User:Ancheta Wis/sandbox

Thank you for your suggestions for simplifying the problem; as I edit, please fell free to jump in; here is my plan of attack, so far:

reduce RJ to an efn in Planck's law; leave Planck's law article alone, including history; I'm depending on its previous editors as much as possible
I plan to lean heavily on Planck 1914 (internet archive), as my copy of Planck 1925 (Dover) lives in some box in the basement (I've been working from visual memory)
use content of Wien approximation as the skeleton of the efn in #1, as it has a nice approach for 'scale and scope' of the efn. It uses natural units to emphasize what was known at the time, as well as the experimentally-based constants
Both tails of Planck's law, R-J equation and Wien approximation will be treated in separate efns.

$B_{\lambda }(T)={\frac {2hc^{2}}{\lambda ^{5}}}{\frac {1}{e^{\frac {hc}{\lambda kT}}-1}}$

^[a] ^[b] ^[c] ^[d]

^ Planck's law Bnu the spectral radiance of a body for frequency $ν$ at absolute temperature $T$ is given by $B_{\nu }(\nu ,T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{\exp \left({\frac {h\nu }{k_{\mathrm {B} }T}}\right)-1}},$ where $k B$ is the Boltzmann constant, $h$ is the Planck constant, and $c$ is the speed of light in the medium, whether material or vacuum. The SI units of $B ν$ are W·sr⁻¹·m⁻²·Hz⁻¹.^[1]^[2]^[3]
^ RJ $B_{\lambda }(T)={\frac {2hc^{2}}{\lambda ^{5}}}~{\frac {1}{e^{\frac {hc}{\lambda k_{\mathrm {B} }T}}-1}},$ where h is the Planck constant and $k B$ the Boltzmann constant. The Planck's law does not suffer from an ultraviolet catastrophe, and agrees well with the experimental data, but its full significance (which ultimately led to quantum theory) was only appreciated several years later. Since, $e^{x}=1+x+{x^{2} \over 2!}+{x^{3} \over 3!}+\cdots .$ then in the limit of high temperatures or long wavelengths, the term in the exponential becomes small, and the exponential is well approximated with the Taylor polynomial's first-order term, $e^{\frac {hc}{\lambda k_{\mathrm {B} }T}}\approx 1+{\frac {hc}{\lambda k_{\mathrm {B} }T}}.$ So, ${\frac {1}{e^{\frac {hc}{\lambda k_{\mathrm {B} }T}}-1}}\approx {\frac {1}{\frac {hc}{\lambda k_{\mathrm {B} }T}}}={\frac {\lambda k_{\mathrm {B} }T}{hc}}.$
^ Wien approximation-- Planck's law may be given as^[4] $I(\nu ,T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{\frac {h\nu }{kT}}-1}}$ The Wien approximation may be derived from Planck's law by assuming $h\nu \gg kT$ . When this is true, then^[4] ${\frac {1}{e^{\frac {h\nu }{kT}}-1}}\approx e^{-{\frac {h\nu }{kT}}}$ and so Planck's law approximately equals the Wien approximation at high frequencies.
^ RJ Comparison to Planck's law $B_{\lambda }(T)={\frac {2ck_{\mathrm {B} }T}{\lambda ^{4}}},$

History of scientific method#Epicurus

In his work Kαvώv ('canon', a straight edge or ruler, thus any type of measure or standard, referred to as 'canonic'), Epicurus laid out his first rule for inquiry in physics: 'that the first concepts be seen,^[5]^: p.20 and that they not require demonstration '.^[5]^{: pp.35–47}

His second rule for inquiry was that prior to an investigation, we are to have self-evident concepts,^[5]^{: pp.61–80} so that we might infer [ἔχωμεν οἷς σημειωσόμεθα] both what is expected [τò προσμένον], and also what is non-apparent [τò ἄδηλον].^[5]^{: pp.83–103}

Epicurus applies his method of inference (the use of observations as signs, Asmis' summary, p. 333: the method of using the phenomena as signs (σημεῖα) of what is unobserved)^[5]^{: pp.175–196} immediately to the atomic theory of Democritus. In Aristotle's Prior Analytics, Aristotle himself employs the use of signs.^[5]^{: pp.212–224}^[6] But Epicurus presented his 'canonic' as rival to Aristotle's logic.^[5]^{: pp.19–34} See: Lucretius (c. 99 BCE – c. 55 BCE) De rerum natura (On the nature of things) a didactic poem explaining Epicurus' philosophy and physics.

Asmis, Elizabeth (January 1984), Epicurus' Scientific method, vol. 42, Cornell University Press, p. 386, ISBN 978-0-8014-6682-3, JSTOR 10.7591/j.cttq45z9

paraphrasing Asmis. How do 'its concepts correspond to the words used to state the problem, in order to have standards by which to judge the problem?', as Asmis puts it (pages 10-11)

The way I read the article, Rust is a vehicle for getting beyond Haskell notation, in the same vein as the informal tone. The Rust syntax is a way of rewriting a functional programming concept using another notation. Monad (functional programming)#Sample adjunct supposition is another vehicle, for illustrating adjunction using bind or >>=. That way the article can illustrate the concatenation of parameters, as arguments in a record tuple. This minimizes boilerplate, and also encourages the developer to use more function composition rather than to hard-code special cases.

https://web.archive.org/web/20140125154343/http://www.mda.mil/system/aegis_bmd.html https://news.usni.org/2022/02/02/u-s-offered-russians-aegis-ashore-inspections-to-ease-ukraine-tensions-more-american-troops-headed-to-europe https://getpocket.com/read/3134195958 De-escalation https://www.defensenews.com/industry/2022/12/02/sarcos-defense-to-test-robotic-arm-for-us-army-in-1m-deal/ https://www.airandspaceforces.com/b-21-to-be-capable-of-holding-at-risk-any-target-on-the-face-of-the-earth/ https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN31331-AR_71-9-000-WEB-1.pdf https://katu.com/news/nation-world/defense-secretary-says-us-in-pivotal-point-with-china-ukraine-russia-vladimir-putin-xi-jinping-authoritarian-values-b-21-raider-nuclear-weapons-hegemony-ronald-reagan-europe-icbms By 2022 the 25th Secretary of the Army, Christine Wormuth was able to announce the top six areas for the Army of 2030:^[7] 1) improved Intelligence, surveillance, and reconnaissance (ISR); 2) "Coordination at greater speed";^{[Note 1]} 3) "Win the Fires fight"; 4) §concealment^[8] via improved mobility and reduced signature; 5) "talk often and quickly";^[9]^{[Note 2]} and 6) contested logistics.^[7] ^[10] ^[11] ^[12] ^[13] ^[14] ^[15] ^[16] ^[17] ^[18] ^[19] ^[20] ^{[Note 2]} ^{[Note 1]} ^[21]^[22]

^[a]

In order for IBCS to track a target, it has to build a software entry showing the candidate target's trajectory over the 15-30 minute flight times during mid-course, to record its track of the target. When C2BMC has acquired the target, C2BMC knows the trajectory. In order to hand over the software entry to IBCS, C2BMC's history of the tracked object has to be reformatted to the IBCS tracking format. It is not clear that the two systems (C2BMC/IBCS) are compatible. If they were, the vendors would have said this already. That is the citation I am seeking. Freedberg's citation says this compatibility exists, only "up to a point".^[23] To be specific, let's assume the software entry is a series of XML records. That XML would have to be converted between the two systems. JADC2 would have define the standards for this capability; but that standard has to be agreed upon jointly by the DoD services, and ideally shared with the allies and partners. There is a layer of complexity above this; if I were the vendor, I would encrypt the records; additionally, an adversary could jam the transmissions.

Remember that the design follows that of the Molten-Salt Reactor Experiment which ran for 4 years. The heat remaining in the largely Thorium mixture would need to decay; the molten fuelsalt will not support fission without its being in the graphite moderator; the U233, U235, etc. are needed for the mixture to be fissile. The Thorcon proposal includes a phase where one Can with fuelsalt gets exercised in a series of tests of the design. The regulators will have to approve those tests, before it is actuallly producing electric power.

Faggin et al (1996) p.12 has the timing diagram, a chip-level behavioral diagram, showing which chips activate during operation. Busicom understood their calculator application to this level of detail, as they had already implemented an RTL version (not the PMOS version which Intel was to provide). Busicom had provided timing diagrams to Intel previously (1969); so you can imagine Shima's shock in 1970 when he arrived, to see that Intel had not yet followed through, because the project had not yet been staffed, until Faggin's arrival. --Ancheta Wis (talk | contribs) 10:14, 12 January 2022 (UTC)

There is a misstatement in the attempted section on nonlinear MHD: Maxwell's equations are already partial differential equations, and yes they are linear, so the sentences in this section about understandability do not follow. Can we please revert this section and take it to this page? For starters, the Navier-Stokes equations need to be decoupled from the discussion until any phenomenological aspects of MHD are disentangled from it, such as the speed of magnetic reconnection (not currently explained from known models). Otherwise we are starting from confusion.

^[24]^[25]

On the Foundations of National Resistance is a law of Ukraine (Bill 5557) Про основи національного опору, which came into force 1 January 2022.^[26] It was passed by the Verkhovna Rada on 16 July 2021, and signed by President Volodymyr Zelenskyy on 29 July 2021.

Provisions[edit]

National resistance[edit]

"The basis for preparing Ukrainian citizens for national resistance is their general military training, which is organized on a territorial-zonal basis, based on high motivational attractiveness and consistent with the process of transforming the conscription system in accordance with the principles and best practices of NATO member states".^[26]^[27]

Territorial defense[edit]

See Territorial Defense Forces (Ukraine)

Ukraine's territorial defense consists of military, civilian and military-civilian components.^[28] ^[29]

International order

liberal international order

^[30]

Notes[edit]

^
In standoff, adversaries attempt to project protected areas against each other. Within these protected areas, friends are deemed safe, but foes are endangered by the capabilities of the allies arrayed against them. Outside these projected areas, adversaries compete for control, by projecting their power.

^ Planck 1914, pp. 6, 168
^ Chandrasekhar 1960, p. 8
^ Rybicki & Lightman 1979, p. 22
^ ^a ^b Cite error: The named reference rybickilightman1979 was invoked but never defined (see the help page).
^ ^a ^b ^c ^d ^e ^f ^g Asmis 1984
^ Madden, Edward H. (Apr., 1957) "Aristotle's Treatment of Probability and Signs" Philosophy of Science 24(2), pp. 167-172 via JSTOR discusses Aristotle's enthymeme (70a, 5ff.) in Prior Analytics
^ ^a ^b Andrew Eversden (15 Sep 2022) Wormuth: Here are the 6 areas the Army must be prepared for in 2030
^ Patrick Tucker (14 Sep 2022) Ukraine War Offers Clues to Future War, Joint Chiefs Chairman Says
^ Cite error: The named reference goldfeinRaymond was invoked but never defined (see the help page).
^ U.S. Army (5 October 2022) Army of 2030
^ U.S. Army (10 October 2022) Building ARMY 2030
^ Matthew Beinart (17 May 2022) No Plans To Downgrade Army Futures Command Following Recent Memo, Wormuth Says
^ Jen Judson (10 Oct 2022) Project Convergence exercise has new gateway to test emerging tech
^ Jason Cutshaw (SMDC/ARSTRAT)(23 January 2013 Incoming Army G-3/5/7 learns how SMDC brings space to Soldiers photo: John London, Technical Center, U.S. Army Space and Missile Defense Command/Army Forces Strategic Command, explains the SMDC-One nanosatellite to Maj. Gen. (Promotable) James L. Huggins Jr.
^ AUSA (10 Oct 2022) Opening Ceremony SecArmy Christine Wormuth, Army of 2030 6 areas- min 42:40; EUCOM minute 20:30 ; INDOPACOM ; AFC new focus min 44:55; organizational changes ; IBCS ;
^ Headquarters, Department of the Army (11 Oct 2022) FM 3-0 280 pages; MDO happens now.
^ AUSA (10 Oct 2022) AUSA Contemporary Military Forum: Army 2030 - Preparing Today for Tomorrow’s Fight
^ Randi Stenson, Mission Command Center of Excellence (10 October 2022) U.S. Army Training and Doctrine Command announces release of new Army capstone operations manual FM 3-0, 280 pages
^ Army War College (2019-2020) How the Army Runs HTAR 560 pages
^ [ ( ]
^ Cite error: The named reference csaPaper1 was invoked but never defined (see the help page).
^ Cite error: The named reference csa2 was invoked but never defined (see the help page).
^ Cite error: The named reference joint_ibcs was invoked but never defined (see the help page).
^ John Vandiver (15 Mar 2022) US and NATO allies prepare ideas for strengthening defenses in countries closer to Russia
^ Luke Magee (15 Mar 2022) Germany will buy US-made F-35 fighter jets as it ramps up military spending after Russia's Ukraine invasion
^ ^a ^b Edna Breaking News (1 January 2022) The law of Ukraine on the foundations of national resistance has come into force
^ Brian S. Petit (18 Feb 2022) CAN UKRAINIAN RESISTANCE FOIL A RUSSIAN VICTORY?
^ Ukrinform (28 Dec 2021) Ukraine - Territorial defense forces being created by military, not local authorities - minister
^ Oleksandr Mazur (20 Jan 2022) Odesa City Council makes efforts to strengthen Ukraine's defense
^ FRONTLINE (Mar 15, 2022) Putin's Road to War (full documentary) 53:18

Cite error: There are <ref group=Note> tags on this page, but the references will not show without a {{reflist|group=Note}} template (see the help page).

[Bnu-4] Planck's law Bnu the spectral radiance of a body for frequency $ν$ at absolute temperature $T$ is given by $B_{\nu }(\nu ,T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{\exp \left({\frac {h\nu }{k_{\mathrm {B} }T}}\right)-1}},$ where $k B$ is the Boltzmann constant, $h$ is the Planck constant, and $c$ is the speed of light in the medium, whether material or vacuum. The SI units of $B ν$ are W·sr⁻¹·m⁻²·Hz⁻¹.^[1]^[2]^[3]

[Blam-5] RJ $B_{\lambda }(T)={\frac {2hc^{2}}{\lambda ^{5}}}~{\frac {1}{e^{\frac {hc}{\lambda k_{\mathrm {B} }T}}-1}},$ where h is the Planck constant and $k B$ the Boltzmann constant. The Planck's law does not suffer from an ultraviolet catastrophe, and agrees well with the experimental data, but its full significance (which ultimately led to quantum theory) was only appreciated several years later. Since, $e^{x}=1+x+{x^{2} \over 2!}+{x^{3} \over 3!}+\cdots .$ then in the limit of high temperatures or long wavelengths, the term in the exponential becomes small, and the exponential is well approximated with the Taylor polynomial's first-order term, $e^{\frac {hc}{\lambda k_{\mathrm {B} }T}}\approx 1+{\frac {hc}{\lambda k_{\mathrm {B} }T}}.$ So, ${\frac {1}{e^{\frac {hc}{\lambda k_{\mathrm {B} }T}}-1}}\approx {\frac {1}{\frac {hc}{\lambda k_{\mathrm {B} }T}}}={\frac {\lambda k_{\mathrm {B} }T}{hc}}.$

[Wien-7] Wien approximation-- Planck's law may be given as^[4] $I(\nu ,T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{\frac {h\nu }{kT}}-1}}$ The Wien approximation may be derived from Planck's law by assuming $h\nu \gg kT$ . When this is true, then^[4] ${\frac {1}{e^{\frac {h\nu }{kT}}-1}}\approx e^{-{\frac {h\nu }{kT}}}$ and so Planck's law approximately equals the Wien approximation at high frequencies.

[R-J-8] RJ Comparison to Planck's law $B_{\lambda }(T)={\frac {2ck_{\mathrm {B} }T}{\lambda ^{4}}},$

[standoffDomes-29] 
In standoff, adversaries attempt to project protected areas against each other. Within these protected areas, friends are deemed safe, but foes are endangered by the capabilities of the allies arrayed against them. Outside these projected areas, adversaries compete for control, by projecting their power.

[Planck_1914_6_168-1] Planck 1914, pp. 6, 168

[Chan8-2] Chandrasekhar 1960, p. 8

[Rybicki_1979_22-3] Rybicki & Lightman 1979, p. 22

[rybickilightman1979-6] Cite error: The named reference rybickilightman1979 was invoked but never defined (see the help page).

[Asmis1984-9] ^ ^a ^b ^c ^d ^e ^f ^g Asmis 1984

[10] Madden, Edward H. (Apr., 1957) "Aristotle's Treatment of Probability and Signs" Philosophy of Science 24(2), pp. 167-172 via JSTOR discusses Aristotle's enthymeme (70a, 5ff.) in Prior Analytics

[topSixIn2030-11] Andrew Eversden (15 Sep 2022) Wormuth: Here are the 6 areas the Army must be prepared for in 2030

[milleyOnUkr-13] Patrick Tucker (14 Sep 2022) Ukraine War Offers Clues to Future War, Joint Chiefs Chairman Says

[goldfeinRaymond-14] Cite error: The named reference goldfeinRaymond was invoked but never defined (see the help page).

[2030transform-16] U.S. Army (5 October 2022) Army of 2030

[1pInfographic-17] U.S. Army (10 October 2022) Building ARMY 2030

[afc2030Beyond-18] Matthew Beinart (17 May 2022) No Plans To Downgrade Army Futures Command Following Recent Memo, Wormuth Says

[pc22Gateway-19] Jen Judson (10 Oct 2022) Project Convergence exercise has new gateway to test emerging tech

[smdcNanosat-20] Jason Cutshaw (SMDC/ARSTRAT)(23 January 2013 Incoming Army G-3/5/7 learns how SMDC brings space to Soldiers photo: John London, Technical Center, U.S. Army Space and Missile Defense Command/Army Forces Strategic Command, explains the SMDC-One nanosatellite to Maj. Gen. (Promotable) James L. Huggins Jr.

[wormuthAusa2022-21] AUSA (10 Oct 2022) Opening Ceremony SecArmy Christine Wormuth, Army of 2030 6 areas- min 42:40; EUCOM minute 20:30 ; INDOPACOM ; AFC new focus min 44:55; organizational changes ; IBCS ;

[fm30-22] Headquarters, Department of the Army (11 Oct 2022) FM 3-0 280 pages; MDO happens now.

[1-23] AUSA (10 Oct 2022) AUSA Contemporary Military Forum: Army 2030 - Preparing Today for Tomorrow’s Fight

[2-24] Randi Stenson, Mission Command Center of Excellence (10 October 2022) U.S. Army Training and Doctrine Command announces release of new Army capstone operations manual FM 3-0, 280 pages

[3-25] Army War College (2019-2020) How the Army Runs HTAR 560 pages

[4-26] [ ( ]

[csaPaper1-27] Cite error: The named reference csaPaper1 was invoked but never defined (see the help page).

[csa2-28] Cite error: The named reference csa2 was invoked but never defined (see the help page).

[joint_ibcs-30] Cite error: The named reference joint_ibcs was invoked but never defined (see the help page).

[vandiver-31] John Vandiver (15 Mar 2022) US and NATO allies prepare ideas for strengthening defenses in countries closer to Russia

[magee-32] Luke Magee (15 Mar 2022) Germany will buy US-made F-35 fighter jets as it ramps up military spending after Russia's Ukraine invasion

[edna-33] Edna Breaking News (1 January 2022) The law of Ukraine on the foundations of national resistance has come into force

[petit-34] Brian S. Petit (18 Feb 2022) CAN UKRAINIAN RESISTANCE FOIL A RUSSIAN VICTORY?

[menafn-35] Ukrinform (28 Dec 2021) Ukraine - Territorial defense forces being created by military, not local authorities - minister

[mazur-36] Oleksandr Mazur (20 Jan 2022) Odesa City Council makes efforts to strengthen Ukraine's defense

[5-37] FRONTLINE (Mar 15, 2022) Putin's Road to War (full documentary) 53:18

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Provisions[edit]

National resistance[edit]

Territorial defense[edit]

See also[edit]

Notes[edit]