Draft:Fringe sciences

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Here, the presumed distance of the Oort cloud is compared to the rest of the Solar System using the orbit of Sedna. Credit: NASA / JPL-Caltech / R. Hurt.

On the right, the presumed distance of the Oort cloud is compared to the rest of the Solar System using the orbit of Sedna, "at the very fringe of our solar system."[1]

In physics, fringes are bands of contrasting brightness or darkness produced by diffraction or interference of radiation with a measurable wavelength. The science of studying these fringes is a fringe science. Yes, it's a pun!

In biology, there are organisms that grow fringes on their leaves or on their feet. Like the physics of fringes, these are the biology of fringes, another fringe science.

In the last several centuries, ideas have been studied by scientists and later shown to be wrong. These are often considered to be a fringe science, but with this use of the term science refers to apparent application of the scientific method by scientists that later were proved wrong. It does not refer to an application of the scientific method per se. There are other such endeavors which may turn out to be wrong, and some that may turn out to be right. Efforts to study the "mistakes" of science are also termed fringe sciences, but in many instances these have not been well-studied using the scientific method. These efforts may involve superstition, protoscience or may be just on the fringe of fringe science. These are not the main focus of this resource. A brief section has been included which describes these fringe sciences of the twenty-first century.

The objective of this resource is to give students and others an opportunity to learn about the real and respected sciences of fringes; i.e., real fringe sciences. These are mainstream sciences.

At the conclusion of reading and studying this resource students and others should have a well-rounded understanding of the sciences that benefit from the study of fringes.

The resource is organized into sections. The first introduces and defines types of fringes observed in physics and chemistry in alphabetical order. The second section describes fringes observed in astronomy by radiation. This includes biological fringes found on Earth and used in technology. The final section describes the public policy concerned with the apparent limits and mistakes of contemporary science.


Dark-field image shows two families of Brazil twin lamellae at reflection (1,-1,0,0). Credit: L. van Goethem, J. van Landuyt, and S. Amelinckx.{{fairuse}}

A-fringes are often called α-fringes.

"Since the crystal axes in both parts of a Brazil twin are parallel, it is expected that if the boundary produces diffraction contrast fringes, then these will be a-fringes."[2]

"The fringes from such a boundary have been termed a-fringes by Amelinckx".[2]

In the image on the right, the a-fringes occur at or immediately next to the twin boundaries. Some are dark fringes. Others are smooth and lighter due to the overlap of two boundaries.

Brewster fringes[edit]

The Production of Brewster's Fringes is diagrammed. Credit: R. N. O'Brien.{{fairuse}}

Def. "Fringes of Equal Inclination"[3] are called Brewster's Fringes, or Brewster fringes.

"Tolansky has given an excellent treatment of fringes of equal inclination.10 However the difference between wedge or fizeau type fringes and Brewster's fringes will briefly be considered."[3]

The "two types can exist simultaneously, it is easy to confuse the two."[3]

Per the image on the right, "If the incident light is at an angle to the wedge whose angle is small (about 2 minutes of arc), instead of getting wedge fringes, that is, a continuous set of equally spaced parallel fringes, rings of fringes [END VIEW through the lens in the image on the right] are produced."[3]

"For wedge fringes, the fringes appear on a uniform wedge at positions where the thickness of the wedge is an integral multiple of the wavelength of the monochromatic light, that is since nλ = 2μt Cos ø, whenever the thickness has increased by λ/2 from the last fringe, bright or dark, a new fringe appears. n is the order of interference, μ the refractive index, t the thickness and ø the angle of incidence of the light. If ø becomes a very little less than 90° for thick wedges, Brewster's fringes result."[3]

In the experimental set up used glass plates were in contact with the wedge, "Brewster's fringes are located at infinity and appear on the wedge as rings as shown in [the diagram on the right], End View. The fringes will appear at positions governed by nλ = μt(Cosine of the angle of refraction in the first glass flat minus Cosine of the angle of refraction in the second glass flat) assuming Cos ø is about equal to 1, since the light passes only once through the cell."[3]

Fabry–Pérot fringes[edit]

"Thin films were fabricated from poly(vinylpyrrolidone) (PVPON) and poly(acrylic acid) (PAA) based on hydrogen bonding layer-by-layer (LBL) assembly process. Due to light interference, PVPON/PAA films present Fabry–Pérot fringes in the UV–Vis–NIR spectrum."[4]

"Using the peak positions and amplitude of the Fabry–Pérot fringes, the refractive index and thickness of the film can be evaluated. Furthermore, Fabry–Pérot fringes can be utilized to monitor the film's growth and water content variation in the film."[4]

Fizeau fringes[edit]

A Fizeau scheme spatially filters light from an exoplanet relative to its star. Credit: P. Baudoz, A. Boccaletti, J. Baudrand, & D. Rouan.{{fairuse}}
The Fizeau image in the focal plane shows fringes pinning the intensity distribution of the stellar flux. Credit: P. Baudoz, A. Boccaletti, J. Baudrand, & D. Rouan.{{fairuse}}

The technique [relies] on a simple Fizeau recombination of the science beam [from a beam splitter in the diagram on the right] and the reference beam. It enables to discriminate speckles from a planet without using fast [optical path difference] OPD modulation or deformable mirrors."[5]

The science beam "is spatially filtered using a pinhole or optical fiber. The two beams are recombined in the focal plane in a Fizeau scheme. [...] The Fizeau image in the focal plane will show fringes [see the images on the left, third image] pinning the intensity distribution of the stellar flux. Since the flux of the companion is fully removed from the reference beam by spatial filtering, the intensity of the companion will be unaltered by the reference beam. This is what can be seen in [the images on the left] where the point spread function of the stellar flux interfere with the reference beam creating a fringe pattern over all the diffraction rings and speckles. A companion located at a distance of 2 λ/D and in the upper right quadrant does not show fringes because it is not coherent with the reference beam."[5]

Fresnel fringes[edit]

Fringe pattern produced with a Michelson interferometer using white light. Credit: Alain Le Rille.{{free media}}
The image diagrams the Michelson-Morley interferometer. Credit: Albert Abraham Michelson and Edward Morley.{{free media}}
Fresnel fringes are produced in a field emission electron microscope. Credit: Akira Tonomura, Tsuyoshi Matsuda, Junji Endo, Hideo Todokoro and Tsutomu Komoda.{{fairuse}}

In the image on the right are the Fresnel fringes produced with a Michelson interferometer using white light configured so that the central fringe is white rather than black.

The image on the left diagrams the Michelson-Morley interferometer, where a is the light source, an oil lamp; b is a beam splitter; c is a compensating plate so that both the reflected and transmitted beams travel through the same amount of glass (important since experiments were run with white light which has an extremely short coherence length requiring precise matching of optical path lengths for fringes to be visible; monochromatic sodium light was used only for initial alignment); d, d' and e are mirrors; e' is a fine adjustment mirror; and f is a telescope.

"The formation of Fresnel fringes is illustrated in [the image second down on the right]. Nearly plane wave [of electrons] with a divergent angle of 2β illuminates the edge of a specimen. The transmitted wave and the diffracted waves from the edge interfere with each other on [an] observation plane [to] form Fresnel fringes. The spacing of the fringes becomes smaller with the distance from the edge. The minimum spacing is limited by the diameter of an illumination cone on the observation plane [middle horizontal line in the image]."[6]

Haidinger fringes[edit]

The diagram shows the generation of Heiginger fringes of equal inclination and the inverse process of beam propagation. Credit: Wei Wang, Hirokazu Kozaki, Joseph Rosen, and Mitsuo Takeda.{{fairuse}}

Def. "interference fringes produced by light passing through thick glass plates at near-normal incidence"[7] are called Haidinger fringes.

These interference fringes were "named after Wilhelm Karl von Haidinger (1795-1871), [an] Austrian mineralogist".[7]

The diagram on the right demonstrates the generation of Haidinger fringes. By analogy, the distance ΔZ can also refer to the thickness of a flat, polished glass plate with its upper surface acting as a mirror M1, and lower surface acting as an effective reference mirror, M2'. The observation point P as in an optical microscope used in optical mineralogy is above the optical axis of lens L.

"f is the focal length of the lens, AH is a normal from point A to ray CLP, and A' is a mirror image of point A with respect to plane M2'."[8]

"A ray from the source that is incident upon the plane-parallel plate at a small angle θ is reflected by the upper and lower surfaces, M1 and M2', to form parallel rays [AB] and [AC]."[8] These are then focused by lens L to point P in the ring.

Maker fringes[edit]

This diagram shows the X-cut location of a quartz crystal including symmetry elements. Credit: Raquel Alicante.{{fairuse}}

Here's a theoretical definition:

Def. interference fringes produced by near-normal incident radiation passing through a plate rotated about an axis within the plate, perpendicular to the direction of irradiation, are called Maker fringes.

In the diagram on the right, the thick dashed line marked X Cut represents the plate cut from a quartz crystal perpendicular to the crystal's X-axis, parallel to the Z-axis (into the plane of the image). The X-axis is the direction of irradiation and the Z-axis is the axis of rotation.

Moiré fringes[edit]

Animation of changing angle between two identical line grids is shown. Credit: P. Fraundorf.{{free media}}
Definition of the variables used for the calculation of the distance between dark lines for a rotational Moiré pattern is shown, where "ligne claire" means "pale line". Credit: Christophe Dang Ngoc Chan.{{free media}}

"If two fine patterns are superposed multiplicatively, a beat pattern - moiré fringes - will appear in their product [see image at top right]."[9]

In the lower right diagram the variables used for the calculation of the distance between dark lines for rotational Moiré fringes are defined.

Def. "an optical effect formed when one family of curves is superposed on another, the lines of the overlapping figures crossing at an angle less than about 45°; the moiré lines are then the locus of the points of intersection"[10] is called a moiré pattern, or moiré fringes.

Pendellösung fringes[edit]

Def. interference fringes produced by radiation passing through thick wedge plates at near-normal incidence are called Pendellösung fringes.

The "dark and light fringes (Pendellösung fringes) will have a narrower spacing at the edges of the diffraction region and a wider spacing in the centre[.] [The] central part of the fringe turns out to be bent towards the thick part of the wedge. The degree of bending of the fringes depends on L [the source-film distance as in a camera or length to the plane of focus]. In the limit L ⟶ ∞ the fringes are straight, which corresponds to the plane-wave incidence at the Bragg angle [...]. In practice, the fringes are always bent due to L finiteness, and the first fringe broadens out in the centre."[11]

Ramsey fringes[edit]

Ramsey pattern is obtained for P(4)F1 SF6 line with four traveling waves (interaction geometry illustrated by the inset). Credit: Ch. J. Bordé, S. Avrillier, A. Van Lerberghe, Ch. Salomon, D. Bassi and G. Scoles.{{fairuse}}

Def. the fluorescence oscillations from an atom beam[12] are called Ramsey fringes.

Optical "Ramsey fringes [shown in the image on the right have been observed] in the 10 µm spectral region using a supersonic seeded beam of 7% [sulfur hexafluoride] SF6, in He, illuminated by a CO2 laser in spatially-separated field zones."[13]

The "P(4) F1 and E components of the ν3 band of SF6, which can be reached with a waveguide CO2 laser oscillating on the P(16) CO2 line at 10.55 µm."[13]

"Four oscillations of the signal could be observed with a 40% contrast with successive minima obtained for a total power of ~1, 4, 9 and 16 mW."[13]

"To obtain fringes, part of the laser beam was intercepted before the interaction region by a screen which transmitted the light only through 1 mm wide slits. Two different geometries were used in these experiments. In the first one, three equidistant standing waves were generated by three equidistant slits of 5 mm separation together with a corner cube placed on the other side of the molecular beam to retroreflect the light back through the slits. In the second geometry, only two of the previous slits were illuminated. An offset between the center of the slits and the center of the corner cube generated two counter-propagating sets of travelling waves with a 5 mm distance between adjacent co-propagating waves of each set. The spacing between the two sets can be arbitrary and was actually l0 mm in this experiment. Highly contrasted fringes have been obtained in both cases and as an example the figure displays the signal corresponding to the four travelling waves case."[13]

"The broad pedestal has a width ~1.4 MHz corresponding to the transit broadening width across a single zone. The fringes themselves have a 23 kHz width (HWHM) consistent with a ~930 m/sec peak velocity of the SF6 molecules [15]."[13]

Talbot fringes[edit]

Schematic of the Talbot fringes experimental setup, where the pulsed metastable helium beam is produced in a switched dc gas discharge, and time-of-flight detection is done by the time-resolving detection scheme. Credit: S. Nowak, Ch. Kurtsiefer, and T. Pfau and C. David.{{fairuse}}
Experimental results are for two different settings of L1: (a) L1 = 0.24 m, (b) L1 = 0.79 m. Credit: S. Nowak, Ch. Kurtsiefer, and T. Pfau and C. David.{{fairuse}}

"The Talbot effect is the self-imaging of a grating il-luminated with plane coherent waves, showing up at a characteristic distance LT = 2d2/λ from the diffraction grating. LT is called the Talbot length. More-general self-images with subharmonic periods also occur at distances LT/(2m) (integer m) but with reduced periodicity d/m. In the paraxial approximation, when an ideal line grating with an infinite slit number is used, a small open fraction and perfect coherent illumination lead to patterns with 100% contrast; self-images then occur at all integer multiples of the Talbot length, nLT, and the subharmonics at all distances nLT/2m, where m can be infinitely large. In practice the achievable contrast is limited by the finite size and slit width of the grating and by the finite transverse coherence length and monochromaticity of the incident beam. In the case of finite geometry (distance L0 from source to grating and L1 from grating to detection plane; [...]), one has to deal with curved wave fronts instead of plane waves. This results in a scaling of the Talbot length15 to an effective Talbot length LTE = 2(1 + L1/L0)d2/λ. In this case the respective diffraction patterns are geometrically magnified, and the periodicity of the fringes takes values deff/m = (1 + L1/L0)d/m."[14]

Plotted are "the spatial atom distribution versus the de Broglie wavelength λdB. The intensity is encoded in the gray scale. The arrows indicate the locations at which Talbot fringes of the mth order are observed. [...] Atomic distributions are shown for λdB = 1–3 pm and λdB = 30–60 pm, where the fast and slow atoms are produced by the source. [Also plotted are] the spatial atom distribution versus the de Broglie wavelength."[14]

Young's fringes[edit]

Measured vertical intensity distribution is taken through the cross section of a set of fringes. Credit: Graham H. Cross and Yitao Ren, Neville J. Freeman.{{fairuse}}

"On the conventional Huygens model each waveguide will act as a source of cylindrical waves diffracting into the far-field where they will overlap to give Young’s interference fringes."[15]

"The full spatial intensity pattern is described by a set of fringes modulated in the x direction and contained within a Gaussian envelope which results from diffraction. According to the simple theory of interference fringes maxima and minima of intensity should be spaced with spacing, a, according to

where λ is the wavelength (632.8 nm in this case) and d, the separation of the sources."[15]

"To confirm the Young’s fringe condition [for the above equation] an intensity scan was taken through the cross section of a set of fringes. At a distance to the screen, s, of 9.6 cm we observed a separation between adjacent fringe maxima, a, of 1.76 cm. At a wavelength of 632.8 nm this gives a waveguide center separation for this sample, d, of 3.45 µm. This compares extremely favorably with the expected separation of between 3.4 and 3.8 µm and is thus within experimental error."[15]

Theoretical fringes[edit]

Interference fringes are produced in overlapping plane waves. Credit: Fffred~commonswiki.

From wave theory, specifically, the interaction of identical waves from at least two sources produces interference fringes, where maxima are separated by the fringe spacing

and df increases with increase in wavelength or decreasing angle θ.


  1. a "decorative border",[16]
  2. a "marginal or peripheral part",[16]
  3. a "light or dark band formed by the diffraction of light",[16]
  4. the "peristome or [border]-like appendage of the capsules of most mosses"[17]

is called a fringe.

Def. in the definite a "method of discovering knowledge about the natural world based in making falsifiable predictions (hypotheses), testing them empirically, & developing theories that match known data from repeatable physical experimentation"[18] is called the scientific method.

Def. the disciplines or branches of learning, especially those "dealing with measurable or systematic principles ... the collective [disciplines] of study or learning acquired through the scientific method; the sum of knowledge gained from such methods and discipline"[19] are called the sciences.

Here's a theoretical definition:

Def. the disciplines or branches of learning, especially those dealing with measurable or systematic principles, the collective disciplines of study or learning acquired through the scientific method regarding fringes in the natural world; the sum of knowledge gained from such methods and discipline, are called fringe sciences.


This colour-composite image of the Helix Nebula (NGC 7293) was created from images obtained using the the Wide Field Imager (WFI). Credit: European Southern Observatory.{{free media}}
The interferogram is of the [O III] 500.7 nm line. Credit: J. Meaburn and N. J. White.{{fairuse}}
The interferogram is of the [N II] 658.4 nm line. Credit: J. Meaburn and N. J. White.{{fairuse}}

"A two-beam, imaging, Fabry-Pérot interferometer (Baddiley et al., 1981) was used [...] during July, 1980. Interferograms of the [O III] 5007 Å and [N II] 6584 Å emission lines were simultaneously detected (by employing a dichroic beamsplitter) with Fabry-Pérot inter-order separations of 3.342 Å for [O III] and 3.182 Å for [N II]."[20]

The "fringes were positioned within the interorder by adjusting the gas (N2) pressure in the etalon chambers so that the centre of the nebula was intersected. The Helix nebula, with an [N II] diameter of ≃ 29 arc min is ideally matched to the ≃ 30 arc min diameter field of the interferometer."[20]

"Calibration of the [O III] and [N II] interferograms was achieved by photographing on the same plate a portion of the fringes produced by the helium and cesium emission lines at 5015.68 Å and 6586.506 Å respectively. Removal of the Fabry-Pérot etalons allows the interferometer to be used as a direct filter camera. Subsequently, complementary [O III] and [N II] photographs taken through narrowband (15 Å) interference filters were also obtained."[20]

"The fringes produced by a single exposure with a classical Fabry-Pérot spectrograph only represent the profile of an emission line if the field is uniformly illuminated by that line and there are no velocity changes in the profile over the field."[20]

In "the present application for fringes, [images on the left] there is only a small change in brightness over the small part of a line profile produced by a distinctly separate velocity component. This applies to the fringes analyzed [...] in the Helix nebula and radial velocities of these components can be determined with accuracy."[20]

In the image on the top left, fringes 1 and 2 are labeled. A third fringe is above fringe 2 at the same spacing. The first fringe in the lower left image is labeled "fringe".

"The most striking new feature revealed [in the interferograms on the left] of the motions within the Helix nebula is apparent in the [O III] interferogram in [the upper left image.] Continuous changes to both negative and positive radial velocities occur from edge to the centre of the Helix nebula. [...] Remarkably, sections of the [N II] velocities [...] from the interferogram in [the lower left image] also show the same tendencies."[20]

"Heliocentric radial velocities from +44 to -51 km s-1 have been detected over the centre of the nebula."[20]


"While I was looking, the object that accompanied the flash burst, and displayed a magnificent mauve and red fringe of light. I say fringe, as it would be impossible for me to describe otherwise the shape, for it appeared to me to project shafts of light, some long and some short, like what would be the rays of a great star."[21]


By bombarding a silicon single crystal wedge with thickness ranging from ~0.3 cm to 1 cm in a slow neutron beam, a series of Pendellösung interference fringes formed by the diffraction of the neutrons appear within Bragg reflections parallel to the thinner edge of the wedge.[22]


"High contrast proton moiré fringes have been obtained in a laser-produced proton beam. Moiré fringes with modulation of 20%–30% were observed in protons with energies in the range of 4–7 MeV. Monte Carlo simulations with simple test fields showed that shifts in the moiré fringes can be used to give quantitative information on the strength of transient electromagnetic fields inside plasmas and materials that are opaque to conventional probing methods."[23]


Map of Kikuchi line pairs is down to 1/1Å for 300 keV electrons in hexagonal sapphire (Al2O3), with some intersections labeled. Credit: P. Fraundorf.{{free media}}

Kikuchi lines pair up to form bands in electron diffraction from single crystal specimens. They serve as "roads in orientation-space" for microscopists not certain at what they are looking. In transmission electron microscopes, they are easily seen in diffraction from regions of the specimen thick enough for multiple scattering.[24] Unlike diffraction spots, which blink on and off as one tilts the crystal, Kikuchi bands mark orientation space with well-defined intersections (called zones or poles) as well as paths connecting one intersection to the next.

Experimental and theoretical maps of Kikuchi band geometry, as well as their direct-space analogs e.g. bend contours, electron channeling patterns, and fringe visibility maps are increasingly useful tools in electron microscopy of crystalline and nanocrystalline materials.[25] Because each Kikuchi line is associated with Bragg diffraction from one side of a single set of lattice planes, these lines can be labeled with the same Miller or reciprocal-lattice indices that are used to identify individual diffraction spots. Kikuchi band intersections, or zones, on the other hand are indexed with direct-lattice indices i.e. indices which represent integer multiples of the lattice basis vectors a, b and c.

Kikuchi lines are formed in diffraction patterns by diffusely scattered electrons, e.g. as a result of thermal atom vibrations.[26] The main features of their geometry can be deduced from a simple elastic mechanism proposed in 1928 by Seishi Kikuchi,[27] although the dynamical theory of diffuse inelastic scattering is needed to understand them quantitatively.[28]

In x-ray scattering these lines are referred to as Kossel lines[29] (named after Walther Kossel).


"A complete theory of Maker fringes in nonabsorbing isotropic and uniaxial crystals has been derived which includes all the corrections necessary for making precise determinations of nonlinear optical co‐efficients. These corrections include finite beamwidth effects and multiple reflection corrections. Comparison of this theory with extensive experimental data on the Maker fringes in quartz, ADP, and KDP shows agreement to within the experimental accuracy of about 5% on the Maker fringe envelopes and to better than 1% on the coherence lengths. We conclude from this study that a careful analysis of Maker fringes can yield precise values of the nonlinear optical coefficients and coherence lengths in isotropic and uniaxial crystals. This is of great importance in establishing accurate and reliable standards in the field of nonlinear optics."[30]

"Andreas Quirrenbach is a Professor of Physics and member of the Center for Astrophysics and Space Sciences at the University of California, San Diego. He became fascinated with the concept of milli-arc-seconds as an undergraduate student while attending a summer school at the Max-Planck-Institut für Radioastronomie (MPIfR). After completing his thesis at MPIfR and obtaining a PhD in astronomy from the University of Bonn, he decided to do "fringe science" at shorter wavelengths and joined the optical interferometry group at the Naval Research Laboratory in Washington, DC, which gave him the opportunity to spend 200 nights on Mt. Wilson observing with the Mark III Interferometer."[31]


The shows a simulation of the Kennedy/Illingworth refinement of the Michelson-Morley experiment. Credit: Stigmatella aurantiaca.{{free media}}

With respect to the image on the right: (a) Michelson-Morley interference pattern in monochromatic mercury light, with a dark fringe precisely centered on the screen, (b) the fringes have been shifted to the left by 1/100 of the fringe spacing, (c) a small step in one mirror causes two views of the same fringes to be spaced 1/20 of the fringe spacing to the left and to the right of the step, (d) a telescope has been set to view only the central dark band around the mirror step (note the symmetrical brightening about the center line), (e) the two sets of fringes have been shifted to the left by 1/100 of the fringe spacing producing an abrupt discontinuity in luminosity is visible across the step.


The figure shows the night-sky spectrum from 650 to 930 nm (Massey & Foltz 2000) and illustrates the large contribution to the sky flux from OH emission bands. Credit: Massey & Foltz 2000 and Steve B. Howell.{{fairuse}}
Top left: I-band neon fringe flat field. Top right: Same CCD section showing a nighttime I-band image of a star field taken with strong OH emission. Bottom: Same section in the final reduced image showing the complete removal of the CCD fringes. Credit: Steve B. Howell.{{fairuse}}

"Fringing in CCD images is troublesome from the aspect of photometric quality and image flatness in the final reduced product. Additionally, defringing during calibration requires the inefficient use of time during the night to collect and produce a "supersky" fringe frame. The fringe pattern observed in a CCD image for a given near-IR filter is dominated by small thickness variations across the detector, with a second-order effect caused by the wavelength extent of the emission lines within the bandpass that produce the interference pattern."[32]

Essentially "any set of emission lines that generally match the wavelength coverage of the night-sky emission lines within a bandpass will produce an identical fringe pattern."[32]

"The production of constructive and destructive interference patterns can cause substantial quantum efficiency variations in thinned CCDs as long-wavelength light is multiply reflected between the front and back surfaces. Fringing begins to be an issue for CCDs when the absorption depth within the silicon becomes comparable with the thickness of the CCD. This occurs for optical wavelengths of ~700 nm or longer, for which the light is internally reflected several times before finally being absorbed (Lesser 1990; Howell 2006)."[32]

"To eliminate the need to use valuable observing time during the night to collect a set of deep-sky exposures in order to produce a "supersky" fringe frame, we used afternoon flat-field exposures of a neon lamp to obtain fringe frames with high signal-to-noise ratios (S/N). The fringe pattern produced in a CCD image is shown to consist of an average pattern from all the emission lines present within a given filter bandpass; thus, the neon emission-line source (Ne lamp) provides a match to the fringe pattern produced by night-sky emission on a filter-by-filter basis. The collection of daytime neon fringe flats provides a fast, efficient method to produce fringe frames, and the defringed CCD images show a complete removal of the night-sky effects."[32]

"Fringing most notably occurs within a CCD when near-monochromatic light is incident on the detector. Spectroscopic observations are prone to fringing, due to their collection of dispersed light placing individual wavelengths across pixels (e.g., Malumuth et al. 2003). Direct images also suffer from fringing (e.g., Gullixson 1992), especially for narrowband observations, primarily due to the bright night-sky emission lines from atmospheric OH molecules. Auroral [O I] emission near 630 nm can also be strong at times and partake in fringe production. Reducing fringing in a CCD can be done by controlling the CCD thinning process to a high level of flatness and by applying an antireflection coating to the back of a thinned CCD. Both of these solutions provide mitigation by reducing the fringe amplitude from near 50% or more to 2% or less."[32]

The "average fringe pattern produced on a CCD image by the summation of all the OH emission lines within a given bandpass can be well approximated by essentially any set of emission lines that generally have the same wavelength distribution within a given bandpass."[32]

The top spectrum in the figures on the right of the night-sky covering the near-IR (Massey & Foltz 2000) has large emission-line bands due to the OH molecule in the Earth’s atmosphere.[32]

"These emission lines are the primary cause of CCD fringing."[32]

The bottom figure shows the emission-line spectrum of a neon lamp shown the same spectral region.[32]

Neon also has groups of emission lines within this region that will provide the same fringe pattern on a CCD as OH emission.[32]

Broadband I and z bandpasses are indicated.[32]

The images on the left contain: (Top left) I-band neon fringe flat field. (Top right) Same CCD section showing a nighttime I-band image of a star field taken with strong OH emission. (Bottom) Same section in the final reduced image showing the complete removal of the CCD fringes.[32]


The "technique of Very Long Baseline Interferometry has been going for four decades. It was developed as a concept in the 1960's and the first fringes were detected in 1969 (Broten et al. 1967; see also the historical review by Clark 2003). The science followed very quickly in the 1970's as compact, extragalactic radio sources were resolved and shown to exhibit superluminal expansion (Whitney et al. 1971; Cohen et al. 1971), which had previously been predicted by (Rees 1966)."[33] [Section title:] "More Fringe Science"[33] "A much-publicized result (Fomalont & Kopeikin 2003) is the measurement of the gravitational deflection of a background quasar by Jupiter, an effect about a thousand times smaller than the solar deflection (for which VLBI produces about the best measurement to date of the post-Newtonian parameter γ in the Robertson expansion of the metric tensor). Although this is undoubtedly a technical tour de force, the interpretation of this result has proven rather controversial. The authors claim that this shows that gravitational effects propagate at the speed of light. It seems to me, though, that there can only be one frame-independent speed in physics and so the answer is, in some sense, already guaranteed by the formalism in which the experiment is usually interpreted."[33]


Time-frequency map contains the frequency peaks detected by the search algorithm from run C7. Credit: I. Fiori, E. Cuoco, F. Paoletti, N. Christensen, and G. Vajente.{{fairuse}}

In preparation for the detection of gravitational radiation at the Virgo interferometer a series of runs was made to measure and identify vibrational frequencies and their origins. One such run "C7" was "work on the detection and investigation of the origin of the frequency lines in the Virgo dark fringe data from run C7. A number of data analysis techniques and experimental methods (in the laboratory) [were] used to identify and characterize these noise lines. [A] first selection of frequency lines [was generated]. Line candidates also come as the by-product of the analysis pipeline of the periodic signal searches (PSS) performed by the Virgo pulsar search group."[34]

Some "lines [were identified] as originating from the WE and NE air conditioning[.] Other lines that were identified include: mirror modes and violin modes of mirror wires [...], includes a measurement of ring-down decay time [...], sidebands of calibration lines [...], and lines due to the residual aliasing in the 4kHz down-sampled data [...]. [One] preliminary list of persistent frequency peaks ("lines") [was produced] by applying the line search algorithm [...] to the dark fringe photodiode signal (channel Pr_B1_ACp). [The] complete dataset of C7 science mode data (about 100 hours) [was processed] by requiring the quality flag Qc_Moni_ScienceMode to be one."[34]

In the image on the right is a time-frequency "map of frequency peaks detected by the search algorithm [...] applied to C7 dark fringe science mode data segments (black). There were 61516 frequency peaks above the [signal to noise resolution] SNR threshold, corresponding to 772 different frequencies. This reduces to 155 persistent ones [...], and finally reduces to 71 lines candidates (plus 18 50Hz harmonics) after merging nearby frequencies."[34]

Ground level motion[edit]

Diagram shows sea level rise. Credit: Kopiersperre.

Ground Motion Service is based on satellite information and its application in interferometry using the Fourier-transform method of fringe-pattern analysis.[35]. This allows a service to provide submillimeter measurements of ground level rise or decline.[36]

Chinese Fringe Flowers[edit]

Loropetalum chinense is the Chinese fringe flower, flowers & foliage. Credit: i_am_jim.
Loropetalum chinense shows leaves with measurement, note fringe on leaves. Credit: darrell.barrell.

Loropetalum is of the family Hamamelidaceae.

Corollar fringes[edit]

Diagram of plain (trimmed) and fringed corollas shows the increase in perimeter produced by the maginal trichomes. Credit: Joseph E. Armstrong.{{fairuse}}

"Attractive features of flowers are adaptations for biotic interactions, and a few floral adaptations are for interactions with the physical environment. Marginal corollar appendages of Nymphoides (Menyanthaceae) can be membranous, a fringe of trichomes, or a ruffle."[37]

"The force needed to dunk flowers with an intact corollar fringe and those whose fringe had been trimmed showed a significant difference. The fringe added a mean of 10.4% to the floral mass, but the upward force generated increased by nearly 50%, a significant difference from the predicted change based upon buoyancy alone."[37]

"A correlation between plant form and type of corolla margin supports the surface-tension hypothesis. The membranous and ruffled corollar margins were found in species whose flowers had less risk of contacting the water's surface."[37]

"Many species of Nymphoides (Menyanthaceae) have a habit similar to waterlilies, with rhizomatous plants rooted in the substrate, floating leaves connected to the rhizome by long petioles, and an emergent axillary inflorescence. The flowers of Nymphoides have conspicuous, attractive, UV-reflecting corollas (Ornduff, 1969⇓) that clearly function to attract insect pollinators. The white or yellow corollas have a short tube and five rotate lobes with a conspicuous marginal appendage, a feature shared with other genera in Menyanthaceae, Goodeniaceae, and with some Hydrophyllaceae and Campanulaceae. The marginal corollar appendage among Nymphoides species ranges from a thin, membranous outgrowth to a fringe of long trichomes to a more robust, mostly fused, ruffled margin. These appendages make the corolla lobes at least two times broader contributing significantly to floral display. The adaptive value of enhanced displays has been demonstrated in many studies, and given the taxonomic occurrence of these corollar appendages and their presence in nonaquatic species, the most parsimonious assumption is that they arose to enhance floral display."[37]

"When Nymphoides flowers with trichome-fringed corollas were pulled beneath the water's surface, they reemerged completely dry and functional. If the water level rose around an inflorescence tethered to its rhizome, the corolla lobes of open flowers bent upward into a valvate, bud-like configuration. The fringe from adjacent corolla lobes met and entrapped an air bubble, not unlike a plastron of aquatic insects (Hinton, 1976⇓), which traps a bubble of air for respiration within a mat of nonwettable hairs. This observation prompted an investigation of the corollar fringe as an adaptation to an aquatic environment."[37]

"Floating is the most common interaction between organisms and the water-air interface, a function of the organism's density (mass by volume) generating an upward buoyancy to overcome the pull of gravity (mass by acceleration). Surface tension interaction also generates an upward force, so negligible in most cases that it is ignored. However, a few organisms generate a significant upward force from surface tension interactions. Insects like water striders can actually walk and jump on the water surface. Vogel (1988)⇓ calculated a walk-on-water index (WOWI) as the ratio of the force holding the organism up to the force pulling the organism down. To overcome the force generated by gravity (approximately gravity [g] times an organism's density [p], times it's volume or length [l] cubed), an upward force is generated by the organism's contact perimeter (l) with the water's surface times the surface tension (γ). Combining terms after canceling length in the numerator produces a unitless index (Vogel, 1988⇓); the formula is"[37]

"Because surface tension, gravity, and the density of the study organism are all essentially constants, the variable term is the square of the length, the perimeter of contact with the water surface (Vogel, 1988⇓). Given the mass of an organism, one can calculate the perimeter needed for the organism to walk on water, or conversely, given a perimeter one can calculate the mass that can be supported by surface tension. Clearly as the mass of the organism increases, the perimeter of contact must increase greatly for walking on water to remain possible. This interaction also requires nonwettable surfaces, so the cuticular layer of plants is preadapted for surface tension interaction. Like many plant surfaces, the flowers of Nymphoides have a conspicuous waxy cuticle."[37]

"A fringe greatly increases the corolla perimeter without greatly increasing the mass, so it could generate a significant upward force. The fringe increases the corollar perimeter by two times the length of the trichomes times the number of trichomes less the length of the fringeless perimeter [in the diagram on the right]. With many long, narrow, closely spaced trichomes, the increase in perimeter (l) is considerable. The membranous or ruffled corolla margins would not significantly increase the corolla perimeter because of their continuous, although slightly irregular, margin."[37]

Dianthus superbus[edit]

A "fringed pink, large pink" flower of Dianthus superbus. Credit: Takashi Hososhima from Tokyo, Japan.{{free media}}

In the image on the right is a "fringed pink, large pink" flower of Dianthus superbus.

"(kawara nadeshiko, “fringed pink, large pink”, Dianthus superbus)"[38]

Papaver somniferum[edit]

Here is Papaver somniferum in the herb garden of Burg Lindenfels, Lindenfels in Odenwald. Credit: Hartmann Linge.{{free media}}

"'Venus' is a laciniatum type [of Papaver somniferum such as in the image on the right] with large fringed petals of rosy red with white on the underside at the base of the petals."[39]

Basking shark fringes[edit]

The image shows a basking shark filter feeding. Credit: Greg Skomal / NOAA Fisheries Service.{{free media}}

"MY notice of Prof. Steenstrup's paper was written in the autumn of 1875, to accompany an electrotype of the woodcut in that paper of the baleen-like fringes of the basking shark, sent to me for NATURE from Copenhagen."[40]

Lizard toe fringes[edit]

Triangular fringes are shown for: A Phrynocephalus mystaceus, B Uma notata, C Crossobamon eversmanni, D Cross-section of Uma scoparia fringe. Credit: Claudia Luke.{{fairuse}}
Projectional fringes are shown: A Eremias acutirostris, B Scincus scincus, C Cross-section of Scincus scincus toe. Credit: Claudia Luke.{{fairuse}}
Conical fringes are shown: A Teratoscincus scincus, B Plenopus garrulus, and C Cross-section of Teratoscincus scincus fringe. Credit: Claudia Luke.{{fairuse}}
Rectangular fringes are shown for A Hydrosaurus pustulosus, B Holaspis guentheri, C Kentropyx calcaratus, and D Cross-section of Hydrosaurus amboinensis fringe. Credit: Claudia Luke.{{fairuse}}

"Lizard toe fringes are composed of laterally projecting elongated scales and have arisen independently at least 26 times in seven families of lizards. Four different fringe types are identified: triangular [top right image], projectional [top left image], conical [second down, right image] and rectangular [second down, left image]."[41]

For the triangular fringes, image on the right, there is a cross-section drawing of a Uma scoparia fringe, where d.s. is dorsal scale, d.-dermis, e.-epidermis, and v.s.-ventral scale. Bars represent 1 cm.

For the projectional fringes, image on the left, there is a cross-section drawing of a Scincus scincus toe, where b. is bone, f.s.--fringe scale, and v.s.-ventral scale. Bars represent 1 cm.

For the conical fringes, image second down on the right, there is a cross-section drawing of a Teratoscincus scincus fringe, where d.s. is dorsal scale, d.-dermis, e.-epidermis, and v.s.-ventral scale. Bars represent 1 cm.

For the rectangular fringes, image second down on the left, there is a cross-section drawing of a Hydrosaurus amboinensis fringe, where d.s. is dorsal scale, d.-dermis, e.-epidermis, and v.s.-ventral scale. Bars represent 1 cm.

"Variation in fringe morphology shows a strong association with substrate type: triangular, projectional and conical fringes with windblown sand; and rectangular fringes with water."[41]

Oort clouds[edit]

2015 TG
(nicknamed The Goblin for the letters TG and because its discovery was near Halloween),[1][42] is a trans-Neptunian object (TNO) and sednoid in the outermost part of the Solar System.[43]


Dynamic radio spectrum is from the pulsar PSR B0834+06. Credit: Barney J. Rickett, Andrew G. Lyne and Yashwant Gupta.{{fairuse}}

Very "fine modulations of the dynamic spectra of interstellar scintillation (ISS) from pulsar PSR B0834+06 [have been observed]. These fringes have a period in radio frequency of 45 kHz, which is about 100 times smaller than the largest bandwidth due to normal ISS of the pulsar at the central observing frequency of 408 MHz."[44]

A "model [shows good consistency] in which two ray-bundles intersect and interfere creating the fringes, from which a 22-µs delay difference is inferred. The separation between the bundles is greater than 4 mas which is more than 10 times their angular diameter. Such a large ratio cannot be due to an inner scale that cuts off the pervasive turbulent density spectrum responsible for the diffractive angular broadening."[44]

"The fringing was observed on four occasions over 30d and so is similar to the 'extreme scattering event' observed in other sources. 3 au is the scale inferred [. Stochastic refraction model:] many isolated regions in a layer of parsec thickness randomly build up enhanced angles of refraction. Normally neighboring ray-paths do not intersect. However, occasionally their angles are large enough to cause the interference and the associated fringes. [The] ionized refracting layer surrounds a warm H I cloud, with anisotropic density irregularities of 0.25 electron cm-3, which could be in equilibrium with the normal interstellar pressure."[44]


Visibility curves of Betelgeuse. Credit: F. Roddier, C. Roddier, and, R. Petrov, F. Martin, G. Ricort, and C. Aime.
Speckle observation of Betelgeuse uses the Steward Observatory 2.25 m telescope. Credit: M. Karovska, P. Nisenson, and R. Noyes.

The "famous red supergiant has two close companions [...] based on speckle interferometry work done in the early 1980s at Kitt Peak, Arizona, and Cerro Tololo, Chile. It revealed that the inner of the two stars orbits Betelgeuse every two years or so at a mean distance of about 5 astronomical units and little is known about the outer companion except that it lies some 40 or 50 astronomical units from Betelgeuse (December, 1985, Sky and Telescope)."[45]

"A careful look to our visibility curves [on the right, full line is our data and broken line is speckle data from Aime et al. 1985] reveals a small periodic modulation that we have interpreted as possibly due to a stellar companion (Roddier, Roddier, and Karovska 1984). The estimated position angle is 85° ± 5° (mod. 180°). The period of modulation corresponds to an angular distance of 0.4"-0.5" and the depth of modulation to a magnitude difference of the order of 3.5-4."[46]

"Both observations reveal a similar modulation giving confidence about the reality of such a companion. Given its observed distance to the main star, its angular motion is expected to be negligible during the 8 months which separate the two observations."[46]

"The existence of such a companion suggested [...] that another companion might also be present close to the disk. It would explain the bright feature observed by Roddier and Roddier (1983) and Goldberg et al. (1981) as well as the observed rapid rotation of the plane of polarization (Haynes 1980). [...] The existence of both companions has recently been confirmed from speckle observations (Karovska et al. 1985)."[46]

"Detection of two close optical companions to the red supergiant α Ori was accomplished in 1983 November on the Steward Observatory 2.25 m telescope. [...] The closer of the two sources is located at 0.06" ± 0.01" from α Ori (P.A. = 273°), the more distant at 0.51" ± 0.01" (P.A. = 278°)."[47]

"Speckle observation [of Betelgeuse uses the Steward Observatory 2.25 m telescope during November 1983, where] (a) and (b) [are the] recovered power spectrum and phase; (c) and (d) autocorrelation and the reconstructed image for the distant companion; (e) and (f) autocorrelation and image for the close companion."[47]


Heliocentric velocity is plotted vs distance from the solar apex. Credit: Sidney van den Bergh.{{fairuse}}

"Local Group members [have] D < 1.0 MPc [. A] few galaxies with distances slightly larger than 1.0 MPc have radial velocities which appear to indicate that they might be dynamically bound to the Local Group. [Those] galaxies [may be] possible outlying members of the Local Group. [The] Local Group is not isolated in space and [...] interactions with neighboring galaxies and groups may have been important in the distant past (Valtonen et al. 1993; Dunn & Laflamme 1993)."[48]

"The spatial separation between IC 10 and M31 (assumed to be at a distance of 725 kpc) is only 0.7 MPc. On the basis of its small distance and location in the V versus cos θ diagram IC 10 is almost certainly a physical member of the Local Group."[48]

Andromeda IV "was discovered by van den Bergh (1972) who concluded that it was either a relatively old star cloud in the outer disk of M31 or a background dwarf galaxy. Jones (1993) argues convincingly that And IV is, in fact, a star cloud in the disk of M31."[48]

At right is a plot of heliocentric velocity V versus distance θ from the solar apex at galactic coordinates = 97.2 °, b = -5.6 ° of Sandage (1986b).[48]

"Local Group envelope lines are ± 60 km/s from the center line with V(θ) = -295 cos θ. Filled circles represent certain Local Group members with D < 1.0 MPc, and Mv < -14.0. Crosses are fainter Local Group members. Local Group suspects are marked as open circles. Note that the dwarf spheroidal galaxy Leo I falls well outside the band occupied by most other certain Local Group members."[48]

Active galactic nuclei[edit]

BSSpM reconstruction is of a disk-jet model of M87 at 1.3 mm. Credit: Vincent L. Fish, Kazunori Akiyama, Katherine L. Bouman, Andrew A. Chael, Michael D. Johnson, Sheperd S. Doeleman, Lindy Blackburn, John F. C. Wardle, William T. Freeman, the Event Horizon Telescope Collaboration.{{free media}}

"The angular resolution of the [Event Horizon Telescope] EHT is especially well matched to the scale of emission in the black holes in the center of the Milky Way (known as Sagittarius A* or Sgr A*) and the giant elliptical galaxy M87. General relativity predicts that if a black hole is surrounded by optically thin emission, the black hole will cast an approximately circular shadow with a diameter of around 10 gravitational radii (1 rg = GMc−2), which corresponds to about 50 μas in Sgr A* and 40 μas in M87. Fringe spacings of EHT baselines at 1.3 mm span a range of approximately 25 to 300 μas, providing both the resolution needed to image the shadow region and shorter spacings to be sensitive to the accretion and outflow region out to a few tens of rg. The very high angular resolution of the EHT is also useful for studying compact structures in other [Active galactic nuclei] AGN sources. For instance, EHT observations of the quasars J1924−2914 and 3C 279 have demonstrated that the small structures seen at 1.3 mm have lower brightness temperatures than seen at centimeter wavelengths [2–4]."[49]

The "effective angular resolution provided by CLEAN is coarser than that provided by, e.g., the Maximum Entropy Method (MEM) [30]. The diameters of the predicted black hole shadows in Sgr A* and M87 are only approximately twice the fringe spacing of the longest baselines at 1.3 mm. This is sufficient for producing an image of the shadow region to examine the morphology and size of the shadow, but angular resolution finer than the fringe spacing is desirable in order to produce a clearer image that is more suitable for testing general relativity [1,31,32]. It is possible to create slightly superresolved images with CLEAN. (We define superresolution as λ/(Bα), where λ is the observing wavelength, B is the projected length of the longest baseline, and α > 1. Slightly superresolved (α ≳ 1) reconstructed images are not uncommon, but the data do not contain enough information to reconstruct images with arbitrarily high superresolution (α ≫ 1).) However, MEM is better at squeezing more angular resolution out of a dataset [33]."[49]

The center image is a "Bi-Spectrum Sparse Modeling (BSSpM) reconstruction of a disk-jet model of M87 at 1.3 mm. (a) The original model [48]; (b) The model convolved with a 10 μas Gaussian; (c) The BSSpM reconstruction of the image from simulated data [47]. The fringe spacing of the longest baseline is approximately 25 μas; (d) The BSSpM reconstruction convolved with a 10 μas Gaussian. BSSpM successfully recovers features of the model at a superresolution of 40% of the fringe spacing. A linear transfer function is used in all panels."[49]



A combination of fluorite, UD and Super UD elements are used in many of today's super-telephoto L series lenses, telephoto zooms and wide-angle lenses. Credit: Canon.

"The Jena makers have directed their attention to the production of glasses, which, when properly paired, will give a tertiary spectrum, a colour near the middle of the ordinary spectrum being brought to the same focus as two other colours, one near the red end and one near the blue end. The foci are thus collected into a much smaller space along the axis, and the fringes of colours, which an ordinary achromatic shows in certain circumstances, are no longer seen."[50]

"If you hold a prism up against sunlight, a rainbow spectrum will appear. This is due to the fact that different wavelengths of light refract – or bend – at different points within the prism. The same phenomenon occurs to a lesser degree in photographic lenses, where it is known as chromatic aberration. It's most noticeable in photographs as colour fringing at the edges of objects. Combining convex and concave lenses helps to correct the problem but does not entirely resolve it."[51]

"Fluorite, which boasts a very low dispersion of light, is capable of combatting the residual aberration that standard optical glass fails to eliminate. Canon succeeded in artificially creating crystal fluorite in the 1960s, producing the first interchangeable SLR lenses with fluorite elements. In the 1970s, Canon achieved the first UD (Ultra Low Dispersion) lens elements incorporating low-dispersion optical glass. This technology was further improved to create Super UD lenses in the 1990s. A combination of fluorite, UD and Super UD elements are used in many of today's super-telephoto L series lenses, telephoto zooms and wide-angle lenses."[51]

Charge-coupled devices[edit]

"Fringing is a well-known problem in thinned [Charge-coupled devices] CCDs such as the one used in [Space Telescope Imaging Spectrograph] STIS. [Light] entering the CCD will undergo a series of internal reflections which produces an interference pattern in the spectrum. This fringing pattern is a complicated function of wavelength, CCD face non-planarity and source spectrum […]. The fringing becomes apparent at approximately 7000 Å, where the chip becomes semi-transparent to incoming light."[52]

"For point source targets, the best solution in general is to take an observation of the STIS internal tungsten lamp with a short slit as close in time as possible to the primary observation."[52]

Laser diode arrays[edit]

"Using diffraction gratings as beam splitters in LDA systems the resulting fringe spacing becomes achromatic. Thus employing unstabilized laser diodes of different wavelengths, distinguishable fringe systems with identical fringe spacings in the measuring volume can be generated. The evaluation of at least two LDA burst signals and their signal phase corresponding to the different fringe systems locally parallel shifted and/or tilted against each other allows the directional measurement of lateral and axial velocity components without using frequency shift techniques."[53]

Computer search techniques[edit]

"Depth- first search always expands the deepest node in the current fringe of the search tree."[54]


Def. "an economic condition in which a small number of sellers exert control over the market of a commodity"[55] is called an oligopoly.

The "case of asymmetric oligopoly [is] where a dominant group of producers imposes a selling price to a competitive fringe of producers, each too small to exert a perceptible influence on price through individual output decisions."[56]

Exploitative "pricing abuses may arise not only under conditions of monopoly, where a single dominant company abuses its market power but also in markets jointly dominated by several actors (oligopoly)."[57]

"Besides the usual model-estimation errors and additional stochastic influences not captured by the regression, the difference is likely to occur due to the fact that we do not explicitly model competition between the players of the dominant group. In order to capture this, we could use an oligopoly model with a competitive fringe, rather than a quasi-monopoly model, but that would complicate the mathematics significantly."[58]

Economics of Market Dominance[edit]

This two-page illustration portrays the powerful railroad monopoly as an octopus, with its many tentacles controlling such financial interests as the elite of Nob Hill, farmers, lumber interests, shipping, fruit growers, stage lines, mining, and the wine industry. Credit: G. Frederick Keller.

Monopolistic practices are actions that reduce the fair market competition between enterprises or entrepreneurs.

"Monopolistic market structures and their consequences have for long been part of established economic analysis ... However, real-world monopolies do not always fit the textbook categories ... The matter has been brought to a head in recent years by cases initiated by antitrust authorities against allegedly monopolistic firms ... These cases have served to highlight the inadequacies of traditional monopoly analysis ... From these cases has emerged a much better understanding of dominant firms."[59]

"If such a fringe existed and became a threat to the dominant firm then we would expect the dominant group, by predatory action, to do something about it."[60]

A state could be said to "succeed" if it maintains, according to philosopher Max Weber, a monopoly on the legitimate use of physical force within its borders. When this is broken (e.g., through the dominant presence of warlords, paramilitary groups, or terrorism), the very existence of the state becomes dubious, and the state becomes a failed state.

"In each instance, the politically dominant group is attempting to design a constitution that will legitimize its hold on power and allow it to continue to monopolize resource allocation."[61]

"In 1972, the ruling elites in Cameroon hurriedly put together a constitution that abolished the country's federal system and made Cameroon a one-party dictatorship."[61]


"Mainstream science is scientific inquiry in an established field of study that does not depart significantly from orthodox theories. In the philosophy of science, mainstream science is an area of scientific endeavor that has left the process of becoming established. New areas of scientific endeavor still in the process of becoming established are generally labelled protoscience or fringe science. A definition of mainstream in terms of protoscience and fringe science[62] can be understood from the following table:[63]

Systematized as scientific definition
Treated with scientific method
Attempts to be scientific or resembles science
Superstition Pseudoscience Protoscience Fringe science (Mainstream) science

Def. a "belief, not based on human reason or scientific knowledge,[64] that future events may be influenced by one's behaviour in some magical or mystical way"[65] is called a superstition.

Def. any "body of knowledge purported to be scientific or supported by science but which fails to comply with the scientific method"[66] is called a pseudoscience.

"Pseudoscience is notoriously lax in rigorous application of the scientific method. Reproducability is typically a problem."[67]

"Bad science might more properly be labelled "poor science" in that it is typically characterized by substandard or "sloppy" methodology."[67]

"Junk science is used to describe agenda-driven research that ignores certain standard methodologies and practices in an attempt to secure a given result from an experiment."[67]

Def. an "unscientific field of study which later becomes a science",[68] a "field of study at the initial phase of the scientific method, involving information gathering and hypothesis formulation,[69] but is not yet falsifiable, or if it is, its predictions have not yet been observed",[68] or a "new area or field of science in the process of being established"[70] is called a protoscience.

"A protoscience is a field of inquiry which is not yet considered a real "science", but which nevertheless bears some resemblance to the norms of the scientific method."[67]

Def. fringe science: "Wiktionary does not have any English dictionary entry for this term. This is because the term, though it may be attested, is not idiomatic or fails to meet our criteria for inclusion in another way."[71]

Fringe science may be an "inquiry into an established field of science which departs significantly from mainstream theories in that field and is considered questionable by the mainstream"[72] is called a fringe science.

"We used to have a reasonable definition of "fringe science", and Wikipedia still has an entry for it. It was the subject of a "Request for Deletion" and was deleted and replaced with a "no entry" template in December last year. Not all of us approved of this change. Among the Google book search hits, none supports the definition of "science of fringes"."[73]

"Fringe science is a phrase used to describe scientific inquiry in an established field that departs significantly from mainstream or orthodox theories."[67]

"Fringe science is, by definition, at the fringes of an already accepted discipline."[67]

"Reproducability is not so [typically a problem] in fringe science."[67]

"Fringe science maintains the normal standards of methodology."[67]

"Fringe science is, simply, real science that is on the edges of mainstream and widely-accepted theories. In other words, it's the kind of science/theory that stands at least a chance of becoming respected at some point, just not quite at the moment. This means that the researchers have to be real researchers [...] and they have to use the scientific method."[67]

The "best alternative label would maybe be "speculative theories" that don't have quite the weight of established doctrine."[67]

"Fringe science, as in standard methodology, proceeds from theory to conclusion with no attempt to direct or coax the result."[67]

"Fringe science is seen by most scientists as unlikely but not irrational: many of today's most widely-held theories had their origins as fringe science. As with all categories, disagreement is widespread regarding what ideas are legitimate fringe science, and what ideas belong to the other four categories listed above. Traditionally, the term "fringe science" is generally used to describe unusual or fantastic theories that have their basis in some established scientific principle, and which are advocated by a published (or somehow recognized) mainstream scientist."[74]

"The phrase "fringe science" is sometimes considered pejorative."[75]

The "pejorative nature of the phrase may or may not reflect any objective shortcoming, or failure to conform to the norms of the scientific method, of the idea, thesis, or area of study in question, and if it does so reflect, the reflection may (or may not) endure. Fringe science is an idea or field of inquiry which is not considered, and is unlikely ever to be considered, legitimate or "real" by the majority of living scientists, though it may be born out by research in future generations, and finally generally accepted. This multi-generational perspective was underscored by physicist Max Planck with his candid remark that "a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it"[76]."[77]

"It remains one of the most neglected insights into the nature of science, that it progresses not steadily but by revolution and against continuing resistance. Four decades ago already, Thomas Kuhn (1970) described scientific revolutions and Bernard Barber (1961) described "Resistance by scientists to scientific discovery". Barber pointed out that contrarian facts or ideas are routinely and inevitably resisted at first by the scientific community; he mentions Abel (mathematics), Arrhenius and Faraday (physical chemistry), Ampĕre and Ohm and Maxwell (electricity and magnetism), Heaviside (radio reflection from the ionosphere), Karl Pearson (biometry), Magendie (chemistry in medicine), Lister (antisepsis), Pasteur (fermentation as biologically caused), Darwin (evolution as a result of natural selection) -- a panoply of now-revered names who were anything but revered by their peers when they first proposed their discoveries."[78]

"Again, these are exceptions rather than the rule; most hypotheses and new ideas do not survive; "revolutionary" new theses are found to be rubbish more often than they eventually vindicate themselves. The customary procedures, institutions, and power politics of the world of science constitute a formidable barrier against such rubbish, which is of course to the good. Unfortunately they form a comparable barrier against genuinely revolutionary findings and innovations, which can be held up for decades or even generations, at great cost. Fringe science and pseudoscience -- convenient "sound bite" terms of opprobrium -- can have a devastating effect, regardless of whether or not there existed a sound basis for such judgement.[79] Hence such terms should be used with great care, and those who use them should be held to a high standard -- even though in any given instance they are more likely right than wrong. As in the U.S. legal system, it is important to prosecute and punish the guilty, but it is even more important to protect and absolve the innocent."[77]

"While most scientists and nonbelievers would like to see more skepticism about fringe science and the paranormal, this clearly is not happening."[80]

"As unsubstantiated claims receive significant backing, skeptics and defenders of mainstream science enter the fray."[80]

By its standard practices of applying good scientific methods, mainstream is distinguished from pseudoscience as a demarcation problem and specific types of inquiry are debunked as junk science, cargo cult science, scientific misconduct, etc." From Wikipedia:Mainstream science.

"Hidden beneath the public image of science as a rational intellectual enterprise lurk many secrets, many boundary stories, and the treatment of so-called 'fringe science'".[81]

'Fringe science': "The term itself works to consign certain types of scientific activity as outside (or at best marginal to) so-called 'mainstream science'. Fringe science continues to be written off as pseudoscience, hobbyism or quackery (and, increasingly, as New Age mumbo-jumbo) -- a move which reveals the cultural formations of science as a ring-fenced, professionalized practice (despite, or maybe because of, its legitimation crisis)."[81]

"Fringe science is an inquiry in an established field of study which departs significantly from mainstream theories in that field and is considered to be questionable by the mainstream." From Wikipedia:Fringe science.

Toby McMaster: "I will explore some of these issues and their potential solutions, whilst also showing how science's "Big Three" (biology, chemistry, and physics) may have to learn to share the spotlight with each other, and how, what I call fringe sciences, such as psychology and economics, may also have their own roles to play."[82]

"The sciences, especially perhaps the fringe sciences that impinge directly on the human-—medicine, biology, archaeology, paleontology—-have a strongly anthropomorphic value system, indeed a system that might be called neoanthropomorphic in that it models the world in terms of the interests and assumptions of twentieth-century Western culture."[83]

"That most scientific studies are ultimately wrong is normal for science. There are more theories in the graveyard of science than theories that stand the test of time. Why? Because new data is always emerging and theories have to be adjusted. Theories are only as good as theories are, until new data comes along and ruins them. Theories give a best guess at what is going on based on things we observe (data), but they are not immutable. If you only have a few data points, then your working theory is more likely to turn out to be wrong. This is not news to science, this is science."[84]

"The great thing about science is its ability to be flexible enough to change when it needs to. In science, if all the sudden "black" really does become "white", theories must be adjusted. Individual scientists themselves, being human beings, might have trouble adjusting and be disappointed; but if they know how science works they shouldn't be confused. In science if you can't adjust your theories to new data, the body of science will just, eventually, leave you behind. Einstein famously refused to believe in some aspects of quantum mechanics, and the field moved on without him."[84]

"The more data, the more reliable the theories. Given that [...] linking genes with diseases is a huge area of growth, it is unsurprising that in a newly emerging growth area many, if not most, of the initial working theories may turn out to be wrong."[84]

The "data doesn't seem to support the theory that the majority of scientists are more interested in funding and fame than "truth". What the data shows is business as usual: that scientists can be biased (not news), and that most scientific theories, in the end, are thrown on the garbage heap."[84]


  1. The formal term fringe science or fringe sciences is used for detectable variations, including second order harmonics.
  2. The public policy topic 'fringe science' is at best a protoscience.

See also[edit]


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External links[edit]