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William Nordhaus

William Nordhaus
Nordhaus in Stockholm, December 2018
Born
William Dawbney Nordhaus

(1941-05-31) May 31, 1941 (age 83)[2]
EducationYale University (BA, MA)
Sciences Po
Massachusetts Institute of Technology (PhD)
AwardsBBVA Foundation Frontiers of Knowledge Award (2017)
Nobel Memorial Prize in Economic Sciences (2018)
Scientific career
FieldsEnvironmental economics
InstitutionsYale University
ThesisA theory of endogenous technological change (1967)
Doctoral advisorRobert Solow[1]

William Dawbney Nordhaus (born May 31, 1941) is an American economist. He was a Sterling Professor of Economics at Yale University, best known for his work in economic modeling and climate change, and a co-recipient of the 2018 Nobel Memorial Prize in Economic Sciences.[3] Nordhaus received the prize "for integrating climate change into long-run macroeconomic analysis".[4]

Education and career

Nordhaus was born in Albuquerque, New Mexico, the son of Virginia (Riggs) and Robert J. Nordhaus,[5] who co-founded the Sandia Peak Tramway.[6][7] Robert J. Nordhaus was from a German Jewish family – his father Max Nordhaus (1865–1936) had immigrated from Paderborn in 1883, and became a manager of The Charles Ilfeld Company branch in Albuquerque.[8][9]

Nordhaus graduated from Phillips Academy in Andover and subsequently received his BA and MA from Yale in 1963 and 1972, respectively, where he was a member of Skull and Bones.[10] He also holds a Certificate from the Institut d'Etudes Politiques (1962) and a PhD from MIT (1967).[11][10][12] He was a Visiting Fellow of Clare Hall, Cambridge in 1970–1971. He has been a member of the faculty at Yale since 1967, in both the Economics department and the School of the Environment.[13][12] Nordhaus also served as its Provost from 1986–1988 and its Vice President for Finance and Administration from 1992–1993. He has been on the Brookings Panel on Economic Activity since 1972. During the Carter administration, from 1977–1979, Nordhaus was a member of the Council of Economic Advisers.[12]

Nordhaus was elected to the American Philosophical Society in 2013.[14] He served as the chairman of the board of directors of the Federal Reserve Bank of Boston between 2014 and 2015.[15]

Nordhaus lives in New Haven, Connecticut, with his wife, Barbara, a social worker recently retired from the Yale Child Study Center.[12]

Contributions to economics and the study of climate change

Nordhaus is the author or editor of over 20 books. One of his early works is the wildly popular introductory textbook, Economics, co-authored with Paul Samuelson. Originally a project of Samuelson's alone, Nordhaus worked on the textbook from the 12th edition until the 19th (the most recent edition), starting in 1985.[16][17] The book was first published in 1948 and has appeared in nineteen different editions and seventeen different languages since then. It was a best-selling economics textbook for decades and is still extremely popular today. Economics has been called a “canonical textbook”, and the development of mainstream economic thought has been traced by comparing the nineteen editions over the 1948–2010 period.[18]

Nordhaus has also written several books on global warming and climate change, one of his primary areas of research. Those books include, Managing the Global Commons: The Economics of Climate Change (1994), which won the 2006 award for "Publication of Enduring Quality" from the Association of Environmental and Resource Economists. Other notable books include, Warming the World: Economic Models of Global Warming (2000), co-authored with Joseph Boyer; The Climate Casino: Risk, Uncertainty, and Economics for a Warming World;[19] and The Spirit of Green: The Economics of Collisions and Contagions in a Crowded World (2021).

In 1972, Nordhaus, along with fellow Yale economics professor James Tobin, published, "Is Growth Obsolete?",[20] an article that introduced the Measure of Economic Welfare (MEW), or Index of Sustainable Economic Welfare (ISEW), as the first attempt to develop environmental accounting.

Nordhaus is also known for his critique of current measures of national income. For example, in a 1996 article, he wrote,[21]

If we are to obtain accurate estimates of the growth of real incomes over the last century, we must somehow construct price indexes that account for the vast changes in the quality and range of goods and services that we consume, that somehow compare the services of horse with automobile, of Pony Express with facsimile machine, of carbon paper with photocopier, of dark and lonely nights with nights spent watching television, and of brain surgery with magnetic resonance imaging.

Economist Filip Palda summarizes the importance of Nordhaus's insight when he writes,[22]

The practical lesson to be drawn from this fascinating study of lighting is that the way we measure the consumer price index is severely flawed. Instead of putting goods and their prices directly into the index we should reduce all goods to their constituent characteristics. Then we should evaluate how these goods can best be combined to minimize the cost of consuming these characteristics. Such an approach would allow us to include new goods in the consumer price index without worrying about whether the index of today is comparable to that of ten years ago when the good did not exist. Such an approach would also allow governments to more precisely calculate the rate at which welfare and other forms of aid should be increased. At present, such calculations tend to overestimate the cost of living because they do not take into account the manner in which increases in quality reduce the monetary cost of maintaining a certain standard of living.

Contributions on economics of climate change

Nordhaus has written on the economics of climate change. He is the developer of the DICE and RICE models, integrated assessment models of the interplay between economics, energy use, and climate change. In Reflections on the Economics of Climate Change (1993), he writes,[23]

Mankind is playing dice with the natural environment through a multitude of interventions–injecting into the atmosphere trace gases like the greenhouse gases or ozone-depleting chemicals, engineering massive land-use changes such as deforestation, depleting multitudes of species in their natural habitats even while creating transgenic ones in the laboratory, and accumulating sufficient nuclear weapons to destroy human civilizations.

According to the climate change models Nordhaus has developed, sectors of the economy that depend heavily on unmanaged ecosystems–that is, are heavily dependent upon naturally occurring rainfall, runoff, or temperatures–will be most sensitive to climate change, generally. Agriculture, forestry, outdoor recreation, and coastal activities fall in this category.[23] Nordhaus takes seriously the potentially catastrophic impacts of climate change.[24]

In 2007, Nordhaus, who has done several studies on the economics of global warming, criticized the Stern Review for its use of a low discount rate, writing,[25]

The Review's unambiguous conclusions about the need for extreme immediate action will not survive the substitution of discounting assumptions that are consistent with today's market place. So the central questions about global-warming policy–how much, how fast, and how costly–remain open. The Review informs but does not answer these fundamental questions.

In 2013, Nordhaus chaired a committee of the National Research Council that produced a report discounting the impact of fossil fuel subsidies on greenhouse gas emissions.[26]

In 2015, Nordhaus published an article promulgating his concept of a "climate club".[27] This publication has become widely debated and cited within and outside economics.[28] He conceptualizes this as a coalition of the willing among countries that wish to adopt more stringent climate mitigation policies. The climate club introduces carbon pricing among the club's member states and levies a fee on all imports of goods from countries that are outside the club and have not introduced similar carbon pricing.[29] It has been argued that the carbon border adjustment mechanism (CBAM) of the European Union could become a climate club.[30][31][32]

In a January 2020 interview with Neue Zürcher Zeitung, Nordhaus claimed that achieving the 2 °C goal of the Paris agreement was "impossible", stating that, "even if we make the fastest possible turn towards zero emissions, CO2 will continue to accumulate in the atmosphere, because we cannot simply shut down our economy". He asserted that he was not alone in making this assessment, claiming that half of the simulations arrived at the same conclusion. He also remarked that the two-degree target was set without reference to the costs of meeting the target.[33][34]

Honors

Scientific and engineering academies

Among many honors, he is a Member of the United States National Academy of Sciences, the American Philosophical Society, and an Elected Fellow of the American Academy of Arts and Sciences.[12] He has been a foreign member of the Royal Swedish Academy of Engineering Sciences since 1999. He was awarded the Daniel Patrick Moynihan Prize by the American Academy of Political and Social Science in 2020.

American Economic Association

In 2004, Nordhaus was designated a Distinguished Fellow of the American Economic Association (AEA), along with George P. Shultz and William A. Brock.[35] The accompanying AEA statement referred to his "knack for asking large questions about the measurement of economic growth and well-being, and addressing them with simple but creative insights," among them, his pioneering work on the political business cycle,[36] ways of using national income accounts data to devise economic measures reflecting better health, increases in leisure and life expectancy, and "constructing integrated economic and scientific models to determine the efficient path for coping with climate change".[37] In 2013, Nordhaus became president-elect of the AEA, and served as the association's president between 2014 and 2015.[38][15]

Nobel Memorial Prize in Economics

Nordhaus was awarded the Nobel Memorial Prize in Economic Sciences in 2018, which he shared with Paul Romer.[15] In detailing its reasons for giving the prize to Nordhaus, the Royal Swedish Academy of Sciences specifically recognized his efforts to develop "an integrated assessment model, i.e. a quantitative model that describes the global interplay between the economy and the climate. His model integrates theories and empirical results from physics, chemistry and economics. Nordhaus' model is now widely spread and is used to simulate how the economy and the climate co-evolve."[4]

Many of the news outlets that reported on Nordhaus's prize noted that he was in the early wave of economists who embraced a carbon tax as a preferred method of carbon pricing.[39][40] Some climate scientists and commentators were disappointed with the Nobel Prize going to Nordhaus due to his embrace of substantially lower carbon taxes per ton than most scientists, along with his past history of arguing for low carbon taxes.[41]

Evaluations

The Nobel Foundation described Nordhaus's work as follows: "William Nordhaus’s findings deal with interactions between society, the economy and climate change. In the mid-1990s, he created a quantitative model that describes the global interplay between the economy and the climate. Nordhaus’s model is used to examine the consequences of climate policy interventions, for example carbon taxes." Additionally, the Nobel Prize announcement commented that Nordhaus had “significantly broadened the scope of economic analysis by constructing models that explain how the market economy interacts with nature."[42] In an evaluation of the work, Lint Barrage summarizes its impact, stating that the "body of work also represents science at its best: integrative across disciplines, visionary in scope yet incremental in progress, transparent, and producing knowledge for the benefit of humankind."[43]

Critics of Nordhaus's DICE model focus on several aspects. One of the most important, incorporating political and moral philosophy, is the use of discounting, with an early study by William Cline.[44] Another branch, represented by Robert Pindyck, holds that integrated assessment models cannot capture the complexity of the climate-economy nexus.[45] Nicholas Stern argued that the damage function does not capture many of the most important risks to society.[46] A particularly important critique, developed by Martin Weitzman, is that the economy-climate system may have "fat tails" and therefore inadequately deal with low probability, high consequence outcomes.[47]

In an article by Christopher Ketcham on "theintercept.com"[48] there are a number of critical insights and critical views of Nordhaus' methods and assumptions, which didn't recognise or value tipping-cascades or non-elastic eco and environmental risk.

Post-Keynesian economist Steve Keen criticises the economics of climate change generally and the 2018 work by Nordhaus in particular: "economists made their own predictions of damages, using three spurious methods: assuming that about 90% of GDP will be unaffected by climate change, because it happens indoors; using the relationship between temperature and GDP today as a proxy for the impact of global warming over time; and using surveys that diluted extreme warnings from scientists with optimistic expectations from economists." When specifically speaking about Nordhaus, he says that "Nordhaus has misrepresented the scientific literature to justify the using a smooth function to describe the damage to GDP from climate change. Correcting for these errors makes it feasible that the economic damages from climate change are at least an order of magnitude worse than forecast by economists, and may be so great as to threaten the survival of human civilization."[49]

See also

References

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  2. ^ Biographical Directory of the Council of Economic Advisers. Council of Economic Advisers (U.S.). 2007. p. 171. ISBN 978-0313225543. Retrieved October 11, 2018.
  3. ^ Appelbaum, Binyamin (October 8, 2018). "2018 Nobel in Economics Awarded to William Nordhaus and Paul Romer". The New York Times.
  4. ^ a b "The Prize in Economic Sciences 2018" (PDF) (Press release). Royal Swedish Academy of Sciences. October 8, 2018.
  5. ^ "Albuquerque Journal Obituaries". obits.abqjournal.com.
  6. ^ Davenport, Coral (May 10, 2014). "Brothers Battle Climate Change on Two Fronts". The New York Times.
  7. ^ "Sandia Peak Ski & Tramway – History & Technology". sandiapeak.com.
  8. ^ Nuzzo, Regina (June 27, 2006). "Profile of William D. Nordhaus". Proceedings of the National Academy of Sciences. 103 (26): 9753–9755. Bibcode:2006PNAS..103.9753N. doi:10.1073/pnas.0601306103. PMC 1502525. PMID 16803963.
  9. ^ Rochlin, Harriet; Rochlin, Fred (2018). Pioneer Jews: A New Life in the Far West. Houghton Mifflin Harcourt. ISBN 978-0618001965 – via Google Books.
  10. ^ a b "William Dawbney Nordhaus Will Marry Barbara Feise". The New York Times. May 3, 1964. Retrieved October 8, 2018.
  11. ^ Nordhaus, William Dawbney (1967). A theory of endogenous technological change (Ph.D.). Massachusetts Institute of Technology. OCLC 24679365 – via ProQuest.
  12. ^ a b c d e "William D. Nordhaus". economics.yale.edu. Yale Department of Economics. Archived from the original on February 11, 2019. Retrieved October 8, 2018.
  13. ^ Harris, Richard (February 11, 2014). "Economist Says Best Climate Fix A Tough Sell, But Worth It". Washington, D.C.: National Public Radio. Retrieved October 1, 2017.
  14. ^ "APS Member History". search.amphilsoc.org. Retrieved March 17, 2021.
  15. ^ a b c "Yale's William Nordhaus wins 2018 Nobel Prize in Economic Sciences". YaleNews. October 8, 2018. Retrieved October 8, 2018.
  16. ^ Samuelson, Paul A.; McGraw, Harold W.; Nordhaus, William D.; Ashenfelter, Orley; Solow, Robert M.; Fischer, Stanley (1999). "Samuelson's "Economics" at Fifty: Remarks on the Occasion of the Anniversary of Publication". The Journal of Economic Education. 30 (4): 352–363. doi:10.2307/1182949. JSTOR 1182949.
  17. ^ Samuelson, Paul A.; Nordhaus, William D. (2009). Economics. McGraw-Hill Education. ISBN 9780073511290.
  18. ^ Smith, Leanne (2000). "Introduction". A study of Paul A. Samuelson's Economics : making economics accessible to students : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Economics at Massey University, Palmerston North, New Zealand (Thesis). Massey University. p. 2. hdl:10179/2178.
  19. ^ William D. Nordhaus (2013). The Climate Casino: Risk, Uncertainty, and Economics for a Warming World. Yale University Press. ISBN 978-0300189773.
  20. ^ Nordhaus, William D.; Tobin, James (1973). "Is Growth Obsolete?" (PDF). In Moss, Milton (ed.). The Measurement of Economic and Social Performance (Reprinted ed.). New York, NY: National Bureau of Economic Research. pp. 509–564. ISBN 0-870-14259-3.
  21. ^ Nordhaus, William D. (1996). "Do Real-Output and Real-Wage Measures Capture Reality? The History of Lighting Suggests Not" (PDF). In Bresnahan, Timothy F.; Gordon, Robert J. (eds.). The Economics of New Goods. University of Chicago Press. p. 30. ISBN 978-0-226-07415-3.
  22. ^ Palda, Filip (2013). The Apprentice Economist: Seven Steps to Mastery. Cooper-Wolfling. ISBN 978-0-9877880-4-7.
  23. ^ a b Nordhaus, W. D. '"Reflections on the economics of climate change", Journal of Economic Perspectives (1993); 7(4) 11–25 at pp. 11, 15
  24. ^ Nordhaus WD (November 1992). "An Optimal Transition Path for Controlling Greenhouse Gases" (PDF). Science. 258 (5086): 1315–1319. Bibcode:1992Sci...258.1315N. doi:10.1126/science.258.5086.1315. PMID 17778354. S2CID 23232493.
  25. ^ Nordhaus, William (May 3, 2007). "The Stern Review on the Economics of Climate Change" (PDF). Yale University.
  26. ^ "U.S. Tax Code Has Minimal Effect on Carbon Dioxide and Other Greenhouse Gas Emissions, Report Says". National Academies. Retrieved July 7, 2015.
  27. ^ Nordhaus, William (April 1, 2015). "Climate Clubs: Overcoming Free-riding in International Climate Policy". American Economic Review. 105 (4): 1339–1370. doi:10.1257/aer.15000001. ISSN 0002-8282.
  28. ^ "William Nordhaus". scholar.google.com. Retrieved December 10, 2023.
  29. ^ Tarr, David G.; Kuznetsov, Dmitrii E.; Overland, Indra; Vakulchuk, Roman (June 1, 2023). "Why carbon border adjustment mechanisms will not save the planet but a climate club and subsidies for transformative green technologies may". Energy Economics. 122: 106695. Bibcode:2023EneEc.12206695T. doi:10.1016/j.eneco.2023.106695. ISSN 0140-9883.
  30. ^ Szulecki, Kacper; Overland, Indra; Smith, Ida Dokk (2022). "The European Union's CBAM as a de facto Climate Club: The Governance Challenges". Frontiers in Climate. 4. doi:10.3389/fclim.2022.942583. hdl:11250/3024350. ISSN 2624-9553.
  31. ^ Overland, Indra; Sadaqat Huda, Mirza (September 1, 2022). "Climate clubs and carbon border adjustments: a review". Environmental Research Letters. 17 (9): 093005. Bibcode:2022ERL....17i3005O. doi:10.1088/1748-9326/ac8da8. hdl:11250/3056333. ISSN 1748-9326. S2CID 252179609.
  32. ^ Smith, Ida Dokk; Overland, Indra; Szulecki, Kacper (July 5, 2023). "The EU's CBAM and Its 'Significant Others': Three Perspectives on the Political Fallout from Europe's Unilateral Climate Policy Initiative". JCMS: Journal of Common Market Studies. 62 (2): 603–618. doi:10.1111/jcms.13512. hdl:11250/3092796. ISSN 0021-9886. S2CID 259617760.
  33. ^ "Global warming goals impossible, Nobel laureate tells Swiss paper". Swissinfo. January 26, 2020. Retrieved January 27, 2020.
  34. ^ Voigt, Birgit; Meier, Jürg (January 25, 2020). "Nobelpreisträger Nordhaus: Wir erreichen das 2-Grad-Ziel nicht". Neue Zürcher Zeitung. Retrieved January 27, 2020.
  35. ^ American Economic Association "Distinguished Fellows".
  36. ^ • William D. Nordhaus, 1975. "The Political Business Cycle," The Review of Economic Studies, 42(2), pp. 169–190.
       • _____, 1989:2. "Alternative Approaches to the Political Business Cycle," Brookings Papers on Economic Activity, pp. 1–68.
  37. ^ American Economic Association, 2004. "William D. Nordhaus, Distinguished Fellow".
  38. ^ "American Economic Association". aeaweb.org.
  39. ^ Strauss, Delphine (October 8, 2018). "Economics Nobel recognises work on climate change and innovation: William Nordhaus and Paul Romer showed how to achieve sustained and sustainable growth". Financial Times. Mr Nordhaus was an early advocate of carbon taxes, but the committee noted that the models he developed also allowed policymakers to calculate quantitative paths for the best tax showing how they would depend on [assumptions regarding the values of disparate climate and economic variables].
  40. ^ Appelbaum, Binyamin (October 8, 2018). "2018 Nobel in Economics Awarded to William Nordhaus and Paul Romer". The New York Times. The Yale economist William D. Nordhaus has spent the better part of four decades trying to persuade governments to address climate change, preferably by imposing a tax on carbon emissions. His careful work has long since convinced most members of his own profession . ...
  41. ^ Linden, Eugene (October 25, 2018). "The economics Nobel went to a guy who enabled climate change denial and delay". Los Angeles Times. Retrieved October 31, 2018.
  42. ^ "The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2018". NobelPrize.org. Retrieved June 17, 2021.
  43. ^ "The Scandinavian Journal of Economics". Wiley Online Library. doi:10.1111/(ISSN)1467-9442. Retrieved June 17, 2021.
  44. ^ Cline, William (1992). The economics of global warming. Institute for International Economics.
  45. ^ Pindyck, Robert S. (May 2012). "Uncertain outcomes and climate change policy". Journal of Environmental Economics and Management. 63 (3): 289–303. doi:10.1016/j.jeem.2011.12.001. hdl:1721.1/66946. ISSN 0095-0696.
  46. ^ Stern, Nicholas (April 1, 2008). "The Economics of Climate Change". American Economic Review. 98 (2): 1–37. doi:10.1257/aer.98.2.1. ISSN 0002-8282. S2CID 59019533.
  47. ^ Weitzman, Martin L. (July 1, 2011). "Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change". Review of Environmental Economics and Policy. 5 (2): 275–292. doi:10.1080/14747731.2020.1807856. ISSN 1750-6816. S2CID 225300874.
  48. ^ Ketcham, Christopher (October 29, 2023), When Idiot Savants Do Climate Economics, How an elite clique of math-addled economists hijacked climate policy.
  49. ^ Keen, Steve (September 1, 2020). "The appallingly bad neoclassical economics of climate change". Globalizations. 18 (7): 1149–1177. doi:10.1080/14747731.2020.1807856. ISSN 1750-6816. S2CID 225300874.

Further reading

External links

Academic offices
Preceded by President of the American Economic Association
2014– 2015
Succeeded by
Awards
Preceded by Laureate of the Nobel Memorial Prize in Economics
2018
Succeeded by
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Abdul Sattar Edhiعبدالستار ایدھیLahir1928[1][2]Bantva, Bantva Manavadar, Gujarat, India Britania[1]Meninggal8 Juli 2016(2016-07-08) (umur 88)[3]Karachi, Sindh, PakistanSebab meninggalGagal ginjalMakamEdhi Village, KarachiKebangsaanPakistanNama lainMalaikat Belas Kasih[4]Orang Miskin Terkaya[5][6]بابائے خدمتDikenal atasKarya sosialGaya hidup sederhanaHumanitarian[7]Suami/istriBilquis EdhiOrang t…

Patung Chullachaki dari Peru Chullachaki[1] (Quechua, berkaki satu, dari kata chulla atau ch'ulla = tunggal, ganjil, tidak berpasangan, chaki = kaki;[2][3][4] ejaan yang juga kadang digunakan dalam bahasa Spanyol)[5] atau Chullachaqui (ejaan Spanyol), juga dikenal dengan nama Shapishico, adalah makhluk hutan dalam mitologi penduduk asli di kawasan hutan Amazon yang terletak di Peru dan Brasil. Ia biasanya digambarkan sebagai makhluk yang pendek dan buruk r…

Kepolisian Daerah Sulawesi Tengah dipimpin oleh seorang perwira tinggi Polri berpangkat Jenderal bintang dua atau Inspektur Jenderal Polisi dan saat ini di jabat oleh Inspektur Jenderal Polisi Agus Nugroho. Daftar Pejabat Berikut adalah para perwira tinggi Polri yang pernah menjabat sebagai Kepala Kepolisian Daerah Sulawesi Tengah: No. Kapolda Mulai Selesai Ref. Komandan Resor Angkatan Kepolisian Sulawesi Tengah 1. AKBP.Soekaryadi 1964 1966 2. AKBP.R. Katamsi 1966 1970 Komandan Komdim 3. AKBP.Pa…

County Mason, KentuckyGedung pengadilan County Mason di MaysvilleMap of Kentucky highlighting County MasonLokasi di negara bagian KentuckyLokasi negara bagian Kentucky di Amerika SerikatDidirikan1788Asal namaGeorge MasonSeatMaysvilleKota terbesarMaysvilleWilayah • Keseluruhan246 sq mi (637 km2) • Daratan240 sq mi (622 km2) • Perairan63 sq mi (163 km2), 2.6Populasi • Kepadatanauto/sq mi (Kesalahan ek…

Taman Nasional Gunung Mulu Protected Area Gunung Mulu dilihat dari kejauhan Negara Malaysia Provinsi Sarawak Titik tertinggi  - lokasi Mount Mulu Area 754 km2 (291 sq mi) Plant Nepenthes Animal Gibon, Orangutan, Rhinoceros Hornbill, Badak Sumatra, Beruang Madu Founded 1974 Management Kehutanan Sarawak UNESCO World Heritage Site Name Taman Nasional Gunung Mulu Year 2000 (#24) Number 1013 Region Asia Pasifik Criteria vii, viii, ix, x Taman Nasional Gunung Mulu dekat M…

Großdeutschland beralih ke halaman ini. Untuk kegunaan lain, lihat Großdeutschland (disambiguasi). Peta sejarah Eropa yang menampilkan situasi linguistik pada sekitar tahun 1918 di Eropa Tengah. Pan-Jermanisme ([Pangermanismus atau Alldeutsche Bewegung] Error: {{Lang-xx}}: text has italic markup (help)) adalah sebuah pemikiran politik pan-nasionalis. Pan-Jermanis awalnya ingin menyatukan seluruh penduduk pemakai bahasa Jerman di Eropa dalam sebuah negara tunggal yang dikenal sebagai Jerman Ray…

Agar perkalian matriks dapat dilakukan, matriks A perlu memiliki jumlah kolom yang sama dengan jumlah baris pada matriks B. Hasil perkalian keduanya adalah matriks dengan jumlah baris yang sama dengan matriks A dan jumlah kolom yang sama dengan matriks B. Dalam matematika, perkalian matriks adalah suatu operasi biner dari dua matriks yang menghasilkan sebuah matriks. Agar dua matriks dapat dikalikan, banyaknya kolom pada matriks pertama harus sama dengan banyaknya baris pada matriks kedua. Matri…

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