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Giants of Antiquity & The Mind

" There are some, King Gelon, who think that the number of the sand is infinite in multitude; ... Again there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its magnitude ... But I will try to show you by means of geometrical proofs ... that, of the numbers named by me ... , some exceed not only the number of the mass of sand equal in magnitude to the Earth ... , but also that of the mass equal in magnitude to the universe."

-- Archimedes , The Sand Reckoner

1.1 Nature of Number

1.2 Sys. of Numeration
1.3 Arithmetic
1.4 Properties
1.5 Catalog of Numbers
2.1 Cosmic Horizons
2.2 SI Prefixes
2.3 Imagining Numbers
2.4 The -illion Series
3.1 Intro to Recursion

3.2 Common Notations

3.3 Large No. Arithmetic

4.1 Jonathan Bowers

4.2 Fast Growing

4.3 Extensible-E

    In this Chapter we explore large numbers as they occurred in antiquity. Ancient people were as fascinated by large numbers as we are, perhaps even more. Large numbers served to inspire awe, strike fear, and describe the divine. Large numbers were as much spiritual as intellectual objects to the ancients.

 In the previous two chapters we explored numbers as they occur in nature, and as "tools". In this chapter we free numbers of this practical obligation and consider them instead as products of the human imagination.

 The following articles are filled with telling anecdotes about large numbers. At the end of this chapter we will try and imagine really large numbers ourselves and see just how far our imagination can take us.


 Although you can always read the articles in sequential order, in this case it is not strictly necessary as each article can work as a stand-alone article.

2.3.1 - Skewes' Number 

            We explore the mathematics behind the origin of Skewes' Number and then try to comprehend it's sheer size! Prepare for some mind boggling mathematics.

2.3.2 - Imagining Big Numbers

            Now let's take the concepts we already know and take our own journey through the upper echalons of the finite.

2.3.3 - Archimedes The Sand Reckoner (ON HIATUS)

2.3.4 - The Wheat & The Chessboard (ON HIATUS)

2.3.5 - Huge Arabic Decimal Numbers (ON HIATUS)