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Pyrite

The mineral pyrite, or iron pyrite, also known as fool's gold, is an iron sulfide with the chemical formula FeS2 (iron (II) disulfide). Pyrite is the most abundant sulfide mineral. Pyrite's metallic luster and pale brass-yellow hue give it a superficial resemblance to gold, hence the well-known nickname of fool's gold. The color has also led to the nicknames brass, brazzle, and brazil, primarily used to refer to pyrite found in coal.

The name pyrite is derived from the Greek πυρίτης λίθος (pyritēs lithos), 'stone or mineral which strikes fire', in turn from πῦρ (pŷr), 'fire'. In ancient Roman times, this name was applied to several types of stone that would create sparks when struck against steel; Pliny the Elder described one of them as being brassy, almost certainly a reference to what is now called pyrite.

By Georgius Agricola's time, c. 1550, the term had become a generic term for all of the sulfide minerals.

Pyrite is usually found associated with other sulfides or oxides in quartz veins, sedimentary rock, and metamorphic rock, as well as in coal beds and as a replacement mineral in fossils, but has also been identified in the sclerites of scaly-foot gastropods. Despite being nicknamed "fool's gold", pyrite is sometimes found in association with small quantities of gold. A substantial proportion of the gold is "invisible gold" incorporated into the pyrite (see Carlin-type gold deposit). It has been suggested that the presence of both gold and arsenic is a case of coupled substitution but as of 1997 the chemical state of the gold remained controversial.

Uses

Pyrite gain a brief popularity in the 16th and 17th centuries as a source of ignition in early firearms, most notably the wheellock, where a sample of pyrite was placed against a circular file to strike the sparks needed to fire the gun.

Pyrite is used with flintstone and a form of tinder made of stringybark by the Kaurna people of South Australia, as a traditional method of starting fires.

Pyrite has been used since classical times to manufacture copperas (ferrous sulfate). Iron pyrite was heaped up and allowed to weather (an example of an early form of heap leaching). The acidic runoff from the heap was then boiled with iron to produce iron sulfate. In the 15th century, new methods of such leaching began to replace the burning of sulfur as a source of sulfuric acid. By the 19th century, it had become the dominant method.

Pyrite remains in commercial use for the production of sulfur dioxide, for use in such applications as the paper industry, and in the manufacture of sulfuric acid. Thermal decomposition of pyrite into FeS (iron(II) sulfide) and elemental sulfur starts at 540 C; at around 700 C, pS 2 is about 1 atm.

A newer commercial use for pyrite is as the cathode material in Energizer brand non-rechargeable lithium metal batteries.

Pyrite is a semiconductor material with a band gap of 0.95 eV. Pure pyrite is naturally n-type, in both crystal and thin-film forms, potentially due to sulfur vacancies in the pyrite crystal structure acting as n-dopants.

During the early years of the 20th century, pyrite was used as a mineral detector in radio receivers, and is still used by crystal radio hobbyists. Until the vacuum tube matured, the crystal detector was the most sensitive and dependable detector available—with considerable variation between mineral types and even individual samples within a particular type of mineral. Pyrite detectors occupied a midway point between galena detectors and the more mechanically complicated perikon mineral pairs. Pyrite detectors can be as sensitive as a modern 1N34A germanium diode detector.

Pyrite has been proposed as an abundant, non-toxic, inexpensive material in low-cost photovoltaic solar panels. Synthetic iron sulfide was used with copper sulfide to create the photovoltaic material. More recent efforts are working toward thin-film solar cells made entirely of pyrite.

Pyrite is used to make marcasite jewelry. Marcasite jewelry, using small faceted pieces of pyrite, often set in silver, has been made since ancient times and was popular in the Victorian era. At the time when the term became common in jewelry making, "marcasite" referred to all iron sulfides including pyrite, and not to the orthorhombic FeS2 mineral marcasite which is lighter in color, brittle and chemically unstable, and thus not suitable for jewelry making. Marcasite jewelry does not actually contain the mineral marcasite. The specimens of pyrite, when it appears as good quality crystals, are used in decoration. They are also very popular in mineral collecting. Among the sites that provide the best specimens are Soria and La Rioja provinces (Spain).

In value terms, China ($47 million) constitutes the largest market for imported unroasted iron pyrites worldwide, making up 65% of global imports. China is also the fastest growing in terms of the unroasted iron pyrites imports, with a CAGR of +27.8% from 2007 to 2016.

Research
In July 2020 scientists reported that they have observed a voltage-induced transformation of normally diamagnetic pyrite into a ferromagnetic material, which may lead to applications in devices such as solar cells or magnetic data storage.

Researchers at Trinity College Dublin, Ireland have demonstrated that FeS2 can be exfoliated into few-layers just like other two-dimensional layered materials such as graphene by a simple liquid-phase exfoliation route. This is the first study to demonstrate the production of non-layered 2D-platelets from 3D bulk FeS2. Furthermore, they have used these 2D-platelets with 20% single walled carbon-nanotube as an anode material in lithium-ion batteries, reaching a capacity of 1000 mAh/g close to the theoretical capacity of FeS2.

In 2021, a natural pyrite stone has been crushed and pre-treated followed by liquid-phase exfoliation into two-dimensional nanosheets, which has shown capacities of 1200 mAh/g as an anode in lithium-ion batteries.

Formal oxidation states for pyrite, marcasite, molybdenite and arsenopyrite
From the perspective of classical inorganic chemistry, which assigns formal oxidation states to each atom, pyrite and marcasite are probably best described as Fe2+[S2]2−. This formalism recognizes that the sulfur atoms in pyrite occur in pairs with clear S–S bonds. These persulfide [–S–S–] units can be viewed as derived from hydrogen disulfide, H2S2. Thus pyrite would be more descriptively called iron persulfide, not iron disulfide. In contrast, molybdenite, MoS2, features isolated sulfide S2− centers and the oxidation state of molybdenum is Mo4+. The mineral arsenopyrite has the formula FeAsS. Whereas pyrite has [S2]2– units, arsenopyrite has [AsS]3– units, formally derived from deprotonation of arsenothiol (H2AsSH). Analysis of classical oxidation states would recommend the description of arsenopyrite as Fe3+[AsS]3−.

Crystallography

Iron-pyrite FeS2 represents the prototype compound of the crystallographic pyrite structure. The structure is cubic and was among the first crystal structures solved by X-ray diffraction. It belongs to the crystallographic space group Pa$\overline{3}$ and is denoted by the Strukturbericht notation C2. Under thermodynamic standard conditions the lattice constant $$a$$ of stoichiometric iron pyrite FeS2 amounts to 541.87 pm. The unit cell is composed of a Fe face-centered cubic sublattice into which the ions are embedded. (Note though that the iron atoms in the faces are not equivalent by translation alone to the iron atoms at the corners.) The pyrite structure is also seen in other MX2 compounds of transition metals M and chalcogens X = O, S, Se and Te. Certain dipnictides with X standing for P, As and Sb etc. are also known to adopt the pyrite structure.

The Fe atoms are bonded to six S atoms, giving a distorted octahedron. The material is a semiconductor. The Fe ions is usually considered to be low spin divalent state (as shown by Mössbauer spectroscopy as well as XPS). The material as a whole behaves as a Van Vleck paramagnet, despite its low-spin divalency.

The sulfur centers occur in pairs, described as S22−. Reduction of pyrite with potassium gives potassium dithioferrate, KFeS2. This material features ferric ions and isolated sulfide (S2-) centers.

The S atoms are tetrahedral, being bonded to three Fe centers and one other S atom. The site symmetry at Fe and S positions is accounted for by point symmetry groups C3i and C3, respectively. The missing center of inversion at S lattice sites has important consequences for the crystallographic and physical properties of iron pyrite. These consequences derive from the crystal electric field active at the sulfur lattice site, which causes a polarization of S ions in the pyrite lattice. The polarisation can be calculated on the basis of higher-order Madelung constants and has to be included in the calculation of the lattice energy by using a generalised Born–Haber cycle. This reflects the fact that the covalent bond in the sulfur pair is inadequately accounted for by a strictly ionic treatment.

Arsenopyrite has a related structure with heteroatomic As–S pairs rather than S-S pairs. Marcasite also possesses homoatomic anion pairs, but the arrangement of the metal and diatomic anions differ from that of pyrite. Despite its name, chalcopyrite does not contain dianion pairs, but single S2− sulfide anions.

Crystal habit
Pyrite usually forms cuboid crystals, sometimes forming in close association to form raspberry-shaped masses called framboids. However, under certain circumstances, it can form anastomosing filaments or T-shaped crystals. Pyrite can also form shapes almost the same as a regular dodecahedron, known as pyritohedra, and this suggests an explanation for the artificial geometrical models found in Europe as early as the 5th century BC.

Varieties
Cattierite (CoS2), vaesite (NiS2) and hauerite (MnS2), as well as sperrylite (PtAs2) are similar in their structure and belong also to the pyrite group.

Bravoite is a nickel-cobalt bearing variety of pyrite, with > 50% substitution of Ni2+ for Fe2+ within pyrite. Bravoite is not a formally recognised mineral, and is named after the Peruvian scientist Jose J. Bravo (1874–1928).

Distinguishing similar minerals
Pyrite is distinguishable from native gold by its hardness, brittleness and crystal form. Pyrite fractures are very uneven, sometimes conchoidal because it does not cleave along a preferential plane. Native gold nuggets, or glitters, do not break but deform in a ductile way. Pyrite is brittle, gold is malleable.

Natural gold tends to be anhedral (irregularly shaped without well defined faces), whereas pyrite comes as either cubes or multifaceted crystals with well developed and sharp faces easy to recognise. Well crystallised pyrite crystals are euhedral (i.e., with nice faces). Pyrite can often be distinguished by the striations which, in many cases, can be seen on its surface. Chalcopyrite (CuFeS2) is brighter yellow with a greenish hue when wet and is softer (3.5–4 on Mohs' scale). Arsenopyrite (FeAsS) is silver white and does not become more yellow when wet.

Hazards
Iron pyrite is unstable when exposed to the oxidizing conditions prevailing at the Earth's surface: iron pyrite in contact with atmospheric oxygen and water, or damp, ultimately decomposes into iron oxyhydroxides (ferrihydrite, FeO(OH)) and sulfuric acid. This process is accelerated by the action of Acidithiobacillus bacteria which oxidize pyrite to first produce ferrous ions, sulfate ions , and release protons (, or ). In a second step, the ferrous ions are oxidized by  into ferric ions  which hydrolyze also releasing  ions and producing FeO(OH). These oxidation reactions occur more rapidly when pyrite is finely dispersed (framboidal crystals initially formed by sulfate reducing bacteria (SRB) in argillaceous sediments or dust from mining operations).

Pyrite oxidation and acid mine drainage
Pyrite oxidation by atmospheric in the presence of moisture  initially produces ferrous ions  and sulfuric acid which dissociates into sulfate ions and protons, leading to acid mine drainage (AMD). An example of acid rock drainage caused by pyrite is the 2015 Gold King Mine waste water spill.

Dust explosions
Pyrite oxidation is sufficiently exothermic that underground coal mines in high-sulfur coal seams have occasionally had serious problems with spontaneous combustion. The solution is the use of buffer blasting and the use of various sealing or cladding agents to hermetically seal the mined-out areas to exclude oxygen.

In modern coal mines, limestone dust is sprayed onto the exposed coal surfaces to reduce the hazard of dust explosions. This has the secondary benefit of neutralizing the acid released by pyrite oxidation and therefore slowing the oxidation cycle described above, thus reducing the likelihood of spontaneous combustion. In the long term, however, oxidation continues, and the hydrated sulfates formed may exert crystallization pressure that can expand cracks in the rock and lead eventually to roof fall.

Weakened building materials
Building stone containing pyrite tends to stain brown as pyrite oxidizes. This problem appears to be significantly worse if any marcasite is present. The presence of pyrite in the aggregate used to make concrete can lead to severe deterioration as pyrite oxidizes. In early 2009, problems with Chinese drywall imported into the United States after Hurricane Katrina were attributed to pyrite oxidation, followed by microbial sulfate reduction which released hydrogen sulfide gas. These problems included a foul odor and corrosion of copper wiring. In the United States, in Canada, and more recently in Ireland,  where it was used as underfloor infill, pyrite contamination has caused major structural damage. Concrete exposed to sulfate ions, or sulfuric acid, degrades by sulfate attack: the formation of expansive mineral phases, such as ettringite (small needle crystals exerting a huge crystallization pressure inside the concrete pores) and gypsum creates inner tensile forces in the concrete matrix which destroy the hardened cement paste, form cracks and fissures in concrete, and can lead to the ultimate ruin of the structure. Normalized tests for construction aggregate certify such materials as free of pyrite or marcasite.

Occurrence
Pyrite is the most common of sulfide minerals and is widespread in igneous, metamorphic, and sedimentary rocks. It is a common accessory mineral in igneous rocks, where it also occasionally occurs as larger masses arising from an immiscible sulfide phase in the original magma. It is found in metamorphic rocks as a product of contact metamorphism. It also forms as a high-temperature hydrothermal mineral, though it occasionally forms at lower temperatures. Pyrite occurs both as a primary mineral, present in the original sediments, and as a secondary mineral, deposited during diagenesis. Pyrite and marcasite commonly occur as replacement pseudomorphs after fossils in black shale and other sedimentary rocks formed under reducing environmental conditions. Pyrite is common as an accessory mineral in shale, where it is formed by precipitation from anoxic seawater, and coal beds often contain significant pyrite.

Notable deposits are found as lenticular masses in Virginia, U.S., and in smaller quantities in many other locations. Large deposits are mined at Rio Tinto in Spain and elsewhere in the Iberian Peninsula.

Cultural beliefs
In the beliefs of the Thai people (especially those in the south), pyrite is known as Khao tok Phra Ruang, Khao khon bat Phra Ruang (ข้าวตอกพระร่วง, ข้าวก้นบาตรพระร่วง) or Phet na tang, Hin na tang (เพชรหน้าทั่ง, หินหน้าทั่ง). It is believed to be a sacred item that has the power to prevent evil, black magic or demons.

title: Pyrite


text:
User:24.150.61.63/Foundation ontology

See Talk:Foundation ontology

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

title: User:24.150.61.63/Foundation ontology


text:
Talk:Particle physics foundation ontology

Please, someone add below "This entry is not required because there can be no conceivable challenge to the particle physics foundation ontology". Go ahead. I dare ya. :-)

Some scientists openly admit there are probably infinite particles, or that political inability to do some experiments skews quantum mechanics as a science rather badly, I'll try to find some of these and add them in... the Yudkowsky quote may also be an extreme example of a PPFO absolutist - who are mostly in the AI field it seems...

This ontology is also called the "particle physics zoo", which is interesting, as a "zoo" is also a place where we try to gather what exists and look at it all at once. Not sure if the "foundation ontology" phrasing has come into common use. But it's handy as "foundation ontology" itself needs definition, and it's not obvious that the 'particle physics zoo' the same thing. Some would say that the 'zoo' represents the stuff we still are looking for, and isn't a foundation in the sense that "proton, neutron, electron" can be considered a foundation for the periodic table of the elements.

Also there is some stuff which attempts to put cognition and chemistry at the foundation level, explaining quantum mechanics as one of many types of bonds that hold up to observer-observed. Not sure if this is very easy to find... it's quite radical and the particle physics boys obviously hate it very much.

weakened the revised statement re: the challenge from cogsci of math... it isn't Lakoff and Nunez suggesting that *physics* is somehow not objective, they are claiming to *prove* that *math* is not *provably* objective, and this throws all claims to universal "true for all cognitive creatures" mathematical models into doubt. But it's a little less of a direct challenge, i.e. L&N are not out picketing to shut down particle accelerators, just questioning the degree to which humans can be sure of their own models - including very very basic ones.

Talk to some mathematicians and physicists -- you might find them to be less arrogant and more concerned with philosophical issues that you think. You may be attacking a straw man here. We're completely in sync here, actually. I wrote this as you wrote that:

"It separates, by definition, radically autonomous particles from the choice-making observers. It assigns all choice, in particular all ethical choices, to the observer or experimenter."

The ethical choices being that to construct the test infrastructure, hire the scientists, and spend money on this field rather than on say competing theory. I think it's fair to say that the immense expense of that is an ethical choice.

However, as a whole, this claim was probably too strong to include - not all PPFO advocates are really saying that their funding is justified, some actually say otherwise, and some say that they think that the particles are actually laughing at us.

This may just prove they are nut cases.

But anyway the paragraph is probably not true "by definition", and should be weakened. It can stay out, as it's not really essential to the definition.

It would be better to try to define 'radically autonomous process' making those points there instead.

--- "no direct ethical consequences -- and no, it does not 'radically separate', it may link them together into a larger system] "

Umm.. if it did, wouldn't that be necessarily an ethical system? That may be a theology versus philosphy issue. But the larger system being another radical autonomous process versus it being a choice made by human values... hard to avoid.

--

Wigner's raising of the "other species" issue in 1960 was a surprise - I just found that.

I framed the ethical debate, a bit, so that this would be two objections that lead in three directions. It's a bit radical to include in philosophy of science, or philosophy of mathematics, or epistemology, because debate is really focused on this issue around hard-to-verify physics and medical theory.

I'm guessing, but I think the average reader is going to read this, conclude that "ok this is treating particle physics' output like religion, I get it... it happens every time they fund something - but that's life."

The more philosophically inclined, say half of them, mgiht say "these objections aren't so serious - philosophy of science as it stands can resolve them" and read that next.

Maybe 15% of readers will say "this is quite serious and interesting - why do I believe in math anyway?" and go off to philosophy of mathematics - getting into a more general treatment of foundations debates (of which this is one).

Maybe 5% of readers will say "I always thought so" and head off to cognitive science of mathematics or body philosophers.

I'm not sure the Yudkowski quote is that relevant. It's from an article about building an ontology for an AI, and is not meant to imply that that's really all there is or ever will be--only that it is a reasonable foundation for building an AI that can interact with us at our present level of understanding. Besides, he's not a particle physicist, he's an AI researcher (and a friend of mine, which I why I know this). And he's certainly not in the academic mainstream. I like the kid, but let's not make it sound like this is a quote from some real university physicist or something. --Lee Daniel Crocker

-

I think his quote is important because it shows that more limited AIs and other simulations are going to assume that the PPFO is "real" and perhaps convince people to put them in charge of hot fusion or nuclear weapons or DNA extruders or something. That the *cultural* impact of the PPFO is very real, and it guides funding decisions, and huge amounts of human effort one way or another...

Yudkowsky is like Lakoff, an extremist who lays out the simplest assumption... I agree he's more useful to illustrate the point about the impact of the PPFO than he is as a physicist. But this article is not actually about how physicists see the PPFO - it's more about how it affects everything else in our culture, which of course is what's funding big science itself...

The use of the term "ontology" in theology and computer science is ultimately convergent... theology is more ambitious and is more concerned with "finding" rather than "doing". Also, Yudkowsky is very careful and consistent - his glossaries are impressive - he's probably the best voice for the "particle physics is really really real" view... doesn't he intend to hand over all technology to a "Friendly AI" which would more or less become a sort of god?

That takes big-T Trust... :-)

It's fair then to put Yudkowsky and Pope John Paul II and Lakoff in the same article... and Monty Python too. Shows the extreme breadth of the debate...

Thanks also to whoever added the point about the anti-reductionist solid state physicists, it makes the link to the 'hard' scientists concerned about this, which is important, for physicists who happen to read this article...

...not that I think they're the main audience.

-- This is plain wrong. Anti-reductionist physicists don't object particle physics foundation ontology on experimental or epistemological grounds.

 * Objections to these assumptions arise mostly in the "soft" sciences, but are increasingly heard in "hard" science:

 * A number of physicists, particularly in solid state physics, question the notion of particle physics as the foundation for all other understanding. Their objections fit into a continuum of issues with experimental methods, with human cognitive bias, with falsifiability, and with reductionism.

- This is also amazingly bad non-sense. The person who wrote this has no clue as to what the actual debate is. There was a really good article in the New York Times on the reductionist/anti-reductionist debate and it pops up as a topic on Physics Today. The debate is *NOT* about the nature of truth, the validity of mathematics, or the philosophical foundations of science.

 * === it's only a model? ===

 * The reaction of such physicists to mathematical abstractions that fully predict physical phenomena may be characterized in the same terms as the fictional knights in Monty Python And The Holy Grail, encountering (the simulated) Camelot for the first time: "It's only a model."

 * Most practicing scientists would agree with that sentiment, rejecting reductionism as a philosophy, even if they must appeal to it for grant money. A common objection of scientists to "anti-reductionist" views is that scientific method itself requires constant investigation and challenge - and that it is computer science, simulation, artificial intelligence, other technology and the funding process that assume or require any kind of "foundation ontology".  In other words, then:  "It's only a model."

There are several debates going on.

The reductionist/anti-reductionist debate (physicists versus physicists)

The nature of truth debate (theologians, mathematical foundationists)

The validity of mathematics debate (cognitive scientists, linguists, postmodernists),

The philosophical foundations of science (all of the above minus physicists).

If you want to claim that the physicists' family squabble with each other is categorically different than the other objections, fine, but I call that differentiation a bias of yours.

That said, I have no objection to separating their specific objection, and taking it out of the "continuum"... fair enough?

The "it's only a model" section is an attempt to debunk the idea that scientists themselves believe in their models. Maybe it fails at doing that, but it was an attempt to argue that scientists themselves don't see the "zoo" as an "ontology"... any more than zookeepers see a zoo as a full unbiased representation of the ecology the animals and plants come from.

If you claim to understand the reductionist/anti-reductionist debate better than I, fair enough, likely true, but this article is about *all* currently debated issues re: the zoo as ontology.

It would be ideal to get Yudkowsky, Lakoff, the Pope, you, David Bohm, Monty Python, and a few of us in the room for a debate.

But, failing that, please do not say that several debates which exist, don't.

Instead, please fix the characterization of the anti/reductionist debate, CITING SOURCES.

If the original explanation of the debate was wrong, I'm sorry, I didn't write it, I wrote the stuff about all the other debates, and just included that anti/reductionist stuff which someone else had jammed in. So I have no conceivable objection to your fixing it or characterizing it as different from the other debates. No promises about relating it to those debates once you've fixed what it "actually is..."

Why not cite the Times article itself?

Also, if you read the objectionable passages, neither of them say that the 'hard' scientists objection is ON THE SAME GROUND AS the 'soft' ones... only that they question some of the same *assumptions*... different thing.

If this isn't clear, it can be fixed.

OK, a quick read establishes that the article reads better without those "bridging" passages you deleted - I added them so that non-scientists would understand this better, but if you claim they're not correct, fine... two different debates on reductionism on two different grounds.

I'd like to know if this section as I modified it is accurate:

anti-reductionist physicists

Some solid state physicists more deeply question the notion of particle physics as the foundation for all other understanding. They point out that large numbers of objects can undergo statistical behavior and have properties that are indepedent of the properties of the particles themselves.

Furthermore, they note, there are systems with radically different components that can undergo very similar behavior, and it has been argued that the similarities in behavior can best be understood through universal rules which are independent of the properties of the components of the systems themselves. These rules or methods or processes would then be "more real than matter" in that they would determine how observers shared an understanding of matter, and would set limits on investigative feasibility.

If so, then I'm very clued out, since a rules-based universe is exactly what the other objections also seem to point to...

-

All right, this is starting to make sense now... vaguely. This is a tough subject and I find it difficult to believe that I could have understood the argument well enough to extend the above, but somehow got it all wrong in relation to the other objections.

I suspect there are two objections arising from physicists - "shallow" ones to the current zoo, and "deep" ones to the existence of a zoo... the "deep" are maybe best characterized by David Bohm, and maybe this isn't different from the cognitive bias argument.

lumping in the cognitive bias guys with the anti-reductionist guys may have been more common in the older sources I read... since cognitive bias (Wigner's "other species" issue etc) established its own literature, leading up to the Lakoff stuff etc., these people have generally not been called "anti-reductionist" but rather "pro-cognitive" or "cognitive paradigm" - by their enemies. To themselves, they are just sensible people with no paradigm... questioning the establishments' trust in inertial theory...

The term "zoo" is not NPOV and needs to be removed. Furthermore, the times of a "zoo" of hundreds of bewildering particles is over; nowadays we just have a small well organized set of particles that make up everything, as explained in particle physics.

 * who's "we"? The anti-reductionists too?

 * Yes. You don't even understand the genuine reductionist/anti-reductionist debate in physics. The anti-reductionists don't claim that the standard model is wrong; they just say that finding the ultimate particle model is not as important as studying the emergent properties that arise at higher levels, and that indeed knowledge of the underlying particle model will not help much in studying the emergent properties. AxelBoldt

 * I agree with the anti-reductionists that particle insight isn't necessary - they still think it's ok to explore, I happen to believe I can prove that if the a-r types are right, particle physics is at best a dangerous distraction. It's the issues involved in propagating the zoo/ontology and the cult of accelerators that bother me - and they are discussed in funding circles quite a bit.  If the PPFO/zoo "will not help much", just shut 'em down.

 * Anyway, that's nice. I don't believe in it.

 * Nobody cares. If you can cite well-established researchers which have evidence that the neat standard model is in fact a bewildering zoo and far from complete, add that to particle physics. AxelBoldt

 * do you really want particle physics all cluttered up with issues of it being a cosmology, foundation ontology, gift from god, etc.? I wanted to respect the nice clean article that was there, and keep this issue separate.  Particle physics won't be "changed" or "fixed" by such criticism, it would simply go away like medieval scholastics arguing angels per heads of pins...

 * the term "particle zoo" or "particle physics zoo" is in common use - you claim it is now out of common use and that the zoo is accepted as a true foundation ontology. I believe that too, thus the title.  So what's wrong?  If you want to add "particle physics standard model" to the list of acronyms, or even make that the primary title of the article, that's not a problem, as it is the "standard" claim of the "model" that is actually under debate.  In that case, as with "Ecoregional" vs. "Bioregional" Democracy, we'd just make "particle physics foundation ontology" and "particle physics zoo" two alternate names that are seemingly less NPOV than the term "standard model".  Fair?

 * I submit you have nothing but a zoo that is an incomplete explanation of something else. If what you said were true, particle accelerators would already have been shut down.  But they still run, so this is still in dispute.  We will remove "zoo" when they stop searching for more.  Fair?

 * No. Zoo is not NPOV and it goes. The accelerators are running because some predictions by the standard model have not yet been observed, since apparently we haven't tried high enough energies. AxelBoldt

 * Sorry. Zoo goes back the minute you take it out.  Your fetish for "high enough energies" and your use of "we" is also not NPOV, quite obviously.  Note that you assume that these predictions *will* be observed, and you acknowledge (implicitly and in flat contradiction of your "no zoo" claim) that there is need to test this.

 * consider this settled. If "zoo" is mentioned up front so that people can do their own searches to find that community of people still using it, and the contrast between zoo and standard model is clearly described, and neither is in the title, then I think we have found an NPOV here - at the expense of having to coin a term, which I believed was necessary from day one (thus inventing it).  I better explained the alternate terms for search purposes and to help people better understand NPOV and why we won't take sides on things like "zoo versus standard" and etc.

Has the term "particle physics foundation ontology" been used in the literature before? We don't want original research in Wikipedia. AxelBoldt

 * "particle ontology" is the most common term, probably due to its brevity. However it is clearly w.r.t. particle *physics*, not dust particles, and it is clearly a "foundation ontology" in exactly the sense understood in logic, computer science,

and theology. "particle physics ontology" is the most exact term that assumes the least. However the use of this zoo as a foundation ontology, as Axel just proved it is used to claim "we just have a small well organized set of particles that make up everything," which is very obviously a claim that it is a foundation ontology. If this claim is shared by many physicists, as I believe it is, then "particle physics foundation ontology" is a correct description of the claim... and "particle physics ontology" is a correct description of the zoo. Fair?

 * "particle physics" "foundation ontology" throws up zero matches in Google - this seems to me to indicate that it is too original for an encyclopedia. Unless anyone else has heard of this subject, I would suggest that it would be better moved to meta. Enchanter

 * no, look up "particle ontology", and "particle zoo", the brief terms. For a "non-NPOV" term, "particle zoo" does seem to be the most common term in use.  If we split the article into two, it has to be "ontology as foundation" (as Axel understands it) versus "ontology as guide to further searching" as particle accelerator studies seem to use it...

here's Karl Popper's view of this which uses the term "cosmology". That is an acceptable substitute for "foundation ontology" but then this needs more about astronomy, anthropics, and theology, which I was deliberately avoiding by using "foundation ontology".

 * The current zoo and these methods are explained under particle physics. This article is concerned with the impact of the zoo on activities other than particle physics.

Why can't you then find a clear title for your article? "Impact of standard model outside of particle physics". Everybody would understand that. Put your anti-accelerator propaganda there and be done with it. Instead, you create layers and layers of impenetrable new-age speak. AxelBoldt

 * my only remaining issue with the accelerator issue is that you treat it as if the issue is "accelerators versus other science and education" rather than say "accelerators versus foreign aid or investment in extreme outsider views or housing homeless people" or more succinctly "accelerators versus general expenditures"

 * the term "standard model" is itself less NPOV than I think we'd prefer...

 * accordingly, I am quite satisfied by the solution of keeping it out of the title - so that neither "zoo" nor "standard model" are claimed in the title, but both are mentioned and explained clearly in context several times in the article. This is very well balanced now.  Thanks.

 * if it's "new-age speak" then a lot of old-age people speak it - Karl Popper, the Pope, etc. here's Karl Popper's view of this.

 * The clearest title for this article would be "particle physics cosmology" - but as I say that would require broader treatment of issues like the Anthropic Principle, cognitive bias beyond the particle physics zoo, etc.

 * as to accelerators, it's clear that while they are in use, someone is still looking for particles. So this is not yet a settled "cosmology" so certain that we abandon the search... nor is it an arbitrary foundation ontology as you suggest, not subject to question.

WHAT are you guys talking about - if you understood the subject you wouldn't be having this discussion.

This isn't some theological debate where everybodys view is just as good as any other, there isn't any disagreement between particle physicists and solid state physicists about who has the true view of the universe.

Reading this it sounds like you come from a discipline with a completely different way of thinking and you have just transferred it wholesale into the arena of physics, with results that frankly are very unimpressive. I suspect that the response to attempts to help you resolve your confusion are likely to be territorial, especially as the best suggestion would be for you to spend - a not inconsiderable amount of - time learning the physics, rather than some second-hand theory discussing the physics, at the end of which you would no longer ask those questions.

Particle physics is good for the physics of particles, statistical physics for the statistical properties of assemblies of particles, vector field theory for electricity and magnetism, General Relativity for large-scale phenomena, quantum mechanics for small-scale phenomena. The methods of these different fields do not compete, they are appropriate in their domains.

This is a common thing in the world. The methods of the car mechanic do not compete with those of the historian, indeed it would arguably be inappropriate to try to analyse a faulty exhaust from a historical perspective - you could do it, but it would probably be as foolish as trying to apply particle physics to analysing the thermal efficiency of different work cycles for gas engines.

See what I mean ?

Anyway the upshot is that the article at http://en.wikipedia.org/wiki/Foundation_ontology just looks foolish to anyone who knows some physics. It is immediately apparent that it is written by someone trained in one of the social sciences, who doesn't really understand the physics.

 * sorry but that's the truth :-(

I think it would be appropriate to change the article to make it clear that the debate is not amongst physicists, but some other group of people. The page will be more accurate


text:
Fushimi

Fushimi may refer to:

 * Emperor Fushimi of Japan
 * Fushimi, Kyoto, a ward of Kyoto city
 * Fushimi, Nagoya, a neighbourhood in Nagoya
 * Fushimi (surname), a Japanese surname
 * Fushimi-no-miya, a branch of the Japanese Imperial Family

title: Fushimi


text:
Emperor Go-Fushimi

Emperor Go-Fushimi (後伏見天皇) was the 93rd emperor of Japan, according to the traditional order of succession. His reign spanned the years from 1298 to 1301.

This 13th-century sovereign was named after his father, Emperor Fushimi and go- (後), translates literally as "later"; and thus, he is sometimes called the "Later Emperor Fushimi". The Japanese word go has also been translated to mean the "second one"; and in some older sources, this emperor may be identified as "Fushimi, the second", or as "Fushimi II".

Family
Before his ascension to the Chrysanthemum Throne, his personal name (his imina) was Tanehito-shinnō (胤仁親王).

He was the eldest son of Emperor Fushimi. They belonged to the Jimyōin-tō branch of the Imperial Family.

 * Court Lady: Saionji (Fujiwara) Neishi / Yasuko (西園寺（藤原）寧子) later Kōgimon'in (広義門院; 1292–1337), Saionji Sanekane's daughter
 * First daughter: Imperial Princess Junshi (珣子内親王)
 * Third son: Imperial Prince Kazuhito (量仁親王) later Emperor Kōgon
 * Fifth son: Imperial Prince Kagehito (景仁親王; b. 1315)
 * Second daughter: Imperial Princess Kenshi / Kaneko (兼子内親王)
 * Ninth son: Imperial Prince Yutahito (豊仁親王) later Emperor Kōmyō
 * Jibukyō-no-tsubone (治部卿局), Priest's daughter
 * First Son: Imperial Prince Priest Sonin (尊胤法親王; 1306–1359）
 * Takashina Kuniko (高階邦子), Takashina Kunitsune's daughter
 * Second Son: Imperial Prince Priest Shuho (法守法親王; 1308–1391）
 * Ogimachi Moriko (正親町守子; d. 1322), Ogimachi Michiakira's daughter
 * Sixth Son: Imperial Prince Priest Shōin (承胤法親王; 1317–1377）
 * Seventh Son: Imperial Prince Priest Chōjo (長助法親王; 1318–1361）
 * Eighth Son: Imperial Prince Priest Ryosei (亮性法親王; 1318–1363）
 * Fifth Daughter: Imperial Princess Kōshi (璜子内親王) later Shotokumon’in (章徳門院)
 * Taiyo-no-kata（対御方; 1297–1360), Ogimachi Michiakira's daughter
 * Fourth Son: Imperial Prince Son Imperial Prince Priest Jishin (慈真法親王; b. 1314)
 * Fourth Daughter: Princess Kakukō (覚公女王)
 * Tenth Son: Imperial Prince Priest Sondō (尊道入道親王; 1332–1403）
 * Ukyōnodaibu-no-tsubone (右京大夫局)
 * Third daughter
 * Sixth daughter

Events of Go-Fushimi's life
Tanehito-shinnō was named Crown Prince or heir in 1289.

Fushimi acted as cloistered emperor for a period, but after a while, from 1313 to 1318, Go-Fushimi acted in that function.
 * 30 August 1298 (Einin 6, 22nd day of the 7th month): In the 11th year of Fushimi-tennō's reign (伏見天皇十一年), the emperor abdicated; and the succession (senso) was received by his son.
 * 17 November 1298 (Einin 6, 13th day of the 10th month): Emperor Go-Fushimi acceded to the throne (sokui) and the nengō was changed to Shōan to mark the beginning of a new emperor's reign.
 * 1 November 1299 (Shōan 1, 8th day of the 10th month): Chinese Chan master Yishan Yining arrived in Kamakura as a last Mongol envoy.
 * 2 March 1301 (Shōan 3, 21st day of the 1st month): Abdicates due to rally of the Daikakuji Line
 * 11 September 1308 (Tokuji 3, 26th day of the 8th month): Younger brother becomes Emperor Hanazono, retired emperor
 * 17 May 1336 (Engen 1, 6th day of the 4th month): Died

During Hanazono's reign, negotiations between the Kamakura shogunate and the two lines resulted in an agreement to alternate the throne between the two lines every 10 years (the Bumpō Agreement). This agreement did not last long, as it was broken by Emperor Go-Daigo.

Go-Fushimi was the author of a famous plea to the god of the Kamo Shrine for help in gaining the throne for his son. This plea was ultimately successful, but it was not until thirty-three years after his abdication that Go-Fushimi's son, Emperor Kōgon became emperor. Kōgon was the first of the northern court emperors backed by the Ashikaga shogunate.

Emperor Go-Fushimi is enshrined with other emperors at the imperial tomb called Fukakusa no kita no misasagi (深草北陵) in Fushimi-ku, Kyoto.

Kugyō
Kugyō (公卿) is a collective term for the very few most powerful men attached to the court of the Emperor of Japan in pre-Meiji eras. Even during those years in which the court's actual influence outside the palace walls was minimal, the hierarchic organization persisted.

In general, this elite group included only three to four men at a time. These were hereditary courtiers whose experience and background would have brought them to the pinnacle of a life's career. During Fo-Fushimi's reign, this apex of the Daijō-kan included:
 * Sesshō, Takatsukasa Kanetada, 1298
 * Sesshō, Nijō Kanemoto, 1298–1300
 * Kampaku, Nijō Kanemoto,	1300–1305
 * Sadaijin
 * Udaijin
 * Nadaijin
 * Dainagon

Eras of Go-Fushimi's reign
The years of Go-Fushimi's reign are more specifically identified by more than one era name or nengō.
 * Einin      (1293–1299)
 * Shōan (1299–1302)

title: Emperor Go-Fushimi


text:
Emperor Go-Nijō

Emperor Go-Nijō (後二条天皇) was the 94th emperor of Japan, according to the traditional order of succession. He reigned from 1301 to his death in 1308.

This 14th-century sovereign was named after the 12th-century Emperor Nijō, and go- (後), translates literally as "later"; and thus, he is sometimes called the "Later Emperor Nijō", or, in some older sources, may be identified as "Nijō, the second" or as "Nijo II".

Genealogy
Before his ascension to the Chrysanthemum Throne, his personal name (his imina) was Kuniharu-shinnō (邦治親王).

Go-Nijō was the eldest son of the 91st emperor Emperor Go-Uda. He belonged to the Daikakuji-tō branch of the Imperial Family.

Empress: Fujiwara no Kinshi (藤原忻子) later Chōrakumon-in (長楽門院), Tokudaiji Kintaka's daughter

Naishi: Fujiwara Tamako (藤原 頊子) later Banshūmon-in (万秋門院; 1268 - 1338), Ichijō Sanetsune’s daughter

Lady-in-waiting: Fujiwara Muneko (藤原 宗子) also Chunagon'no-tenji (中納言典侍), Itsutsuji Munechika’s daughter
 * First Son: Imperial Prince Kuniyoshi (邦良親王; 1300 - 1326）
 * Second Son: Imperial Prince Hanamachi-no-miya-Kunimi (花町宮邦省親王; 1302-1375)

Naishi: Koto Naishi, Taira Munetoshi’s daughter
 * First Daughter: Imperial Princess Benshi (㛹子内親王; 1302 - 1362）later Jyuseimon'in/jyujoumon'in (壽成門院/寿成門院)

Court Lady: Dainagon-no-tsubone (fujiwara), Sanjo Kinyasu’s daughter
 * Third Son: Imperial Prince Priest Yujo (祐助法親王; 1302 - 1359）
 * Fourth Son: Imperial Prince Priest Shoson (聖尊法親王; 1303 - 1370）
 * Third Daughter: Imperial Princess Eiko (栄子内親王)
 * Fifth Daughter

Court Lady: Lady Mikushige (fujiwara), Sanjo Kinchika
 * Fifth Son: Imperial Prince Sonsai (尊済法親王; 1304 - 1329)

Court Lady: Taira Nobusuke’s daughter
 * Fourth Daughter: Imperial Princess Choshi (瑒子内親王)

Court Lady: Shindainagon-no-Tsubone
 * Second daughter: Imperial Princess Minshi (珉子内親王)

Events of Go-Nijō's life
Kuniharu-shinnō was made an imperial prince by Imperial proclamation in 1286.

In 1296, he became crown prince (heir) to the Jimyōin-tō Emperor Go-Fushimi, his second cousin.

 * 2 March 1301 (Shōan 3, 21st day of the 1st month): In the 5th year of Go-Fushimi-tennō's reign (後伏見天皇五年), the emperor was forced to abdicate; and the succession (‘‘senso’’) was received by his cousin. Shortly thereafter, Emperor Go-Nijō is said to have acceded to the throne (‘‘sokui’’).

Go-Nijō's father, the Emperor Go-Uda reigned as cloistered emperor during his reign.

The succession dispute between the Daikakuji and Jimyōin branches of the Imperial Family continued during his reign. His grandfather, the retired Emperor Emperor Kameyama was said to have acted through the Bakufu to ensure Go-Nijō's enthronement.

On 10 September 1308, Go-Nijō died of illness.

Go-Nijō is buried at Kitashirakawa no misasagi (北白河陵) in Sakyō-ku, Kyoto.

Kugyō
Kugyō (公卿) is a collective term for the very few most powerful men attached to the court of the Emperor of Japan in pre-Meiji eras. Even during those years in which the court's actual influence outside the palace walls was minimal, the hierarchic organization persisted.

In general, this elite group included only three to four men at a time. These were hereditary courtiers whose experience and background would have brought them to the pinnacle of a life's career. During Nijō's reign, this apex of the Daijō-kan included:
 * Kampaku, Nijō Kanemoto, 1300–1305
 * Kampaku, Kujō Moronori, 1305–1308
 * Sadaijin
 * Udaijin
 * Nadaijin
 * Dainagon

Eras of Go-Nijō's reign
The years of Go-Nijō's reign are more specifically identified by more than one era name or nengō.
 * Shōan (1299–1302)
 * Kengen       (1302–1303)
 * Kagen       (1303–1306
 * Tokuji      (1306–1308)

title: Emperor Go-Nijō


text:
Hanazono

Hanazono may refer to:

Places

 * Hanazono University in Kyoto, Japan
 * Higashi Osaka Hanazono Rugby Stadium in Higashi Osaka, Osaka Prefecture, Japan
 * Hanazono, Saitama, former town in Saitama Prefecture, Japan
 * Hanazono, Wakayama, former village in Wakayama Prefecture, Japan
 * Hanazono Shrine, a Shinto shrine in Shinjuku, Tokyo, Japan

People

 * Emperor Hanazono, the 95th emperor of Japan
 * Utako Hanazono, Japanese geisha

Fictional characters

 * Hikari Hanazono, in the anime and manga series Special A
 * Karin Hanazono, in the anime and manga series Kamichama Karin
 * Sakura Hanazono, in the anime and manga series Kaichō wa Maid-sama!
 * Shizuma Hanazono, in the anime Strawberry Panic
 * Tae Hanazono, a character in the multimedia franchise BanG Dream!
 * Yurine Hanazono, in the anime and manga series Dropkick on My Devil!

title: Hanazono


text:
Talk:Where Mathematics Comes From

Terrible example
The following is actually a good example of the ignorance with which the book has been received in some quarters:

"It's difficult for me to conceive of a metaphor for a real number raised to a complex power, but if there is one, I'd sure like to see it." Joseph Auslander

Apparently Joseph Auslander did not read the book, because if he had he would have found a discussion of the conceptual metaphors involved in raising real numbers to an imaginary power at the very beginning of the section on Euler's equation. The whole point of that discussion is that raising a real number to a complex power is the metaphor.

I think this is a bad and misleading example of criticism of the book, and should be removed.

K.S. —Preceding unsigned comment added by 99.231.49.9 (talk) 01:25, 27 April 2009 (UTC)

A more charitable reading of Auslander would have him saying that he read the metaphor multiple times and carefully, and -- in his terms -- has difficulty conceiving of it. Metaphors, after all, aren't universal. Stacking them as high as WMCT does strains credulity of the resulting stack as a metaphor. Gene B. Chase 14:25, 15 March 2012 (UTC)

Random crap people couldn't bother to put a heading to themselves
''This page represents the latest discussion of Where Mathematics Comes From. For older discussion, ranging all over the map and including a discussion of quantum mechanics, see Talk:Where Mathematics Comes From/Archive.''
 * The archive should be mentioned at the top of this page. Otherwise the archive is difficult to find.  Tkuvho (talk) 16:14, 24 March 2010 (UTC)
 * Ok, I added an archive box at top. But I've never done this before and I'm not sure I understood all the instructions at Template:Archives. In particular, the archives were given a non-standard name, so the box cannot access them automatically. If someone knows how to do this better, please do. --seberle (talk) 22:01, 24 March 2010 (UTC)

I've renamed the article to the name of the Lakoff/Nunez book. The article "Cognitive science of mathematics" should be broader, covering all the findings of cognitive science related to math (and not just those identified in the book), and perhaps being less attached to these two authors' "embodied realism". --Ryguasu 06:11 Dec 27, 2002 (UTC)
 * all good moves

Now that structure of these articles is agreed on, and old talk gone, can we please discuss the book and the implications of the book and what can be said about it? If you look in the article history there was a great deal of material directly related to the book, including commentary on reviews etc.. This appears to have been deleted, contrary to wikipedia conventions, by people who evidently had not read the book nor understood its claims - perhaps bad writing was the issue - and perhaps some of that old text should be reviewed and re-incorporated by third parties? The book also has undergone some revisions and the authors have responded to criticisms. Does that response go here, or in cognitive science of mathematics ?

 * I think it would be highly appropriate to discuss criticisms about the book and responses thereto in this particular article. We can always move it somewhere else if that later turns out to be more appropriate. --Ryguasu

Am I missing something, or does the book not provide a way to conceptualize multiplication of a*b or a/b, when a and b are both non-integer, for any of the "4 Gs"? (The book provides ways to conceptualize many other simple operations, including these ones for integers.) If not, could somebody suggest a way to visualize such multiplications, or at least suggest why the standard procedure is reasonable? --Ryguasu 01:51 Feb 25, 2003 (UTC)

---

"This idea analysis is distinct from mathematics itself and cannot be performed by mathematicians not sufficiently trained in the cognitive sciences."

 * This is clearly a fantastic argument that beats all others: "my analysis is based on special techniques that you cannot understand, former experts in {insert subject here}".

 * Although there is certainly some room for the criticism that Lakoff, in particular, is too quick to presume himself one of the leading authorities on anything he's thought about, your paraphrase here is not particularly accurate. The argument is not that mathemeticians cannot understand the ideas in Where Mathematics Comes From; it's that a normal mathematical education doesn't teach anything like this. In particular, a normal mathematical education devotes approximately no time to considerations of A) what about the mind/brain allows it to do mathematics, or B) the philosophy of mathematics. These are precisely the topics that the book is about. Of course, the article could probably be clearer about all this. --Ryguasu 16:11 Mar 21, 2003 (UTC)

Well, your explanation sounds reasonable. How about replacing

"Idea analysis is distinct from mathematics and cannot be performed by mathematicians unless they are trained in cognitive science."

with

"A standard mathematical education does not develop such idea analysis techniques because it does not pursue considerations of A) what structures of the mind allow it to do mathematics, or B) the philosophy of mathematics."

Giving 'er the good ol' college try, now. —Preceding unsigned comment added by 70.68.103.27 (talk) 00:23, 23 September 2010 (UTC)
 * Ok, hang on. We agree that Lakoff and Núñez are perhaps a bit too forceful in their argument that mathematicians cannot understand cognitive science and that your restatement is probably more palatable. However, the goal here is not to be more palatable. I believe that the original statement you deleted is a more accurate statement of what Lakoff and Núñez presented in WMCF. Please remember that this article is supposed to be presenting the argument from WMCF (unless clearly reporting criticism), not our own views. --seberle (talk) 13:31, 23 September 2010 (UTC)

Check me on this: "If one accepts logicism in its only coherent form, one must reject the outright denial of Lakoff, even if one accepts the findings of his research." Discarding the premise and looking only at the conclusion ("one must reject the outright denial of Lakoff, even if one accepts the findings of his research"), let me reword this to the semantically equivalent "if one accepts the findings of his (Lakodff's) research, one must reject the outright denial of Lakoff." Substituting "deny" for "reject" and "accept" for "deny the (outright) denial," we get "if one accepts the findings of his (Lakodff's) research, one must accept Lakoff." That's certainly true, but I do not understand why a tautology should be included. I'm writing a science fiction story, and I am no expert on logic or mathematics, but tautologies hurt my head. Can someone fix or explain?" -- Kencomer 8:06AM 23-Apr-2004 (UTC)

Kencomer, I've just rewritten that sentence to make what I take the original author's intentions to be a little more clear. See if the revision doesn't help you out. -Ryguasu 17:06, 24 Apr 2004 (UTC)~

Is it really necessary for every section to be headed with a question?? On a different note, this article needs a little NPOVing and input from math people. I've read parts of the book (esp. the infamous Euler identity part) and the authors are presumptuous about the way mathematicians do their work. In fact, many of the processes they accuse mathematicians of being unaware of or sufficiently informed about, are actually processes quite common in everyday mathematical thought and teaching. (For example, analogies and applications to the sciences and the "real world".) The way the Euler identity part of the book reads is virtually identical to the way I would explain it to someone learning it, and very similar to how it's presented in the classroom (not just textbooks). The authors may be talented cognitive scientists, but they are poor sociologists and observers of human behaviour. They should spend several months or a year following a mathematician around, just watching, observing, they would learn a lot. Revolver 01:52, 12 Jul 2004 (UTC)Revolver 01:50, 12 Jul 2004 (UTC)

Is this article about a book or about where math comes from? If it is about a book and is a faithful summary of this book, I think that it is a tragedy that such a book was ever written. If the article is indeed intended as an account of "where math comes from", then there is quite a bit lacking.

The entire article seems to mistake the subject of mathematics for the subject of applied mathematics, which I maintain are separate subjects. Applied mathematicians are not actually mathematicians at all, they are simply scientists in their field of application. A pure mathematician is one who concerns himself solely with the validity of mathematical statements. Whether they realize it or not, most pure mathematicians are formalists.

A formalist beleives that all of mathematics is just a game. A branch of mathematics is simply a set of deduction rules (a formal logic) and a set of axioms stated in this logic. Mathematicians concern themselves with the "game" of deciding what can and can't be deduced from these axioms using these rules. The question of their interpretation, their validity in the "real world", and their application is of no concern to a mathematician. That is the job of applied mathematicians who, I maintain, are not truly mathematicians at all. The doctrine of formalism is arguably the most successful answer to the question of where math comes from.

The question which is the title of this article is never truly addressed in this article. The title should maybe be renamed "How can we jusify the application of mathematics?". I think that the article on the philosophy of math addresses the question of where math comes from much more thoroughly.

??
I don't understand how people can put forth things such as this in the Criticisms section: "WMCF does not explain where arithmetic comes from (if that is even possible or makes sense). Rather, it merely concluded that humans possess innate arithmetical ability." ?? I'd say it quite clearly follows, and should be obvious to any sensible person, that mathematics is but mathematical thought which directly maps to the physical world through the neural correlates of said thought--this is so trivial that I'm startled at the need to point it out! There is no contradiction in having mathematics both reflecting a structuring in the physical world and the subjective mental aspect, since mind is just an aspect of brain and part of that world. Thus saying "WMCF is entirely consistent with the Platonic philosophy which it rejects" is ludicrous since Platonism not only proposes mathematics is independent of mind, but that it is independent of the physical world, and that is a religious proposition and hardly has a place in a technical, rational discussion. ThVa (talk) 13:35, 21 July 2008 (UTC)

M.F.
Well, I know where this article comes from and someone should get a shovel. It reads like a bad review of the book or a personal essay, not an article in an encyclopedia. And who gives a fouc what the post-modernists have "developed" anyway?

 * Meanwhile, the postmodernists, most notably Michel Foucault, developed a deep critique of Western ethics, theology and philosophy, which focused on the absence of any model of the living and acting human body...

too much opinion
This article in general has too much opinion, e.g. René Descartes' "cogito ergo sum" seems to be under serious challenge. Wikipedia articles should be factual reports on what different sides in a controversy say.

The page is 'interesting', however not very encyclopic. As noted above, contains alot of opinion, and seems more like a book review.

This entry is seriously deficient
I own a copy of WMCF, and this entry does not do justice to the book at all. For starters, WMCF is a wonderful meditation on the cognitive origins of real analysis, complex numbers, the exponential function, and so on. There are also nice chapters on Boolean algebra, first order logic, and set theory, although the deepest passion of Lakoff and Nunez rests with analysis. Certain aspects of WMCF trace back to Lakoff's 1987 Women Fire and Dangerous Things. Nobody seems to notice that.

I think that Lakoff and Nunez have made a major contribution to our civilization's ongoing conversation about the philosophy of mathematics. The entry does not do justice to that conversation. For my part, I have long been suspicious of Platonism and the associated notion that mathematics is "discovered" rather than "invented." I agree with Lakoff when he writes "there is no way we can ever find out." No way, that is, until we interact with another technogically advanced civilization, which is unlikely to ever happen, if you agree with Barrow & Tipler, and Ward and Brownlee, that homo sapiens is the only technology manipulating species in our Galaxy.

I tell my students that mathematics is a vast "toolbox for the mind" and that mathematics, like all tools, was crafted by humans to serve human purposes. Euclidian geometry and number theory excepted, nearly all of our mathematics came into being after the start of the scientific revolution that began with Copernicus and Galileo, not before.

(I would except also plane and spherical trigonometry, probability, Gaussian elimination by Chinese to solve simultaneous linear equations, election theory, the mathematical logic of Ramon Llull, and so many other things that I can hardly count. In short, the Renaissance wasn't the beginning of an awful lot of things. -- Gene B. Chase 14:44, 15 March 2012 (UTC)) — Preceding unsigned comment added by GeneChase (talk • contribs)

It is very true that the education of all mathematicians does not prepare them at all to take on board claims like those of WMCF. And I can attest to the intense hostility nearly all mathematicians have for those sorts of claims. Nearly all working mathematicians are unwitting unreflective Platonists. Finally, it is incredibly true that nearly all mathematicians under 50 years of age take no interest in the philosophy of mathematics. No grants, no possible Fields medal, therefore worthless.

I believe that mathematics is the most successful human symbolic activity. This implies that understanding mathematics requires understanding the role of symbols in human communication, the subject matter of semiotics. This implies that the notation of mathematics is deserving of close scientific study. I doubt there is a single mathematician alive who thinks in this manner. A dead one who would have agreed was Charles Peirce.

 * Though this may be true, just in the same way that you praise the book, changing the article reflects your personal opinion about mathematics, mathematicians and the book, which, just as the article, may do no justice to mathematicians or mathematics. I suppose the best option is that if you feel strongly about this, you find sources that both agree and disagree with the book, as this would be the purpose of an encyclopedia. At the same time, someone could interpret your thoughts on mathematicians to be very opinionated such as "unwitting" and "unreflective". Any group can make such a claim about any other group and I think we can agree that it rarely holds. So even if understand your dismay towards this article, its problem is precisely that it reflects opinions whereas it should reflect a general consensus.GabKBel (talk) 23:20, 14 May 2010 (UTC)

Mathematics and Politics?
Does this article need the "Mathematics and Politics" section? The authors of the book make conscientious attempts to disassociate themselves and their theses from the excesses of postmodernism, and I think this article should preserve that sentiment.

In addition, I think the argument that "the failure of Principia Mathematica to ground arithmetic in set theory and formal logic" was a "failure" needs a link to Godel's incompleteness theorem or better citations. Was this stated or implied goal of Principia? Has Godel "plagued" philosophers of mathematics? On the contrary I think it took about 50+ years to digest Godel but mathematical philosophy is alive and kicking, "thanks" to Godel. (Witness Chaitin, Wolfram ...)

As someone with a deep (but not professional) interest in the history and philosophy of mathematics and someone who generally would describe himself as a Platonist, I found this book to be frustratingly thought-provoking and refreshing, and I respected its strongly worded and generally well-constructed arguments, who's points could be refuted or conceded line-by-line. Its positives were its style and tone, which were smart enough NOT to attach mathematics to politics or the Baghavad Ghita. Unfortunately it seems as if the leftist intellectuals have co-opted Lakhoff/ Nunez's bold yet constrained theses and hence somehow we get this Wikipedia article.--209.128.81.201 00:45, 22 March 2006 (UTC)

 * I like the substance and thrust of nearly everything you write above. It seems, however, that much of the material to which you (and I) objected strongly has been excised, to be replaced by -- nothing.
 * Principia is historically very important, but a substantive failure. Its notation is wallpaper, and its proofs turgid and pedantic, a long winded horror. A much better approach is that of Norm Megill's Metamath, although even his approach is long winded. One day someone will write a taught little book showing how to ground analysis, algebra, and geometry in first order logic (a logic which is simply than the way it is typically taught) and a minimum of set theory.

 * Thanks anon202. (I did the revert, and I'm 209 above.)  I agree that the knife was widely cut.  The article could be a little longer, with some mention on the critique of mathemetician's emphasis on the concept of closure (which I appreciated), the critique of mathematical induction, the overall importance of metaphor...  Can you think of a way to expand it?
 * I agree with you about Principia. But I didn't read WMCF as a critique of formalism or Hilbert's Program in general.  Godel & Turing & recently as mentioned above Chaitin & Wolfram & Robins & ... did it better.  WMCF seemed more a critique of "Platonism," or what Nunez and Lakhoff have described as the "Romance of Mathematics."  Thoughts? --M a s 23:33, 9 May 2006 (UTC)

Expand tag
The article is long enough as it is. I'm going to remove the tag unless someone can explain why I shouldn't. Gene Ward Smith 19:32, 12 May 2006 (UTC)

 * Go for it. Could you then desection some?  (It might look strange to have a section with only 2 sentences.)  Thanks!  --M a s 20:04, 12 May 2006 (UTC)

I did that and a lot more; the section on the response of the mathematical community was incorrect and seriously failed the NPOV test, and I've completely rewritten and expanded that section so it's not just an ad for the book any more. Gene Ward Smith 19:07, 13 May 2006 (UTC)

 * Good edits Mr. Smith. Thanks! --M a s 01:08, 15 May 2006 (UTC)

 * Now the article has turned back to crap. No wonder I'm giving up on Wikipedia.

Unclosed bracket
Can someone add the missing bracket to the quote in the first section? Should it enclose "and human communities"? —Viriditas | Talk 01:41, 17 October 2006 (UTC)

Mathematics and nature stimuli
Most of mathematics is analogious to easy navigation or to moving objects in a seen landscape. The pictorial form of thinking is humans' most efficient way of handling information. The capacity of humans who live in a nature environment is enermous: compare the number of technical kind of details in a nature landscape (lines, curves, shapes, structures, etc) to the number of them in a city landscape. My memory for mathematical things used to be much better when I had wandered in nature. Has there been any research on this?Htervola 10:30, 8 December 2006 (UTC)

The romance of mathematics
I think the following can be deleted:

 * It can be argued that only the first of the above quotes really describes Platonism. The second is rather vague, the third is obviously true (logic is a subset of mathematics), while the fourth is not necessarily associated with Platonism. For example, the Platonists Kurt Godel and Roger Penrose deny that artificial intelligence is possible.

"It can be argued" is classic weasel wording - who argues this? Secondly, the section above does not appear to be direct critique of platonism anyway, but rather a critique of several common romantic ideas about mathematics. Thirdly, the third statement is not "obviously true" to me, nor to the authors of the book who apparently "dismiss it as an intellectual myth"! Reasoning can be non-logical (eg. linguistic or emotional reasoning).

Any objections to removing this small paragraph? ntennis 03:36, 4 May 2007 (UTC)

P.S. The same anonymous editor made some |other additions to the article at the same time, which begin with "it has been pointed out that..." and "another criticism is..." but what follows looks like an original critique.

Further, there's a large section at the bottom of the article in the "summing up" section that looks like it needs to go:

 * Mathematics has grown into an extremely powerful toolbox for the mind, one whose potential applications extend well beyond those traditional bastions of mathematical application, science and technology. For example, logic and abstract algebra have much to offer to the social sciences and humanities. But communicating these riches to the wider community of nonmathematicians has proved difficult, and the problem is worsening. Even formal systems as basic as first order logic and axiomatic set theory are nowadays learned only by the more technical philosophy majors, and by a small fraction of mathematics students. Hence only a few specialists learn any mathematics beyond calculus, applied statistics, differential equations, and a bit of linear algebra. Just how many persons with a university education know what an equivalence class, partial order, or morphism are? What it means for a collection of axioms to have a model? If the cognitive approach to mathematics suggests improvements to the basic mathematical toolbox and better ways to communicate that toolbox to nonspecialists, it will move humanity closer to the fulfillment of Leibniz's great dream of a universal symbolistic.

Again, any objections? ntennis 03:59, 4 May 2007 (UTC)

 * OK, a week has passed so I removed the passsages. They are retained here on the talk page should anyone want to argue for their reinclusion. ntennis 01:20, 11 May 2007 (UTC)

material removed from Critical response
I have removed the text below, which is variously irrelevant, OR, unencyclopedic in style, ungrammatical, or doesn't reflect a coherent understanding of the text. Please feel free to hash this out in sandbox or talk, and be sure that it fits the book before posting in the article. And cite sources.

 * But this critique can also be challenged under the light of theory of multiple intellegences provided by Howard Gardner. So a person might posses good intellegence of certain types but not necessarily of other types. One such example is Munshi Premchand - the famous story writer and novelist in Hindi literature - who was weak in mathematics. Further, by the same logic, the claim - " ... it would be required to show that intelligence and mathematical ability are separable, and this has not been done" can also be said to be untenable, since here the author seems to presume that intellegence is of one universal nature.

 * From this point of view, whatever one's views on Platonism (right, wrong, meaningless), the 'invention' of mathematical concepts such as number would be impossible since they are hard-wired into our brains from the moment we are born. Also, the word "invention" insinuates that things could somehow be different, so that we could have invented a number theory where 1+1=3, or prime decomposition is false. However, any such number theory immediately falls apart in the face of simple reasoning. In reality, 1+1=3 is obviously false, and Euclid and the ancient Indians stumbled upon prime decomposition rather than inventing it. [But - It can be said that these critics have not enough grounding in the ideas of Lakoff to raise the relevant, valid criticism. Lakoff, Nunez can be interpreted that the experiences of the bodies we have with the external world has resulted in the emergence of unique 'affordance' ( J.J. Gibson's term) characteristic of the type of bodies we have. This has laid down the basis of emergence of mathematics we have. So it is merely regarding the origin of basis of 'ours type' of mathematics which the work of Lakoff, Nunez is refering.]

 * Another criticism is that WMCF does not explain where arithmetic comes from (if that is even possible or makes sense).[ Again, they have but simply the critic don't seem to have understood that]. Rather, it merely concluded that humans possess innate arithmetical ability. Some argue that WMCF is entirely consistent with the Platonic philosophy which it rejects. [ No way it seems tenable. Rather the central attack of Lakoff is to undermine Platonic view of mathematics]

"alyosha" (talk) 05:51, 6 April 2009 (UTC)

original research
I agree with Seberle's criticism that this article contains a considerable amount of original research and synthesis. Much of it is less than entirely sympathetic to the book under discussion. Tkuvho (talk) 15:04, 21 March 2010 (UTC)
 * It should not be too difficult to clean this article up, but I am unfamiliar with the criticism of this book beyond the single working link offered in the criticism section. Here is what needs to be done by someone knowledgeable of the criticism of the book:

 * There are two criticism sections that need to be combined. The first one appears to be entirely original research. (If it is, it can simply be deleted.)
 * Any criticism which is original research should be removed.
 * Any criticism which is explaining what critics have said needs to be referenced.
 * The two quotes need to have their links fixed. If there are no longer valid links, simple footnoted references would suffice.
 * There are a few good sentences which can be kept, such as the criticism of math error and the authors' response, which is properly linked. This sentence could be expanded to include some of the other responses included in that link, such as the authors' insistence that the embodiment aspect of their claims is being overlooked. It might also be good to reference the original Bonnie Gold review which the authors are responding to and mention the criticisms contained in that review.
 * As Tkuvho pointed out, everything should be stated as a neutral report on what critics have said and the authors have responded. Some of the current sentences are POV in that they are directly criticizing the authors rather than stating what critics have said. This is both POV and original research. We don't want to know Wikipedia editors' thoughts on this book; we want to know what the public reaction of experts has been. --seberle (talk) 16:24, 22 March 2010 (UTC)
 * I would like to raise the following additional issue. Jbottoms76 reports above that the link to the book site is, regrettably, a prohibited one.  Who prohibited it and why?  The link should certainly be included here.  Is it correct to assume that the site was prohibited by an overzealous wikipedian who happens to disagree with the thesis contained in the book?  Tkuvho (talk) 17:00, 22 March 2010 (UTC)
 * I am not sure what Jbottoms76 is referring to. The link actually no longer works. You can access an archived copy of the link from June 20, 2008, at http://web.archive.org/web/20071101135617/perso.unifr.ch/rafael.nunez/2ndprint.html. But I don't think it is proper to link to an archived copy. (Is that what he meant by "prohibited"?) I have not yet been able to locate the new site. Perhaps there is not one? In that case, this link should simply be removed. --seberle (talk) 20:06, 22 March 2010 (UTC)

removing POV tag with no active discussion per Template:POV
I've removed an old neutrality tag from this page that appears to have no active discussion per the instructions at Template:POV:
 * This template is not meant to be a permanent resident on any article. Remove this template whenever:
 * There is consensus on the talkpage or the NPOV Noticeboard that the issue has been resolved
 * It is not clear what the neutrality issue is, and no satisfactory explanation has been given
 * In the absence of any discussion, or if the discussion has become dormant.

Since there's no evidence of ongoing discussion, I'm removing the tag for now. If discussion is continuing and I've failed to see it, however, please feel free to restore the template and continue to address the issues. Thanks to everybody working on this one! -- Khazar2 (talk) 00:02, 30 June 2013 (UTC)

External links modified
Hello fellow Wikipedians,

I have just added archive links to 1 one external link on Where Mathematics Comes From. Please take a moment to review my edit. If necessary, add after the link to keep me from modifying it. Alternatively, you can add to keep me off the page altogether. I made the following changes:
 * Added archive https://web.archive.org/20060718161407/http://www.unifr.ch:80/perso/nunezr/warning.html to http://www.unifr.ch/perso/nunezr/warning.html

When you have finished reviewing my changes, please set the checked parameter below to true to let others know.

Cheers. —cyberbot II  Talk to my owner :Online 05:51, 28 August 2015 (UTC)

Removed criticism
Well, it had been tagged as possibly (and is hard to see it otherwise) OR for about 7 years, so I went ahead and removed it. Here's what I cut out: In set theories such as Zermelo–Fraenkel one can indeed have {1,2} = (0,1), as these are two different symbols denoting the same object. The claim that there is an anomaly because these are "fully distinct concepts" is on the one hand not a clear scientific statement, and on the other hand, is on par with such statements as: ""The positive real solution of $$x^2=2$$" and "$$\sqrt{2}$$" cannot be equal because they are fully distinct concepts.".

The apparent anomaly stems from the fact that Lakoff and Núñez identify mathematical objects with their various particular realizations. There are several equivalent definitions of ordered pair, and most mathematicians do not identify the ordered pair with just one of these definitions (since this would be an arbitrary and artificial choice), but view the definitions as equivalent models or realizations of the same underlying object. The existence of several different but equivalent constructions of certain mathematical objects supports the platonistic view that the mathematical objects exist beyond their various linguistical, symbolical, or conceptual representations.

As an example, many mathematicians would favour a definition of ordered pair in terms of category theory where the object in question is defined in terms of a characteristic universal property and then shown to be unique up to isomorphism (this was recently mentioned in an article on mathematical platonism by David Mumford).

The above discussion is meant to explain that the most natural and fruitful approach in mathematics is to view a mathematical object as having potentially several different but equivalent realizations. On the other hand, the object is not identified with just one of these realizations. This suggests that the intuitionistic idea that mathematical objects exist only as specific mental constructions, or the idea of Lakoff and Núñez that mathematical objects exist only as particular instances of concepts/metaphors in our embodied brains, is an inadequate philosophical basis to account for the experience and de facto research methods of working mathematicians. Perhaps this is a reason why these ideas have been met with comparatively little interest by the mathematical community.

Non-existent Mac Lane
In the article it is written: "Lakoff and Núñez cite Saunders Mac Lane (the inventor, with Samuel Eilenberg, of category theory) in support of their position. Mathematics, Form and Function (1986), an overview of mathematics intended for philosophers, proposes that mathematical concepts are ultimately grounded in ordinary human activities, mostly interactions with the physical world."

I have searched the book by Lakoff and Nunez for this fact. However, Mac Lane is never mentioned (except of listing his book in a general bibliography, without any comment).

Zbisem (talk) 14:31, 7 November 2018 (UTC)

Criticism deletion
The last few paragraphs under the "Human cognition and mathematics" section were recently deleted. User:Metalmikebot explained the deletion as follows:
 * I deleted the last several paragraphs, which were attached as criticisms without relevant citations; these would be better suited to a separate section under "criticisms", in which criticisms were **cited** rather than written into the entry like an op-ed. They appeared to use original research and did not accurately represent the book.)

I do not have sufficient expertise on this book and its criticism to judge the quality of the deleted paragraphs. However, in apparent contradiction to the stated reasons for the deletion, the deleted paragraphs did have several citations. Also, there does exist a separate "Critical response" section where the paragraphs could have been moved to, in contradiction to the implication that such a section needs creating. I am restoring the deleted paragraphs until a better justification can be given for their removal. Perhaps there are genuine reasons for believing the references were not valid? Perhaps these paragraphs should be moved to the "Critical response" section? --seberle (talk) 15:28, 8 January 2022 (UTC)

title: Talk:Where Mathematics Comes From


text:
Emperor Go-Daigo

Emperor Go-Daigo (後醍醐天皇 Go-Daigo-tennō) (26 November 1288 – 19 September 1339) was the 96th emperor of Japan, according to the traditional order of succession. He successfully overthrew the Kamakura shogunate in 1333 and established the short-lived Kenmu Restoration to bring the Imperial House back into power. This was to be the last time the emperor had real power until the Meiji Restoration in 1868. The Kenmu restoration was in turn overthrown by Ashikaga Takauji in 1336, ushering in the Ashikaga shogunate. The overthrow split the imperial family into two opposing factions between the Ashikaga backed Northern Court situated in Kyoto and the Southern Court based in Yoshino. The Southern Court was led by Go-Daigo and his later successors.

This 14th-century sovereign personally chose his posthumous name after the 9th-century Emperor Daigo and go- (後), translates as "later", and he is thus sometimes called the "Later Emperor Daigo", or, in some older sources, "Daigo, the second" or as "Daigo II".

Biography
Before his ascension to the Chrysanthemum Throne, his personal name (imina) was Takaharu-shinnō (尊治親王).

He was the second son of the Daikakuji-tō emperor, Emperor Go-Uda. His mother was Fujiwara no Chūshi/Tadako (藤原忠子), daughter of Fujiwara no Tadatsugu (Itsutsuji Tadatsugu) (藤原忠継/五辻忠継). She became Nyoin called Dantenmon-in (談天門院). His older brother was Emperor Go-Nijō.

Emperor Go-Daigo's ideal was the Engi era (901–923) during the reign of Emperor Daigo, a period of direct imperial rule. An emperor's posthumous name was normally chosen after his death, but Emperor Go-Daigo chose his personally during his lifetime, to share it with Emperor Daigo.

Events of Go-Daigo's life
In 1324, with the discovery of Emperor Go-Daigo's plans to overthrow the Kamakura shogunate, the Rokuhara Tandai disposed of his close associate Hino Suketomo in the Shōchū Incident.
 * 1308 (Enkyō 1): At the death of Emperor Go-Nijō, Hanazono accedes to the Chrysanthemum Throne at age 12 years; and Takaharu-shinnō, the second son of former-Emperor Go-Uda is elevated as Crown Prince and heir apparent under the direction of the Kamakura shogunate.
 * 29 March 1318 (Bunpō 2, 26th day of 2nd month): In the 11th year of Hanazono's reign (花園天皇十一年), the emperor abdicated; and the succession (senso) was received by his cousin, the second son of former-Emperor Go-Uda. Shortly thereafter, Emperor Go-Daigo is said to have acceded to the throne (sokui).
 * 1319 (Bunpō 3, 4th month): Emperor Go-Daigo caused the nengō to be changed to Gen'ō to mark the beginning of his reign.

In the Genkō Incident of 1331, Emperor Go-Daigo's plans were again discovered, this time by a betrayal by his close associate Yoshida Sadafusa. He quickly hid the Sacred Treasures in a secluded castle in Kasagiyama (the modern town of Kasagi, Sōraku District, Kyōto Prefecture) and raised an army, but the castle fell to the shogunate's army the following year, and they enthroned Emperor Kōgon, exiling Daigo to Oki Province (the Oki Islands in modern-day Shimane Prefecture), the same place to which Emperor Go-Toba had been exiled after the Jōkyū War of 1221.

In 1333, Emperor Go-Daigo escaped from Oki with the help of Nawa Nagatoshi and his family, raising an army at Senjo Mountain in Hōki Province (the modern town of Kotoura in Tōhaku District, Tottori Prefecture). Ashikaga Takauji, who had been sent by the shogunate to find and destroy this army, sided with the emperor and captured the Rokuhara Tandai. Immediately following this, Nitta Yoshisada, who had raised an army in the east, laid siege to Kamakura. When the city finally fell to Nitta, Hōjō Takatoki, the shogunal regent, fled to Tōshō temple, where he and his entire family committed suicide. This ended Hōjō power and paved the way for a new military regime.

Upon his triumphal return to Kyoto, Daigo took the throne from Emperor Kōgon and began the Kenmu Restoration. The Restoration was ostensibly a revival of the older ways, but, in fact, the emperor had his eye set on an imperial dictatorship like that of the emperor of China. He wanted to imitate the Chinese in all their ways and become the most powerful ruler in the East. Impatient reforms, litigation over land rights, rewards, and the exclusion of the samurai from the political order caused much complaining, and his political order began to fall apart. In 1335, Ashikaga Takauji, who had travelled to eastern Japan without obtaining an imperial edict in order to suppress the Nakasendai Rebellion, became disaffected. Daigo ordered Nitta Yoshisada to track down and destroy Ashikaga. Ashikaga defeated Nitta Yoshisada at the Battle of Takenoshita, Hakone. Kusunoki Masashige and Kitabatake Akiie, in communication with Kyoto, smashed the Ashikaga army. Takauji fled to Kyūshū, but the following year, after reassembling his army, he again approached Kyōto. Kusunoki Masashige proposed a reconciliation with Takauji to the emperor, but Go-Daigo rejected this. He ordered Masashige and Yoshisada to destroy Takauji. Kusunoki's army was defeated at the Battle of Minatogawa.

When Ashikaga's army entered Kyōto, Emperor Go-Daigo resisted, fleeing to Mount Hiei, but seeking reconciliation, he sent the imperial regalia to the Ashikaga side. Takauji enthroned the Jimyōin-tō emperor, Kōmyō, and officially began his shogunate with the enactment of the Kenmu Law Code.

Go-Daigo escaped from the capital in January 1337, the regalia that he had handed over to the Ashikaga being counterfeit, and set up the Southern Court among the mountains of Yoshino, beginning the Period of Northern and Southern Courts in which the Northern Dynasty in Kyoto and the Southern Dynasty in Yoshino faced off against each other.

Emperor Go-Daigo ordered Imperial Prince Kaneyoshi to Kyūshū and Nitta Yoshisada and Imperial Prince Tsuneyoshi to Hokuriku, and so forth, dispatching his sons all over, so that they could oppose the Northern Court.

 * 18 September 1339 (Ryakuō 2, 15th day of the 8th month): In the 21st year of Go-Daigo's reign, the emperor abdicated at Yoshino in favor of his son, Noriyoshi-shinnō, who would become Emperor Go-Murakami.
 * 19 September 1339 (Ryakuō 2, 16th day of the 8th month): Go-Daigo died;

The actual site of Go-Daigo's grave is settled. This emperor is traditionally venerated at a memorial Shinto shrine (misasagi) at Nara.

The Imperial Household Agency designates this location as Go-Daigo's mausoleum. It is formally named Tō-no-o no misasagi.

Consorts and children

 * Empress (Chūgū): Saionji Kishi (西園寺禧子) later Empress Dowager Go-Kyōgoku-in (後京極院), Saionji Sanekane's daughter
 * Princess (b. 1314)
 * Second Daughter: Imperial Princess Kanshi (懽子内親王, 1315–1362) later Empress Dowager Senseimon-in (宣政門院), Saiō at Ise Shrine; later, married to Emperor Kōgon

 * Empress (Chūgū): Imperial Princess Junshi (珣子内親王) later Empress Dowager Shin-Muromachi-in (新室町院), Emperor Go-Fushimi's daughter
 * Imperial Princess Sachiko (幸子内親王, b. 1335)

 * Nyōgo: Fujiwara no Eishi (藤原栄子) also Anfuku-dono (安福殿), Nijō Michihira's daughter

 * Court lady: Fujiwara no Chikako (藤原親子) also Chūnagon-tenji (中納言典侍), Itsutsuji Munechika's daughter
 * Eleventh Son: Imperial Prince Mitsuyoshi (満良親王)

 * Lady-in-waiting: Dainagon'nosuke, Kitabatake Moroshige's daughter

 * Lady-in-waiting: Shin-Ansatsu-tenji (新按察典侍), Jimyoin Yasufuji's daughter

 * Lady-in-waiting: Sochi-no-suke (帥典侍讃岐)

 * Court lady: Koto no Naishi (勾当内侍), Saionji Tsunafusa's daughter
 * Princess

 * Court lady: Shōshō no Naishi (少将内侍), Sugawara no Arinaka's daughter
 * Imperial Prince Seijo (聖助法親王) – Head Priest of Onjō-ji

 * Court lady: Fujiwara (Ano) no Renshi (藤原廉子/阿野廉子) later Empress Dowager Shin-Taikenmon-in (新待賢門院, 1301–1359), Ano Kinkado's daughter
 * Imperial Prince Tsunenaga (also Tsuneyoshi) (恒良親王)
 * Imperial Prince Nariyoshi (also Narinaga) (成良親王)
 * Imperial Prince Noriyoshi (義良親王) later become Emperor Go-Murakami
 * Imperial Princess Shoshi (祥子内親王) – Saiō at Ise Shrine 1333–1336; later, nun in Hōan-ji
 * Imperial Princess Ishi (惟子内親王) – nun in Imabayashi
 * Speculated - Imperial Princess Noriko (憲子内親王) later Empress Dowager Shinsenyō-mon-in (新宣陽門院)

 * Court lady: Minamoto no Chikako (源親子), Kitabatake Morochika's daughter
 * Imperial Prince Moriyoshi (or Morinaga) (護良親王) – Head Priest of Enryakuji (Tendai-zasu, 天台座主) (Buddhist name: Prince Son'un, 尊雲法親王)
 * Imperial Prince Kōshō (恒性, 1305–1333) – priest
 * Imperial Princess Hishi (妣子内親王) – nun in Imabayashi
 * princess – married to Konoe Mototsugu (divorced later)
 * Imperial Prince Sonsho (尊性法親王)

 * Court lady: Fujiwara no Ishi/Tameko (藤原為子, d. c. 1311–12), Nijō Tameyo's daughter
 * Imperial Prince Takanaga (also Takayoshi) (尊良親王)
 * Imperial Prince Munenaga (also Muneyoshi) (宗良親王) – Head Priest of Enryakuji (Tendai-zasu, 天台座主) (Buddhist name: Prince Sonchō, 尊澄法親王)
 * Imperial Princess Tamako (瓊子内親王, 1316–1339) – nun
 * Princess

 * Nyōgo: Fujiwara no Jisshi (実子). Tōin Saneo's daughter
 * Princess

 * Court lady: Fujiwara no Shushi/Moriko (藤原守子, 1303–1357), daughter of Tōin Saneyasu (洞院実泰)
 * Imperial Prince Gen'en (玄円法親王, d.1348) – Head Priest of Kōfuku-ji
 * Imperial Prince Saikei (最恵法親王) – priest in Myōhō-in

 * Princess: Imperial Princess Kenshi (憙子内親王, 1270–1324) later Empress Dowager Shōkeimon'in (昭慶門院), Emperor Kameyama's daughter
 * Mumon Gensen (無文元選, 1323–1390) – founder of Hōkō-ji (Shizuoka)

 * Court lady: Fujiwara (Nijo) Michiko (二条道子) also Gon-no-Dainagon no Sammi no Tsubone (権大納言三位局, d. 1351) later Reisho-in (霊照院), Nijō Tamemichi's daughter
 * Imperial Prince Hōnin (法仁法親王, 1325–1352) – priest in Ninna-ji
 * Prince Kaneyoshi (also Kanenaga) (懐良親王, 1326–1383) – Seisei Taishōgun (征西大将軍) 1336–?
 * princess

 * Court lady: Ichijō no Tsubone (一条局) later Yūgimon'in (遊義門院), Saionji Sanetoshi's daughter
 * Imperial Prince Tokiyoshi (also Yoyoshi) (世良親王) (c. 1306–8 – 1330)
 * Imperial Prince Jōson (静尊法親王) (Imperial Prince Keison, 恵尊法親王) – priest in Shōgoin (聖護院)
 * Imperial Princess Kinshi (欣子内親王) – nun in Imabayashi

 * Court lady: Shōnagon no Naishi (少納言内侍), Shijō Takasuke's daughter
 * Sonshin (尊真) – priest

 * Nyōgo: Dainagon-no-tsubone (大納言局), Ogimachi Saneakira's daughter
 * Imperial Princess Naoko (瑜子内親王)

 * Nyōgo: Saemon-no-kami-no-tsubone (左衛門督局), Nijō Tametada's daughter
 * Nun in Imabayashi

 * Court lady: Gon-no-Chūnagon no Tsubone (権中納言局), Sanjō Kinyasu's daughter
 * Imperial Princess Sadako (貞子内親王)

 * Nyōgo: Yoshida Sadafusa's daughter

 * Nyōgo: Bōmon-no-tsubone (坊門局), Bomon Kiyotada's daughter
 * Princess (Yōdō?)

 * Nyōgo: Horikawa Mototomo's daughter
 * Princess

 * Nyōgo: Minamoto-no-Yasuko (源康子) also Asukai-no-tsubone (飛鳥井局) later Enseimon'in Harima (延政門院播磨), Minamoto-no-Yasutoki's daughter

 * Nyōgo: Wakamizu-no-tsubone (若水局), Minamoto-no-Yasutoki's daughter

 * Nyōgo: Horiguchi Sadayoshi's daughter
 * daughter married Yoshimizu Munemasa

 * Court lady: Konoe no Tsubone (近衛局) later Shōkunmon'in (昭訓門院)
 * Prince Tomoyoshi (知良王)

Go-Daigo had some other princesses from some court ladies.
 * (unknown women)
 * Yōdō (d. 1398) – 5th Head Nun of Tōkei-ji
 * Rokujō Arifusa's wife
 * Ryusen Ryosai (竜泉令淬, d.1366)
 * Kenkō (賢光)

Kugyō
Kugyō (公卿) is a collective term for the very few most powerful men attached to the court of the Emperor of Japan in pre-Meiji eras. Even during those years in which the court's actual influence outside the palace walls was minimal, the hierarchic organization persisted.

In general, this elite group included only three to four men at a time. These were hereditary courtiers whose experience and background would have brought them to the pinnacle of a life's career. During Go-Daigo's reign, this apex of the Daijō-kan included:
 * Kampaku, Nijō Michihira, 1316–1318
 * Kampaku, Ichijō Uchitsune, 1318–1323
 * Kampaku, Kujō Fusazane, 1323–1324
 * Kampaku, Takatsukasa Fuyuhira, 1324–1327
 * Kampaku, Nijō Michihira, 1327–1330
 * Kampaku, Konoe Tsunetada, 1330
 * Kampaku, Takatsukasa Fuyunori, 1330–1333
 * Sadaijin
 * Udaijin
 * Naidaijin
 * Dainagon

Eras of Go-Daigo's reign
The years of Go-Daigo's reign are more specifically identified by more than one era name or nengō. Emperor Go-Daigo's eight era name changes are mirrored in number only in the reign of Emperor Go-Hanazono, who also reigned through eight era name changes.

 * Pre-Nanboku-chō court

 * Bunpō               (1317–1319)
 * Gen'ō         (1319–1321)
 * Genkō       (1321–1324)
 * Shōchū (1324–1326)
 * Karyaku             (1326–1329)
 * Gentoku             (1329–1331)
 * Genkō         (1331–1334)
 * Kenmu               (1334–1336)

 * Nanboku-chō southern court

 * Eras as reckoned by legitimate sovereign's Court (as determined by Meiji rescript)
 * Engen               (1336–1340)

 * Nanboku-chō northern Court

 * Eras as reckoned by pretender sovereign's Court (as determined by Meiji rescript)
 * Shōkei       (1332–1338)
 * Ryakuō       (1338–1342)

In popular culture
Emperor Go-Daigo appears in the alternate history novel Romanitas by Sophia McDougall.

title: Emperor Go-Daigo


text:
Emperor Chōkei

Emperor Chōkei (長慶天皇) was the 98th emperor of Japan, according to the traditional order of succession. He reigned from 1368 through 1383. His personal name was Yutanari (寛成) and his regal name roughly translates to "Long Celebration".

Genealogy
His father was Emperor Go-Murakami and his mother may have been Kaki Mon'in.

 * Empress (chūgū): Saionji Kinshige's daughter
 * Gyōgo (行悟; 1377–1406)
 * Nyōgo: Noriko (father and family unknown)
 * First son: Imperial Prince Tokiyasu (世泰親王)
 * Unknown
 * Kaimonji Kosho (海門承朝; 1374–1443)
 * Sonsei (尊聖; 1376–1432),
 * son: founder of Tamagawa family (玉川宮)

Biography
On March 29, 1368 (Shōhei 23, 11th day of the 3rd month), following the death of Emperor Murakami II, he was enthroned in the house of the Chief Priest at the Sumiyoshi Grand Shrine in Sumiyoshi, Osaka, where the Southern Court had made its capital. However, because the Southern Court's influence was declining, the enthronement remained in some doubt until the Taishō period. In 1926, the enthronement was officially recognized and inserted into the Imperial Line.

Emperor Chōkei insisted throughout his reign on fighting the Northern Dynasty, but it was already too late. In 1383 or 1384, he abdicated to Emperor Go-Kameyama, who supported the peace faction.

After the reunification of the rival courts, he went into retirement and eventually returned to Yoshino where he died on August 27, 1394. The kami of Emperor Chōkei is venerated at Shishō jinja in Totsugawa, Yamato province.

Kugyō
Kugyō (公卿) is a collective term for the very few most powerful men attached to the court of the Emperor of Japan in pre-Meiji eras. Even during those years in which the court's actual influence outside the palace walls was minimal, the hierarchic organization persisted.

In general, this elite group included only three to four men at a time. These were hereditary courtiers whose experience and background would have brought them to the pinnacle of a life's career. During Chōkei's reign, this apex of the Daijō-kan included:
 * Sadaijin
 * Udaijin
 * Nadaijin
 * Dainagon

Eras of Chōkei's reign
The years of Chōkei's reign are more specifically identified by more than one era name or nengō.

 * Nanboku-chō southern court

 * Eras as reckoned by legitimate Court (as determined by Meiji rescript)
 * Shōhei   (1346–1370)
 * Kentoku         (1370–1372)
 * Bunchū   (1372–1375)
 * Tenju           (1375–1381)
 * Kōwa       (1381–1384)

 * Nanboku-chō northern court

 * Eras as reckoned by pretender Court (as determined by Meiji rescript)
 * Ōan         (1368–1375)
 * Eiwa            (1375–1379)
 * Kōryaku (1379–1381)
 * Eitoku          (1381–1384)

title: Emperor Chōkei