# Pythagoras' Revenge: A Mathematical Mystery

By Arturo Sangalli | Go to book overview

Chapter 10
RANDOM NUMBERS

Johanna Davidson’s fascination with randomness dated back to her first course in probability and statistics. What she had found most intriguing was the fact that the teacher could not provide a satisfactory definition of “random” (or of “probability,” for that matter), even though notions such as “random variable” and “random sample” lie at the heart of the theory. She would later learn that this was not due to the lecturer’s imperfect knowledge of the subject, but rather to the difficulty of specifying what, for example, a random sequence of 0s and 1s precisely is. In fact, this question has a long history and no definitive answer.

A simple—if not very practical—way of generating a string of 0s and 1s in a random fashion is to repeatedly flip a perfectly balanced (or “fair”) coin and to write down the outcomes as “1” for heads, and “0” for tails. Thus, after ten tosses of the coin, we may have obtained the sequence

0 1 0 0 1 1 0 0 1 0

whose binary digits (or bits) are totally unpredictable: the eleventh bit is equally likely to be 0 or 1, and the same is true for any subsequent bit. On the other hand, sequences that exhibit some kind of pattern or regularity, such as

0 1 0 1 0 1 0 1 0 1… or 0 1 1 0 1 1 1 0 0 1 0 1…

-69-

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

#### Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.
Citations (0)
Some of your citations are legacy items.
Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
• Saved book/article
• Highlights
• Quotes/citations
• Notes
• Bookmarks
Notes

#### Cited page

Style
Citations are available only to our active members.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited page

Pythagoras' Revenge: A Mathematical Mystery

• Title Page iii
• Contents v
• Preface ix
• List of Main Characters (Chapter in Which They Are Introduced) xi
• Prologue xiii
• Part I- A Time Capsule? 1
• Chapter 1- The Fifteen Puzzle 3
• Chapter 2- The Impossible Manuscript 10
• Chapter 3- Game over 19
• Chapter 4- A Trip to London 25
• Chapter 5- A Letter from the Past 32
• Chapter 6- Found and Lost 38
• Chapter 7- A Death in the Family 46
• Part II- An Extraordinarily Gifted Man 51
• Chapter 8- The Mission 53
• Chapter 9- Norton Thorp 63
• Chapter 10- Random Numbers 69
• Chapter 11- Randomness Everywhere 76
• Chapter 12- Vanished 82
• Part III- A Sect of Neo­ Pythagoreans 83
• Chapter 13- The Mandate 85
• Chapter 14- The Beacon 87
• Chapter 15- The Team 98
• Chapter 16- The Hunt 106
• Chapter 17- The Symbol of the Serpent 115
• Chapter 18- A Professional Job 122
• Chapter 19- with a Little Help from Your Sister 126
• Part IV- Pythagoras' Mission 137
• Chapter 21- Kidnapped 152
• Chapter 22- The Last Piece of the Puzzle 158
• Epilogue 169
• Appendix 1- Jule's Solution 171
• Appendix 2- Infinitely Many Primes 173
• Appendix 3- Random Sequences 175
• Appendix 4- A Simple Visual Proof of the Pythagorean Theorem 177
• Appendix 5- Perfect and Figured Numbers 178
• Notes, Credits, and Bibliographical Sources 181
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen
/ 183

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.