Clifford A. PickoverBesprekingen

Quando é que os seres humanos ataram os primeiros nós? Por que razão foi assassinada a primeira mulher matemática? Será possível voltar uma esfera do avesso? Estas são apenas algumas perguntas provocadoras que obtêm resposta neste livro maravilhoso. O autor, Clifford A. Pickover, revela-nos a magia e o mistério por trás de alguns dos marcos mais significativos da matemática, assim como os objetos e os pensamentos mais antigos que a Humanidade alguma vez contemplou, recuando 150 milhões de anos, até aos últimos progressos tecnológicos de ponta. A matemática está presente em qualquer domínio do esforço científico. Pode ser usada para explicar as cores do pôr do Sol ou a arquitetura do nosso cérebro e ajudar-nos a explorar as realidades da quântica subatômica e a retratar as galáxias longínquas.

A little too much code and the code is outdated of course since I read it in 2022, but with some really cool subjects but also a few subjects that were just boring to me.

The book is attractive. An illustration for each one of the 250 milestones. Arranged chronologically. The very first entry is about ant odometers; the date is 150 milion BC, when ants appear to have evolved from wasps. The last is "The Mathematical Universe Hypothesis"; the date is 2007. The ones about animals aren't really all that interesting; especially the monkeys counting one. The first real math one is "Magic Squares"; dated 2200 BC. Guess ones that old have been found? The magic squares article inspired me to develop a standard 3-sided magic square, so now I actually know some basic principles about the simplest magic square there is.

There was enough information in the book for me to make my own computer programs to draw the images, which I really liked. The Sci-fi story, not so much.

Indeholder "Preface", "Acknowledgments", "Chapter 1. How to Calculate a Black Hole's Mass", "Chapter 2. The Black Hole's Event Horizon Circumference", "Chapter 3. Black-Hole Tidal Forces", "Chapter 4. A Black Hole's Gravitational Lens", "Chapter 5. A Black Hole's Gravitational Blueshift", "Chapter 6. Gravitational Time Dilation", "Chapter 7. Anatomical Dissection of Black Holes", "Chapter 8. Embedding Diagrams for Warped Space-Time", "Chapter 9. Gravitational Wave Recoil", "Chapter 10. Optical Appearance of a Collapsing Star", "Chapter 11. Gravitational Distension Near a Black Hole's Heart", "Chapter 12. Quantum Foam", "Chapter 13. Black-Hole Recreations", "Chapter 14. Mathematical Black Holes", "Chapter 15. Black Holes Evaporate", "Chapter 16. Wormholes, Cosmological Doughnuts, and Parallel Universes", "Postscript 1. Could We Be Living in a Black Hole?", "Postscript 2. The Grand Internet Black-Hole Survey", "Author's Musings", "Smorgasbord for Computer Junkies", "Notes", "Further Reading", "Index".

"Preface" handler om introduktion til emnet. Siyah-Chal var et fængsel, kaldet Det sorte hul. Bogen handler om objekter, der kan fange selv lys. Og menneskeheden er kun et lille ubetydeligt blink i det store, store univers.
"Acknowledgments" handler om en særlig tak til Kip Thorne og til computerprogrammører og nogle af billederne er lavet på en IBM RISC System/6000 computer, men man kan også bruge en hjemmecomputer og bare bruge lidt mere tid.
"Chapter 1. How to Calculate a Black Hole's Mass" handler om ???
"Chapter 2. The Black Hole's Event Horizon Circumference" handler om ???
"Chapter 3. Black-Hole Tidal Forces" handler om ???
"Chapter 4. A Black Hole's Gravitational Lens" handler om ???
"Chapter 5. A Black Hole's Gravitational Blueshift" handler om ???
"Chapter 6. Gravitational Time Dilation" handler om ???
"Chapter 7. Anatomical Dissection of Black Holes" handler om ???
"Chapter 8. Embedding Diagrams for Warped Space-Time" handler om ???
"Chapter 9. Gravitational Wave Recoil" handler om ???
"Chapter 10. Optical Appearance of a Collapsing Star" handler om ???
"Chapter 11. Gravitational Distension Near a Black Hole's Heart" handler om ???
"Chapter 12. Quantum Foam" handler om ???
"Chapter 13. Black-Hole Recreations" handler om ???
"Chapter 14. Mathematical Black Holes" handler om ???
"Chapter 15. Black Holes Evaporate" handler om ???
"Chapter 16. Wormholes, Cosmological Doughnuts, and Parallel Universes" handler om ???
"Postscript 1. Could We Be Living in a Black Hole?" handler om ???
"Postscript 2. The Grand Internet Black-Hole Survey" handler om ???
"Author's Musings" handler om tidligere bøger og andres breve og hvad nu ellers forfatteren synes hører til her.
"Smorgasbord for Computer Junkies" handler om ???
"Notes" handler om et par noter til hvert kapitel, hvor forfatteren uddyber nogle ting.
"Further Reading" handler om forslag til yderligere læsning.
"Index" er et opslagregister.

???

A sort of autobiography and sort of collection of essays that Pickover could not fit into his other books, I'd reckon. As such, it meanders and sometimes does not really hang together, but a lot of the stuff is interesting. I don't understand, though, why Pickover has never mentioned Jorge Luis Borges. The math and the books. He's acres better than Proust, yet Pickover devotes a chapter to Proust and his connections to brains and such. A huge section on DMT was quite interesting. Some advice on writing. Well worth it if you like Pickover; well worth it if you can find it cheaply.

It was more like a picture book than any math book I ever read. It's still on my shelf, but I may not ever read it again.

Use as a research project book for the history of math.

After nearly a year, I have finally finished the book about math.

It may sound daunting, especially for your average person. But if you really love math concepts, and you really love reading, then perhaps you might want to give this one a go. The writing is great, and the picture that accompanies each description offers a perfect balance to an otherwise not-so-interesting subject for many. At over 500 pages, you'll be reading this for a long time; at least, if you're the type of person that literally likes to read from cover to cover.

The subtitle of this book is; "From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics". That about says sit all. This is a really cool encyclopedia-like book with great images and one-page anecdote about math, from across time. They range from cicada's calculating prime numbers, to the Infinite Monkey Theorem to how they solved Checkers. I used it like a nightly devotional, reading one or two stories every night. (probably why it took me 2 years to finish).

One interesting story is about Benford's Law, where the probability of the first digit of a set of numbers is known. In any set of numbers there is a 30% chance that a number will begin with 1. This idea is used by accounting auditors sometimes to look for fraud. Cooked books are unlikely to follow the law, natural ones would.

Very interesting reading.

10/10

S: 2/19/14 - F: 5/26/16 ( 838 Days)

This book was disconcerting and seemed rather chaotic. I think I got to page 5. I will try again.

The sub-title gives the best summary of this gorgeous book. I find the iridescent prime numbers on the cover particularly charming. Haven't made it through all chronologically ordered 250 milestones--that would simply be a forgettable gorge--but am trying to ponder a) familiar concepts or theorems such as The Golden Ratio (de Pacioli 1509), the Mobius Strip (Mobius 1858) or the Riemann Hypothesis (Riemann 1859), whose incantatory titles are fun to pronounce and b) a dawning comprehension of the mathematical mind's deployment of functions with symbols (numbers etc.) to identify the infrastructure/laws of reality, like the geometry of a spiral shell or the ear canal. Here is where I start to understand why famous mathematicians were/are often philosophers or deeply religious people--the theorems and proofs ultimately aim to answer all life's questions and we will finally know who we are and then why we are here. I still don't get how mathematicians can put forth conjectures or theorems that require centuries to prove; or problems that we don't yet have the technology to solve?!

The empirical method is so much more agreeable--to me any-way.

Pickover almost always succeeds in helping us innumerates appreciate the importance of each milestone, only occasionally furnishing explanations as impenetrable as the problems themselves.

9 out of 10 Recommended to lifelong learners readers of history and science and fans of lavishly illustrated books.

For a non-mathematician such as this reviewer, Pickover's book starts off with several interesting thought problems pertaining to the concept of infinity. From there, more mathematical angles are introduced but gradually so that one is eased into the more complex and sometimes dizzying heights of extremely large numbers. An entertaining and fascinating read, perfect for both mathematician and non-mathematician alike.

This was a very pretty book with page long descriptions of historically significant mathematical concepts. Each description was accompanied with a full page related image. However, you will need to search further for any significant understanding of the ideas.

Drugs, me, me, me, Proust, me, me, I love me, and more me. Ps. Technology=God. Did I mention, me?

Like a homeless Alzheimer’s patient, Sex, Drugs, Einstein, & Elves meanders over so much terrain that writing a review is a bit like tracking the trajectory of every pellet in a shotgun blast. It’s filled with the kind of cocktail party chatter you might use to pick up a Mensa member at their convention after-party. He spends a paragraph on an idea and then moves on without staking out any true analytical critique. It feels much like an aging indie rocker going on about “Yeah, I dig Yo La Tengo’s cover of Speeding Motorcycle; no, not the version on Fake Book, the one they recorded live with Daniel Johnston who was patched over the phone when they were doing a show at WFMU, it’s on Genius Love = Yo La Tengo, disk 1.” Puts me off lunch.

To be fair, I didn’t mind the meandering nature. Although numerous sections were uninteresting, he changes subjects so rapidly that something more intriguing comes up quickly. And a quick read is what I recommend…skim over the subjects that don’t do it for you. Computer generated poetry? I’d rather boil my hand.

The one chapter that did rivet me was the one on DMT. Like most of the book, it’s a survey of other people’s experiences with a bit of speculation mixed in. And yet, the epitome of this author’s naïveté is that he cheerily admits he’s never taken a psychedelic drug…but oooh, his novels and his art work are so psychedelic, he doesn’t need to! Even so, reading about the similarities between many of the drug experiences is fascinating. Pickover plays up the similarities so much that he thinks it’s possible that there really is a parallel dimension out there that DMT puts us in touch with. Unfortunately, he never considers the cultural similarities and influences that might be linking these experiences…nor does he contrast the modern tripper with the true tribal shamans who communed with Nature Gods rather than the Machine Elves of Timothy Leary fame. Regardless of the truth of the matter, just reading about these mind-bending experiences is quite a treat and worth the price of this book.

I’m also glad he brings up the history of Ibogaine (Iboga), a psychedelic substance that some users in the 60s found had completely eliminated their addiction to heroine, cocaine, and even alcohol. Unfortunately, the U.S. government declared it a controlled substance due to its psychedelic nature. It was not even permitted for laboratory testing purposes and still is not. A great example of moralistic suppression of a potentially life-saving medication. Pickover does a great service by highlighting this substance made from the bark of a tree.

Sadly, the book goes on 150 pages further.

It’s Pickover’s pomposity and blind optimism that really got to me. I was nauseated by his self-love. Oh, he’s so fascinating…clearly. He quite frequently mentions and recommends his other books throughout this book. Because they’re just so great too, you wouldn’t want to miss them. He’s really proud of how many books he’s written. In his chapter on publishing, he blithely tosses off the actual monetary advances he gets for his books. Some of his ideas on reality are so clever, you can read more about them in his clever sci fi novels. He spends a bit of time on his previous book dedications and drops how he’s been interviewed “countless times.” His love affair with his own quaint little town of Shrub Oak and its “mall” (seriously, he loves the mall) are embarrassingly parochial.

He spends a lot of time on Proust. Yeah, Proust is awesome. Too bad Pickover’s overindulgent references to Proust give the impression that he’s trying to create a halo around his own book by filling it with the romantic language of Swann’s Way—whether intentionally or not. The commentary on Proust is merely summarized criticism by more thoughtful reviewers. (Pickover attempts to cast a similarity between himself and Walter Benjamin, too). Here are some examples of how he indirectly attempts to associate himself with Proust’s greatness, “Thinking about Proust’s strange realities, I developed several novels that deal with what I call neorealities” and “Proust’s town of Combray, like my own Shrub Oak, is the kind of small town where…” and so on. He conveniently mentions how many times Proust’s novel was rejected and lo-and-behold, this very work by Pickover was rejected repeatedly as well! I wonder why?

His chapter on “writing tips” is absolutely embarrassing and guarantees beyond any prayer of a doubt that I will never read his fiction. “Avoid using an omniscient narrator” “Short better than long for dialogue.” “Buy a National Geographic. Page through it and select a setting for your novel. Look at the photos to help you create a vivid description.” HURL!!!!

I could have handled the la-di-dah arrogance, but what really made me angry bubbled up in the last fourth of the book: his techno-apologism. He foresees all of society’s problems as being solved in the future by technology and science. This Wired-enamor minus the rah-rah capitalism (in fact, he seems oblivious to almost all economic issues) is dangerously naïve at best and criminally ignorant at worst. We still have war and torture and rape and murder and starvation. And global warming (caused by technology) which he conveniently never mentions. But somehow being able to “download our consciousness into a computer” or robot is going to solve the worlds problems. Not only do I not believe this technology is possible, but his optimism is not born out by history. Better technology just means better ways to kill and maim. More efficient, more brutal war. Is an iPhone 3Gs really worth it? Does it make us happier? Who is the “we” made happier by technology? The rich continue to be privileged and live easier lives. The shanty towns in Sao Paolo continue to overflow. The homeless refugees in Iraq. The genocide in Darfur. These folks don’t give a shit about your goddamn AI program that frankly will NOT become conscious like a Terminator despite your confidence it will. All we really need are a very few tangible things. Fresh water. Food. Some shelter. Companionship and community. Technology is just what we crave because we’re alienated. We’ve constructed a society that requires it. In order to keep growth going. Economics depends on growth. Too bad growth is also cancer. I read somewhere that the Mayan’s may have killed themselves off by overpopulating/overusing the environment where they lived. Who says that can’t happen to our species as a whole?

Don’t get me wrong, I’m not a Luddite. I desire product as much as the next joe. But I don’t believe in its value. I know it’s because I’m culturally brainwashed. I think every time I exchange money for product it steals a piece of me. Whether it be my safety or my soul. But I do it anyway. Until I get bored with product and buy next product. Or want better, more advanced product.

Pickover is a sort of spiritualist materialist, without ever reconciling the two. (God is a mathematician.) Unfortunately, his materialist view is typically reductionist: biological or psychological phenomena, can be reduced to physical phenomena and can thus be programmed into a computer. This assertion isn’t much more than a religious belief. There is no accepted reductionist theory of consciousness. DNA replication can’t be explained by subatomic properties. Even subatomic properties only lend themselves to probabilities NOT programming. How do numbers capture the feeling of a breeze? The phenomenon itself, not the neurons that trigger the feeling. There is no subroutine for self-awareness. Do androids dream of electric sheep? “Nature is mathematics,” he says. Somewhere in the infinitely repeating digits of Pi, for example, is a representation of you. I assert against his assertion that a living thing cannot be capture in numbers. Living is a process, not a thing. It can’t be frozen in digits. The universe just IS. Math is a human way to interpret the universe. Pickover’s universe is like The Matrix, if a good one instead of an evil one. Is a breath of air math? Is a dream mathematical? Or is it just what it is?

“The Internet will dissolve away nations as we know them today. Humanity becomes a single hive mind, with a group intelligence, as geography becomes putty in the hands of the Internet sculptor.” You don’t think that it might be more likely that we find new and better ways to enslave each other for wealth? “Some researchers have even suggested that humans are at less risk for extinction now than at any other time in history, and that this risk decreases proportionately to advances made in technology…in this century we will probably become immortal from our understanding of the biological basis of aging and our merging with computers.” (italics mine)

To me the quintessence of technology is the nuclear bomb. We should have stopped at dental floss and the bicycle. But unfortunately, humans have a really hard time applying breaks. “…at this time in history…” there exists a way that humanity could make this planet uninhabitable. Sorry, technology doesn’t seem like my savior.

I’m sure in person, Pickover is a sweet guy. Too bad he’s a narcissist as a writer.

I had to check it out, just from curiousity. It actually does teach the basic concepts of calculus, starting from Luigi's pizza toss into the air. "Easy to digest." I would recommend it.
And he's got tantalizing other titles, too.

Some of the most incendiary minds of science have also verged on pathology; a few of them clearly have been mentally ill. Cliff Pickover describes the quirks and eccentric behaviors of some of these people, including Nikola Tesla (Chapter 1!), Oliver Heaviside, Richard Kirwan, Henry Cavendish, Francis Galton, and Theodore Kaczynski, among others. "Strange Brains ..." also includes discussion of some of the disorders that these people suffered: obsessive-compulsive disorder, bipolar disorder, schizophrenia, and others. This is a fascinating book that will enrich my teaching about the contributions of these strange men with their (sometimes) wonderful ideas. Check out Dr. Pickover's Web page (above) to see the contributions of a true polymath.

Similar in format to _The Math Book_ -- 2 pages for each "milestone", one comprising a big color image. Idiosyncratic and annoyingly sprinkled with bits of God-talk, like every Pickover book. If it gets high-schoolers (or whoever) interested in physics, more power to him.

THis book is both very cool and very frustrating. I'm not sure how the physics work, or what was missed. But, generally, some articles were explained nicely, others with nothing but formula. Same goes with the pictures... They are beautiful, but generally don't add much to the explanation.

This was a great book to read at night. I would read a few segments right before bed.½

I only just started this book and ... weird, already have feelings about it. Stay tuned, though, because I plan to finish it and those feelings may change.

I guess I feel like Clifford Pickover is the Stephen King of popular science. His books are numerous and when I see one, I think "oh, that looks great," but inevitably wind up feeling as though the books would individually be better if there weren't so dang many of them! They tend to have a thrown-together, slightly chintzy, not-quite-fully-edited feel to them. There is typically stuff in a Pickover book I'm glad to have encountered, but in sum they feel somewhat dashed off, and this one is no exception.

I also am not sure I like theological speculation in my science.

A professor of technology but with both feet securely in the air.

Indeholder "Introduction", "c. 150 Million B.C. Ant Odometer", "c. 30 Million B.C. Primates Count", "c. 1 Million B.C. Cicada-Generated Prime Numbers", "c. 100,000 B.C. Knots", "c. 18,000 B.C. Ishango Bone", "c. 3000 B.C. Quipu", "c. 3000 B.C.Dice", "c. 2200 B.C. Magic Squares", "c. 1800 B.C. Plimpton 322", "c. 1650 B.C. Rhind Papyrus", "c. 1300 B.C. Tic Tac Toe", "c. 600 B.C. Pythagorean Theorem and Triangles", "548 B.C. Go", "c. 530 B.C. Pythagoras Founds Mathematical Brotherhood", "c. 445 B.C. Zeno's Paradoxes", "c. 440B.C. Quadrature of the Lune", "c. 350 B.C. Platonic Solids", "c. 350 B.C. Aristotle's Organon", "c. 320 B.C. Aristotle's Wheel Paradox", "300 B.C. Euclid's Elements", "c. 250 B.C. Archimedes: Sand, Cattle & Stomachion", "c. 250 B.C. Pi", "c. 240 B.C. Sieve of Eratosthenes", "c. 240 B.C. Archimedean Semi-Regular Polyhedra", "225 B.C. Archimedes' Spiral", "c. 180 B.C. Cissoid of Diocles", "c. 150 B.C. Ptolemy's Almagest", "250 Diophantus's Arithmetica", "c. 340 B.C. Pappus's Hexagon Theorem", "c. 350 B.C. Bakhshali Manuscript", "415 The Death of Hypatia", "c.650 Zero", "c. 800 Alcuin's Propositiones ad Acuendos Juvenes", "830 Al-Khwarizmi's Algebra", "834 Borromean Rings", "850 Ganita Sara Samgraha", "c. 850 Thabit Formula for Amicable Numbers", "c. 953 Chapters in Indian Mathematics", "1070 Omar Khayyam's Treatise", "c. 1150 Al-Samawal's The Dazzling", "c. 1200 Abacus", "1202 Fibonacci's Liber Abaci", "1256 Wheat on a Chessboard", "c. 1350 Harmonic Series Diverges", "c. 1427 Law of Cosines", "1478 Treviso Arithmetic", "c. 1500 Discovery of Series Formula for Pi", "1509 Golden Ratio", "1518 Polygraphiae Libri Sex", "1537 Loxodrome", "1545 Cardano's Ars Magna", "1556 Sumario Compendioso", "1569 Mercator Projection", "1572 Imaginary Numbers", "1611 Kepler Conjecture", "1614 Logarithms", "1621 Slide Rule", "1636 Fermat's Spiral", "1637 Fermat's Last Theorem", "1637 Descartes' La Geometrie", "1637 Cardioid", "1638 Logarithmic Spiral", "1639 Projective Geometry", "1641 Torricelli's Trumpet", "1654 Pascal's Triangle", "1657 The Length of Neile's Semicubical Parabola", "1659 Viviani's Theorem", "c. 1665 Discovery of Calculus", "1669 Newton's Method", "1673 Tautochrone Problem", "1674 Astroid", "1696 L'Hopital's Analysis of the Infinitely Small", "1702 Rope around the Earth Puzzle", "1713 Law of Large Numbers", "1727 Euler's Number, e", "1730 Stirling's Formula", "1733 Normal Distribution Curve", "1735 Euler-Mascheroni Constant", "1736 Konigsberg Bridges", "1738 St. Petersburg Paradox", "1742 Goldbach Conjecture", "1748 Agnesi's Instituzioni Analitiche", "1751 Euler's Formula for Polyhedra", "1751 Euler's Polygon Division Problem", "1759 Knight's Tours", "1761 Bayes' Theorem", "1769 Franklin Magic Square", "1774 Minimal Surface", "1777 Buffon's Needle", "1779 Thirty-Six Officers Problem", "c. 1789 Sangaku Geometry", "1795 Least Squares", "1796 Constructing a Regular Heptadecagon", "1797 Fundamental Theorem of Algebra", "1801 Gauss's Disquisitiones Arithmeticae", "1801 Three-Armed Protractor", "1807 Fourier Series", "1812 Laplace's Theorie Analytique des Probabilites", "1816 Prince Rupert's Problem", "1817 Bessel Functions", "1822 Babbage Mechanical Computer", "1823 Cauchy's Le Calcul Infinitesimal", "1827 Barycentric Calculus", "1829 Non-Euclidean Geometry", "1831 Mobius Function", "1832 Group Theory", "1834 Pigeonhole Principle", "1843 Quaternions", "1844 Transcendental Numbers", "1844 Catalan Conjecture", "1850 The Matrices of Sylvester", "1852 Four-Color Theorem", "1854 Boolean Algebra", "1857 Icosian Game", "1857 Harmonograph", "1858 The Möbius Strip", "1858 Holditch's Theorem", "1859 Riemann Hypothesis", "1868 Beltrami's Pseudosphere", "1872 Weierstrass Function", "1872 Gros's Theorie du Baguenodier", "1874 The Doctorate of Kovalevskaya", "1874 Fifteen Puzzle", "1874 Cantor's Transfinite Numbers", "1875 Reuleaux Triangle", "1876 Harmonic Analyzer", "1879 Ritty Model I Cash Register", "1880 Venn Diagrams", "1881 Benford's Law", "1882 Klein Bottle", "1883 Tower of Hanoi", "1884 Flatland", "1888 Tesseract", "1889 Peano Axioms", "1890 Peano Curve", "1891 Wallpaper Groups", "1893 Sylvester's Line Problem", "1896 Proof of the Prime Number Theorem", "1899 Pick's Theorem", "1899 Morley's Trisector Theorem", "1900 Hilbert's 23 Problems", "1900 Chi-Square", "1901 Boy's Surface", "1901 Barber Paradox", "1901 Jung's Theorem", "1904 Poincare Conjecture", "1904 Koch Snowflake", "1904 Zermelo's Axiom of Choice", "1905 Jordan Curve Theorem", "1906 Thue-Morse Sequence", "1909 Brouwer Fixed-Point Theorem", "1909 Normal Number", "1909 Boole's Philosophy and Fun of Algebra", "1910-1913 Principia Mathematica", "1912 Hairy Ball Theorem", "1913 Infinite Monkey Theorem", "1916 Bieberbach Conjecture", "1916 Johnson's Theorem", "1918 Hausdorff Dimension", "1919 Brun's Constant", "c. 1920 Googol", "1920 Antoine's Necklace", "1921 Noether's Idealtheorie", "1921 Lost in Hyperspace", "1922 Geodesic Dome", "1924 Alexander's Horned Sphere", "1924 Banach-Tarski Paradox", "1925 Squaring a Rectangle", "1925 Hilbert's Grand Hotel", "1926 Menger Sponge", "1927 Differential Analyzer", "1928 Ramsey Theory", "1931 Godel's Theorem", "1933 Champernowne's Number", "1935 Bourbaki: Secret Society", "1936 Fields Medal", "1936 Turing Machines", "1936 Voderberg Tilings", "1937 Collatz Conjecture", "1938 Ford Circles", "1938 The Rise of Randomizing Machines", "1939 Birthday Paradox", "c. 1940 Polygon Circumscribing", "1942 Hex", "1945 Pig Game Strategy", "1946 ENIAC", "1946 Von Neumann's Middle-Square Randomizer", "1947 Gray Code", "1948 Information Theory", "1948 Curta Calculator", "1949 Csaszar Polyhedron", "1950 Nash Equilibrium", "c. 1950 Coastline Paradox", "1950 Prisoner's Dilemma", "1952 Cellular Automata", "1957 Martin Gardner's Mathematical Recreations", "1958 Gilbreath's Conjecture", "1958 Turning a Sphere Inside Out", "1958 Platonic Billiards", "1959 Outer Billiards", "1960 Newcomb's Paradox", "1960 Sierpinski Numbers", "1963 Chaos and the Butterfly Effect", "1963 Ulam Spiral", "1963 Continuum Hypothesis Undecidability", "c. 1965 Superegg", "1965 Fuzzy Logic", "1966 Instant Insanity", "1967 Langlands Program", "1967 Sprouts", "1968 Catastrophe Theory", "1969 Tokarsky's Unilluminable Room", "1970 Donald Knuth and Mastermind", "1971 Erdos and Extreme Collaboration", "1972 HP-35: First Scientific Pocket Calculator", "1973 Penrose Tiles", "1973 Art Gallery Theorem", "1974 Rubik's Cube", "1974 Chaitin's Omega", "1974 Surreal Numbers", "1974 Perko Knots", "1975 Fractals", "1975 Feigenbaum Constant", "1977 Public-Key Cryptography", "1977 Szilassi Polyhedron", "1979 Ikeda Attractor", "1979 Spidrons", "1980 Mandelbrot Set", "1981 Monster Group", "1982 Ball Triangle Picking", "1984 Jones Polynomial", "1985 Weeks Manifold", "1985 Andrica's Conjecture", "1985 The ABC Conjecture", "1986 Audioactive Sequence", "1988 Mathematica", "1988 Murphy's Law and Knots", "1989 Butterfly Curve", "1996 The On-Line Encyclopedia of Integer Sequences", "1999 Eternity Puzzle", "1999 Perfect Magic Tesseract", "1999 Parrondo's Paradox", "1999 Solving of the Holyhedron", "2001 Bed Sheet Problem", "2002 Solving the Game of Awari", "2002 Tetris Is NP-Complete", "2005 NUMB3RS", "2007 Checkers Is Solved", "2007 The Quest for Lie Group E8", "2007 Mathematical Universe Hypothesis", "Notes and Further Reading", "Index", "Photo Credits ".
Et opslag pr emne. Det hele i kronologisk orden. Flot!
Mange søde detaljer som at et af de semiregulære arkimediske legemer et afskåret dodecaeder blev brugt som mønster for detonatorerne i Fat Man bomben. Borromeanske ringe kan ikke være helt plane. Bruns konstant er summen af reciprokværdierne af alle primtalstvillinger. En cirkel omskrevet med en trekant omskrevet med en cirkel omskrevet med en firkant osv konvergerer mod en cirkel med radius lidt over 8.7.
Et sjovt terningespil kaldet pig - beskrevet af John Scarne.
Et polyeder uden diagonaler og som ikke er en trekantet pyramide. 78557 * 2^n + 1 er aldrig et primtal! - 78557 er måske det mindste af den slags - kaldet et Sierpinski tal.
2008 Hans Andersson bygger en legomindstormsrobot der kan løse rubiks terning helt selv. Et Szilassi polyeder har 7 sekskantede flader og hver flade deler en kant med alle de andre flader - det var ellers kun den trekantede pyramide, der gjorde det.
Andrica's formodning siger at sqrt(primtal nr n+1) - sqrt(primtal nr n) er mindre end 1.
Parrondo's paradoks er to spil, som hver ruinerer spilleren hvis han spiller dem, men som giver gevinst, hvis man skifter mellem dem.

Glimrende matematikbog med mange udfordringer

For each of his 250 idiosyncratically-chosen math "milestones," Pickover allocates two facing, somewhat oversized, pages, with the recto one consisting of a gorgeous color image. There's the usual Pickoverian trait of annoyingly sprinkling religiony allusions throughout the text. The images I especially liked include some by computer artists Jos Leys (www.josleys.com) and Paul Nylander (www.bugman123.com).

A 500-page collection of eponymous laws of physical science (Hooke's Law, Ohm's Law, etc), many emanating from 1800s Europe. That the prolific Pickover is probably incapable of writing a non-idiosyncratic book is evidenced as early as p 8 when he says, "Many of the laws in this book that excite me the most deal with electrical discoveries of highly religious people." Huh? A subset of the innumerable exogenous quotations he includes drip with theology, and this is really quite annoying.

A quirky, fun, wide-ranging collection of explorations revolving generally around the theme of infinity, chock-full of interesting puzzles, stories, illustrations, and even computer programs for experimenting. This was one of my favorite books in high school!