={\left(hf\right)}^2+{\left(h{f}^{\prime }\right)}^2-2h^{2}f{f}^{\prime }\cos \theta ,}$

which, after evaluating the square and canceling and rearranging terms, further yields

${\displaystyle 2hf{m}_{\text{e}}{c}^2-2h{f}^{\prime }{m}_{\text{e}}{c}^2=2h^{2}f{f}^{\prime }\left(1-\cos \theta \right).}$

Dividing both sides by 2hff′m_ec yields

${\displaystyle \frac{c}{f^{\prime }}-\frac{c}{f}=\frac{h}{m_{\text{e}}c}\left(1-\cos \theta \right).}$

Finally, since fλ = f′λ′ = c,

$${\displaystyle {\lambda }^{\prime }-\lambda =\frac{h}{m_{\text{e}}c}(1-\cos \theta ).}$$

3

It can further be seen that the angle φ of the outgoing electron with the direction of the incoming photon is specified by

$${\displaystyle \cot \phi =\left(1+\frac{hf}{m_{\text{e}}{c}^2}\right)\tan (\theta /2).}$$

4

Applications

Compton scattering

Compton scattering is of prime importance to radiobiology, as it is the most probable interaction of gamma rays and high energy X-rays with atoms in living beings and is applied in radiation therapy.

Compton scattering is an important effect in gamma spectroscopy which gives rise to the Compton edge, as it is possible for the gamma rays to scatter out of the detectors used. Compton suppression is used to detect stray scatter gamma rays to counteract this effect.

Magnetic Compton scattering

Magnetic Compton scattering is an extension of the previously mentioned technique which involves the magnetisation of a crystal sample hit with high energy, circularly polarised photons. By measuring the scattered photons' energy and reversing the magnetisation of the sample, two different Compton profiles are generated (one for spin up momenta and one for spin down momenta). Taking the difference between these two profiles gives the magnetic Compton profile (MCP), given by ${\displaystyle J_{\text{mag}}({\mathbf{p}}_z)}$ – a one-dimensional projection of the electron spin density. $${\displaystyle J_{\text{mag}}({\mathbf{p}}_z)=\frac{1}{\mu }{\iint }_{-\mathrm{\infty }}^{\mathrm{\infty }}(n_{\uparrow }(\mathbf{p})-n_{\downarrow }(\mathbf{p}))d{\mathbf{p}}_{x}d{\mathbf{p}}_y}$$ where ${\displaystyle \mu }$ is the number of spin-unpaired electrons in the system, ${\displaystyle n_{\uparrow }(\mathbf{p})}$ and ${\displaystyle n_{\downarrow }(\mathbf{p})}$ are the three-dimensional electron momentum distributions for the majority spin and minority spin electrons respectively.

Since this scattering process is incoherent (there is no phase relationship between the scattered photons), the MCP is representative of the bulk properties of the sample and is a probe of the ground state. This means that the MCP is ideal for comparison with theoretical techniques such as density functional theory. The area under the MCP is directly proportional to the spin moment of the system and so, when combined with total moment measurements methods (such as SQUID magnetometry), can be used to isolate both the spin and orbital contributions to the total moment of a system. The shape of the MCP also yields insight into the origin of the magnetism in the system.

Inverse Compton scattering

Inverse Compton scattering is important in astrophysics. In X-ray astronomy, the accretion disk surrounding a black hole is presumed to produce a thermal spectrum. The lower energy photons produced from this spectrum are scattered to higher energies by relativistic electrons in the surrounding corona. This is surmised to cause the power law component in the X-ray spectra (0.2–10 keV) of accreting black holes.

The effect is also observed when photons from the cosmic microwave background (CMB) move through the hot gas surrounding a galaxy cluster. The CMB photons are scattered to higher energies by the electrons in this gas, resulting in the Sunyaev–Zel'dovich effect. Observations of the Sunyaev–Zel'dovich effect provide a nearly redshift-independent means of detecting galaxy clusters.

Some synchrotron radiation facilities scatter laser light off the stored electron beam. This Compton backscattering produces high energy photons in the MeV to GeV range subsequently used for nuclear physics experiments.

Non-linear inverse Compton scattering

Non-linear inverse Compton scattering (NICS) is the scattering of multiple low-energy photons, given by an intense electromagnetic field, in a high-energy photon (X-ray or gamma ray) during the interaction with a charged particle, such as an electron. It is also called non-linear Compton scattering and multiphoton Compton scattering. It is the non-linear version of inverse Compton scattering in which the conditions for multiphoton absorption by the charged particle are reached due to a very intense electromagnetic field, for example the one produced by a laser.

Non-linear inverse Compton scattering is an interesting phenomenon for all applications requiring high-energy photons since NICS is capable of producing photons with energy comparable to the charged particle rest energy and higher. As a consequence NICS photons can be used to trigger other phenomena such as pair production, Compton scattering, nuclear reactions, and can be used to probe non-linear quantum effects and non-linear QED.

Starship

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https://en.wikipedia.org/wiki/Starship

An updated version (NASA, 1999) of the Project Orion by the United States government (1958–1965). It was the earliest scaled project developing a concept for a spaceship with a propulsion, of fission pulses, that was to be capable to transport humans light years within hundreds of years instead of thousands.

A starship, starcraft, or interstellar spacecraft is a theoretical spacecraft designed for traveling between planetary systems. The term is mostly found in science fiction. Reference to a "star-ship" appears as early as 1882 in Oahspe: A New Bible.

While NASA's Voyager and Pioneer probes have traveled into local interstellar space, the purpose of these uncrewed craft was specifically interplanetary, and they are not predicted to reach another star system; Voyager 1 probe and Gliese 445 will pass one another within 1.6 light years in about 40,000 years. Several preliminary designs for starships have been undertaken through exploratory engineering, using feasibility studies with modern technology or technology thought likely to be available in the near future.

In April 2016, scientists announced Breakthrough Starshot, a Breakthrough Initiatives program, to develop a proof-of-concept fleet of small centimeter-sized light sail spacecraft named StarChip, capable of making the journey to Alpha Centauri, the nearest star system, at speeds of 20% and 15% of the speed of light, taking between 20 and 30 years to reach the star system, respectively, and about 4 years to notify Earth of a successful arrival.

Research

Artist's conception of British Interplanetary Society's Project Daedalus (1978), a fusion powered interstellar probe

To travel between stars in a reasonable time using rocket-like technology requires very high effective exhaust velocity jet and enormous energy to power this, such as might be provided by fusion power or antimatter.

There are very few scientific studies that investigate the issues in building a starship. Some examples of this include:

• Project Orion (1958–1965), mostly crewed interplanetary spacecraft
• Project Daedalus (1973–1978), uncrewed interstellar probe
• Project Longshot (1987–1988), uncrewed interstellar probe
• Project Icarus (2009–2014), uncrewed interstellar probe
• Hundred-Year Starship (2011), crewed interstellar craft

The Bussard ramjet is an idea to use nuclear fusion of interstellar gas to provide propulsion.

Examined in an October 1973 issue of Analog, the Enzmann Starship proposed using a 12,000-ton ball of frozen deuterium to power pulse propulsion units. Twice as long as the Empire State Building is tall and assembled in-orbit, the proposed spacecraft would be part of a larger project preceded by interstellar probes and telescopic observation of target star systems.

The NASA Breakthrough Propulsion Physics Program (1996–2002) was a professional scientific study examining advanced spacecraft propulsion systems.

Types

• Sleeper: Starships that place their occupants into Cryostasis or Temporal Stasis during a long trip. This includes cryonics-based systems that freeze passengers for the duration of the journey. This is a common trope in science fiction, with some notable examples including "To Sleep in a Sea of Stars" by Christopher Paolini and Edward Bellamy's "Looking Backward"
• Generation: Ships in which the destination would be reached by descendants of the original passengers. These ships would necessarily be self-sustaining and self-maintaining for possibly thousands of years. Notable examples of this in fiction are the Godspeed in Beth Revis' "Across the Universe" (and subsequent sequels), as well as the Vanguard from Robert A. Heinlein's "Orphans of the Sky"

Stanford Torus-based generation ship, proposed by Project Hyperion

• Relativistic: Ships that function by taking advantage of time dilation at close-to-light-speeds, so long trips will seem much shorter (but still take the same amount of time for outside observers).
• Frame shift: Ships that take advantage of the fact that certain dimensions are less "folded" than others, to allow shorter travel by shifting one's frame of reference into a higher, more flat dimension to cut down on travel time, such as in science fiction with inter-dimensional hyperspace. Generally this results in speeds close to (but importantly, not greater than) light speed.
• Faster-than-light (FTL): A ship that functions by reaching a destination faster than the speed of light. While according to the special theory of relativity, faster-than-light travel is impossible, drives like a warp drive or using a wormhole, that is in principle similar have been hypothesized.

Theoretical possibilities

Artist's depiction of a hypothetical Wormhole Induction Propelled Spacecraft, based loosely on the 1994 "warp drive" paper of Miguel Alcubierre

The Alcubierre drive is a speculative warp drive conjectured by Mexican physicist Miguel Alcubierre in a 1994 paper which has not been peer-reviewed. The paper suggests that space itself could be topographically warped to create a local region of spacetime wherein the region ahead of the "warp bubble" is compressed, allowed to resume normalcy within the bubble, and then rapidly expanded behind the bubble creating an effect that results in apparent FTL travel, all in a manner consistent with the Einstein field equations of general relativity and without the introduction of wormholes. However, the actual construction of such a drive would face other serious theoretical difficulties.

Fictional examples

Main article: List of fictional spacecraft § Interstellar

The filming model of the 288.6 metres (947 ft) long starship USS Enterprise (NCC-1701) from the Star Trek: The Original Series television show. The model was donated to the Smithsonian Institution in 1974, where it is on public display.

There are widely known vessels in various science fiction franchises. The most prominent cultural use and one of the earliest common uses of the term starship was in Star Trek: The Original Series.

Polymath

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Polymath

Portrait of Benjamin Franklin by David Martin, 1767. Benjamin Franklin is one of the foremost polymaths in American history. Franklin was a writer, scientist, inventor, statesman, diplomat, printer and political philosopher. He further attained a legacy as one of the Founding Fathers of the United States.

A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, but some are gifted at explaining abstractly and creatively.

Embodying a basic tenet of Renaissance humanism that humans are limitless in their capacity for development, the concept led to the notion that people should embrace all knowledge and develop their capacities as fully as possible. This is expressed in the term Renaissance man, often applied to the gifted people of that age who sought to develop their abilities in all areas of accomplishment: intellectual, artistic, social, physical, and spiritual.

Etymology

The word polymath derives from the Greek roots poly-, which means "much" or "many," and manthanein, which means "to learn." Plutarch wrote that the Ancient Greek muse Polyhymnia was sometimes known as Polymatheia, describing her as responsible for "that faculty of the soul which inclines to attain and keep knowledge."

In Western Europe, the first work to use the term polymathy in its title, De Polymathia tractatio: integri operis de studiis veterum (A Treatise on Polymathy: The Complete Work on the Studies of the Ancients), was published in 1603 by Johann von Wowern, a Hamburg philosopher. Von Wowern defined polymathy as "knowledge of various matters, drawn from all kinds of studies ... ranging freely through all the fields of the disciplines, as far as the human mind, with unwearied industry, is able to pursue them". Von Wowern lists erudition, literature, philology, philomathy, and polyhistory as synonyms.

The earliest recorded use of the term in the English language is from 1624, in the second edition of The Anatomy of Melancholy by Robert Burton; the form polymathist is slightly older, first appearing in the Diatribae upon the first part of the late History of Tithes of Richard Montagu in 1621. Use in English of the similar term polyhistor dates from the late 16th century.

Renaissance man

"Renaissance man" redirects here. For other uses, see Renaissance Man.

Portrait of Sir Christopher Wren by Godfrey Kneller, 1711. Best known as an architect, Christopher Wren was also an astronomer, mathematician and physicist

The term "Renaissance man" was first recorded in written English in the early 20th century. It is used to refer to great thinkers living before, during, or after the Renaissance. Leonardo da Vinci has often been described as the archetype of the Renaissance man, a man of "unquenchable curiosity" and "feverishly inventive imagination". Many notable polymaths lived during the Renaissance period, a cultural movement that spanned roughly the 14th through to the 17th century that began in Italy in the Late Middle Ages and later spread to the rest of Europe. These polymaths had a rounded approach to education that reflected the ideals of the humanists of the time. A gentleman or courtier of that era was expected to speak several languages, play a musical instrument, write poetry, and so on; thus fulfilling the Renaissance ideal.

The idea of a universal education was essential to achieving polymath ability, hence the word university was used to describe a seat of learning. However, the original Latin word universitas refers in general to "a number of persons associated into one body, a society, company, community, guild, corporation, etc". At this time, universities did not specialize in specific areas, but rather trained students in a broad array of science, philosophy, and theology. This universal education gave them a grounding from which they could continue into apprenticeship toward becoming a master of a specific field.

When someone is called a "Renaissance man" today, it is meant that rather than simply having broad interests or superficial knowledge in several fields, the individual possesses a more profound knowledge and a proficiency, or even an expertise, in at least some of those fields. Some dictionaries use the term "Renaissance man" to describe someone with many interests or talents, while others give a meaning restricted to the Renaissance and more closely related to Renaissance ideals.

In academia

Robert Root-Bernstein and colleagues

Robert Root-Bernstein is considered the principal responsible for rekindling interest in polymathy in the scientific community. His works emphasize the contrast between the polymath and two other types: the specialist and the dilettante. The specialist demonstrates depth but lacks breadth of knowledge. The dilettante demonstrates superficial breadth but tends to acquire skills merely "for their own sake without regard to understanding the broader applications or implications and without integrating it". Conversely, the polymath is a person with a level of expertise that is able to "put a significant amount of time and effort into their avocations and find ways to use their multiple interests to inform their vocations".

A key point in the work of Root-Bernstein and colleagues is the argument in favor of the universality of the creative process. That is, although creative products, such as a painting, a mathematical model or a poem, can be domain-specific, at the level of the creative process, the mental tools that lead to the generation of creative ideas are the same, be it in the arts or science. These mental tools are sometimes called intuitive tools of thinking. It is therefore not surprising that many of the most innovative scientists have serious hobbies or interests in artistic activities, and that some of the most innovative artists have an interest or hobbies in the sciences.

Root-Bernstein and colleagues' research is an important counterpoint to the claim by some psychologists that creativity is a domain-specific phenomenon. Through their research, Root-Bernstein and colleagues conclude that there are certain comprehensive thinking skills and tools that cross the barrier of different domains and can foster creative thinking: "[creativity researchers] who discuss integrating ideas from diverse fields as the basis of creative giftedness ask not 'who is creative?' but 'what is the basis of creative thinking?' From the polymathy perspective, giftedness is the ability to combine disparate (or even apparently contradictory) ideas, sets of problems, skills, talents, and knowledge in novel and useful ways. Polymathy is therefore the main source of any individual's creative potential". In "Life Stages of Creativity", Robert and Michèle Root-Bernstein suggest six typologies of creative life stages. These typologies are based on real creative production records first published by Root-Bernstein, Bernstein, and Garnier (1993).

• Type 1 represents people who specialize in developing one major talent early in life (e.g., prodigies) and successfully exploit that talent exclusively for the rest of their lives.
• Type 2 individuals explore a range of different creative activities (e.g., through worldplay or a variety of hobbies) and then settle on exploiting one of these for the rest of their lives.
• Type 3 people are polymathic from the outset and manage to juggle multiple careers simultaneously so that their creativity pattern is constantly varied.
• Type 4 creators are recognized early for one major talent (e.g., math or music) but go on to explore additional creative outlets, diversifying their productivity with age.
• Type 5 creators devote themselves serially to one creative field after another.
• Type 6 people develop diversified creative skills early and then, like Type 5 individuals, explore these serially, one at a time.

Finally, his studies suggest that understanding polymathy and learning from polymathic exemplars can help structure a new model of education that better promotes creativity and innovation: "we must focus education on principles, methods, and skills that will serve them [students] in learning and creating across many disciplines, multiple careers, and succeeding life stages".

Peter Burke

Peter Burke, Professor Emeritus of Cultural History and Fellow of Emmanuel College at Cambridge, discussed the theme of polymathy in some of his works. He has presented a comprehensive historical overview of the ascension and decline of the polymath as, what he calls, an "intellectual species".

He observes that in ancient and medieval times, scholars did not have to specialize. However, from the 17th century on, the rapid rise of new knowledge in the Western world—both from the systematic investigation of the natural world and from the flow of information coming from other parts of the world—was making it increasingly difficult for individual scholars to master as many disciplines as before. Thus, an intellectual retreat of the polymath species occurred: "from knowledge in every [academic] field to knowledge in several fields, and from making original contributions in many fields to a more passive consumption of what has been contributed by others".

Given this change in the intellectual climate, it has since then been more common to find "passive polymaths", who consume knowledge in various domains but make their reputation in one single discipline, than "proper polymaths", who—through a feat of "intellectual heroism"—manage to make serious contributions to several disciplines. However, Burke warns that in the age of specialization, polymathic people are more necessary than ever, both for synthesis—to paint the big picture—and for analysis. He says: "It takes a polymath to 'mind the gap' and draw attention to the knowledges that may otherwise disappear into the spaces between disciplines, as they are currently defined and organized".

Bharath Sriraman

Bharath Sriraman, of the University of Montana, also investigated the role of polymathy in education. He poses that an ideal education should nurture talent in the classroom and enable individuals to pursue multiple fields of research and appreciate both the aesthetic and structural/scientific connections between mathematics, arts and the sciences.

In 2009, Sriraman published a paper reporting a 3-year study with 120 pre-service mathematics teachers and derived several implications for mathematics pre-service education as well as interdisciplinary education. He utilized a hermeneutic-phenomenological approach to recreate the emotions, voices and struggles of students as they tried to unravel Russell's paradox presented in its linguistic form. They found that those more engaged in solving the paradox also displayed more polymathic thinking traits. He concludes by suggesting that fostering polymathy in the classroom may help students change beliefs, discover structures and open new avenues for interdisciplinary pedagogy.

Kaufman, Beghetto and colleagues

James C. Kaufman, from the Neag School of Education at the University of Connecticut, and Ronald A. Beghetto, from the same university, investigated the possibility that everyone could have the potential for polymathy as well as the issue of the domain-generality or domain-specificity of creativity.

Based on their earlier four-c model of creativity, Beghetto and Kaufman proposed a typology of polymathy, ranging from the ubiquitous mini-c polymathy to the eminent but rare Big-C polymathy, as well as a model with some requirements for a person (polymath or not) to be able to reach the highest levels of creative accomplishment. They account for three general requirements—intelligence, motivation to be creative, and an environment that allows creative expression—that are needed for any attempt at creativity to succeed. Then, depending on the domain of choice, more specific abilities will be required. The more that one's abilities and interests match the requirements of a domain, the better. While some will develop their specific skills and motivations for specific domains, polymathic people will display intrinsic motivation (and the ability) to pursue a variety of subject matters across different domains.

Regarding the interplay of polymathy and education, they suggest that rather than asking whether every student has multicreative potential, educators might more actively nurture the multicreative potential of their students. As an example, the authors cite that teachers should encourage students to make connections across disciplines, use different forms of media to express their reasoning/understanding (e.g., drawings, movies, and other forms of visual media).

Waqas Ahmed

In his 2018 book The Polymath, British author Waqas Ahmed defines polymaths as those who have made significant contributions to at least three different fields. Rather than seeing polymaths as exceptionally gifted, he argues that every human being has the potential to become one: that people naturally have multiple interests and talents. He contrasts this polymathic nature against what he calls "the cult of specialisation". For example, education systems stifle this nature by forcing learners to specialise in narrow topics. The book argues that specialisation encouraged by the production lines of the Industrial Revolution is counter-productive both to the individual and wider society. It suggests that the complex problems of the 21st century need the versatility, creativity, and broad perspectives characteristic of polymaths.

For individuals, Ahmed says, specialisation is dehumanising and stifles their full range of expression whereas polymathy "is a powerful means to social and intellectual emancipation" which enables a more fulfilling life. In terms of social progress, he argues that answers to specific problems often come from combining knowledge and skills from multiple areas, and that many important problems are multi-dimensional in nature and cannot be fully understood through one specialism. Rather than interpreting polymathy as a mix of occupations or of intellectual interests, Ahmed urges a breaking of the "thinker"/"doer" dichotomy and the art/science dichotomy. He argues that an orientation towards action and towards thinking support each other, and that human beings flourish by pursuing a diversity of experiences as well as a diversity of knowledge. He observes that successful people in many fields have cited hobbies and other "peripheral" activities as supplying skills or insights that helped them succeed.

Ahmed examines evidence suggesting that developing multiple talents and perspectives is helpful for success in a highly specialised field. He cites a study of Nobel Prize-winning scientists which found them 25 times more likely to sing, dance, or act than average scientists. Another study found that children scored higher in IQ tests after having drum lessons, and he uses such research to argue that diversity of domains can enhance a person's general intelligence.

Ahmed cites many historical claims for the advantages of polymathy. Some of these are about general intellectual abilities that polymaths apply across multiple domains. For example, Aristotle wrote that full understanding of a topic requires, in addition to subject knowledge, a general critical thinking ability that can assess how that knowledge was arrived at. Another advantage of a polymathic mindset is in the application of multiple approaches to understanding a single issue. Ahmed cites biologist E. O. Wilson's view that reality is approached not by a single academic discipline but via a consilience between them. One argument for studying multiple approaches is that it leads to open-mindedness. Within any one perspective, a question may seem to have a straightforward, settled answer. Someone aware of different, contrasting answers will be more open-minded and aware of the limitations of their own knowledge. The importance of recognising these limitations is a theme that Ahmed finds in many thinkers, including Confucius, Ali ibn Abi Talib, and Nicolas of Cusa. He calls it "the essential mark of the polymath." A further argument for multiple approaches is that a polymath does not see diverse approaches as diverse, because they see connections where other people see differences. For example da Vinci advanced multiple fields by applying mathematical principles to each.

Examples

Further information: List of Renaissance figures

Polymaths include the scholars and thinkers of the Renaissance and Enlightenment, who excelled at several fields in science, technology, engineering, mathematics, and the arts. In the Italian Renaissance, the idea of the polymath was allegedly expressed by Leon Battista Alberti (1404–1472), a polymath himself, in the statement that "a man can do all things if he will". Leonardo da Vinci is often used as the archetypal example of a polymath.

Many polymaths didn't identify as such, since the term was first coined in the 17th century; they were instead described as polymaths by later historians. This includes several philosophers of Ancient Greece and the Islamic Golden Age. Whether or not a person is a polymath is often a subject of debate because of the term's broad definition by nature.