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== '''[[Four color theorem]]''' ==
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The '''four color theorem''', sometimes known as the '''four color map theorem''' or '''Guthrie's problem''', is a [[problem]] in [[cartography]] and [[mathematics]]. It had been noticed that it only required four [[color]]s to fill in the different [[contiguous]] [[shape]]s on a [[map]] of regions or [[country|countries]] or [[province]]s in a flat surface known as a [[plane (geometry)|plane]] such that no two [[adjacent]] regions with a common [[boundary]] had the same color. But proving this [[proposition]] proved extraordinarily difficult, and it required [[analysis]] by high-powered [[computer]]s before the problem could be solved. In mathematical history, there had been numerous attempts to prove the supposition, but these so-called [[proof (mathematics)|proofs]] turned out to be flawed. There had been accepted proofs that a map could be colored in using more colors than four, such as six or five, but proving that only four colors were required was not done successfully until 1976 by mathematicians Appel and Haken, although some mathematicians do not accept it since parts of the proof consisted of an analysis of [[discrete]] cases by a computer.<ref name=Math1>{{cite news
==Footnotes==
|title= Four-Color Theorem
|publisher= Wolfram MathWorld
|quote= Six colors can be proven to suffice for the g=0 case, and this number can easily be reduced to five, but reducing the number of colors all the way to four proved very difficult. This result was finally obtained by Appel and Haken (1977), who constructed a computer-assisted proof that four colors were sufficient. However, because part of the proof consisted of an exhaustive analysis of many discrete cases by a computer, some mathematicians do not accept it. However, no flaws have yet been found, so the proof appears valid. A shorter, independent proof was constructed by Robertson et al. (1996; Thomas 1998).
|date= 2010-04-18
|url= http://mathworld.wolfram.com/Four-ColorTheorem.html
|accessdate= 2010-04-18
}}</ref> But, at the present time, the proof remains viable, and was confirmed independently by Robertson and Thomas in association with other mathematicians in 1996&ndash;1998 who have offered a simpler version of the proof, but it is still complex, even for advanced mathematicians.<ref name=Math1/> It is possible that an even simpler, more elegant, proof will someday be discovered, but many mathematicians think that a shorter, more elegant and simple proof is impossible.
 
''[[Four color theorem|.... (read more)]]''
 
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Latest revision as of 10:19, 11 September 2020

Nuclear weapons proliferation is one of the four big issues that have held back worldwide deployment of peaceful nuclear power. This article will address the proliferation questions raised in Nuclear power reconsidered.

As of 2022, countries with nuclear weapons have followed one or both of two paths in producing fissile materials for nuclear weapons: enrichment of uranium to very high fractions of U-235, or extraction of fissile plutonium (Pu-239) from irradiated uranium nuclear reactor fuel. The US forged the way on both paths during its World War II Manhattan Project. The fundamental aspects of both paths are well understood, but both are technically challenging. Even relatively poor countries can be successful if they have sufficient motivation, financial investment, and, in some cases, direct or illicit assistance from more technologically advanced countries.

The International Non-proliferation Regime

The International Atomic Energy Agency (IAEA) has a vigorous program to prevent additional countries from acquiring nuclear weapons. The Treaty on the Non-Proliferation of Nuclear Weapons (NPT) is the cornerstone arrangement under which strategic rivals can trust, by independent international verification, that their rivals are not developing a nuclear weapons threat. The large expense of weapons programs makes it very unlikely that a country would start its own nuclear weapons program, if it knows that its rivals are not so engaged. With some notable and worrying exceptions, this program has been largely successful.

Paths to the Bomb

It is frequently claimed that building a civil nuclear power program adds to the weapons proliferation risk. There is an overlap in the two distinct technologies, after all. To build a bomb, one needs Highly Enriched Uranium (HEU) or weapons-grade plutonium (Pu-239). Existing reactors running on Low Enriched Uranium (LEU, under 5% U-235) or advanced reactors running on High Assay LEU (HALEU,up to 20% U-235) use the same technology that can enrich uranium to very high levels, but configured differently. Enrichment levels and centrifuge configurations can be monitored using remote cameras, on-site inspections, and installed instrumentation -- hence the value of international inspections by the IAEA. Using commercial power reactors as a weapons plutonium source is an extremely ineffective, slow, expensive, and easily detectable way to produce Pu. Besides the nuclear physics issues, refueling pressurized water reactors is both time-consuming and obvious to outside observers. That is why the US and other countries developed specialized Pu production reactors and/or uranium enrichment to produce fissile cores for nuclear weapons.

Future Threats and Barriers

Minimizing the risk of future proliferation in states that want to buy nuclear reactors or fuel might require one or more barriers:
1) Insisting on full transparency for all nuclear activities in buyer states, including monitoring and inspections by the International Atomic Energy Agency (IAEA).
2) Limiting fuel processing to just a few supplier states that already have weapons or are approved by the IAEA.
3) Ensuring that fuel at any stage after initial fabrication has an isotopic composition unsuitable for weapons. "Spiking" the initial fuel with non-fissile isotopes, if necessary.
4) Limiting the types of reactors deployed to buyer states. In general, breeders are less secure than burners. Sealed reactor modules are more secure than reactors with on-site fuel processing.
5) Providing incentives and assurances for buyer states to go along with all of the above.
6) Application of diplomatic pressure, sanctions, and other economic measures to non-compliant states.
7) Agreement that any reactor declared rogue by the IAEA will be "fair game" for any state feeling threatened.

Footnotes