Math and the Ancient World

[jay gw]

I was looking through some old books on business, and noticed that the information was very outdated, pre computer days etc.

The mathematical ratios used to analyze revenues, expenses/other business related data were the same as is used today, but were never more advanced than one or two variables. There was no regression analysis, not one single book covered anything as advanced as multiple regression.

This led me to the question:

Prior to computers and calculators, were humans restricted to using relatively simple mathematical formulas?

Look at the pyramids of Egypt. How much math is really involved in their design and construction? What about the roman aqueducts? The Colisseum? Statue of Liberty? Notre Dame?

Without the knowledge like calculus and the ability technology has provided, is it true to say that the human world until 50 years ago or so was literally constructed by series of low level, elementary mathematical formulas?

 

[Brown]

In the age before calculators, a lot of engineering pursuits were "table-driven." Sines, cosines, logarithms, square roots and the like had to be looked up in books, and interpolations had to be performed. Slide rules could be used to do some of the calculations quickly, but only with an accuracy of about three digits. Tables usually had far more digits and were more accurate.

Preparing a table was a lot of work, but it could be a very valuable tool.

Bridge-builders, building designers and public works engineers, among others, used tables to design their projects.

Some engineering disciplines are still table-driven. Thermodynamics texts include tables of enthalpy, entropy and the like, which have been derived by experimentation. Materials science also uses tables of material properties.

But nobody looks up a cosine or a square root anymore. There is no need.

 

[Kiless]

I had a Log book. When younger, I used to use an abacus until a teacher said that we had to do more computer skill work and took them away from us. I miss my abacus and I'm planning to get one for a friend's child as a birthday present.

 

[Iconoclast]

I was looking through some old books on business, and noticed that the information was very outdated, pre computer days etc.

The mathematical ratios used to analyze revenues, expenses/other business related data were the same as is used today, but were never more advanced than one or two variables. There was no regression analysis, not one single book covered anything as advanced as multiple regression.

The invention of the first spreadsheet -- VisiCalc -- for the first time made complex financial calculations and "what if" scenarios simple and fast.

Prior to computers and calculators, were humans restricted to using relatively simple mathematical formulas?

By the very definition of the word "relative" this statement MUST be true. Faster computational devices allow relatively more complex equations to be solved faster than they were in the past.

Look at the pyramids of Egypt. How much math is really involved in their design and construction? What about the roman aqueducts? The Colisseum? Statue of Liberty? Notre Dame?

How did they known the Cathedral at Notre Dame wouldn't collapse under it's own weight?

Without the knowledge like calculus and the ability technology has provided, is it true to say that the human world until 50 years ago or so was literally constructed by series of low level, elementary mathematical formulas?

Just when do you think calculus was invented? Newton published the first edition of his Principia in 1687 which includes what we today call calculus.

 

[anor277]

Posted by Iconoclast
Just when do you think calculus was invented? Newton published the first edition of his Principia in 1687 which includes what we today call calculus.

Actually I believe calculus was invented a long time before the 17th century. Archimedes, I believe, published something called the Sand Reckoner , which dealt with most problems of integral calculus (and he drew on more ancient sources). Differential calculus, as you say, was the invention of Newton and Leibniz.

 

[Iconoclast]

Thanks for clearing that up anor.

 

[LW]

Look at the pyramids of Egypt. How much math is really involved in their design and construction?

Not much. Most of Egyptian mathematics worried about practical problems: how to compute areas of various plots of land, how to find out the size of the rations of individual workers, and like. A good source for all that is Mathematics in the Time of the Pharaohs.

 

[drkitten]

Actually I believe calculus was invented a long time before the 17th century. Archimedes, I believe, published something called the Sand Reckoner , which dealt with most problems of integral calculus (and he drew on more ancient sources).

No. Archimedes didn't have a decent formulation of the infinite, either conceptually or using the more modern limit process, and of course had no notion of the antiderivative available to him. Given that those are the two most fundamental concepts of integral calculus, I'd hardly consider his work to "[deal] with most problems of integral calculus."

A good treatise, and well worth reading. It's the first real attempt to deal with the idea that there are, in fact, very very large but distinct numbers and the measurement of large quantities. But hardly calculus.

 

[Soapy Sam]

Wasn't there a chap did something with how apples fall from the moon?

Jacob Newman? Einaar Newcomen?
Something like that.

 

[Iconoclast]

Wasn't there a chap did something with how apples fall from the moon?

Jacob Newman? Einaar Newcomen?
Something like that.

I believe that was Alfred E. Newman.

 

[CBL4]

About a dozen years ago, I took a class on manufacturing quality assurance. To make the math simple, they were always making approximations and assumptions (e.g. everything is bell shaped) that they knew were untrue. This let them look stuff up in tables rather than have to do the math.

With computer data tracking, all of these approximation could be removed but I have no idea whether this is actually happening.

CBL