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Ancient Egyptian Mathematics        (11 December 1999)

Hello,

You don't know me but I was wondering if you could be of some help. Is there any information that you could give me about the ancient Egyptians being the first civilization to really study and use math? Also, any information on how they incorporated math with the building of pyramids would be greatly appreciated.

Thank you so much for your time. I'm so sorry to be a bother to you. Good day!

Respectfully,

Emma B.        EmmaG707@aol.com

Re: Ancient Egyptian Mathematics        (15 December 1999)

Dear Emma,

Yes, the Egyptians were among the first to develop a practical knowledge of mathematics for their everyday needs, they used the decimal system of notation that we nowadays still use (computers, for instance, use the binary system, the ancient Mesopotamians used a very different one based on the number 60) already from 3,000 BC (the Narmer Palette). Although they didn't reach as far as we know, the abstraction that later the Greeks would achieve, they knew basic geometry and arithmetic, they could calculate volumes of different geometric entities, they could work with fractions, they knew a value of Pi of 3.16, better than the one used by others at the same of time of just 3. They used this for all their activities, also for building the pyramids.

You'll find more information in a specialized forum on ancient mathematics, at:

http://forum.swarthmore.edu/epigone/historia_matematica/

I hope this helps.

Sincerely,

José        jjvalent8@yahoo.com

Los Charlatanes y la Egiptología        (23 de Diciembre de 1999)

Creo que de cierta manera tienen ustedes razón, pero en cuanto al ejemplo del poder de una pirámide les digo que están muy equivocados, pues yo mismo hice construir una pirámide de gran tamaño y puedo decirles que en pleno verano, la época más húmeda de Canadá, yo puse dos zanahorias a secar dentro de la pirámide, hace dos años, y aún las tengo, aunque cada día se secan más y más sin pudrirse. También puse un ramo de hojas de menta y ahí están completamente deshidratadas con todo su sabor e incluso a veces las he utilizado para hacer té, después de 24 meses.

Un saludo desde Canadá,

Armando Hidalgo        homar@colba.net

NOTA DEL MODERADOR - Ud. tiene derecho a creer lo que desee, pero nosotros nos remitimos a nuestro sentido común que nos dice que no hay razón para que una forma geométrica en particular preserve o altere o actúe de un modo distinto a otras formas geométricas y a los hallazgos de la Universidad de Guelph que dieron "el beso de la muerte" a esas teorías extrañas. Pruebe con un cubo o un icosaedro o una simple copa invertida y verá que el resultado es el mismo...

World Pyramids and Ziggurats                (2 January 2000)

I've read in books about the pyramids by which Egypt is famous but also pyramids or similar monuments have been found in ancient America (Mexico, Peru) and in Mesopotamia (Iraq). I've found it difficult to tell the difference between them, if there was any, why did they build them? What were they used for? Since the explanations I've seen in some literature seem a bit far-fetched, to say the least, I'd like to know more about this subject, which I haven't found discussed at all in the serious books I've read so far.

Andrés Suárez                suarez@starting-point.com

Re: World Pyramids and Ziggurats                (10 January 2000)

In my humble opinion, they represent the human wish to build mountains in which to worship their gods or to procure means to enable the souls of their dead rulers to ascend to heaven. In ancient Egypt that seems to have been the main purpose, also perhaps to show to everybody the power of the ruler who could have them built. In Mesopotamia, it seems they were just temples, high places to worship the gods, let's not forget that it is a rather flat land (especially southern Iraq) and they had to build their own mountains. In America, they seem to have fulfilled that purpose and also occasionally acted as tombs, as in Mexico. The difficulty some people have to imagine those ancient peoples building them with rudimentary technology merely reflects their modern inability to realize what ancient people could accomplish with limited resources. G. Belzoni, the Italian explorer who worked in Egypt at the beginning of the 18th century, illustrates this point very well. In his book of memoirs, he tells us that once he tried to move a huge fragment of a colossus near the river to ship it to Alexandria and then to London, England, but was unable to make it move one inch, even after trying all his European skills. Then a group of local peasants came and offered to help. To his astonishment, with the assistance of some long sticks and using their lifelong peasant techniques, they managed to move the object to where Belzoni wanted. Illiterate, apparently primitive natives had accomplished what the modern European couldn't do. It is a sobering example, isn't it? Let's not write off ancient people's abilities just because we can't figure out how effective their simple but practical resources can be.

Duart                (duart@my-deja.com)

Elementos extranjeros en el arte arcaico egipcio        (24 de Enero de 2000)

En algunos de los objetos fechables al Protodinástico egipcio se pueden apreciar motivos que no son originarios de Egipto, como por ejemplo en la Paleta de Narmer los dos monstruos mitológicos con los largos cuellos entrelazados, en el cuchillo de Gebel el Arak, el héroe mitológico dominando o estrangulando dos leones, etc. En la bibliografía antigua se reconocía que esos motivos eran de origen mesopotámico, donde abundan tales representaciones, de modo que se menciona en ellos una temprana influencia mesopotámica sobre Egipto que llevó probablemente a la aparición de la escritura en Egipto, la arquitectura en ladrillo secado al sol de especiales características y otros elementos. En los libros más recientes sobre tal período en Egipto ya no se habla más de estos temas y no veo por ninguna parte la supuesta influencia mesopotámica. ¿Qué ha causado el cambio de postura? ¿Por qué no se hallan en Egipto posteriormente más ejemplos de esa influencia? Hay autores populares que ahora hablan nuevamente de una conquista de Egipto temprana por invasores mesopotámicos, ¿es ésto aceptable?

Zoser        (zoser8@my-deja.com)

Re: Elementos extranjeros en el arte arcaico egipcio    (26 de Enero de 2000)

Yo creo que debemos tomar en cuenta que esos motivos artísticos tempranos en Egipto sólo aparecen en algunos objetos y luego nunca más los vemos en el arte egipcio, fueron aparentemente una moda pasajera, quizás producto de copias efectuadas por artistas egipcios de decoraciones de objetos provenientes de Mesopotamia, en una época en que el arte egipcio estaba definiendo sus parámetros de estilo y forma.

La supuesta conquista mesopotámica en esa época, me cuesta creer que alguien la esté sosteniendo aún hoy día, pues la arqueología egipcia reciente ha aventado definitivamente toda posibilidad de conquista extranjera, tal como la definieron Petrie y otros posteriormente, pues no se ven por ningún lado en Egipto rastros de una dominación de ese tipo en esta época tan temprana. Hay una continuidad innegable que habría sido rota en el registro arqueológico si hubieran ingresado a Egipto conquistadores extranjeros.

Según parece, en el Protodinástico egipcio (Naqada III) parece haber habido una colonización egipcia del sur de Palestina, que por razones oscuras cesó a fines de este período (Bronce Temprano I). Así que lejos de una conquista de Egipto por extranjeros, la situación parece haber sido justamente lo contrario... Muchos autores populares generalmente se manejan con bibliografía anticuada y no creen necesario enterarse del estado actual de las cuestiones, pues probablemente piensan que su público jamás detectará sus gruesos errores de apreciación con tal que su prosa sea lo suficientemente florida y entretenida. Creo que el público debería disfrutar de lo ameno de la narrativa de esos autores, pero no otorgarles mucha confianza que debería reservarse para obras más serias.

Vignolo        (luisvignolo@yahoo.com)

Black Pharaohs - Egypt's Nubian Rulers         (8 February 2000)

This message announces the publication in February 2000 of a new book entitled The Black Pharaohs - Egypt's Nubian Rulers, presenting in-depth research, fresh analysis, and perhaps a controversial reassessment of the Kushite kingdom in ancient Egypt.

Many thanks for taking the time to read this. We hope the information is of interest. If you know anyone else who may be interested, please feel free to pass this information on to others.

Yours truly,

Robin Page

The Rubicon Press

57 Cornwall Gardens

London SW7 4BE

United Kingdom

Tel/Fax: +44 (0) 207 937 6813

Book Description

The Black Pharaohs - Egypt's Nubian Rulers

How did modern Sudan's ancient civilisation conquer, rule then lose its dominion over Pharaonic Egypt? The Rubicon Press is pleased to announce the publication of a new book, The Black Pharaohs - Egypt's Nubian Rulers - a major historical and archaeological study on the rise and fall of ancient Egypt's one-time black rulers. The Black Pharaohs is a detailed and provocative reassessment of the Kushite kingdom, which, at its height, stretched from the Mediterranean far into modern Sudan, while influencing large parts of Black Africa and much of western Asia including Syria and The Lebanon. Written by Dr Robert Morkot, a renowned scholar and Egyptologist specialising in the ancient Kushite civilisation, The Black Pharaohs describes the extraordinary scope and influence of the Kushites at a time of remarkable social, cultural and military upheaval in north and north east Africa and the Near East. For nearly one hundred years, between 750 and 650 BC, the Kushite kingdom was one of the greatest powers on earth. The Kushites were seen by the princes of western Asia, notably the kings of Israel and Judah, as their defenders against the might of the Assyrian empire. Inevitably, their championing of the Asiatic kingdoms brought the Kushites into conflict with the Assyrian empire. It was the strength of Assyria combined with the self-interest of the Libyan dynasts of the Egyptian Delta that eventually forced the Kushites out of Egypt, putting a stop to Nubia's Pharaonic ambitions. In this major work of more than 350 pages and 116 illustrations, Robert Morkot examines Nubia's legacy in ancient Egypt, describing the impact of this often under-estimated people. Where did the powerful Kushite kingdom come from? How was it able to conquer Egypt and gain such influence in western Asia? What influence did the Kushites wield in Egypt and amongst Egypt's neighbours in Africa? Until recently, the Kushite kingdom was thought to have burst from an historical void. But, over the past decade, there has been a considerable reassessment of the origins of this powerful state. Indeed, the archaeology of this period of Nubian history has become the focus of heated academic debate. Much of this debate and subsequent controversy has focussed on the minutiae of archaeology. As a leading scholar in this field, Dr Morkot seeks to give a more expansive view of the era, incorporating a great deal of new evidence and interpretation. The Black Pharaohs takes a much broader approach, placing the Kushite kingdom in its greater historical context, and in a long tradition of formidable opposition to Egyptian southward expansion. As well as significant Egyptian and Nubian evidence, the mass of Assyrian texts, some of which have been published only recently, sheds further light on the cultures and conflicts of these ancient super-powers. Altogether, this book draws on fresh evidence and analysis, and presents a new, and perhaps controversial, reassessment of the Kushite kingdom.

Publication Details

Full title: The Black Pharaohs - Egypt's Nubian Rulers

Hardback ISBN: 0-948695-23-4 Price Hardback: UK£ 29.95 US$ 59.95

Paperback ISBN: 0-948695-24-2 Price Paperback: UK£ 19.95 US$ 29.95

Format: 234 x 156 mm

Date of Publication: February 2000 (Rights available.)

Research Questions        (4 March 2000)

> Prof. Castillos,

>

> Thank you so much in advance for responding to my request. I'll really appreciate it.

> Thanks again.

>

>Niki

> _________________________________________________________

> QUESTIONS

>

> 1. Are there any classes that you can take in high school that apply directly to egyptology?

>

Unfortunately not. Egyptology is a highly specialized branch of history and archaeology, so you only get general glimpses in History at the High School level. It would be as unlikely as finding in High School courses on brain surgery or particle physics, they are usually graduate studies at universities.

>

> 2. Are there any classes that you can take in high school that apply indirectly to egyptology?

>

Yes, History, Archaeology, Classics, modern languages (you'll need these since besides English, German and French are the official languages of Egyptology).

>

> 3. What does it cost to go to college to become an egyptologist?

>

It depends on the college. I'd say about the same as for other careers, a few thousand dollars a year, depending on how many courses you take, etc.

>

> 4. What is the amount of time that you go to college for?

>

It also depends on the university, but I'd say on average about 4 years for a BA, another 2 to 3 for your MA and then, another 2 or 3 for your PhD, as a minimum.

>

> 5. Are there any requirements for getting into college to become an egyptologist?

>

It depends on the university, but I think requirements are not so high as for other careers where you find many applicants and selection is a must. With your High School Diploma and fairly good marks, you should be all right.

>

> 6. What are the graduation requirements?

>

First you have to take as an undergraduate courses on Anthropology, History, Archaeology, etc., with a major in one of those, then you take up Egyptology as a graduate student, the times are roughly as outlined above.

>

> 7. Can you get financial aid?

>

Again, each university has its policies, some do or you can get student loans you can repay later. You have to find out for yourself.

>

> 8. Are there any technical requirements to become an egyptologist?

>

I don't know exactly what you mean, but I think that being observant, meticulous, organized, with some mathematical skills since statistics are becoming more important every day, are basic, besides having the ability to work with others (archaeology is teamwork now) and to be a motivator and a leader.

>

> 9. Are there any internships available?

>

As before, you have to find out at your intended college.

>

> 10. Is there any training that is taught while on a job?

>

Yes, you usually go on field projects with your professors.

>

> 11. Is there any experience needed to become an egyptologist?

>

Not really.

>

> 12. Do you need to have any special skills?

>

Well, I answered this above.

>

> 13. What are the average amount of hours you work a day?

>

Well it depends on your responsibilities. As a professor, with my teaching duties, my research, administrative duties, student guidance after regular hours, lectures, popularization duties, etc., I'd say about 10 - 12 hours a day, but I just get carried away...

>

> 14. Explain what traveling is like for you and where you most often go?

>

Egypt is the destination and to wherever your studies take you. Also to important libraries and museums in Europe or North America in search of data.

>

> 15. Are there any physical requirements?

>

I don't think so. A strong constitution helps if you will work in the field, sometimes in the middle of nowhere.

>

> 16. What are extra duties that come with the job? (ex. committees, meetings, community service, etc.)

>

Like I said, you are often expected to popularize your subject because universities need to entice students to take up your subject or you'll be out of a job, also if there is an Egyptian collection there, you may become involved in its conservation and publication, if they can't afford their own people for that. You must set some limits to what they will try to get you into, otherwise you won't be able to cope trying to do everything and achieving nothing.

>

> 17. Are there any standards? (ex. drug testing, etc.)

>

No, unless you are into (recreational) drug consumption and/or dealing which is severely penalized in Egypt.

>

> 18. Is there any independent vs. group planning and productivity?

>

You'll find that the old fashioned individual approach will bring you worse results than teamwork, besides you'll most likely be expected to integrate yourself into existing ongoing projects. As a general rule, if you don't do research, publish little and just teach, if your position is not tenured, you'll soon be chucked out. If you managed to achieve tenure, they'll relegate you to one side and ignore you, not a nice prospect for anyone. Although productivity is less demanded than in business, there is a minimum expected from you.

>

> 19. Do you have to do a lot of paper work? If so, what kind?

>

Yes, but because of shortage of staff in our Uruguayan Institute which has very limited financial resources, in bigger places you'll have secretarial staff available to take up many of the menial chores, but some of it you'll have to do anyway. You have to write your papers, reports, prepare your classes, reply to all your mail, etc.

>

> 20. How flexible is your schedule? Why or why not?

>

It's not flexible at all, because of personnel shortages here.

>

> 21. Is your job stressful? Why or why not?

>

Any job is as stressful as you let it be. To the outside pressure and the one from within yourself, you must set limits that have to do with efficiency and job satisfaction, but without barring you from the normal human being recreational activities that will make you a relaxed and balanced person, in control of his/her life, as it should be.

>

> 22. What is you salary?

>

I will not answer questions of a personal nature, but in the States I think that you may start at about $ 20 - 30,000 a year and if you land a tenured teaching position in a good place, you might earn $ 40 - 50,000 a year.

>

> 23. What was you starting salary?

>

I answered this above with an approximate estimation for the United States.

>

> 24. What are the terms of your sick, vacation, and maternity leave?

>

No such thing in our Institute with its honorary teaching positions, but I understand they can be quite generous at most universities.

>

> 25. What are perks that come with the job?

>

Respect, admiration for the subject you deal with that is very popular everywhere and rubs off unto you, the chance to travel and meet different people and see exotic places.

>

> 26. What will the demand for egyptologists be in 7-10 years?

>

I think it will be stable, as people retire or pass away, newcomers will take those jobs, besides countries that are just now opening up to Egyptology like China, are offering positions to qualified foreigners.

>

> 27. What is the size of the field now and what will it be in the future?

>

I think it's a very restricted area of knowledge that will never become a mass activity like medicine or law, but a certain number of talented people will always be required to dig, study, publish, teach and preserve the countless monuments of Egypt and the objects at the Museums.

>

> 28. What is the competiveness of the field?

>

I think very high, positions are relatively few and the aspiring graduates many, but there is always room for bright people who want to leave their mark and contribute to the common goal.

>

> 29. What are the areas of availability and what will they be in 7-10 years?

>

I'd say that the destination of the new experts will be universities as teaching staff, museums as curators, archaeological institutions dealing with fieldwork, even travel agencies as guides and many others that might come up as we move towards an increasingly service-oriented world in which people will enjoy more time for leisure and longer retirement years to fill with new hobbies and interests.

I would like to say that some of my opinions may be debatable, so I would suggest you get feedback from other colleagues in order to have a balanced view. Good luck with your project !

J. J. Castillos         (juancast@yahoo.com)

>

> Thanks a lot,

>

> Niki Spear         (lvedbyall@hotmail.com)

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