Fun! Not since Mandebrot's FRACTAL GEOMETRY OF NATURE and ...
359578
Reflecting the wide ranging spectrum of fractals in mathematics, science, technology, art, and engineering, the authors have produced a 'must have'  for anyone with curiousity with this fascinating topic. While some of  the math will be tough going for those not so inclined, all they have to do is turn the page for a different and well written explanation of a different fractal application. Fun!  Not since Mandebrot's FRACTAL GEOMETRY OF NATURE and Barnsley's FRACTALS EVERYWHERE has there been such a definitive and essential book on fractals. Richly illustrated.
263316
The highest compliment I can give this game is that an eleven year old - who hates math - actually wanted to play more of it after I taught him how to play! It's fun, engages the mind (for adults and kids alike), and it was clearly designed by a very clever mathematician. It takes no time at all to set up, and games are quick to play. There are a few "Sorry" elements that come into play with the Prime Cards, which I didn't care for, as their vindictive nature does not seem to fit well with the concept of "Math for Love" - especially if you're trying to encourage anti-math kids to embrace it. Also, the blank cards in the stack... why??? Interesting design choices. I dinged it one star because the build quality of the components is subpar when compared to today's high standards for tabletops (the board is already warping after only two weeks of ownership), but it's otherwise a sold game.
3246026
The author quoted John von Neuman in his introduction:  "In mathematics you don't understand things; you just get used to them", but this quote serves also as a summary of the whole book. So first, don't expect to understand things after reading this book and second, don't expect to get used to them either, unless you are a mathematician. This book is an anecdotal and very light reading that concentrates on the "story" of one of the greatest quests in mathematics. It will give you a better idea of the main mathematicians involved and what they contributed to this almost two century long quest of finding and constructing the "atoms of symmetry" and afterwards of classifying them during the so called "Thirty Years War" (70's - 2000) in a sort of "periodic table" plus 26 non fitting "exceptional symmetry atoms" or sporadic groups. The "monster" is the biggest of these groups.

What this book really shows is that 16-hour days of arduous number-crunching can make you get used to math in a way that the interrelations or patterns between numbers and their basic operations or permutations become "hard-wired" into your brain. Consider following conversation between two "Monsters of Maths"  (I summarized the anecdote and changed the wording; T=Thompson, C=Conway). C: "I think there might be some exceptional group in Leech's Lattice". T: "I am not sure...give me the size." 12 1/2 hours later C: "It's  2^22*3^9*5^4*7^2*11*13*23 or half of it". 20 minutes later T:"Yes, it's half of it, I can see it now...It's...the monster! and... look, it has a baby!...Let's find out if they really exist..."  The figure mentioned by Conway equals  8,315,553,613,086,720,000 and is expressed as factors of prime numbers for simplicity. (yes, simplicity!) How these factors can seem obvious to anybody in the first place is already a mystery for me, but  mathematicians seem to send each other postcards with these numbers, and apparently they make sense to them.

This book will reveal you the existence of a 196,883 dimensional space, which by the way seems to be the world in which mathematicians live in and, since "the Monster" might be linked to the way the Universe is constructed, we probably also live in it without being aware of it. On the other hand, some anecdotes could have been omitted in order to explain some concepts more deeply, like what makes the exceptions different from the other groups in the "periodic table", what exactly is a lie algebra, how does a character table work (maybe he could have explained it using a 4 x 4 table), etc. For an understanding of rotations in three dimensional space, read the chapters on lie algebra and group theory in&nbsp;<a data-hook="product-link-linked" class="a-link-normal" href="/Deep-Down-Things-The-Breathtaking-Beauty-of-Particle-Physics/dp/080187971X/ref=cm_cr_arp_d_rvw_txt?ie=UTF8">Deep Down Things: The Breathtaking Beauty of Particle Physics</a>.
515143
I'll be honest, because you're seriously trying to consider whether to buy this book, aren't you? By Design leaves me with that pesky taste of the more misleading proponents of conservatively partisan economics: it's not insincere in what it propounds, but it certainly mixes impressively blinkered methodology and the distinct flavor that someone more technically competent really should have written the thing.
Case in point: The anthropic principle argues that the universe was designed with human life as its intended goal? Hmm, I seem to remember something a little different in Stephen Hawking's 'A Brief History of Time'... Rather than giving substance to the idea of intelligent design, the anthropic principle argues that even if this universe that so amazingly bears us turns out to be improbable compared to all possible permutations, we are proof that luck (NOT God) was on this universe's side. In other words, it is the statistical law of insufficiently small samples applied to our universe, which for the sake of the anthropic principle, is treated as one sample (which any statistician knows has infinite variance).
Ironically, another one of the books unfortunate additions might be able to be cured by the REAL anthropic principle (maybe his ailment was a symptom of his apparent belief in the perverse version of anthrop-acy). You see, the poor scientist couldn't seem to believe his eyes at human phenomena like blood-clotting, and his intellectual laziness made him easy prey for the christian scientist cult. But wait! What if some (admittedly impressive) seemingly providence-inspired phenomena could be explained by the anthropic principle too?
It turns out this isn't necessary -- Herr Doctor can still go do a google search on the biochemistry, organic biology, simple physics, or even the sheer probability of molecular hemomorphing (blood clotting).
As for you, chr reader, I suggest you turn to Hawking's already classic updates on contemporary science ('A Brief History of Time' or more recently 'The Universe in a Nutshell') for a more informative treatment to satisfy your spiritual curiosity.
3823036
Hiding in the Mirror:  The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond, by Lawrence M. Krauss with glossary and index. Science popularized, but hard science, not soft or fanciful science.  Since I have no physics or math theory this book was a challenge, but with concentration I was able to follow along. My reward was to gain a rudimentary comprehension of Einstein's Special and General Relativity theories, to gain some insight into "dimensions" as well as to understand what quarks, neutrinos and gravitons are.  I'll forget it all, of course, but next time I hear of them an echo will remain that will enable me to know what's being talked about.  I read this book in seven consecutive evenings.  Krauss's lucidity, his occasional wry humor and tantalizing style made me catch the excitement.  What will happen next?  The description of string theories was indeed hairy, partly because these are still mathematical theories as yet unprobed physically and partly because they are frankly mind-boggling.  The author, an eminent particle physicist (Case Western University) on the interface with cosmology, watered nothing down, nor did he once fail to distinguish between empirical and speculative.  He places this book in the historical, cultural context of physics and cosmology.
1486378
Well...it's fun/high speed/mind candy. Can't we have some NEW twists?
521532
This is interesting introduction in fractal geometry. It's just amazing how geometry and proportions are represent many things in our live. I never thought that antenna in our cell phones based on this geometry and because of that it become possible to use the same structure of antenna for many uses in cell phone. Fractals can describe as complicated things as a human blood vessels and formation of mountains. Who do not like math won't be disappointed also because movie made in popular simple language. It just looks like God is master in math (not that old man with beard) and we can see and use his creations if we can understand how.
4184848
Clifford A. Pickover, "Surfing through Hyperspace," 239 pages, numerous illustrations

This book discusses higher-dimensional geometry, the fourth dimension, philosophy, religion, mathematics and string theory.  The author begins by saying that he knows of no subject in mathematics that has intrigued both children and adults as much as the idea of a fourth dimension -- a spatial direction different from all the directions of our normal three-dimensional space.  Philosophers and parapsychologists have meditated upon this dimension that no one can point to but may be all around us.  Theologians have speculated that the afterlife, heaven, hell, angels, and our souls could reside in a fourth dimension -- that God and Satan could literally be lumps of hypermatter in a four-dimensional space inches away from our ordinary three-dimensional world.  The book's table of contents gives a good indication of topics and people covered.  I have given more information about the topic in parentheses.

Preface

Introduction

Chapter 1. Degrees of Freedom (history of fourth dimension, string theory, hyper-time)

Chapter 2. The Divinity of Higher Dimensions (Flatland, 4-D creatures, God)

Chapter 3. Satan and Perpendicular Worlds (parallel universes, wormholes, 4-D chess)

Chapter 4. Hyperspheres and Tesseracts (Hinton Cubes, tesseracts, hyperspheres)

Chapter 5. Mirror Worlds (Zollner, aliens, Mobius words, Klein bottles)

Chapter 6. The Gods of Hyperspace (Hypothetical access to the 4th dimension)

Concluding Remarks

Appendix I.  Mind-Bending Four-Dimensional Puzzles

Appendix II.  Higher Dimensions in Science Fiction

Appendix III. Banchoff Klein Bottle

Appendix IV.  Quaternions

Appendix V.  Four-Dimensional Mazes

Appendix VI.  Smorgasbord for Computer Junkies

Appendix VII. Evolution of Four-Dimensional Beings

Appendix VIII.  Questions for Further Thought

Appendix IX.  Hyperspace Titles

A fun story involving fictional FBI agents exploring the fourth dimension weaves the topics together.  A mixture of humor and mathematics.
1372467
The Posterior Analytics is a rather dull and uninspired work even by Aristotelian standards. Aristotle's trademarked method of pointless classification is here running at high gear at its pointless best. Although the relation between Aristotle and mathematicians such as Euclid is never made explicit in the historical record, it seems clear to me that the mathematicians owe nothing to Aristotle, and that the Posterior Analytics is an awkward attempt at saying something about the geometrical method by an outsider who is not really attuned to it. To understand the essence of the geometrical method one will be better off reading philosophers with a natural affinity with mathematics, such as Plato and Descartes. Aristotle puts it well when he says that "you should not argue about geometry among non-geometers---for those who argue poorly will escape detection" (77b). Unfortunately, generations of geometrically ignorant readers have ignored this sound advice and ended up greatly overestimating this rather trifling treatise.

Be that as it may, the essence Aristotle's view of the axiomatic-deductive method is summed up in the following sentence: "Demonstrative understanding ... must proceed from items which are true and primitive and immediate and more familiar than and prior to and explanatory of the conclusions." (71b)

Three notable consequences of this thesis are:

The axiomatic-deductive method is much more than mere logic. "There can be a deduction even if these conditions are not met, but there cannot be a demonstration---for it will not bring about understanding." (71b)

There is a fundamental distinction between "demonstrations which are said to demonstrate and those which lead to the impossible" (85a), i.e., proofs by contradiction, which must be seen as intrinsically inferior (87a).

Axioms stem from perception. "I call prior and more familiar in relation to us items which are nearer perception" (72a), so immediate perception must be the ultimate foundations of "demonstrative understanding." "We must get to know the primitives [i.e., axioms] by induction; for this is the way in which perception instills universals." (100b) However, "for the principles [i.e., axioms] a geometer as geometer should not supply arguments" (77b). Note the two coextensive words for "axiom"---indeed, "I call the same things principles and primitives" (72a), since immediately given truths and logical starting points of a deductive system should be the same thing.
2183643
Highly stimulating and extremely hard to read, written for mathematicians in physics. However, the chapter on Riemannian Geometry can be worked through, up to a point, without any knowledge of exterior differential forms, and is notable if for only one fact alone: a simple calculation is provided that explains explicitly that spheres in four and eight dimensions (3-spheres and 7-spheres) are flat with torsion! I don't know another reference that a physicist without special background in math can consult to understand this highly nonintuitive fact.
268274
I was a fan of Brian Greene's previous books "Elegant Universe" and "Fabric of the Cosmos". About half way through this book I became disappointed and disenchanted. He is moving beyond an exposition of modern physics and becoming more the cheerleader of string theory. I enjoyed first hearing the details of string theory in his Elegant Universe. But as more time passes string theory has nothing more to show for its standing as physics rather than speculation. Also, there is little here you won't find covered in other recent physics popularizations such as Susskind's "Cosmic Landscape".  My conclusion is that the attempt of string theorists to postulate infinite universes based on anthropic principles is a last gasp defense of a theory that has over a generation of time to produce scientifically valid results but instead has nothing to show except mathematics divorced from reality.

We are asked to accept 10^500 (or more) possible universes with different physical constants and 11-dimensional structures, which of course we won't be verifying by experiment in anyone living's lifetime. This is no longer physics or science, this is science fiction or theology. How much longer should physics be allowed this mathematical speculation to continue? If after 30 years string theory cannot predict anything verifiable in a lab and cannot even define why undetectable infinite multiverses are worthy of being called science, it is time to admit defeat and start over. I'd rather we be discussing angels dancing on the head of pins, at least there isn't a half dozen other books on that subject cluttering up the popular science shelves as there are currently about multiverses.

It reminds me of the proof of god arguments that start with imagining a being with perfect qualities. Then the most perfect of beings is one that had all of these properties plus existence. Ergo the most perfect being exists. Well, Mr. Greene, just because you need an infinite number of multiverses to shore up your collapsing theory of strings doesn't make their existence any more real than the existence of a supernatural being.

I have one specific mathematical argument to make on this topic. The first of Greene's multiverses is an infinite universe which he insists requires an infinite number of copies of every being who ever lived acting out every action that ever could be acted out. I think there is a logical fallacy in his argument. First, Mr. Greene speculates there may be an infinite size to the universe. Is this universe countably infinite, or an infinity of a higher order? Regardless, I can point to the infinity of real numbers between 0 and 1. I can point to the infinity of rational numbers between 0 and 1. However, the fact that the interval between 0 and 1 contains an infinity of numbers does not allow me to say I will find the number 2 or 5 or pi there. Why should I be convinced that Mr. Greene's infinite universe has infinite copies of me or even an infinite number of planets, or even one, overrun by, say, blue unicorns, within its infinite domain? What if the infinity of planets, suns and galaxies contain only one of us and an infinity of cold dead moons and black holes?

On page 186 the author cites the success of modern physics in predicting the magnetic moment of the electron to 12 decimal places. When string theory can calculate that and other physical constants to even one decimal place it will be an accomplishment. But until then string theory and the arguments for an infinity of multiverses seem more and more a desperate attempt to justify a wasted generation of mathematical speculation with no basis in reality. The title "The Hidden Reality" is very apt. String theory's "hidden reality" is no more real than the "hidden" worlds of Valhalla, Hades, Oz or Pepperland.  I give Mr. Greene 3 stars only for a well-written book, but I don't wish to read any similar speculative fantasies by him in the future.
1062800
As a mathematical derivatives trader for a decade - and quite skeptical of stocks, bonds, funds and such - I was amused and bit scared to recognize my own thoughts here (Yes, this book tastes better with a nice Malbec) ... Moving beyond its bit convoluted philosophical backdrop, I found it (well, on a second read) surprisingly hands-on and practical. Two hands-on implications:

1. Compared to arithmetic and geometry (thousands years old) and, say, physics (actively studied since medieval universities), probability is in its pre-Newtonian - say "medieval" stage. Gaussian statistics is less than couple of centuries old, non-Gaussian, say Mandelbrot-type probability is only few decades old ... Relying on probability in investing specifically (or human interactions in general) may be a mistake - field needs few centuries to mature, I think.

2. Traditional approach views derivatives as derived from underlying security, which itself derives from primary entity. Speaking for myself only, I find it useful and more practical to visualize derivative as a primary building block - say a Lego piece - of financial universe. If an option - or "contingent claim" in Ayache's words - is a primitive building block, it can be used to derive a synthetic futures contract, then building blocks of entire capital structure (debt, equity) and markets (or Ayache's "technology"), possibly reversing flow of time and causality. After another bottle of Malbec, perhaps Soros and his concept of "Reflexivity" provides additional food for thought ... I thinks such approach helps in hands-on decision making, with concept of risk divorced from notion of probability.
2894756
The person who wrote this book is definitly crazy. But then probably so am I.

If you don't like this book why were you reading it? If you don't like the subject then why were you reading this book? I imagine some people think sacred geometry is easier than ordinary geometry or math, and that this is an easy way to get information,without putting in effort.

Unfortunately sacred geometry is harder than applied math,so persons not actually practising and creating will find little to latch onto and feel cheated. They should read some obscure mathematical Phd instead, since they will obtain similar benefit.

If one feels Drunvalo rants then one should read Kepler. The poetical efforts of Mandelbrot reveal the passion which drives creation versus the dull monotony of committing to memory the discoveries of times past.

Unfortunately when math and science is taught at school very little of the life history of the creator is taught as well.

Newton for instance, spent a huge amount of time on alchemical

experiments. He took it completely seriously. Since Newton was undoubtly a genius there was likely something of worth in this activity, even if it was just to raise the level of mental activity to a point above the mundane where that new discovery on a more practical level became possible.

The fantasy in which Drunvalo has embedded his message is part of the rich ore which has been mined by Hollywood to create Stargate,Battlestar Galactica and other science fiction fantasies. It has already turned into gold.
4301901
I don't know about you, but I get tired of evolutionists trying to tell us that there's no real design in nature, that it's only "apparent design" we're looking at. We're told that these things only look designed but they couldn't actually be designed because we "know" they are the product of chance natural processes. This disingenuous dodge is offered by folks who are unwilling to allow a Divine Foot in the door.

Apparently, this dodge is also offered by folks who hope their audience doesn't look at nature too terribly deeply! Made in Heaven is made-to-order to deal with anti-design arguments. Ray Comfort's book presents 40 cases in which scientists are copying nature's alleged lack of design to design new technology!

From misquitoes that gives us painless needles  to termite mounds that give us better air conditioning, to spider webs that give us better armor, and even moth's eyes to inspire new solar cells, Ray Comfort shows us that without a doubt scientists and engineers are stealing God's designs without giving him the slightest bit of credit!

I enjoyed this book very much. My only criticism is that each topic is so brief, spanning only two pages apiece, so that each 2-page spread is a new article. While it is lavishly illustrated, this doesn't leave much room for content, which left me wanting much more. Of course, part of the reason for this is that it appears to be meant for children at about the middle school to high school level. As such, it presents an overview of the argument against "apparent design" with many brief supporting examples of design in nature - and it gets the point across quite admirably! What's more, these articles stir the imagination and whet the appetite to learn more, so I wholly expect it will become fodder for many a home school and Christian school science assignment!

Parents and children alike will enjoy this book, especially those who already love science. I definitely recommend it.

-Rev Tony Breeden, from the Bookwyrm's Lair

Disclosure of Material Connection: I received this book free from the publisher through the New Leaf Publishing Group Book review program on CreationConversations.com. I was not required to write a positive review. The opinions I have expressed are my own. I am disclosing this in accordance with the Federal Trade Commission's 16 CFR, Part 255  : "Guides Concerning the Use of Endorsements and Testimonials in Advertising."
2358168
it is hard not to fall in love with topology after reading "euler's gem." this book is the epitome of outstanding mathematical exposition, presenting the history and consequences of euler's humble looking polyhedron formula with extraordinary clarity. richeson takes the reader on a leisurely journey of mathematical exploration to get to the land of algebraic topology, while visiting along the way the surrounding territories of graph theory, knot theory, and classical and differential geometry. by the end, the reader should have realized that the various branches of mathematics are intimately intertwined and the journey itself was of significant value. the reader will see mathematical truth and beauty in the process of creation, as well as in its results.

euler's polyhedron formula is: v - e + f = 2, where v is the number of vertices, e is the number of edges, and f is the number of faces. such a simple formula, and yet so deep! if by some chance you've never plugged this formula before, try it now with a cube. draw a cube and start counting the number of vertices, edges and faces. you will get: v = 8, e = 12, f = 6, and so 8 - 12 + 6 = 2. incidentally, euler was a highly "experimental" mathematician in the sense that he was not afraid of calculations and would crunch things out to see if a pattern emerges. that was how euler found this formula in the first place, even wondering how such a simple observation could have escaped other mathematicians before him.

euler's original proof of his formula was combinatorial in nature and somewhat interesting, but it was legendre's proof that completely blew me away. legendre's proof made me utter the words, "so beautiful!!!" (actually, i also used an f-word in there, but amazon is a family website.) legendre's ingenious idea was to consider the images of the vertices, edges and faces as projected onto a sphere encompassing the convex polyhedron. the projection is with respect to a point light source inside the polyhedron. the problem then transforms into a counting problem of areas on the sphere, completely out of left field! everyone who has an interest in mathematics should see the details of this proof before leaving this world. legendre's contribution to uncovering the truly topological aspect foreshadows some of the later consequences of euler's polyhedron formula. we see here an entrance to the road leading to triangulations of surfaces and the results that followed that development.

while richeson's book is suitable for a large readership, its potential is perhaps greatest among high school students who show promise in mathematics. this book expounds the history of the polyhedron formula, offers biographical sketches of great mathematicians, goes through different proofs, explores connections and cross-fertilization in the mathematical empire, and gives the reader a sense of the art of mathematical thinking. it is almost certain that not everything in "euler's gem" will be fully understood by a student at the high school level, but that's perfectly ok. it is good for the mind to see glimpses of where mathematics is heading in future courses so that math doesn't feel like meaningless memorization without any direction. i hope "euler's gem" will gain popularity among high school faculty members so that they will recommend it to their brightest students; i hope this book will be used to stoke the fires in the minds of those who will later walk the path of math and science.

in writing "euler's gem," richeson has done the mathematical community a tremendous service. topology has never before been so lucidly explained to so wide an audience. well done.
3814952
In time many fields can get taken over by mathemeticians, who are not bad people-- they are artists who make beautiful formulas and impress each other with their brilliance.  Mathematicians have no responsibility to pay attention to the universe we live in.  Their work is in symbolic truth.  Often times it is extremely useful in understanding the universe, but that is another kind of work- applied math.

Scientists are supposed to learn Natures secrets, regardless of whether the math is beautiful, though it quite often is.

Economics is a field totally dominated by people who love math a bit more than they ought to - and their predictive ability suffers.

Physics likes to study how many strings can dance on the head of a pin, because theoretical work is cheaper than real work.
In the mean time important laboratory findings are ignored.  Like the seasonal nature of beta decay. (Fishbach).  Or LENR / Cold Fusion which is now totally repeatable, but nobody cares.  Having too much fun being mathematicians.

This book is a refreshing view on what has happened to physics lately.
1306008
Over all I enjoyed this book, the author introduces many true and theoretical science ideas. Many things like "Lake Las Vegas", "Cheyenne Mountain" I've never heard of and and found interesting. Human nature was realistically depicted. I found the idea of time travel back 45 millionths of a second amusing and worth thinking about. I struggled with the duplication idea in that to my mind the duplicate should only last the duration of the time traveled. The author wrote a great afterword and in it mentioned Zeno's Paradox, about the tortoise and the hare which always seemed to me to be a semantic trick in that the race's participants movements are stated as separate expressions, if you combine the equations by simple algebra there is no paradox. Also it seemed to me split second time travel could revolutionize computer hardware. Other than these nitpicky complaints the book is fun, informative, thought provoking, and well worth reading.