Questions tagged [computation]

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38 votes
6 answers
4k views

What is so mysterious about Archimedes' approximation of $\sqrt 3$?

In his famous estimation of $\pi$ by inscribed and circumscribed polygons, Archimedes uses several rational approximations of irrational values; a typical example is that he states, without ...
Mark Dominus's user avatar
31 votes
3 answers
6k views

How did Napier come to invent logarithms?

What was Napier's original logic, leading to his invention of logarithms? In other words, how did Napier, using the mathematics that was available at that time, derive them?
AbdElWadoud's user avatar
22 votes
1 answer
1k views

What sorts of calculations called for the invention of logarithm tables?

It's often stated that Napier invented logarithms in order to simplify the task of engineers and scientists who had to crunch numbers by hand. Now, logarithms obviously do simplify calculations (as I ...
Jack M's user avatar
  • 3,119
13 votes
3 answers
5k views

What was the first electronic computer?

I would like to know what is considered to be the first electronic digital computer. A literature ambiguous on this. I found these claims: ENIAC - a computer constructed by Mr. Eckert and Mr. ...
Martin Vesely's user avatar
12 votes
2 answers
3k views

How did the shift from constructed mathematical objects to modern mathematics occur?

How did the shift from the times of Thales, Pythagoras, and even Euclid, where mathematical objects were found, exhibited, or constructed from given entities, to modern mathematics occur? In modern ...
Leandro Caniglia's user avatar
12 votes
3 answers
2k views

Did anybody know Pi well enough in 1592 to celebrate Pi day?

Pi to 7 decimal digits is: 3.1415926 Many people are familiar with Pi day. Celebrated on March 14 as per American date format, the holiday brings attention to the fact that the date resembles the ...
dotancohen's user avatar
11 votes
1 answer
476 views

Does Blum's speedup theorem have any conceptual predecessors?

Blum's speedup theorem seems to me that bears at least some superficial resemblance to Gödel's research on the length of proofs under certain axiomatic systems. Does Blum's speedup theorem have any ...
GEP's user avatar
  • 1,515
9 votes
1 answer
329 views

Have the results from Computational Physics disprove any physics theory?

We are familiar with the instances when experimental results disproved physics theories, such as the Michelson-Morley experiment. What about computational physics results? To date, is there any ...
Graviton's user avatar
  • 193
8 votes
2 answers
562 views

Day-to-day tasks of human computers, à la Hidden Figures movie

I was fascinated by the film Hidden Figures, and a related article from New Scientist magazine Gifted and black: The brilliant woman who got the US into space. I'm trying to understand more about ...
nealmcb's user avatar
  • 221
6 votes
6 answers
2k views

Has a digit ever been used to represent the number "10"?

Ten is special to humans, as there are 10 fingers on two hands, and fingers are still the basic counting medium for people. So, was there any digit representing the number "10" in a positional system ...
Barun's user avatar
  • 209
6 votes
1 answer
257 views

What did Delaunay invent Delaunay triangulations for before computers were developed?

I was teaching my students about Delaunay Triangulation which is a method for dividing a surface into triangles. This triangulation method is the basis of most computer calculations that require a ...
Hugh's user avatar
  • 162
6 votes
1 answer
363 views

Why were British WWII computing machines and their projects destroyed after the war ended?

I've seen from a number of sources that both the Colossus and the cryptological bombes operating for England were dismantled after the war ended. The Wikipedia article even says that all of Colossus' ...
Tarc's user avatar
  • 163
5 votes
1 answer
160 views

Was Charles Sanders Peirce aware of Charles Babbage's difference engine?

Is there any indication that Charles Peirce was aware of Babbage and his work on mechanical computing?
GEP's user avatar
  • 1,515
5 votes
1 answer
159 views

History of computing/computation in higher education

A Google search for the first academic computer science program a couple of years ago cited a half-dozen programs in France and England that were considered proto-computer science. Current searches ...
user avatar
5 votes
0 answers
116 views

Where is the first reference to the "Z combinator", a call-by-value fix-point combinator?

I'd like to know the earliest reference to the Z-combinator. This could be either where the name was first coined, or even the first discussion of a need for an applicative-order Y combinator. I didn'...
Jason Hemann's user avatar
4 votes
3 answers
219 views

What is the most number of digits of a mathematical transcendental constant that have been required for a real computation?

What is the most number of digits of a transcendental mathematical constant (for example, $\pi$ or $\mathrm{e}$) that have been necessary for an actual computation? Note that I am asking about the ...
ajd's user avatar
  • 151
4 votes
1 answer
104 views

What/When was the first radio nav system capable of triangulating your position?

What was the first radio navigation system capable of triangulating your position, and when was it built? How accurate was it and what was its range? This does not have to be GPS or a satellite ...
DrZ214's user avatar
  • 861
4 votes
0 answers
150 views

Who bet against the usefulness of matrix inversion – or is it a myth?

In my linear-algebra and numerics courses, I frequently heard an anecdote about some professor betting – literally, with money – that there would never be any application where computing the actual ...
Wrzlprmft's user avatar
  • 1,022
4 votes
1 answer
624 views

Using paper of known density to calculate area under a curve [duplicate]

Ive never seen a source for this, but I had a professor a few years back that a low tech way of calculating the area under a curve (definite integral) was to use a piece of paper with known thickness/...
guest92929's user avatar
3 votes
1 answer
274 views

Tools of the trade: were early scientists and mathematicians really "writing with feathers using light from burning animal fat?"

I've used the phrase more than once, but in this answer I wrote: closing thoughts: Realistic orbits are not perfect conics, and so they and their Keplerian elements do not represent realistic orbits. ...
uhoh's user avatar
  • 2,163
3 votes
1 answer
70 views

Who is Wanner from Rosenrock-Wanner (ROW) methods?

I've spent some time with a search engine trying to find out about Wanner, a person whose surname is mentioned in the name of Rosenbrock-Wanner (ROW) methods primarily used for iteratively solving ...
sequence's user avatar
  • 133
3 votes
0 answers
215 views

How were sine and cosine functions computed before the notion of Taylor series?

We know using modern analysis techniques that $\sin x$ and $\cos x$ can be computed by their Taylor series (in fact the Taylor series are given as the definitions of these functions in today's real ...
Maximal Ideal's user avatar
2 votes
1 answer
295 views

Has Penrose ever acknowledged criticism of the Penrose-Lucas argument?

So, Roger Penrose is a bright guy, I mean, he won the Nobel Prize, but the Penrose-Lucas argument that the human mind is a hypercomputer based on Godel's Second Incompleteness Theorem is laughably bad....
Thomas Anton's user avatar
2 votes
0 answers
89 views

Bureau human computing services

Prior to the development of electronic computers, human computers were used and computer departments consisted of a room with humans at desks performing calculations. Large scientific organizations, ...
Fred's user avatar
  • 348
1 vote
1 answer
245 views

Newton as the first one to establish numerical analysis as a new field of study

I was reading about the history of Newton's Method. Newton used a cubic equation, $x^3 - 2x - 5 = 0$, to show the efficacy of his method around 1670. I was wondering that why Newton would choose this ...
PG1995's user avatar
  • 377
1 vote
0 answers
99 views

Quotation reference: "functions which can be evaluated under 1 sec are as good as analytically available"

I have a vague memory of a (possibly-apocryphal) quote by a physicist (I remember it as being Giorgio Parisi, which could be wrong), saying something to the effect of "any function which can be ...
πr8's user avatar
  • 111
0 votes
3 answers
278 views

Why were early electronic computers mutually incompatible?

At the beginning of the electronic computing era in the 1950s, computers were mutually incompatible both in terms of hardware and software. It was impossible to use peripherals (e.g. punched card or ...
Martin Vesely's user avatar
0 votes
0 answers
54 views

Frege alluded to a logic algorithm?

Somewhere (I wish I remember where) I read that Gottlob Frege, although he didn't invent a logic algorithm, alluded to one (the Quine–McCluskey algorithm? something else? converting truth tables to ...
Geremia's user avatar
  • 5,289
0 votes
0 answers
42 views

What is the (economic, social) value of STEM archives?

I'm trying to convince my institution to improve their internal Computer Science archives, and want one of my argument angles to be based on empirical value-adds of archiving. History, library science,...
Maggie's user avatar
  • 129