6 ms·

Rhind Mathematical Papyrus

42 points by abudabi123 4y ago

olddustytrail 4y ago
I'm a bit in two minds about these things. On the one hand it feels wrong it was removed from the country of origin. On the other hand would it have been as well preserved if it hadn't been? On the third hand, this is clearly a cultural concern as had I been born 100 years ago I wouldn't have cared in the slightest about removing a document from primitive people. And had I been born 100 years in the future I wouldn't have the slightest regard for the biological humans' concerns. Perhaps it all works out.
- credit_guy 4y ago
  The people who live in Egypt now are not any closer to the writers of the Rhind Papyrus than the people who live in Norway or Argentina. The Rhind Papyrus belongs to the world heritage, not to the Egypt heritage.
  - pestatije 4y ago
    It was stolen... what are you thinking?
    - credit_guy 4y ago
      Egypt (like probably every other place on Earth) experienced countless migrations. Egypt was under Persian rule for 300 years, then under Greco-Roman rule for 1000 years. After that (1400 years ago) it was conquered by the Arabs, and to this day it considers itself an Arab state. For many hundreds of years during this period (roughly from 1200 to 1800) Egypt imported lots of slaves that became soldiers (the "mamluks"). Most of these slaves were of Slavic origin, thus resulting in the English word "slave" coming from "Slav". Bottom line, Egypt was a huge melting pot for at least 3000 years, and most likely before too. People who live now in Egypt can probably trace most of their ancestors to regions outside of Egypt. They are not more heirs of the writers of the Rhind Papyrus than you and me. But let's say that they are. What did the inhabitants of Egypt do about the Pharaonic era historical artifacts? They looted them time and again. Looted and sold them to the highest bidder. Maybe you want to claim that people from Egypt don't "loot" the Ancient Egypt artifacts, they only "take possession" of them, since they are the rightful owners. But if you claim that, then you are not in luck, my friend. This is what happened to the Rhind Papyrus. It was found (or looted) by the locals, who sold it to the highest bidder, who happened to be a guy from the Great Britain. The papyrus was not stolen, it was simply bought.
      - pestatije 4y ago
        What about all the art looted from the jews and subsequently sold overseas? > was not stolen, it was simply bought.
        credit_guy 4y ago
        How is that related with what we are discussing here? We are talking about a thing that was made 3500 years ago. Who is its rightful owner? It's a completely different situation than stealing from someone who is alive. How in the world do these things seem similar to you?
        pestatije 4y ago
        It's exactly the same thing: you bought a stolen good, please return it
        credit_guy 4y ago
        Return means return to the rightful owner. Who is the rightful owner here?
- cperciva 4y ago
  I think my answer to this would be "thanks for preserving this for us; we're ready to take it back now". These artifacts absolutely belong to their countries of origin, but we have a collective duty to ensure that they are protected -- and museums should ensure that conditions are in place for them to be properly handled before returning them.
  - olddustytrail 4y ago
    That's a good answer. I think you're right.
  - lupire 4y ago
    World heritage objects (over 1000years old?) should be under multilateral supervision and spread across the world, with every region having a sampling of artifacts from the whole world.
- lupire 4y ago
  Casually calling for worldwide genocide (anthrocide) in the next century isn't cool. Humanity isn't going virtual.
bee_rider 4y ago
The table of translations is great. > 1, 2, 6, 7, 8 and 9 loaves of bread (respectively, in each problem) are divided among 10 men. In each case, represent each man's share of bread as an Egyptian fraction. I guess it shouldn’t be surprising, but wow, this form of question really goes back.
qsort 4y ago
What never ceases to amaze me when reading ancient mathematics is how much harder everything is without proper notation. For example, you don't have rational numbers, so you are forced to represent everything as awkward sums. Even computing, say, three fifths of a number is a challenge under that system! You don't have \pi to represent "ratio of circumference to diameter", so you have to use ad-hoc approximations. You don't have notation for polynomials, so even basic equations are ad-hoc problems. Another example: (almost) the entire work of Diophantus, the man diophantine equations are named after, is basically obsoleted by \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Mind you, it's not that these people were dumb. That they were solving those problems with limited tools is proof enough that they were very smart. It's like trying to write a program in 80s Basic, at a certain point the incidental complexity is eating you alive.
- jacobolus 4y ago
  > (almost) the entire work of Diophantus, the man diophantine equations are named after, is basically obsoleted by \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. This is nowhere close to an accurate statement, even if we only consider works that have survived to the present (most of his work has been lost). Have you tried to read the work of Diophantus or any modern summary?
- jameshart 4y ago
  The question this should inspire: what do we find hard that would be trivial if we developed better notation? Einstein tensors are a great example of notation as an enabling technology - it’s a mistake to think we have thought of all the notation tricks we might need. I wonder if, for example, in attempting to reason about neural networks in terms of ‘gradients’ and ‘matrix operations’ we might look, to future mathematicians, like poor ancients struggling to handle arithmetic without a clean notation for rational fractions…
  - qsort 4y ago
    The hard part of course is that genuinely new notation (i.e. not just a more convenient way to write the same thing as before) requires genuinely new mathematics to go along with it. People had been doing derivatives (at least sort of) before Newton and Leibniz, Cardano (sort of) used complex numbers before Euler, algebra before Galois, categories before Mac Lane. But these people "connected the dots", as it were. It's not merely a trick -- it's a fundamental contribution.
pyinstallwoes 4y ago
Last time similar was posted: https://news.ycombinator.com/item?id=33691603 https://news.ycombinator.com/item?id=33691603 > One of the modern applications of Egyptian fractions is the request of a specific resistance value needed in the design of an electrical circuit, a problem called in the literature the 2- Ohm problem. College students know well from their physics class, that the equivalent resistance R of two parallel resistances and is given from a law very easy to deduce, based on equating the current passing through the fictitious equivalent resistance R with the two currents passing through both resistances while maintaining same potential. One direct application of this, suppose an engineer wishes to incorporate in one of his designs a resistor of so many ohms which the manufacturer does not produce; for it is impossible that the latter displays in the market all possible ohm-values for his resistors. First, the market cannot possibly sustain it, but more important, one cannot feasibly produce resistors with values as elements of a dense subset of the real line, being, as analysis taught us, an uncountable set. Rather, manufacturers display only in the market what they call an "E12 series", i.e. resistors in sets of 12 different values, namely > 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 ...... > 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820...... > 1000, 1200.......... Ohms, etc..... > Now suppose an engineer needs in one of his designs a resistor of 7 ohms, then he would resort to a parallel combination from the fraction 1/7=1/10+1/56+1/100+1/120+1/150 in which all the resistors belong to the E12 series, i.e. he will replace his 7 ohms resistor with 5 parallel resistors; this he reaches using a special software (computer programmes exist for such designs, yet the exact solution is by no means trivial). What I did myself instead, is to resort to Ahmes 2/n table and wrote 2/7=1/4+1/28 or that 1/7=1/8+1/56. Decomposing further 1/8 into 1/12+1/24=1/12+1/48+1/48, but then I shall have to use instead of the 48 ohms resistor a resistor of 47 ohms from the E12 table. My final fraction is 1/7=1/12+1/ 47+1/47+1/56, i.e. my resistor of 7 ohms will be simulated by 4 parallel resistors instead of 5 (I am accepting equal fractions). My solution is both minimal and optimal based on Ahmes table. The relative error of my design will not exceed 0.6 per cent, being negligible; especially that any manufactured resistor will itself be subject to some allowed tolerance of the same order. https://web.archive.org/web/20130625181118/http://weekly.ahr https://web.archive.org/web/20130625181118/http://weekly.ahr... So, a thousands of years ago? Ancient Egypt and before? :) Also: > The measured values of voltages and currents in the infinite resistor chain circuit (also called the resistor ladder or infinite series-parallel circuit) follow the Fibonacci sequence. The intermediate results of adding the alternating series and parallel resistances yields fractions composed of consecutive Fibonacci numbers. The equivalent resistance of the entire circuit equals the golden ratio.

42 points by abudabi123 4y ago

I'm a bit in two minds about these things. On the one hand it feels wrong it was removed from the country of origin. On the other hand would it have been as well preserved if it hadn't been? On the third hand, this is clearly a cultural concern as had I been born 100 years ago I wouldn't have cared in the slightest about removing a document from primitive people. And had I been born 100 years in the future I wouldn't have the slightest regard for the biological humans' concerns. Perhaps it all works out.

credit_guy 4y ago
The people who live in Egypt now are not any closer to the writers of the Rhind Papyrus than the people who live in Norway or Argentina. The Rhind Papyrus belongs to the world heritage, not to the Egypt heritage.
- pestatije 4y ago
  It was stolen... what are you thinking?
  - credit_guy 4y ago
    Egypt (like probably every other place on Earth) experienced countless migrations. Egypt was under Persian rule for 300 years, then under Greco-Roman rule for 1000 years. After that (1400 years ago) it was conquered by the Arabs, and to this day it considers itself an Arab state. For many hundreds of years during this period (roughly from 1200 to 1800) Egypt imported lots of slaves that became soldiers (the "mamluks"). Most of these slaves were of Slavic origin, thus resulting in the English word "slave" coming from "Slav". Bottom line, Egypt was a huge melting pot for at least 3000 years, and most likely before too. People who live now in Egypt can probably trace most of their ancestors to regions outside of Egypt. They are not more heirs of the writers of the Rhind Papyrus than you and me. But let's say that they are. What did the inhabitants of Egypt do about the Pharaonic era historical artifacts? They looted them time and again. Looted and sold them to the highest bidder. Maybe you want to claim that people from Egypt don't "loot" the Ancient Egypt artifacts, they only "take possession" of them, since they are the rightful owners. But if you claim that, then you are not in luck, my friend. This is what happened to the Rhind Papyrus. It was found (or looted) by the locals, who sold it to the highest bidder, who happened to be a guy from the Great Britain. The papyrus was not stolen, it was simply bought.
    - pestatije 4y ago
      What about all the art looted from the jews and subsequently sold overseas? > was not stolen, it was simply bought.
      - credit_guy 4y ago
        How is that related with what we are discussing here? We are talking about a thing that was made 3500 years ago. Who is its rightful owner? It's a completely different situation than stealing from someone who is alive. How in the world do these things seem similar to you?
        pestatije 4y ago
        It's exactly the same thing: you bought a stolen good, please return it
        credit_guy 4y ago
        Return means return to the rightful owner. Who is the rightful owner here?
cperciva 4y ago
I think my answer to this would be "thanks for preserving this for us; we're ready to take it back now". These artifacts absolutely belong to their countries of origin, but we have a collective duty to ensure that they are protected -- and museums should ensure that conditions are in place for them to be properly handled before returning them.
- olddustytrail 4y ago
  That's a good answer. I think you're right.
- lupire 4y ago
  World heritage objects (over 1000years old?) should be under multilateral supervision and spread across the world, with every region having a sampling of artifacts from the whole world.
lupire 4y ago
Casually calling for worldwide genocide (anthrocide) in the next century isn't cool. Humanity isn't going virtual.

bee_rider 4y ago

The table of translations is great. > 1, 2, 6, 7, 8 and 9 loaves of bread (respectively, in each problem) are divided among 10 men. In each case, represent each man's share of bread as an Egyptian fraction. I guess it shouldn’t be surprising, but wow, this form of question really goes back.

qsort 4y ago

What never ceases to amaze me when reading ancient mathematics is how much harder everything is without proper notation. For example, you don't have rational numbers, so you are forced to represent everything as awkward sums. Even computing, say, three fifths of a number is a challenge under that system! You don't have \pi to represent "ratio of circumference to diameter", so you have to use ad-hoc approximations. You don't have notation for polynomials, so even basic equations are ad-hoc problems. Another example: (almost) the entire work of Diophantus, the man diophantine equations are named after, is basically obsoleted by \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Mind you, it's not that these people were dumb. That they were solving those problems with limited tools is proof enough that they were very smart. It's like trying to write a program in 80s Basic, at a certain point the incidental complexity is eating you alive.

jacobolus 4y ago
> (almost) the entire work of Diophantus, the man diophantine equations are named after, is basically obsoleted by \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. This is nowhere close to an accurate statement, even if we only consider works that have survived to the present (most of his work has been lost). Have you tried to read the work of Diophantus or any modern summary?
jameshart 4y ago
The question this should inspire: what do we find hard that would be trivial if we developed better notation? Einstein tensors are a great example of notation as an enabling technology - it’s a mistake to think we have thought of all the notation tricks we might need. I wonder if, for example, in attempting to reason about neural networks in terms of ‘gradients’ and ‘matrix operations’ we might look, to future mathematicians, like poor ancients struggling to handle arithmetic without a clean notation for rational fractions…
- qsort 4y ago
  The hard part of course is that genuinely new notation (i.e. not just a more convenient way to write the same thing as before) requires genuinely new mathematics to go along with it. People had been doing derivatives (at least sort of) before Newton and Leibniz, Cardano (sort of) used complex numbers before Euler, algebra before Galois, categories before Mac Lane. But these people "connected the dots", as it were. It's not merely a trick -- it's a fundamental contribution.

pyinstallwoes 4y ago

Last time similar was posted: https://news.ycombinator.com/item?id=33691603 https://news.ycombinator.com/item?id=33691603 > One of the modern applications of Egyptian fractions is the request of a specific resistance value needed in the design of an electrical circuit, a problem called in the literature the 2- Ohm problem. College students know well from their physics class, that the equivalent resistance R of two parallel resistances and is given from a law very easy to deduce, based on equating the current passing through the fictitious equivalent resistance R with the two currents passing through both resistances while maintaining same potential. One direct application of this, suppose an engineer wishes to incorporate in one of his designs a resistor of so many ohms which the manufacturer does not produce; for it is impossible that the latter displays in the market all possible ohm-values for his resistors. First, the market cannot possibly sustain it, but more important, one cannot feasibly produce resistors with values as elements of a dense subset of the real line, being, as analysis taught us, an uncountable set. Rather, manufacturers display only in the market what they call an "E12 series", i.e. resistors in sets of 12 different values, namely > 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 ...... > 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820...... > 1000, 1200.......... Ohms, etc..... > Now suppose an engineer needs in one of his designs a resistor of 7 ohms, then he would resort to a parallel combination from the fraction 1/7=1/10+1/56+1/100+1/120+1/150 in which all the resistors belong to the E12 series, i.e. he will replace his 7 ohms resistor with 5 parallel resistors; this he reaches using a special software (computer programmes exist for such designs, yet the exact solution is by no means trivial). What I did myself instead, is to resort to Ahmes 2/n table and wrote 2/7=1/4+1/28 or that 1/7=1/8+1/56. Decomposing further 1/8 into 1/12+1/24=1/12+1/48+1/48, but then I shall have to use instead of the 48 ohms resistor a resistor of 47 ohms from the E12 table. My final fraction is 1/7=1/12+1/ 47+1/47+1/56, i.e. my resistor of 7 ohms will be simulated by 4 parallel resistors instead of 5 (I am accepting equal fractions). My solution is both minimal and optimal based on Ahmes table. The relative error of my design will not exceed 0.6 per cent, being negligible; especially that any manufactured resistor will itself be subject to some allowed tolerance of the same order. https://web.archive.org/web/20130625181118/http://weekly.ahr https://web.archive.org/web/20130625181118/http://weekly.ahr... So, a thousands of years ago? Ancient Egypt and before? :) Also: > The measured values of voltages and currents in the infinite resistor chain circuit (also called the resistor ladder or infinite series-parallel circuit) follow the Fibonacci sequence. The intermediate results of adding the alternating series and parallel resistances yields fractions composed of consecutive Fibonacci numbers. The equivalent resistance of the entire circuit equals the golden ratio.