Posts Tagged ‘sigfigs0mg’

iPad Notebook export for Significant Figures: The Lives and Work of Great Mathematicians

Sunday, April 29th, 2018

Some quick quotes from
Significant Figures: The Lives and Work of Great Mathematicians Stewart, Ian
Citation (MLA): Stewart, Ian. Significant Figures: The Lives and Work of Great Mathematicians. Basic Books, 2017. Kindle file.
that I really liked

Each short quote below is preceded by the words “Highlight” & indication of the location in the book.

9 The Heat Operator • Joseph Fourier
Highlight(orange) – Page 91 · Location 1439
The precise form of the equation led Fourier to a simple solution, in a special case. If the initial temperature distribution is a sine curve, with a maximum temperature in the middle which tails away towards the ends, then as time passes the temperature has the same profile, but this decays exponentially towards zero.
10 Invisible Scaffolding • Carl Friedrich Gauss
Highlight(orange) – Page 98 · Location 1536
When Gauss was eight, his schoolteacher Büttner set the class an arithmetic problem. It’s often stated that this was to add the numbers from 1 to 100, but that’s probably a simplification.
14 The Laws of Thought • George Boole
Highlight(orange) – Page 146 · Location 2255
The quadratic is then the square (px + qy) 2 of a linear form. A coordinate change is a geometric distortion, and it carries the original lines to the corresponding ones for the new variables. If the two lines coincide for the original variables, they therefore coincide for the new ones. So the discriminants must be related in such a manner that if one vanishes, so does the other. Invariance is the formal expression of this relationship.
21 The Formula Man • Srinivasa Ramanujan
Highlight(orange) – Page 223 · Location 3480
For the first three years of his life, he scarcely said a word, and his mother feared he was dumb. Aged five, he didn’t like his teacher and didn’t want to go to school. He preferred to think about things for himself, asking annoying questions such as ‘How far apart are clouds?’ Ramanujan’s mathematical talents surfaced early, and by the age of 11 he had outstripped two college students who lodged at his home.
23 The Machine Stops • Alan Turing
Highlight(orange) – Page 251 · Location 3929
After the war Turing moved to London, and worked on the design of one of the first computers, ACE (Automatic Computing Engine) at the National Physical Laboratory. Early in 1946 he gave a presentation on the design of a stored-program computer –far more detailed than the American mathematician John von Neumann’s slightly earlier design for EDVAC (Electronic Discrete Variable Automatic Computer). The ACE project was slowed down by official secrecy about Bletchley Park, so Turing went back to Cambridge for a year,
Highlight(orange) – Page 252 · Location 3940
He worked on phyllotaxis, the remarkable tendency of plant structures to involve Fibonacci numbers 2, 3, 5, 8, 13, and so on, each being the sum of the previous two.
24 Father of Fractals • Benoit Mandelbrot
Highlight(orange) – Page 261 · Location 4084
In general, if the rank-n item has frequency proportional to nc, for some constant c, we speak of a cth power law.
Highlight(orange) – Page 261 · Location 4085
Classical statistics pays little attention to power-law distributions, focusing instead on the normal distribution (or bell curve), for a variety of reasons, some good. But nature often seems to use power-law distributions instead.
Highlight(orange) – Page 265 · Location 4147
Julia, and another mathematician Pierre Fatou, had analysed the strange behaviour of complex functions under iteration. That is, start with some number, apply the function to that to get a second number, then apply the function to that to get a third number, and so on, indefinitely. They focused on the simplest nontrivial case: quadratic functions of the form f( z) = z2 + c for a complex constant c. Significant Figures: The Lives and Work of Great Mathematicians eBook: Ian Stewart: Kindle Store

Sunday, April 29th, 2018

Gödel’s incompleteness theorems – Wikipedia

Monday, December 11th, 2017ödel%27s_incompleteness_theorems

Turing machine – Wikipedia

Monday, December 11th, 2017

Halting problem – Wikipedia

Monday, December 11th, 2017

Bletchley Park – Wikipedia

Monday, December 11th, 2017

Phyllotaxis – Wikipedia

Monday, December 11th, 2017

Sierpinski triangle – Wikipedia

Monday, December 11th, 2017

Julia set – Wikipedia

Monday, December 11th, 2017

Syllogism – Wikipedia

Sunday, November 26th, 2017



There are infinitely many possible syllogisms, but only 256 logically distinct types and only 24 valid types (enumerated below). A syllogism takes the form:

Major premise: All M are P.Minor premise: All S are M.Conclusion: All S are P.

(Note: M – Middle, S – subject, P – predicate. See below for more detailed explanation.)

The premises and conclusion of a syllogism can be any of four types, which are labeled by letters[12] as follows. The meaning of the letters is given by the table:

code quantifier subject copula predicate type example
A All S are P universal affirmative All humans are mortal.
E No S are P universal negative No humans are perfect.
I Some S are P particular affirmative Some humans are healthy.
O Some S are not P particular negative Some humans are not clever.

Putting it all together, there are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, though this makes no difference logically). Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. For example, the syllogism BARBARA below is AAA-1, or "A-A-A in the first figure".

Figure 1 Figure 2 Figure 3 Figure 4
Barbara Cesare Datisi Calemes
Celarent Camestres Disamis Dimatis
Darii Festino Ferison Fresison
Ferio Baroco Bocardo Calemos
Barbari Cesaro Felapton Fesapo
Celaront Camestros Darapti Bamalip