LitArk » Books » Children

Seligman - Math mutation classics exploring interesting, fun and weird corners of mathematics

Here you can read online Seligman - Math mutation classics exploring interesting, fun and weird corners of mathematics full text of the book (entire story) in english for free. Download pdf and epub, get meaning, cover and reviews about this ebook. City: Berkeley;CA;New York, year: 2016, publisher: Apress, genre: Children. Description of the work, (preface) as well as reviews are available. Best literature library LitArk.com created for fans of good reading and offers a wide selection of genres:

Romance novel Science fiction Adventure Detective Science History Home and family Prose Art Politics Computer Non-fiction Religion Business Children Humor

Choose a favorite category and find really read worthwhile books. Enjoy immersion in the world of imagination, feel the emotions of the characters or learn something new for yourself, make an fascinating discovery.

$Seligman Math mutation classics exploring interesting, fun and weird corners of mathematics$

Book:
Math mutation classics exploring interesting, fun and weird corners of mathematics
Author:
Seligman / Erik
Publisher:
Apress
Genre:
Books / Children
Year:
2016
City:
Berkeley;CA;New York
Rating:
5 / 5
Favourites:
Add to favourites
Your mark:
- 100
- 1
- 2
- 3
- 4
- 5

Description
Author's other books
Similar books

Math mutation classics exploring interesting, fun and weird corners of mathematics: summary, description and annotation

We offer to read an annotation, description, summary or preface (depends on what the author of the book "Math mutation classics exploring interesting, fun and weird corners of mathematics" wrote himself). If you haven't found the necessary information about the book — write in the comments, we will try to find it.

Seligman: author's other books

Who wrote Math mutation classics exploring interesting, fun and weird corners of mathematics? Find out the surname, the name of the author of the book and a list of all author's works by series.

Math mutation classics exploring interesting, fun and weird corners of mathematics — read online for free the complete book (whole text) full work

Below is the text of the book, divided by pages. System saving the place of the last page read, allows you to conveniently read the book "Math mutation classics exploring interesting, fun and weird corners of mathematics" online for free, without having to search again every time where you left off. Put a bookmark, and you can go to the page where you finished reading at any time.

Light

Font size:

↓

↑

Reset

Interval:

↓

↑

Bookmark:

Make

Erik Seligman 2016

Erik Seligman Math Mutation Classics 10.1007/978-1-4842-1892-1_1

1. Simple Surprises

Erik Seligman 1

(1)

Hillsboro, Oregon, USA

Many of the amusing mathematical tidbits that Ive highlighted in the podcast do not require very deep or complex reasoning: they are simple consequences of logically thinking through our basic notions about numbers, counting, or probability. In this first chapter we discuss some of these very basic but somehow surprising ideas.

City of Mutants

From Math Mutation podcast 1

Did you know that almost everybody in Pittsburgh has an above-average number of fingers? Some say its nuclear waste. Some say its toxic pollution. But I say its just the math.

Suppose a city has 2 million residents. Assuming everyone is healthy, we would expect them to have 20 million fingers among them. So the average number of fingers per person is 20 million divided by 2 million, or 10. But in real life, is there ever a city where everyone is healthy?

In any population, a tiny number of people will have lost a finger due to an industrial accident or over-zealous World of Warcraft keyboard-pounding . So suppose 10 people in the city have lost a finger. Then the total number of fingers is not 20 million, but 19,999,990. (There may be a few with extra fingers to balance this out, but thats a much rarer condition, probably negligible for the purpose of this calculation.) This brings the average per person down to 9.999995. Yet this doesnt change the fact that nearly everybody has 10 fingers, which beats the average by 0.000005! So nearly everyone does have an above-average number of fingers.

As you have probably noticed, were playing with the difference between our casual conversational notion of average, and its mathematical definition. The average is usually formally defined to be the mean , the sum of a measure divided by the size of the population, which we calculated above. But in casual conversation, we think of the word average as denoting a typical member of the population. In terms of formal definitions, this more closely matches the median , where you sort the population by some measurement, and take the middle member as a representative. The median resident of Pittsburgh does indeed have the normal 5 fingers per hand you would expect.

In any case, the statement that opened this episode will work for just about any city. Having lived there for four years back in the 1990s, I think Pittsburgh may indeed be a uniquely mutated city, but if so its for reasons beyond this discussion. So if things get boring at your next social gathering, be sure to liven it up by pointing out that, using the average number of fingers as the measurement, your city is also a city of mutants.

Two Plus Two Equals Five

From Math Mutation podcast 210

Recently I heard someone quote a clever metaphor in a casual conversation, Life is when nature takes 2 and 2 to make 5. Its a nice statement of how living creatures are more than the sum of their parts. If you took all the chemical compounds in my body and dumped them on the ground in the right proportions, all you would get is a mess. Yet somehow I am here, and at least sentient enough to record math podcasts. I went online to try to find the source of this quotation, and was surprised to see the number of references to this seemingly silly nonsense equation, 2 + 2 = 5.

Most of us are probably familiar with the equation from George Orwells classic novel 1984 . As you probably recall, in the book, people are told that if the government says that 2 + 2 = 5, it is the duty of all citizens to believe it not just say it, but actually come to believe that it is true. Surprisingly, Orwell did not come up with this out of thin air: a real-life totalitarian government, the Soviet Union, actually did use 2 + 2 = 5 as part of its propaganda, in a poster with the title 2 + 2 = 5: Arithmetic of a counter-plan plus the enthusiasm of the workers. It wasnt quite as blatantly absurd as in 1984 , but the Soviet propaganda poster used it as a metaphor: supposedly a 5-year plan could be completed in 4 years, because the enthusiasm of the workers provided an invisible additive factor. Sadly, most of this enthusiasm was mainly due to fear of being sent to the Gulag prison camps, which resulted in many managers doctoring the statistics to match the results that the government wanted on paper only. Its also reported that Nazi Hermann Goering actually used this metaphor in real life, once saying If the Fhrer wants it, two and two makes five!

The phrase 2 + 2 = 5 has actually existed in the arts from the early 19th century. According to Wikipedia , the phrase was first coined in a letter from Lord Byron, where he wrote I know that two and two make four& should be glad to prove it too if I couldthough I must say if by any sort of process I could convert 2 & 2 into five it would give me much greater pleasure. He may have been making an indirect reference to Rene Descartes Meditations , where the famous philosopher discussed whether equations such as 2 + 3 = 5 exist outside the human mind, and whether they can be doubted: And further, as I sometimes think that others are in error respecting matters of which they believe themselves to possess a perfect knowledge, how do I know that I am not also deceived each time I add together two and three, or number the sides of a square, or form some judgment still more simple, if more simple indeed can be imagined?

Later, Victor Hugo used this concept in a critique of the mob rule that had led to Napoleons rise to power, foreshadowing Orwells later political metaphor: Now, get seven million five hundred thousand votes to declare that two and two make five, that the straight line is the longest road, that the whole is less than its part; get it declared by eight millions, by ten millions, by a hundred millions of votes, you will not have advanced a step. Russian authors Ivan Turgenev, Leo Tolstoy, and Fyodor Dostoyevsky also made use of this metaphor. Turgenev used it to symbolize divine intervention: Whatever a man prays for, he prays for a miracle. Every prayer reduces itself to this: Great God, grant that twice two be not four. In the 20th century, there were many instances of authors following Orwells lead and again using this metaphor for the struggle against totalitarianism, including Albert Camus and Ayn Rand.

An intriguing question is whether there are cases when it is actually valid to say that 2 + 2 = 5. A well-known mathematicians joke is that 2 + 2 = 5, for particularly large values of 2. This may refer to issues with rounding: if you start, for example, with the obviously correct equation 2.4 + 2.4 = 4.8, and ask someone to round all the numbers to the nearest integer, you do indeed derive 2 + 2 = 5 from this true equation. It also might be a case of playing with the definitions of symbols: perhaps you can define the symbol that we normally write as 2 to actually be an algebraic variable representing the value 2.5. You can also find various tricky proofs that 2 + 2 = 5 circulating the web, where many lines of complex algebra are often used. These many lines usually misdirect you from one invalid step, where a term t is replaced with the square root of t 2 (it should really be the absolute value of that quantity), or both sides are divided by a term that equals 0. Here is an example of one of the simpler ones:

4 4 = 10 10 : Start out with true statement
(2 2) (2 + 2) = 2 5 2 5 : Rewrite both sides in a complex form
(2 2) (2 + 2) = (2 2) 5 : Regroup factors on the right-hand side
==> 2 + 2 = 5 : Divide both sides by (2 2)

Light

Font size:

↓

↑

Reset

Interval:

↓

↑

Bookmark:

Make

Similar books «Math mutation classics exploring interesting, fun and weird corners of mathematics»

Look at similar books to Math mutation classics exploring interesting, fun and weird corners of mathematics. We have selected literature similar in name and meaning in the hope of providing readers with more options to find new, interesting, not yet read works.

ACT - The Official ACT Mathematics Guide

ACT

The Official ACT Mathematics Guide

James D Stein

Seduced By Mathematics: The Enduring Fascination Of Mathematics

Sally Anderson

How Many Ways Can You Make Five?: A Parents Guide to Exploring Math with Childrens Books

Seligman

Modernitys Wager Authority, the Self, and Transcendence

Cheng

How to bake [pi]: an edible exploration of the mathematics of mathematics

David Darling

Weird Math: A Teenage Genius and His Teacher Reveal the Strange Connections Between Math and Everyday Life

Jo Boaler

Whats Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success

Eugenia Cheng

How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics

Zvi Artstein

Mathematics and the Real World: The Remarkable Role of Evolution in the Making of Mathematics

Richard Elwes

The Math Handbook: Everyday Math Made Simple

Jason Rosenhouse

Taking Sudoku Seriously: The Math Behind the Worlds Most Popular Pencil Puzzle

Keith J. Devlin

Life by the Numbers

Reviews about «Math mutation classics exploring interesting, fun and weird corners of mathematics»

Discussion, reviews of the book Math mutation classics exploring interesting, fun and weird corners of mathematics and just readers' own opinions. Leave your comments, write what you think about the work, its meaning or the main characters. Specify what exactly you liked and what you didn't like, and why you think so.