Ancient Mathematics: What's new? | Ancient Mathematics | N J Wildberger

[@imran_rafiq_rather]

This is what my Interest is as well Sir! I have no words to offer my gratitude and thanks for this Sir. God Bless you

[@DanielKBlackwood]

This is perfect Norman Wildberger, I wish I found it earlier.

[@thesmallestatom]

As always, thank you Norman. You have truly influenced my thinking about mathematics in very profound ways.

[@julioezequiel8935]

+TiddlyJack Interesting, I like it

[@tomastamantini]

Great lecture, as always, thank you! I think of the recovery of ancient knowledge and culture as one of the great frontiers of science

[@johnpeter4519]

I am in... Thanks again for the wonderful work that you are doing... I have finished watching your probability series and now I am working on the hyperbolic series.. May God bless you always...

[@argosvu2224]

Thank you Norman. This is a great idea for a series. You have the best math lectures on KZbin! :)

[@wcropp1]

This should prove to be a fascinating topic. Thanks for all the lecture videos!

[@theoremus]

Thank you for the insight.

[@hlogoma]

As usual a delight to embark on one of your many explorations into mathematics and thank you for your generosity in sharing your expertise with us. I have been transcribing my notes on your hyperbolic lecture, now complete, and linear algebra, still a work in progress, to latex complete with figures and worked example, not necessarily correct. If you are interested I can send you the source code etc and in general I can share these notes in pdf format with anyone interested. Okay there is a slightly selfish motivation, I hope that I get feedback on these notes that add to my learning experience and give me an even deeper understanding of the mathematics captured in these notes.

[@njwildberger]

Hi Thomas, I would be delighted to have a look at the pdf summaries of the hyperbolic geometry and linear algebra lectures. Could you please send them to me at my UNSW email address?

[@hlogoma]

Hi Professor, thanks for your reply ... I have sent off both the hyperbolic geometry and linear algebra pdf files to you UNSW email address.

[@hlogoma]

My email starts with hlogoma ... this in case it ends up in your junk mail and you are looking for my name.

[@landspide]

This is brilliant, timing is great, just got back from touring Peru! :)

[@twwc960]

I agree with all the other commenters about what an interesting idea this is. Like them, I do look forward to future videos in this series. Might I also add, this series has the coolest intro music of any of your math video series!

[@njwildberger]

Thanks twwc960, my wife suggests that the intro music is a bit too full on, and I see her point---but it is kind of fun. I hope the series will live up to the musical promise!

[@eskuAdradit0]

great initiative! greetings from a peruvian

[@AMotoVlogger]

Very interesting topic to discuss, professor. I always enjoy your videos (also, cool drumstick emphasis pointer) A very common thread between much of the ancient world, and even our world today, is the effect of sound. You are much more knowledgeable upon the theories and conjectures of mathematics than I am, yet let's set at once in order a few ideas worth exploring. 1) what is the relationship between the ancients' way (let's say, Indians) of composing music and their advancement in arithmetical understanding? 2) the ancient Greeks became the envy of the Roman world because of their culture. Is there any connection between what the Athenians understood in regard to maritime/astrological studies and the Greek culture as a whole? Were ancient celebrities all nerds? 3) in regard to calendars: why were the ancient Hebrew mathematicians so precise in their calculations of days, weeks and years, why did it become part of their core philosophy in Judaism? Lastly) symmetries ("divine" or otherwise) have been a key element of Newtonian (and Einsteinian) physics, music (such as Bach,) architecture, art, etc. etc. Why do you think this is? Why was the application of symmetry so pivitol in the various writings of ancient mathematicians? One need only look at the ancient Chinese to see an entire philosophy built on the concept of symmetries, (art of war, dao de jing, etc.) Anywho thank you for all the videos and information. May God bless you mightily, professor

[@njwildberger]

Thanks for the interesting suggestions for topics. I think most of them will figure in our story: not sure about the sound relation because in the Neolithic we have probably no clues as to the role of singing or music. But astrology, calendars and symmetry are surely topics that we will meet.

[@abdulrazzaq9726]

Make videos on what is Great circle, latitude, longitude,how to find direction of Qibla? explain with examples, how to run calculator in these questions.

[@sharonjuniorchess]

Lol I am sitting in the UK listening to an Aussie talking about ancient artefacts that are within within easy travelling distance from me which got me thinking about one of the oldest civilisations that is on your doorstep, Norman; the aborigines. This was a pre-literate culture that managed to record local information & 'maps' to guide & inform people who might be passing through. Then there are the Polynesians who navigated half the globe with pin point accuracy without the use of a compass but apparently based on their knowledge of winds & currents. Who also seem to have a culture of decorating objects with patterns that look strangely familiar to their Celtic colleagues in the northern hemisphere. Could these patterns be more than just pretty lines? Stories that people tell can themselves be devices for recording (astrological/historical) events that took place and according to some cultures they can be ways of encode numbers as well as words (i.e. the Sanskrit Veda passages). This is a different way of looking at things but it may help us to unlock a few archaeological mysteries.

[@mitchelvalentino1569]

THANK YOU!

[@joeshipper1251]

amazing stuff. i started thinking why they used this markings for ones and tens. after watching other videos about magic number 9, i came up with idea. what if marking 1 means 9° in the circle. then < would mean 90. and if you take 9° from top 0 or 360, 90 would be on the right from 45 to 135 (both add up to 9, 4+5=9 and 1+3+5=9) which would look like

[@Rafael-rn6hn]

Interesting title.

[@Onoma314]

In Naram-Sin's reformation of metrology in Mesopotamia, all units were derived from a theoretical cuboid of water ( The Royal Akkadian gur-cube ) which in turn was based on the " finger / horn " measure ( qarnu in Akkadian - qeren in Hebrew, etc ) with each " finger " representing 1/3600 of the moon's orbit, meaning each finger on a person's hand represents 3600 arcseconds per 1° , in turn being ~ 2 second period of the pendulum under the short angle approximation ( Long time before Huygens ). This meshed with the clypsedra units ( Water clocks, long before Torricelli ) as well as common terminology in " flood literature ", as both new moon and eclipses were referred to as " floods " because the moon's phases were seen as slowly rising floodwaters inundating the moon and then receding ( cf Enuma Anu Enlil tablets for reference ) In turn, the Egyptian Royal cubit was 28 " fingers " ( Teba in Egyptian ) meaning both the Akkadian " finger " and the Egpytian " finger " = 1° If you google the words " finger, astronomy " you'll see these simple hand measures still in use today, that date back almost 6,000 years ( The origin of the " devil's horns ", etc ) and are used to make approximate measures by holding your hand / fingers up to objects in the night sky Of course this is a very simplistic overview If you really want to learn the secrets behind ancient metrology you'll have to learn the languages, traditions, texts, etc, and then ask yourself why at one time that math, languages, beliefs, measurements were all intimately intertwined I guarantee you that if you read some of the rough draft articles on my forum you'll start to see things are not as cut and dry as most would have you believe I'd start with this article where I did a forensic analysis of Newton's interests secretsoftheages.freeforums.net/thread/190/closer-examination-newtons-work-bible

[@njwildberger]

Thanks for the interesting comment.

[@Onoma314]

@@njwildberger Thanks for all the great videos. I meant to add that Naram-Sin was the first known king in ancient literature ( afaik ) to claim divinity ( First man who claimed to be a god on earth ) using the Sumerian ideogram of the star , ( dingir ) which was a determinant in cuneiform, much like the trademark symbol ( silent, unspoken ) attached to the names of deified priest-kings King's Name* Their duties included exegesis of omen and procedural texts, including ephemeris of various astronomical bodies, in fact there are colophon in some texts belonging to a certain lineage - that of Sin-Leqi-Unninni, ( unique 1st person narrator of the so-called Gilgamesh text ), which warn against anybody but a high priest in that lineage from reading the text, as they were doomed to curse themselves by attempting to interpret the tables of astronomy observations ( Ephemeris ) One convention of the priestly literature regarding mathematical astronomy is that the same symbol had multiple meanings, so were one not a high priest who was classically guided by a " tutelary deity " ( Like the guiding voice Socrates wrote about ) they would not understand the text Example, the text would have one single symbol with the following meanings: Sumerian : šuš - ( Akkadian : šuššu ) *1/6 " one sixth "* Sumerian - puzur - ( Akkadian : puzru ) *secret* Sumerian : en - ( Akkadian : bēlu -) *lord; master; ruler, priest* A person, if they were not schooled in mathematical astronomy would have no idea what the fraction 1/6 was used for, and they wouldn't know whether they were reading " priest ", " 1/6 " or " " secret " on the tablet The interesting thing about the dingir* is that you see the convention of silent determinants in later languages like Koine Greek, in which they use the " titlo " to denote divinity, - a line over a word , which is common in Greek Bible manuscripts, over " nomen sacrum " ( sacred names ) of which one is the " number of the beast " ( Something nobody seems to have noticed ) anyhoo, looking forward to your next video/s

[@sangeetasahu8078]

Sir I have seen that the video is not clear because I have to write it. So please don't mind and please check it once

[@julioezequiel8935]

Great !

[@jehovajah]

We also want to avoid presupposing primitive as being less sophisticated and less technically skilled. Rather let us consider it in terms of scarcity of resources.😎

[@oker59]

As I've always said, the second chapter of John D Barrow's "Pi in the Sky" is worth the price of the book. Then, there's Van Der Waerden's "Science Awakening" - I and II. The first is the more mathematical one, the second is the astronomical one. The first book is far more interesting mathematically and scientifically. - I have been distracted from mathematics studies by mythology since about 2002 when I discovered Israel Finkelstein's "The Bible UnEarthed" in the archaeology section of a now defunct bookstore(it was built into a former movie theater; it's really too bad it shut down). Out of all the alternative theory archeaology book in that bookstores archaeology section, that was the only real archaeology book It was the first book I found that might actually decode the bible. I then learned of the sungod hypothesis of Jesus Christ. I felt for awhile that I've read enough, and I can get back to mathematics fulltime, but I've recently been turned on by Robert Graves "The Greek Myths." A lot of christians will argue against the sungod mythology idea because "it's all A.D. time" , "maybe the pagans took from the chrisitans?" For instance, they'll say they can't find any evidence for the sharing of the winter solstice birthday of the pagan sungods(Osirus, Dionysius, Mithras) and Jesus Christ. They'll say well, the Christians took Jesus Christ birthday to be Dec25 around 200 A.D. But, wait a minute; while, yes, we haven't been able to find B.C. time mythology literature quotes for a dec 25 birthday, but if the Christians are making Jesus Christ birthday Dec25 to equal the solstinces birthday of the pagan sungods, then those pagan sungods birthday must have been Dec 25th before they moved Jesus birthday to Dec 25! Anyways, in what little I've read of Robert Graves "The Greek Myths", there's plenty of proof for astrotheology and sungods. Robert Graves "The Greek Myths" also provides tons of evidence for Sir James Frazer's "The Golden Bough" which points that ancient Kings tried to use magic to keep the yearly harvest happening. If they're magic didn't work, then he'd be killed. And someone else would be put in his place, and that new King would try to use magic. Now, the magic is a kind of analogy. They'd think if they acted like something, then they could get something else to act like that. Or, if they ate something, then they'd take on its properties on so on and so forth. Mathematics is an analogy; so, what separated mathematics from magic, and poetry(another artform that is an analogy). Finally, something else I'm struck about Greek mythology is that the Greek mythology and its history shows the transition to a more astronomical consciousness than the previous Earth goddess religions. Archaeologists have found many Venus figurines throughout Europe and up into Russian Asia. These Venus figurines go back tens of thousands of years. Appears to me that the Malta ruins are the last great culture of the Earth goddess religions - in fact, there's the ultimate rather large statue/sculpture of a Venus figurine there.

[@njwildberger]

Thanks oker59, Nice to have some reading suggestions. I can bet that Robert Graves' book is interesting--probably everything he wrote was.

[@nyar2352]

oker59 I would really recommend you look at some more modern research. The Golden Bough is... well. By today's standards, quite shoddy scholarship, particularly in regards to anything that isn't a) Greek, b) European folk practices.

[@oker59]

@@nyar2352 Hello Nyar 23, outside of the Dianna goddess, and the Sacaea Festival, a Babylonian festival, Sir James Frazer mostly relies on, then, contemporary anthropology. A lot of that is probably pretty hard to confirm today. And, so my recent excitement of Robert Graves "The Greek Myths." The point is that Robert Graves research on Greek myths is B.C. timeframe confirmation of Sir James Frazer's "The Golden Bough." Sir James Frazer's "The Golden Bough" is amazing because he derives all this from such an indirect evidence. He doesn't have a explicit quote to the affect(outside of the two references mentioned above). He didn't find this following quotes from Hippocrates of Kos, the Sacred Disease, "As indicated above, the Old Testament preserves remnants from a magical world before god(s). Hippocrates of Kos(of the famous Hippocratic Oath), reveals the connection and reason for the evolution from the magical world to god(s). . . "They who first referred this malady to the gods appear to me to have been just such persons as the conjurors, purificators, mountebanks, and charlatans" About the attribution of diseases to the god(s) . . . ""Men regard its nature and cause as divine from ignorance and wonder," . . . But if it is reckoned divine because it is wonderful, instead of one there are many diseases which would be sacred" - If things that we consider sacred/divine is because of ignorance, then the whole universe(certainly back then) is "of the god(s)". Furthermore . . . "Such persons, then, using the divinity as a pretext and screen of their own inability to of their own inability to afford any assistance, have given out that the disease is sacred, adding suitable reasons for this opinion, they have instituted a mode of treatment which is safe for themselves, namely, by applying purifications and incantations, . . . "All these they enjoin with reference to its divinity, as if possessed of more knowledge, and announcing beforehand other causes so that if the person should recover, theirs would be the honor and credit; and if he should die, they would have a certain defense, as if the gods, and not they, were to blame," The quotes right above show that they say a certain disease they don't know about must be "of the god(s)", and they give magical treatments as the antidote for their and the victim's ignorance. As we've seen some of the evasive thinking quote above from Gregorius of Nyssa, when questioned, they use all kinds of evasive language tactics. Here, the mental trick is that, no matter what happens, god(s) did it. If the person magically gets well, the god(s) are on their side. If not, they say "god works in mysterious ways." We'll see another mental trick to convert people to their religion, "believe, and you will believe" below" I took this out of my Gospel of Truth which is mostly about sungods from B.C. times to Jesus Christ. You might notice some peculiar language.

[@oker59]

Also, I found these a few weeks ago. I forgot which one, but they mentioned sculptures as imitative magic I think it was one of the Carthage videos actually. And, in the Greek videos, there was a piece of stone mentioning "the twelve gods", in case you don't believe in the sungods idea as well.

[@alexandartheserb7861]

Gret topic :) Just one complain, mentioning those civilisation, you are missing maybe one of most important one -Vinca civilization: inventor of first world letters (Vinca letter) from which is derived modern letter, invention of bronze age (oldest world sitest in east Serbia, near copper mines) and resulting from that also first (melting and mixing metals technology): metalurgy, chemistry, alchemy; and maybe even oldest wheel (old toy found in todays Slovenia); society which almost 2 milleniums didnt have wars and where was unthinkable to live from other peoples work but just from yourself work. Climax of this culture was Ancient Greek scients. But later was destroyed by more then 2 milleniums of raids and conquests (Romans, Christianity, Byzanth, Hungarians, Bulgars, Huns, Avars, Albanians, Tursk&islam, Austrians, British, Germans, Soviets...). I am saying all this because if so, this people and civilisation must had great mathematical achievements. Even small in number comparing to other nation, for example even today kids from Serbia (elementary and high school) are in top on worlds math competitions, which is very odd comparing their small number to others. Also lot of other logical features like excellent programing talent (like India but much much smaller population) and finally Tesla, one can not ask himself is there any special gen for this kind of mathematical thinking there which is recidive of that past civilisation (also from math side, question is was Leibnitz Lusatian Serb origin as some say?). Also indo-european language could be born too in this region because when you research ethimology on Wiktionary or elsewhere you will find most of words roots (for example English one or others) are understandable in our languge more clear then in others. Also first European "I" haplogroup was originaly from here and spread into north and west Europe after ice age retreat (they call it I1 there but I2 here even I1 migrated from here, not opposite). Also with invention of bronze, this civilisation had technical advance over other people and conquered East ares all way to India by Ninus and spread their knowledge, letter, philosophy, technology... , same as Alexandar the Great from this very region did later. So, lot of stories, credle of European genetics, language and civilisation, possibly math too, but so small researching worldwide and interest in it. Also, if you chec even older civilisation then Vinca (7000 yrs ago), I.e. Lepenski vir civilisation, about 9000 yrs ago, you will find very interesting math how they geometricaly build their houses and how they position it toward one high mountain-stone on that very site. Very very interesting and even older then Babyloninan and Egypt cultures... Maybe all this is new to someone and hard to comperhend, but lets say it :) Regards :)

[@christopherellis2663]

There is no connection between Serbia and the Vinča, except geography.

[@alexandartheserb7861]

@@christopherellis2663 If "I" haplogroup emerged there 30.000 yrs ago and today most of people on very same place have same haplogroup, who was living in the middle, during Vinca era? Obviously same people. I dont claim that civilisation is only todays Serbian heritage but of all Serbian "I" descendents worldwide which migrated from there during last thousands of yeras... But from other side, I agree with you, during last more then 2 mileniums, mentality and philosophy of those people have been destroying through dozens of foreign invasions which led to restriction of free and mathematical, natural thinking into forcing of thinking in the way which suits current invader. Thats why is today to the observer hard to see it there...but that genes is still in those people, maybe not so obvious on first sight...

[@njwildberger]

Hi Alexander, Thanks for bringing this culture to our attention.

[@alexandartheserb7861]

@@njwildberger Thank you Norman, for all your work, I am currently reading Euclid elements (but trying to understand it deeper, like what if point in math represent everlasting present time,i.e. to look on math as time science) and what Euclid did in his time with collecting all that knowledge on scriprs, you are now doing same collecting on internet and videos :) So, big respect from my side. And yes, those old Danube civilisations like Lepenski Vir, Starcevo, Vinca... should be puzzled in world science and history. Regards, looking forward for new episodes :)

[@homewhite1947]

What about ancient Australian astronomy and Mathematics ?

[@andrdrcks8368]

Ancient Mathematics is way cool. Is there going to be a Algebra of Boole Part III ?

[@njwildberger]

Yes Algebra of Boole Part III is scheduled in a few weeks.

[@flexeos]

In your list you want to add something from latin america. it seems that precolombian civilizations were using quipus ( set of knots on ropes) representing numbers in base 10, before writing was invented as early as 4500 BC.

[@christopherellis2663]

Base sixty and base twenty were more common

[@njwildberger]

@frederic r, Great, we will look out for Latin American megalithic sites too. If you have any particular favourites, let us know.

[@phononify]

i will join and follow

[@Dystisis]

0:45 The wizard teleports!

[@alejandrogarridogouro388]

Veru interesting video. Thank you so much. Are you a mathematician?

[@njwildberger]

Yes I am a mathematician, but I have also done some historical work with Daniel Mansfield on Plimpton 322 and Old Babylonian trigonometry.

[@alejandrogarridogouro388]

@@njwildberger Wow thats amazing. I want to be a mathematician too. Want would you recomend me?

[@christopherellis2663]

@@alejandrogarridogouro388 Watch KZbin, and try out stuff for yourself.

[@jehovajah]

Astrology is a better way to describe and research this area.❤️

[@njwildberger]

I suppose for most of history and pre-history astronomy and astrology were not really separate disciplines. The motion of the objects in the night sky connected with seasons, and the phases of the moon have a tangible effect on both tides and moods: so it was reasonable to suppose that there was a strong link between the heavens and the earth more generally. This would likely have been strengthened by religious beliefs worshiping the sun, moon or planets --- or associated Gods.

[@jehovajah]

njwildberger I know you will find more information when you look under the heading astrology . As a point of fact astrologers were differentiated only in the 18th century from mathematicians and astronomers.

[@brendanward2991]

An ambitious project. Unfortunately, Dr Wildberger is building on the mainstream chronology of ancient history, which I reject. History is not nearly as old as we are told and we do not know nearly as much about the early civilizations as we think.

[@njwildberger]

Hi Brendan: I am quite open to the need for establishing accurate chronologies, and am not wedded to a particular one. I think that is a major challenge with lots of ancient sites: a lot of dating involves a fair amount of guess work, especially when organic material is unavailable or scarce. So that is surely a topic that we can profitably engage with.

[@gausssto570]

What do you mean "history is not nearly as old..."? You mean that our understanding of history was constructed recently, or do you mean that you are a young earth creationist or similar?

[@brendanward2991]

The last Ice age ended around 1500 BCE, not c.10000 BCE. So, Dynastic Egyptian history, Mesopotamian history, Indus Valley history, Chinese Dynastic history, Olmecs and earliest post-glacial South American civilizations all began roughly around 1300 BCE.

[@gausssto570]

@@brendanward2991 I think you've fallen for some nonsense. Trust science, not random conspiracy theory websites.

[@brendanward2991]

I do trust science - good science. The Short Chronology to which I adhere is the result of many years' research by serious scholars. If you are seriously interested, I recommend Charles Ginenthal's series of books "Pillars of the Past" and Emmet Sweeney's "Ages of Alignment".