# Creating Log Tables: Briggs' 400-Year-Old Accomplishment

• B
• Thecla
In summary, 400 years ago, Briggs created a table that was accurate to 14 decimal places. He did this by taking multiple roots of 10. Nowadays, we use computers to produce tables of logarithms, but back then this was a huge undertaking.
Thecla
I haven't used a log table in a long time and the one I used in High School went from 10 to 99 with four significant figures for the logarithms.
I wondered how did Briggs create a log table 400 years ago? How did he find the logarithm of 7(base 10)?
I looked around the internet and You Tube and most sites show how to use logs in multiplication, division and finding roots, but not much on creating a table. I think i know why creating a table is not a point of discussion.
I found a paper on the internet by Denis Roegel (2010):
"A reconstruction of the Tables of Briggs'Arithmetica Logarithmica"

I only read the first two pages because the math is beyond me
Briggs' log table covered the numbers from 1 to 20,000 and 90,001 to 100,000 to 14 decimal places.How did he do it?
He did it by taking multiple roots of 10
log 10=1
log 10^.5=.5
log10^.25=.25
Down to log 10^(.5^54)=.5^54
The author states that Briggs was aided by computers{people} but no names were mentioned.
What a tremendous undertaking this was. As somebody said you only have to do this once and for hundreds of years it saved so much time. Simon Laplace, a 19th century scientist, said that what took months of arithmetical calculations could now be done in a few days.

As an aside, in addition to errors generated by the computer people, some table publishers injected small errors into the tables in order to detect if some other publisher had plagiarized their work.

This injection of small errors became a real issue for the British Admiralty which explained why Babbage's machines were needed to compute these kinds of tables accurately without error.

https://en.wikipedia.org/wiki/Mathematical_table

https://www.maa.org/press/periodica...tical-treasure-babbage-s-tables-of-logarithms

The first thing done with John von Neumann's computer was the printing of a table of logarithms.

jedishrfu said:
This injection of small errors became a real issue for the British Admiralty which explained why Babbage's machines were needed to compute these kinds of tables accurately without error.
I looked at the reference. It appears that the tables were produced by hand, long before the "engine". His innovation appeared to be careful proofreading. Remember, in those day computer was a job description.

It did say that producing the tables convinced Babbage that machines should produce tables of logarithms. But I believe that didn't happen until one hundred years later at the Institute for Advanced Studies.

400 years ago, they would have hired idiot savants to calculate tables. Often, idiot savants can not describe how they do their calculations. When they try, they sometimes say that certain numbers have a taste or color. It doesn't make any sense to other people.

Here's a log table:

SammyS
and here's a couple of Scottish adders as Ireland did snake subtraction:

The winters in Scotland must have been long cold and dark for in the following years Briggs created the log of trig functions(sines, cosines, and tangents ) to the one hundredth of a degree also to 14 decimal places.

Thecla said:
The winters in Scotland must have been long cold and dark for in the following years Briggs created the log of trig functions(sines, cosines, and tangents ) to the one hundredth of a degree also to 14 decimal places.
In those days, 400 years ago, 100 years before Newton, they were fanatically trying to understand the motion of the planets. They did some amazingly accurate calculations.

Thecla said:
The author states that Briggs was aided by computers{people} but no names were mentioned.
They probably weren't named because they acted under his explicit instructions, performing purely "mechanical" arithmetical tasks, much the same way an electronic computer nowadays performs according to a program written by a programmer.

Calculation-intensive projects used rooms full of human computers (usually women) even after World War II.

https://www.smithsonianmag.com/science-nature/history-human-computers-180972202/

jtbell said:
Calculation-intensive projects used rooms full of human computers (usually women) even after World War II.
And (in case you didn't know) they even made a movie about it....

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