Number Systems Ancient to Modern 1: the Egyptians | Sociology and Pure Mathematics | N J Wildberger

[@TemplarX2]

Absolutely love the content. Mixing history and maths is just brilliant. Can't wait for the Sumerian number system. I would also love a brief analysis of the Ishango bone.

[@milansvrcina3512]

I have never seen such an interesting introduction to Egyptian mathematics (usefulness of fractions with numerator 1). The link to the detailed paper is also very helpful. Thanks a lot. Milan Švrčina (teacher of mathematics and physics from Czech Republic)

[@QuestforaMeaningfulLife]

Love how you take the ancients seriously and imagine things from their perspective.

[@jacoboribilik3253]

I just love watching a couple of your videos at night after a long day of work and study.

[@Self-Duality]

Norman, you’re a true treasure to humankind. Your service is uncomputable 😉💭☘️ Studying closely…

[@moshadj]

According to Norman if it's not computable it doesn't exist

[@Self-Duality]

@@moshadj I guess the wink emoji 😉doesn’t give away my sarcasm

[@MisterrLi]

Book: "Where Mathematics Comes From" by Núñez and Lakoff. It discusses a lot of topics close to this youtube channel, like why the "Real numbers" don't exhaust the points on the (geometric) line, why the "Space-filling curves" doesn't fill (geometric) space, various concepts of "Infinity" and if "0.999... = 1.000..." is true or false, amoong many other math questions.

[@WildEggmathematicscourses]

Thanks for the suggestion!

[@QuasarRedshift]

always great to see a new upload

[@thomaskember4628]

At the age of 13 I came to the realisation that we didn't have to use a number system with base 10, but base 8 would work just as well. The character3 8 and 9 were not needed. I wrote out the multiplication table for base 8 which I called the octave system and methods for converting from decimal to octave and octave to decimal using both bases. I wrote all this in a notebook and didn't show anyone. If my teacher had been like Norman, I think I would have shown him the notebook.

[@TimJSwan]

great to see you are still producing content

[@vasanthiviswanathan3150]

Just an absolute treasure. I cannot overstate my gratitude. I wait with bated breath for the next video.

[@kendebusk2540]

Very informative, Dr Norman! I immediately brought to mind the old Hindu fable about the blind men ad the elephant. All "saw" the same thing but the Egyptians were "seeing" the tail, the Babylonians "saw" the trunk, and we modern people "see" the leg. All the same thing, all different!

[@williambowman1317]

Perhaps the Egyptians desired to minimize the number of cuts to subdivide into equal amounts. If you can imagine cutting stone pieces (and needed to cut many of them) minimizing the number of cuts to split them would be important. If you go back in the video to around 22 minute mark and count slices required to give 7 workers equal shares of 5 loaves of bread, you can see that the Egyptian method is superior (i.e. it requires only 17 cuts as opposed to 35 cuts with the modern approach.)

[@CandidDate]

Lately, I've been on a quest to "understand" mathematics and numbers. Not just memorizing the times tables and common derivatives, etc., but really get a feel for how I can better relate to the concept of quantity and eventually quality. Like, today, I thought of the fractions 1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, and 10/10. can you see the exponential or logarithmic values hidden in these? Well, what number do you need to multiply these 10 fractions to get 1? 10, 5, 3.333, 2.5, 2, 1.666, 1.428571, 1.25, 1.111, 1. These values are near exponential don't you think? And that is just one example of how fractions are the key to ALL mathematics. Well at least any math that is "practical" and can be understood rather than memorized. I wish we would develop a greater, simpler relationship to numbers rather than sin, cos, tan, e, pi, i, memorization etc. Don't get me started on linear algebra. But to each his own. Thanks for the video. Great as always. !

[@brendawilliams8062]

Dr. Wildberger. Thankyou

[@yorch802]

I love watching your videos with my dad, occasionally he will fall asleep but he claims to also like them.

[@Onoma314]

Thank you. I have always found it interesting that numbering in Hieroglyphics and Hieratic seem to be based on repdigits ( Iow, the sum of the Hieroglyphic numerals = 1,111,111 and the Hieratic numerals are identical to the sum of the repdigits { 111,222,...888,999 } I've been able to reconstruct a system of calculation using these combined with figurates, employed in geodesy, mathematical astronomy, etc Have you ever spent any time on Royal cubit rods or Naram-Sin's reformation of metrology in 2150 ? Pretty fascinating topics

[@itsinis]

Love the video! Can't wait for more.

[@blasco500]

Very interesting. Thank you

[@sharonjuniorchess]

With ancient tools being found in Egypt dating back to 3.2m years ago it is interesting to speculate where the Egyptians got their 'understanding' of binary counting & arithmetic from. One of the oldest games in Africa which is called Mancala (but goes by many different names) involved dropping small seeds or pebbles into a series of scooped or hollowed out containers. But it also has another purpose as a counting tool (like an abacus) and it is interesting to note that this binary counting system is still used today in some parts of Ethiopia which first involves counting a number stones or pebbles to represent the number and then extracting its binary representation by repeated halving before doing the binary operation of adding or multiplying to get the result and then converting the binary number back into its whole pebble number representation. In fact this method is so simple & practical to use that it makes me wonder why we don't teach children first how to do binary arithmetic as they can handle quite large numbers this way and only when they understand how to do binary arithmetic move from binary to the more compact Denary system. I believe Napier oscillated between different bases to help him do his computations.

[@hanshazlitt4535]

Very interesting. Thanks for the upload!

[@Robinson8491]

This loaf example by Ahmes is brilliant. By the way, have you been able to figure out whether the Euler identity (so imaginary number i and e) is present in base 60 system? I watched your interview on the TOE with Curt Jaimungel and this was one of the unanswered questions asked

[@milenacontreras8690]

Thank you so much!! You are a very good TEACHER ! I discovered you with Howard Crowhurst . Greatings from South America. 🍂🍂🍂

[@txikitofandango]

The fact that 8 loaves divided by 93 equal parts is the same as one loaf divided into 93 pieces, and then you take 8 pieces, is also not trivial. Who figured that one out?

[@OddlingCore]

BUT HOW DO THEY TELL THE DIFFERENCE BETWEEN ONE AND SIXTY?! Edit: Literal seconds after I posted this comment, he answered my question in the video

[@paul-filipilasca1632]

Lovely

[@christopherellis2663]

Confused by fractions? I'll have two halves, and you get the remainder. x-2x/2=0. Great for Trigonometry.

[@sanketparekar]

If we apply mathematical logic to the word "Hindu-arebic number system", it returns FALSE, according to mathematical logic it should be either "Hindu number system" OR "Arebic number system". Thanks sir _/\_

[@orsoncart802]

This is a little off topic but given that it concerns fractions I suppose it’s tangentially related. Here goes: How good a metaphor is “lowest common denominator” when used-universally these days-as a pejorative? Super dumb or what? 😁 My own view of why people use it in this way is that they are simple attracted to its pejorative sounding constituent elements, with ‘denominator’ [whatever one of those is!] being a suitably sounding ‘de-‘ word, such as debased, degraded, defiled, despicable etc. They don’t stop to think what they are actually saying.