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Mathematical accomplishment[edit]

I have heard that Murray's book says that new discoveries in mathematics have declined since 1900. That is utter nonsense; only an illiterate would say such a thing. Is that actually in Murray's book? Michael Hardy 01:06, 29 Nov 2004 (UTC)

The closest to such a thing I can find is pg. 313 of the hardcover edition, where he says:
  1. "The golden age of mathematics ocurred earlier than for any other scientific inventory, over the late 1500s to the end of the 1600s. A short list of the names explain why: Pascal, Fermat, Cavalieri, Descartes, Wallis, Huygens, Barrow, Leibniz, the first Bernouillis, and Newton, who discovered, among much else, logarithms, analytic geomerty, probability theory, and the calculus."
  2. "A lesser but notable period of acheivement came in the early 1800s, led by Gauss, but with a distinguished body..... After mid-19C, all the measures of accomplishment in mathematics, including those based on events, trailed off through the 1950 cutoff."
(Numbered list in the original). Personally, I find such a result to be fairly plausible. I don't know of any figures between 1850-1950 who really rival "Pascal, Fermat, Cavalieri, Descartes, Wallis, Huygens, Barrow, Leibniz, the first Bernouillis, and Newton". --maru (talk) contribs 20:05, 29 April 2006 (UTC)[reply]
Probably nobody rivals Newton. But there has been far more new discovery in mathematics since 1900 the before. Is Murray trying to deny that? --Michael Hardy 19:26, 26 June 2006 (UTC)[reply]
Looks like he's saying that between 1900-1950 accomplishment has declined; he deliberately cuts off all his inventorying at that point (so as to avoid overvaluing contemporary work), so that says nothing about work between 1950-2006. I'm not so sure he's right about the overall progress, though as I have said, I think I agree with his point about individuals. --maru (talk) contribs 23:11, 26 June 2006 (UTC)[reply]
I'd add that besides the issue about the cut off, Murray would probably say that there are fewer eminent individual figures because more is being done through collaboration (I think he explicitly offers this as a reason for the fewer eminent figures: the greater need for large groups working together) and also that per-capita accomplishment has fallen: there may be more accomplishment post-1950 than in Newton's time, but then, there's like 9 or 10 times more humans around. --Gwern (contribs) 01:25 17 February 2010 (GMT)

There is no question that the post-world war II period is the greatest period in the history of mathematics . One has the total refashioning of mathematics in the Eilenberg-Grothendieck era (1945-1970),culminating in the recent work of Connes.dedwards@math.uga.edu--David Edwards,Jan. 18,2010. —Preceding undated comment added 13:43, 18 January 2010 (UTC).[reply]

You obviously know more about mathematics than I do. However 80% of the Eilenberg-Grothendieck era (1945-1970) lies outside the period covered by the book. Jjc2002 (talk) 22:51, 16 February 2010 (UTC)Jjc2002[reply]
You don't need to. Anyone who grandiosely proclaims themselves the culmination of the most glorious period of some field has instantly discredited themselves. --Gwern (contribs) 01:25 17 February 2010 (GMT)

The Mathematics section is a nice example of Murray's shortcomings. Almost everybody literate has read somewhere something about "Fermat's theorem" - it was (probably) the most popular example of an unsolved problem, but it has only made Fermat's name exceedingly popular. Such popularity does not relate directly to his mathematical abilities. The First place for Euler is also easily understood: either you say briefly 'Euler contributed to all branches of mathematics' or you start enumerating, which really takes a lot of place and Murray measures just that.

(Another revealing twist is the absence of Karl Marx among the philosophers - a footnote says his achievements are elsewhere. One would have expected to see a rating of economists, but here Marx is the obvious winner, so Murray had to scrap the category.)

Perhaps some explicit warnings should be included in the article with references to published criticism. Ael 2 (talk) 22:22, 1 December 2010 (UTC)[reply]

Karl Marx as "the obvious winner" among economists? Now that's a terrible joke. 2001:569:7D8E:5300:ED6E:A1EB:16EC:A292 (talk) 07:35, 24 June 2021 (UTC)[reply]


Archimedes is inferior to Fibonacci??? --Michael Hardy 17:09, 26 September 2005 (UTC)[reply]

Not by my reading. Looking through the appendix for the mathematical inventory, they both have index scores of 33. --maru (talk) contribs 20:05, 29 April 2006 (UTC)[reply]

Christian/Western POV[edit]

"Murray explains his finding that the West produced almost all scientific progress by reference to Christianity's emphasis on human intelligence as a gift from God."
That's a pretty obvious instance of ethnocentrism. I would bet that Asians often assert that "the East" has produced almost all scientific progress, citing such contributions as algebra, zero, gunpowder, writing, the Russian invention of the intercontinental ballistic missile, the many remarkable advancements in electronics to come from Japan in the later 20th century, and civilization itself thousands of years ago in what is now the "middle east". To call Murray's conclusion a "finding" makes it seem as though it's an objective fact that has been discovered. I haven't read his book, so I can't critique this article much beyond that. But the article should not embrace his conclusions wholeheartedly, or else it will simply become an echo of his own point of view. --Mr. Billion 19:41, 20 May 2005 (UTC)[reply]
Russians are European. --Jugbo 04:00, 26 October 2006 (UTC)[reply]
He co-wrote "The Bell Curve", what more do I need to know about this crook? Seriously, this book's thesis is just another case of some pseudo-intellectual fellating his employers for cash and glory instead of doing real research. Sweetfreek (talk) 05:06, 1 August 2008 (UTC)[reply]
Of the six specific examples you give in support of your charge of ethnocentrism three are irrelevant as they fall outside the period covered by the book and one of these comes from "the West" (i.e. from Russia). Sometimes contributors to Talk pages ask if the other person read the relevant book. Did you read its title? The politically incorrect fact of the matter is that a hugely disproportionate amount of inventions and discoveries have come from the West. Just ask yourself a simple question - what was the most significant mathematical, mechanical or medical advance to come from outside the West between 1300 and 1950? Jjc2002 (talk) 22:51, 16 February 2010 (UTC)Jjc2002[reply]
Chinese scientific achievements are often underappreciated. Ever heard of variolation? That was discovered in China in the 1400s. Also, Chinese mathematics matched or surpassed that of Europe up until the mid-1500s. (talk) 09:11, 19 June 2016 (UTC)[reply]
Yes, I have heard of variolation, thought at the time I commented I thought it originated in the Islamic World not China.
Variolation is a good example – perhaps THE good example – of a major advance outside of the West in the period I questioned. But I can’t think of another one. If you can kindly let me know.
If we look at the history of advances across a wide range of fields certain trends emerge.
Obviously the first developments happen in Sub-Saharan Africa but once homo sapiens spread beyond there virtually all innovation occurred outside of there.
Once civilizations started things speed up and various discoveries are made in the early centres, the Fertile Crescent, Egypt, China etc and, later, Greece.
If we look at the last few millennia we see that for a long time China led the world in producing important inventions e.g. the “Four Great Inventions” but then things slow down dramatically in China and, around 1300, the West becomes the centre of discovery and invention and has held the lead ever since. (I’m not using Murray only as a source. I’ve a number of books on the history of inventions and they all show the same pattern). The reasons for that are in part what Murray tries to address.
You say that “Chinese scientific achievements are often underappreciated”. I would suggest that that has been the case more in the past than at present, at least in the books that I read and the documentaries I watch. If anything it has been the reverse in my experience. I find that many books and documentaries emphasize areas where China led but not where it lagged e.g. that when the Jesuits arrived there the consensus among educated Chinese was that the earth was flat or that even the great champion of "Science and Civilisation in China" Joseph Needham concluded that ‘one can hardly speak of a developed science of physics,’ in China.
You also say that “Chinese mathematics matched or surpassed that of Europe up until the mid-1500s”. You may know far more than I do about the history of mathematics in general and the history of Chinese mathematics in particular. It would not be difficult. But someone who was in a position to judge, Matteo Ricci - the first man to translate Euclid into Chinese - would write in the 1590's “…if China was the entire world, I could undoubtedly call myself the principal mathematician and philosopher of nature, because it is ridiculously and astonishingly little what they know" and “…the Chinese have no science at all; one may say that only mathematics is cultivated, and the little they know of it is without foundation...They just manage to predict eclipses and in that they make many mistakes. All are addicted to the art of divination, which is most unreliable and also completely false. Physics and metaphysics, including logic, is unknown among them..." Jjc2002 (talk) 14:41, 25 June 2016 (UTC)Jjc2002[reply]
Gunpowder weapons like the cannon and the multistage rocket are good examples of a non-European advancement from 1300-1950.
It's true; logic was virtually unknown in China for most of its history, up until contact with Europeans. However, that didn't stop the Chinese from doing complex calculations (see Zu Chongzhi's calculation of pi and the Shoushi calendar) and making many discoveries through trial and error. Chinese mathematics started to decline by about the mid-1500s, and by then, the West took the lead (Newton, Kepler, etc).
Once homo sapiens spread beyond sub-Saharan Africa virtually all innovations occurred outside? Not really. The achievements of sub-Saharan Africa has been greatly undervalued due to the history of slavery, in which Arabs (and later Europeans) made false claims about the backwardness of Blacks in order to justify them as less than human. See Akala's Oxford Union speech on YouTube for a quick introduction on this topic. (talk) 11:20, 30 June 2016 (UTC)[reply]
Thanks for your comment. I’ll answer it in two parts. The first on China and then, after I’ve seen the video you’ve mentioned, on Africa.
Multiple stage rockets of the sort the Chinese invented aren’t to me a major invention like the wheel, pottery, writing, zero, gunpowder, paper, the magnetic compass, spectacles, the printing press with movable type, the telescope/microscope, the steam engine etc.
The Chinese invention of gunpowder weapons predates 1300. Were there major improvements in China thereafter that weren’t predated elsewhere? In the 17th c. a Chinese emperor pressurized a Jesuit to restore existing Chinese cannon and cast new ones. (Some were still in use during the Opium Wars!) Now what does it say that an emperor rated a foreign theologian higher than his Chinese experts?
In 1925 Alfred North Whitehead wrote, "China forms the largest volume of civilization which the world has seen. There is no reason to doubt the intrinsic capacity of individual Chinamen for the pursuit of science. And yet Chinese science is practically negligible. There is no reason to believe that China if left to itself would have ever produced any progress in science. The same may be said of India."
Over the centuries Chinese cleverness produced a very great deal and the rest of us are greatly in their debt for it. But ingenuity will only bring you so far. You reach a point where you need workable theories and this to me is what they lacked.Jjc2002 (talk) 12:43, 2 July 2016 (UTC)Jjc2002[reply]
I've now watched the Akala talk. He's an engaging speaker and comes across as a nice person but one giving a highly selective presentation and occassionally guilty of that which he criticizes. But it's irrelevant to my point. Yes the achievements of sub-Saharan Africans have been undervalued in the past, though now I think some overvalue them. But my point was about innovation. I ask the question - what was the last major innovation, discovery or idea to come out of sub-Saharan Africa?Jjc2002 (talk) 16:35, 2 July 2016 (UTC)Jjc2002[reply]
Yes, gunpowder weapons came before 1300, but the first cannon (as opposed to a fire lance) was fired by the Chinese in the 14th century CE. Err, no offense, but can't you do research yourself? A quick search online yields several sub-Saharan African inventions like the CyberTracker and cardiopad. I agree that China's lack of logic means that at some point people with logic (namely the West) will overtake them. However, even if left to its own devices, there is no reason to believe that China could not progress, albeit slower than they would have if they had logic. Thomas Edison had little to no theoretical idea of how things work, but that didn't stop him from becoming one of the greatest inventors in recent history, by making device after device until he made one that works.
By the way, can you explain why you think Akala's presentation was "highly selective and occasionally guilty of that which he criticizes"? (talk) 11:48, 8 July 2016 (UTC)[reply]
Books from The Smithsonian, National Geographic and Dorling Kindersley give dates in the 1280s for cannon. If you know why they're wrong please let me know.
I wrote that once homo sapiens spread beyond Sub-Saharan Africa virtually all innovation occurred outside of there. Off the top of my head I would give plant and animal domestication, writing, the wheel, pottery, maths, cities, running water, paper, printing, logic, science, the compass, the waterwheel, the windmill, the steam engine, the electric motor, the internal combustion engine, the wheelbarrow, the cart, the car, the train, the plane, linear perspective, the clock, the computer, antibiotics, and assorted things ending in -scope and -meter etc, etc, etc. You list the CyberTracker and cardiopad. Err, no offense, but can't you spot the difference?
I don’t think it was just the lack of formal logic – or of Euclidian geometry – that prevented the Chinese from progressing further. Their understanding of the universe was fundamentally different from the Western one. It could be said that while Confucian China had technology and magic, Christian Europe had proto-science and miracles – and, later, Protestant Europe would place less emphasis on the miraculous. In believing in a Creator, Europeans believed in a Creation. The mind of the Creator could be read by a careful, scientific study of His Creation.
Edison may have had little theoretical idea of how things work, but he knew that things did work in an orderly fashion in accordance with the correct theoretical underpinning. He lived in a culture that was both the product of and had produced the Scientific and Industrial Revolutions. Whatever else he was trying out he wasn’t trying to balance the yin and yang of the light bulb.
Ingenuity plus trial and error can get you the right mix to make bronze or gunpowder but trial and error isn’t going to produce, say, a radio unless you know, or at least have reason to believe, that radio waves exist. For that you need Science and it has been said that while China had sciences it didn’t have Science.
Re Akala: he himself says that if you look at one piece of evidence in isolation that you're not seeing the whole case. True. The trouble is he sometimes does just that.
He implies that the Sphinx's missing nose was removed by Westerners to hide its African features. That could only have happened after the Napoleonic invasion in 1798. But a drawing of the already noseless Sphinx was published in 1757! Had he done what you suggest I do, i.e., do a search on Google he could have found this in a few minutes (https://www.brooklynmuseum.org/opencollection/archives/image/37200).
He shows red and black images of Tutankhamun, explains that red was a symbolic colour, say he couldn't have been both red and black, "So we need to figure out which one he was". He doesn't mention, and perhaps doesn’t know, that pharaohs were sometimes painted black as a symbol of fertility.
He refers to “The Portrait of the Races” in the tomb of Ramesses II. I presume he means Ramesses III. (If there is such an image in the tomb of Ramesses II then the following point is irrelevant and I apologize in advance). The image he uses is based on a plate in a book not on a photo. If you look at the Wikipedia page on “Ancient Egyptian race controversy” you’ll see that (a) there’s a dispute over whether or not this plate represents what’s actually in the tomb in question and (b) that there are other such “Portrait of the Races”/"Table of Nations” (which can be found by Google) in other tombs that quite literally show a very different picture. If anyone can post a good photo from the tomb that would clarify the issue.
There were 2 instances where I believe he was guilty of that which he criticizes.
(1) He described the Europe of Mansa Musa's time as being in the "Dark Ages".
This is the Europe that had just given the world spectacles, the mechanical clock with a metal escapement and Ockham’s Razor: where Giotto had just revolutionized painting in the Arena Chapel and where Dante had just written the Divine Comedy: a Europe that had just built the first building anywhere to be taller than the Great Pyramid. What were the comparable achievements in Africa around this time?
(2) Talking about the Atlantic slave trade he says that "ancient Greece had slavery, ancient Rome had slavery, there was slavery in the Middle East, there was..." here he paused, "...forced servitude in certain African empires".
Spot the double standard?Jjc2002 (talk) 13:10, 13 July 2016 (UTC)Jjc2002[reply]
Yes, I've spotted Akala's mistake when he said "Dark Ages". I've read several books concerning the "Dark Ages", and they all say that the "Dark Ages" is mostly a myth; that period was actually a period of advancement, such as with the invention of the Carolingian miniscule and the adoption of gunpowder. But other than that, I didn't notice any problems with Akala's speech until you pointed them out, so thank you for that; I see that you are much more knowledgeable than me.
I was just trying to point out a few sub-Saharan African inventions to get you to rethink that maybe sub-Saharan Africa hasn't been sitting on a bench throughout history. Most books I've read tend to only mention the earliest inventors of an invention, even if said invention was independently invented by someone else at a later date. For example, mathematics first originated in Mesopotamia, but few people are aware that sub-Saharan Africa independently developed some form of mathematics; see the Ifá. With that in mind, sub-Saharan Africa probably has produced many inventions and discoveries; they are just much less well known.
The book I have here says the first cannon was fired in 1326, in Ming Dynasty China, but Wikipedia says that the first cannon dated no later than 1290, so I guess my book is wrong. By the way, early Egyptians were probably Black; see the statues of Narmer, Khufu, and the other early dynastic kings. (talk) 01:30, 15 July 2016 (UTC)[reply]
Thanks for your comment. We all know different things. I was unaware of Akala's existence until you referred to him. We can all learn something from everybody else. At 61 I suspect I'm older than you are and if I can pass on one piece of advice without seeming condescending is that you'll really learn by testing your beliefs against the best counter arguments. Akala strikes me as an intelligent, inquisitive young man who, wanting to understand why the world is as it is, came across an explanation that was emotionally satisfying and then failed to ask enough hard questions of it.
By the way "Dark Ages" is a (Northwest) Eurocentric term. There was clearly a falling off in high culture and literacy in parts of Europe after the fall of of the Western Roman Empire but in Eastern Empire, the Islamic, Indian and Chinese worlds the age wasn't dark at all.Jjc2002 (talk) 15:07, 17 July 2016 (UTC)Jjc2002[reply]

Why do I not think that Murray actually said or wrote this, anyway? Is there any reason this line should be in the article, unsourced as it is? If anyone wants something he actually said on the subject, "“Human beings,” he claims, “have been most magnificently productive and reached their highest cultural peaks in the times and places where humans have thought most deeply about their place in the universe and been most convinced they have one.” This for Murray helps explain the preponderance of achievement in the arts and sciences in Europe during the centuries when Christianity was regnant. " Demigord (talk) 19:26, 22 January 2011 (UTC)[reply]

The Murray quote is page 475 in the subsection 'The Aristotelian Principle Recast' of the 'Summation'. --Gwern (contribs) 19:52 22 January 2011 (GMT)


There was no music before Monteverdi? What about the massive achievements of Josquin, Palestrina, Machaut, Ockeghem? That list really presents a 19th-century POV. It made me laugh out loud. Those who carried the Franco-Flemish style to the rest of Europe, and who invented the art of counterpoint, are the ones who made the later achievements possible. Is this guy for real? What sources is he using? --Antandrus (talk) 23:38, 9 November 2005 (UTC)[reply]

Perhaps I am simply unusually ignorant of music, but I haven't heard of a single one of those people listed in your second sentence. --maru (talk) contribs 07:48, 7 May 2006 (UTC)[reply]

yeah it is prettty dumb not to know who palestrina was

Murray knows there's music before Monteverdi. I think certain people should study Murray's book more carefully. His music map for 1400 to 1600 clearly shows the importance of the Low Countries in music. Less heat and more light, please. — Preceding unsigned comment added by (talk) 11:43, 2 December 2013 (UTC)[reply]

Murray a Philistine[edit]

Is there such a category? This books seems the definition of the term. —Preceding unsigned comment added by Editor437 (talkcontribs) 23:28, 3 November 2007 (UTC)[reply]

Well, Luddites are people who don't read books but still have a strong prejudiced opinion -- you know, one not based on any facts, only prejudice. Lkoler (talk) 05:38, 15 March 2012 (UTC)[reply]

Murray has been pretty fair-minded and accurate.

Intelligence Citations Bibliography for Articles Related to Human Intelligence[edit]

You may find it helpful while reading or editing articles to look at a bibliography of Intelligence Citations, posted for the use of all Wikipedians who have occasion to edit articles on human intelligence and related issues. I happen to have circulating access to a huge academic research library at a university with an active research program in these issues (and to another library that is one of the ten largest public library systems in the United States) and have been researching these issues since 1989. You are welcome to use these citations for your own research. You can help other Wikipedians by suggesting new sources through comments on that page. -- WeijiBaikeBianji (talk) 14:35, 28 July 2010 (UTC)[reply]

Way too many tables[edit]

What's the rationale for filling the article with so many tables from the book? Wouldn't that information be a lot more compact as paragraphs of text? (And is it really all necessary in an article about the book?) -- WeijiBaikeBianji (talk, how I edit) 01:16, 17 April 2015 (UTC)[reply]

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