This is an entertaining book about recognizing bullshit, researching and calling it out. Much of the book describes the various types of bullshit, andThis is an entertaining book about recognizing bullshit, researching and calling it out. Much of the book describes the various types of bullshit, and the research required to snoop out its origin. Then, a short portion of the book is about calling it out; how to call it out, and even when to call it out. The book is filled with anecdotal bullshit, and the research the author used to ferret out its origin. Much of the bullshit is unintended--it is simply a matter of passing along incompetent analyses and conclusions. When bullshit is intentional--that is simply called lying.
Selective bias is the reason for a lot of bullshit. This occurs when a survey or a statistic is unintentionally biased in the sampling population. The author describes the situation for waiting for a bus at the airport, for your particular brand of rental car. It always seems like all of the other busses pass you by, before your bus arrives. This is not a coincidence; it is a statistical rule when busses tend to get clumped together instead of arriving equally spaced in time. The author also explains why people who are dating seem to meet nice people who are unattractive, or attractive jerks. This also is not a coincidence; the book describes why this happens!
Then there is the misleading biases in data visualization. After the Florida "Stand Your Ground" law was enacted, a figure seemed to show at first glance, a drop in homicides. A close look at the vertical axis shows that it was inverted, giving the wrong impression. It turns out that the author of the figure did not intend to mislead, but used an unfortunate representation of the truth.
The book describes how scientific journal articles often go awry. It comes down to this: "When a measure becomes a target, it ceases to be a good measure." Scientific journals have a strong preference for a statistical measure called the "p-value" to be less than 0.05. As a result, scientists use the p-value to imply the probability of a hypothesis being true. They often alter the original hypothesis during analysis--absolutely a 'no-no'. Self-selection of statistical groupings that give low p-values is called "P-hacking", and is one reason why so many scientific studies are not reproducible. As a result, p-values no longer serve their original purpose.
The author gives a set of useful suggestions for spotting bullshit on the Internet: 1) Pay attention to where information comes from 2) Find multiple sources for a story 3) Dig back to the origin of a story 4) Use reverse-image lookup; very useful for fact checking 5) Beware of deep-fake media (photoshopping, etc.) 6) Use a fact-checking organization, like Politifact.com, FactCheck.org, or Snopes.com 7) Beware of the illusory truth effect; repetition does not imply truth. 8) Beware of social media: "Think more, share less"
The book contains a set of recommendations on how to call out bullshit. They are: 1) Reductio ad absurdum (very entertaining!) 2) Be memorable 3) Find counter-examples 4) Provide analogies 5) Redraw figures
Finally, the book describes when it is useless to call out bullshit and when it is a moral imperative. And, the chief take-away from the book is this: "If a story sounds too good--or too bad to be true--it probably is!"...more
I loved Jordan Ellenberg's earlier book, How Not to Be Wrong: The Power of Mathematical Thinking, and it was a hard act to follow. But not for EllenbeI loved Jordan Ellenberg's earlier book, How Not to Be Wrong: The Power of Mathematical Thinking, and it was a hard act to follow. But not for Ellenberg, as this book is also great. While the title, "Shape" implies that this book is about geometry--and it is--it is also about so much more. This book shows how mathematics is applicable to just about everything under the sun. And Ellenberg manages to make it all so fascinating! The sheer depth at which he covers an incredibly diverse range of topics is staggering. This is the type of book that I love! Ellenberg is a professor of mathematics, so he certainly knows what he is talking about!
I enjoyed his description of how computers have been taught to play chess. I enjoyed his description of the problem of gerrymandering in states. I had previously thought that, were it not for politics, it would be an easily solved issue. Ellenberg shows why politics is just one of the thorny issues. The geometry, and the issue of fairness is just as difficult! The book describes issues about pandemics, including Covid-19. How can you turn away from a book that talks about politics, eigenvectors, Poincare, neural networks, Euclid and ... and ... Wow! The book does tend to spend a bit too many pages on the subject of gerrymandering, but it is a big problem, and I have never seen such a treatment of the subject....more
This is a marvelous book about all the ways that math errors can infiltrate our day-to-day living. Some of the math errors are just fun (as in older aThis is a marvelous book about all the ways that math errors can infiltrate our day-to-day living. Some of the math errors are just fun (as in older arcade games), while others have life-or-death consequences (like airplanes running out of fuel mid-flight).
Some of the math errors are simply a confusion about units; feet/meters, pounds/kilograms, and so on. One such error was when a jet liner was loaded up with fuel in pounds, instead of kilograms. Luckily, there was a mid-flight landing and refueling. Unluckily, the refueling made the same identical mistake. Luckily, the pilot had experience piloting glider planes! An emergency landing at an abandoned airstrip without engines or power or electricity for the landing gear -- surprised a drag racing party!
Sometimes, a change in versions of equipment or software cause problems when an only partial compatibility is encountered. Sometimes, limited storage for variables (say, 32-bit instead of 64-bit) cause issues when numbers that are expected to be small actually overrun the storage. This happened to the Patriot Missiles that were deployed to protect against incoming missiles during the Desert Storm operation.
Misplaced decimals, misunderstood calculator quirks, bridges and buildings that resonate at unfortunate frequencies, and everyday folk who lack the understanding of how to divide numbers with units, make up many of the fascinating anecdotes in this book.
Matt Parker is an Australian mathematician with a delightful sense of humor. The book is never overly technical--just enough mathematics or engineering background is introduced, to allow an understanding of each episode in the book. Oh--and I did not read this book. I listened to the audiobook, as read by the author. It is absolutely wonderful! ...more
Randall Munroe is the author of the web site xkcd.com, The web site is a collection of science-oriented absurdist cartoons. If you have never had the Randall Munroe is the author of the web site xkcd.com, The web site is a collection of science-oriented absurdist cartoons. If you have never had the opportunity to visit this web site--do so immediately! It's a lot of fun!.
This book follows closely on the web site's approach, and that of his previous book What If?: Randall Munroe Serious Scientific Answers to Absurd Hypothetical Questions Summary & Takeaways. This is obviously a "How To ..." sort of book. Some of the questions it asks, like "How to Throw a Pool Party", "How to Dig a Hole", "How to Play the Piano", or "How to Play Tag" sound like normal How-to questions. At the beginning of each chapter, you might get a standard sort of answer. But it never> stops there. Each answer quickly segues into an altogether absurd approach. The answers often use physics and simple mathematics to illustrate the answers, along with a liberal sprinkling of stick-figure illustrations.
The book is hilarious. The physics/mathematics approach is especially appealing to nerds. The book is highly entertaining. You never know--you might someday have a real need to know how to catch a drone, or how to power your house on Mars. [image]...more
As the title of the book includes the word "brief", I suppose it delivers. The book is only available as an audiobook, divided into ten very short essAs the title of the book includes the word "brief", I suppose it delivers. The book is only available as an audiobook, divided into ten very short essays. Each essay gives a very BRIEF glimpse into the life and accomplishments of a famous mathematician. Perhaps this type of audiobook is good for someone for whom math, in school, "wasn't his thing." For me, each essay isn't enough to even be considered as a teaser. There is no depth here, not much insight. There is just enough here to wonder, "so what?"...more
This book contains memoirs of a mathematician, Cedric Villani, a recipient of the Fields medal. Originally written in French, I read a version that haThis book contains memoirs of a mathematician, Cedric Villani, a recipient of the Fields medal. Originally written in French, I read a version that has been translated into English. The translation seems to be excellent. VIllani collaborated with Clement Mouhot, to derive and prove a theorem related to Landau damping. This is not a pure-mathematics theorem. It is based on a real physical phenomenon that occurs in plasmas. So, it is of great interest to physicists, as well to mathematicians.
The main problem with this book, is that the author does not know who its reader should be. Should the reader be a professional mathematician? Perhaps, but then why would half of the book be devoted to an exploration of how a mathematician works day-to-day? Mathematicians already know that.
Should the reader be an informed layman, with some interest in mathematics? In that case, why are there so many pages scattered throughout the book, filled with very esoteric formulas that only a true expert will understand. Many full pages in the book are filled with equations like this: [image] The words that accompany these pages are not of any help in understanding the equations.
The book also contains many pages of e-mail correspondence, mostly between Villani and Mouhot. This correspondence sheds a little bit of light on how a mathematician might operate during a collaboration. But again, unless you are a professional mathematician, you don't stand a chance in understanding most of the correspondence.
And besides all this, the author makes no effort at all to explain Landau damping, let alone its relationship to his theorem. Landau damping is a real physical phenomenon, with applications in several areas of physics. But having read the book, I still have no idea what it is all about. A quick glance at Wikipedia helps to understand it. But, the book does not even devote a single paragraph to explain what it is about....more
I am sure that Taleb makes new enemies with each book he writes. If, by the end of the book, you have not been offended by something he has written, then you haven't been paying attention. Taleb is blunt, sometimes obtuse, and often right. But it really irks me that his very strong opinions are not always backed up by reasoning. Like a mathematics professor, he will often "let the reader fill in the lines of his proof."
The basic premise of the book, is that one should not believe opinions or forecasts of others, unless they have some "skin in the game." Results are all that count--opinions and talk are worthless. It is so easy for people to spout utter nonsense, so unless they could potentially suffer consequences of being wrong, you should ignore them. This goes especially for intellectuals in academia. However, "hard" science seem to be immune to this problem, because of the redeeming nature of falsification, while "scientism" -- the excessive belief in science is worthless.
The broad sweep of his aphorisms are overwhelming. Here are some examples that actually are given some logical reasoning: Genes follow majority rule. Languages follow minority rule. Islam is widespread because of its rules of conversion and parentage. "Someone with a high public presence who is controversial and takes risks for his opinion is less likely to be a bullxxxt vendor." "Employees are slaves."
And then there are aphorisms that may very well be true, but do not seem to have much back-up reasoning: "Courage (risk taking) is the highest virtue. We need entrepreneurs." "Anything that smacks of competition destroys knowledge." "Academia has a tendency, when unchecked (from lack of skin in the game), to evolve into a ritualistic self-referential publishing game."
Among the people Taleb dislikes: Steven Pinker, Hillary Clinton, journalists, intellectuals who are idiots, the Saudi regime, Monsanto, ... the list goes on and on. Taleb goes into some detail about how psychologists totally misunderstand "loss aversion", due to the concept of ergodicity.
Taleb introduces so many quirky words and expressions, that he devotes a glossary in the back of the book to explain the terms. And, the end of the book is filled with a technical appendix with some very technical mathematical proofs about probability theory.
With so many issues that I have with this book, why do I recommend it with five stars? Because the book is so thought-provoking. It jabs me everywhere, and gets me to think about a lot of things, basic assumptions about life. Take a risk--read this book....more
The subtitle of this book, How Big Data Increases Inequality and Threatens Democracy really says it all. Big data has come into our lives in numerous The subtitle of this book, How Big Data Increases Inequality and Threatens Democracy really says it all. Big data has come into our lives in numerous ways, and many of them are a scourge on our lives. Big data, in and of itself, is not to blame, but the uses to which it is put are often outrageous. Take the case of automated teacher evaluations. These are often based on the improvement of students' scores. It seems like a no-brainer, and since the scores take into account the improvement rather than the absolute scores, they seem to be very fair. However, one New York teacher received an abysmal score of 6 (out of 100) one year, and the following year received a wonderful score of 96. Obviously the teacher did not suddenly improve his teaching methods.
If a mathematician were to analyze the scores from such evaluations, their random scatter would be instantly recognized as meaningless. Yet, these automated evaluations are used for hiring/firing decisions, as well as compensation decisions. The worst aspect, is that there is no attempt to improve the algorithms. The algorithms used in these evaluations are opaque, and no attempt is made to apply feedback to tweak the scores to make them more accurate and fair.
Such algorithms are used in many avenues of life. Credit scores are used by loan companies--and even by auto insurance companies! Police departments use algorithms to plan targeting of police activity, while courts use algorithms to predict recidivism. Colleges, especially for-profit colleges, use algorithms to target potential students.
While this book comes across as very preachy, and very liberal, it does make some very good points. Big data is often used--intentionally or not--to punish the down-trodden and to increase inequality. Profitability is usually the goal, and while fairness is often the purported goal, these algorithms rarely turn out to have the effect of being fair.
I recommend this book to people who are curious about the effects of big data on their lives and on democracy....more
This is a fantastic book about scaling laws and how to understand them. Geoffrey West is a theoretical physicist, who has spent a lot of time at the SThis is a fantastic book about scaling laws and how to understand them. Geoffrey West is a theoretical physicist, who has spent a lot of time at the Santa Fe Institute, deriving theoretical scaling laws, and applying them successfully to biology, cities, and companies. He derives the theories from the structure of networks; arteries, capillaries in organisms, social networks and city infrastructure, and companies.
The scaling laws themselves are fascinating. In the very first chapter, Geoffrey West hits the reader with an astounding set of scaling laws that certainly surprised me. As to biology, there are about 50 different metrics that have interesting scaling laws--and West touches on a few of them. The scaling of metabolism, heart rates, brain matter, growth rates, life spans, aorta lengths, tree heights, and on and on; you get the picture. These scaling laws pertain across organisms, from the tiniest microbe to the blue whale; over 20 orders of magnitude.
But the really surprising aspect is that almost all of the scaling laws are factors of 1/4! For example, metabolic rate scales as Mass to the 3/4 power. Doubling the mass of a mammal increases its time to maturity by 1/4, its lifetime increases by 1/4, and its heart rate decreases by 1/4. And, these laws apply over the entire range of mammals, despite their diversity. Mitochondrial mass, relative to the total mass of an organism, goes as Mass to the -1/4 power. And, Geoffrey West describes how he and colleagues have derived theoretical scaling laws and growth curves from first principles. He shows how remarkably well the data fit his theoretical predictions.
As a physicist, West felt that this universal 1/4-power scaling tells us something fundamental about the dynamics, structure, and organization of life. These laws suggest dynamical processes that constrain evolution. And there are some surprising constants among all mammals. Blood pressure is approximately the same, and the number of heart beats in a lifetime is about the same, among all mammals!
But the discussion of scaling laws don't stop with biology. West finds fascinating scaling laws that apply to cities and to companies. The most perplexing question he addresses is, why do most cities live forever, while companies have short lifetimes? Cities are the prime drivers of economic development, not the nation state. And, most of the scaling laws associated with cities are either to the 0.85 or 1.15 power. That is to say, comparing two average cities, one twice as big as the other in population, the larger city will not have double the number of gas stations, but only 85% more than the smaller one. The larger city will have 115% higher wages, more doctors and lawyers, patents, GDP, number of cases of AIDS, crime and pollution. This scaling applies within all countries, but not across from one country to another.
The average half-life of companies is 10.5 years!And in any given year, the risk of a company disappearing (through bankruptcy, or merger, or acquisition) is the same, regardless of a company's size!
While cities become more diverse as they age and grow, companies do the opposite; they lose diversity, as they become more supportive of tried-and-true products in order to guarantee short-term returns. As companies grow, so too does their bureaucratic control. And, this is at the expense of innovation and R&D (Research and Development).
At times, the narrative deviates from scaling, and goes into various qualitative aspects of cities and companies. The author is rather opinionated in these areas, but his conjectures are interesting, though open to controversy. My only complaint about this book is that, while theoretical scaling laws in biology are developed and tested successfully against data, the book does not offer theoretical scaling laws for cities and companies. To some extent, these are more difficult to develop, because they depend on socio-economic structures and social networks. Data for these, especially for companies, are more difficult or expensive to obtain. Nevertheless, this book offers a wealth of information, and is endlessly fascinating. Highly recommended!...more
This is a fascinating book about the theoretical limits of our knowledge, our ability to make predictions, and to understand the universe. Marcus du SThis is a fascinating book about the theoretical limits of our knowledge, our ability to make predictions, and to understand the universe. Marcus du Sautoy is a professor of mathematics at Oxford University. A central theme of the book, is to show how mathematics works as a powerful tool in helping us understand nature, and the limits to our understanding of how it works.
The book begins with a discussion of throwing a 6-sided die. With perfect knowledge of the position, velocity, and rotation of the die, is the outcome predictable? Actually, the answer depends on the friction of the table onto which the die is thrown. For certain ranges of friction, chaos prevents predictability.c
So the book relates the story of King Oscar II of Norway and Sweden, who celebrated his 60th birthday by offering a gold medal prize to whomever solved a math puzzle; "Is the solar system stable?" Poincare worked on this puzzle, and submitted a paper analyzing the orbits of two planets and a speck of dust. He showed that they followed periodic paths. The editor of the journal showed a gap in the proof, so Poincare tried to stop publication, but it was too late. Poincare had discovered that small perturbations to a stable orbit could make the system fly apart. This led to the discovery of chaos. In 2009, French astronomers modeled the solar system's stability many times, adding slight perturbations. The orbits of Jupiter and Saturn were very stable, but in 1% of the simulations, Mercury's orbit had a resonance with Jupiter, allowing Mercury to collide with Venus, which then collides with the Earth.
It is well known that the Earth's atmosphere is a chaotic system. A small perturbation leads to unpredictable outcomes. This idea feeds the claims of climate-change deniers, that we cannot predict a change in climate. Sautoy brings up the quote,
Not believing in climate change because you can't trust weather reports is a bit like saying you can't tell when the next wave is going to break on Bondi Beach because you don't believe in tides.
Sautoy gives the clearest explanation of wave-particle duality and some of the paradoxes of quantum mechanics, that I have ever read. He discusses elementary particle physics. He brings up the paradox, that electrons behave as if they have no volume, yet they have mass. But then, what is their density? Is it infinite? Is each electron a tiny black hole?
Sautoy brings up a very interesting aspect of Heisenberg's uncertainty principle. Heisenberg's original paper on the subject is often misunderstood. It is not that the act of observation affects a system. Heisenberg was forced to put that example into his paper in order to get it approved by skeptical editors. Even without a direct interaction with a particle, the product of uncertainties in its position and momentum is limited. It's not that we cannot simultaneously precisely measure position and momentum. It is that they do not exist until we measure them.
Many scientists equate God with "things we cannot know." Heisenberg's uncertainty principle also holds for time and energy. When you look at empty space for a short period of time, there is uncertainty in the energy content; space can never be truly empty. Since energy can change into mass, particles can spontaneously appear in a vacuum. So, there is no need for a creator. Some people give the definition of God as the solution to a question, such as "why is there something rather than nothing?" The trouble with most religions, is that God is then given so many properties that god ends up having nothing to do with the definition. It is like working backwards, conjuring up properties without understanding the original definition. One could define God as the existence of things we cannot know. To declare oneself as an atheist is to mean there is nothing we cannot know. But to say that there are things we cannot know, then, is a proof that God exists.
Cosmology is a science where not all questions are, in principle, answerable. This is a "Copernican" aspect of things. The universe is expanding and in the past seven billion years, the expansion rate has been accelerating. Dark energy is hypothesized as the cause. In the distant future, we won't be able to see other galaxies, as space will have disappeared from view, beyond the sphere of our visible universe. But we will still see the stars in our Milky Way galaxy. So, we are lucky to know that other galaxies even exist. Some day in the far future, this knowledge may be lost.
Sautoy describes an interesting set of experiments designed to fool the brain into thinking that your seat of consciousness is located elsewhere--in another person or even in a Barbie doll! Then there is a fascinating discussion of experiments dealing with consciousness. A group of philosophers believes that science can never solve the problem of consciousness. But, we are reminded of the prediction of the philosopher Comte, who foretold that we would never know what is at the heart of a star.
This book is written in a very accessible style. Sautoy gives crystal-clear explanations. I enjoyed every page of this book, as it gave me different ways to think about the universe, and the role of mathematics in unraveling its mysteries. ...more
I enjoy thinking about algorithms as they are applied to technical problems. So, when I saw this book, I thought, "This is a book written just for me.I enjoy thinking about algorithms as they are applied to technical problems. So, when I saw this book, I thought, "This is a book written just for me." And, that assessment was absolutely correct. It is a fascinating book, all about how sophisticated algorithms are applicable to everyday problems.
The book starts out describing the "optimal stopping problem." It is also sometimes called the "secretary hiring problem", and I have seen it applied to dating to find a romantic partner, and this book points out that it can also be applied to looking for an apartment in a seller's market, or searching for a parking space. It can be summed up by the phrase, "Quit while you're ahead." Basically, you have a finite amount of time to complete a search for the "best" item or person. What do you do? It can be shown, mathematically, that you should conduct a search for 37% of your total available time, without making any decisions. Then, at the very next time you find an item or person that is better than all of the previous ones, you should jump on it! I read about this, beforehand, but I didn't realize that 37% comes from 1/e, where "e" is the natural exponent.
The next topic in the book is the dichotomy between explore and exploit. That is to say, when you are looking for something to do, will you try something new (explore), or repeat something that has pleased you in the past (exploit). The answer has to do with how much more time you have in this situation. Movie sequels are all about exploiting, because movie revenues are decreasing. If you are new to an area, you will explore restaurants, but if you are moving away soon, you will return to restaurants you have previously visited. I enjoyed how this issue is related to the "multi-armed bandit" problem. This is a mathematical problem that has lots of applications; choosing the best slot machine in a casino, for example, or designing a web site that will maximize profits for a company.
Sorting is a big topic in the book. It turns out that top poker players sort themselves out, and don't want to play with players they think are better. Libraries use an inefficient caching system, putting recent acquisitions in front. Instead, they should put the most popular books in front. The Naguchi filing system involves returning all files to the extreme left. This goes against the recommendations of efficiency experts, who recommend sorting by topic. Leaving a pile of papers on top of a desk is an example of the MOST efficient filing system! I enjoyed reading an anecdote about Barack Obama visiting Google, before he became president. At Google, he was treated to a pretend job interview. He was asked, "if you had to design an algorithm to sort a million 32-bit integers, what would you do?" He replied that he would not use a bubble-sort algorithm, and all the people in the audience applauded his correct answer!
I enjoyed reading about human memory from an algorithmic point of view. Memory recall is a problem of organization. It was fascinating to read that a graph of the probability of remembering something as a function of elapsed time exactly mimics the probability that a word appears in a newspaper headline twice in a row!
Knowing more makes it harder to remember things; what we call memory decline is actually just learning. A brain fart is actually just a cache miss!
Related to sorting are various problems of scheduling. Examples from the book include multiple laundry loads to minimize total washing plus drying time, and minimizing the rotting of food from a CSA (Community-Supported Agriculture).
No book on everyday applications of algorithms should bypass Bayesian reasoning, and this is an important subject in this book. Our memories of images of plane crashes and car crashes are roughly the same; as a result, we are surprised that there are orders of magnitude more deaths in car crashes, than in plane crashes.
The dangers of over-fitting are discussed at length. As an example, police and FBI agents sometimes over-train; they sometimes use good gun-training etiquette during a shoot-out, with fatal consequences. I really appreciated the discussion of how over-fitting is avoided in biological evolution. It is dangerous for organisms to evolve to over-fit an ecological niche, because the species might not be able to rapidly adapt to an uncertain future environment.
I also thought that the description of "exponential backoff" was very well treated in the book. This esoteric-sounding algorithm is used in all computer networks, but is also used by many of us in treating flaky friends, and in punishment for probation violations.
The last chapter in the book was about game theory. It is helpful, in reading this book, to have some previous background, an understanding of a "Nash equilibrium". The following quote sums it up nicely:
Love is like organized crime. It changes the structure of the marriage game so that the equilibrium becomes the outcome that works best for everybody.
I highly recommend this book. Regardless of your mathematics background, it will intrigue you and amaze you, to see how math permeates our everyday lives....more
This is an amazingly ambitious book. It covers such a wide range of topics--I have never seen such a comprehensive non-fiction book. It starts out witThis is an amazingly ambitious book. It covers such a wide range of topics--I have never seen such a comprehensive non-fiction book. It starts out with a detailed description of theories of the origins of the universe. Here, John Hands is at his best, as he sorts out the various theories. He reasons why some of the theories are still in the running, while others are not borne out by the available evidence.
John Hands continues to discuss the origins of life. He describes the prevalent theories, and gives his opinions about which theories are most realistic. He describes evolution from the earliest microbes to the present-day complex organisms. He considers the evolution of humans and the origins of consciousness. He points out the ways in which humans differ from all other animals.
Then, the book goes into a history of the human race. The development of science, technology, and philosophy are covered in some detail. He points out that many so-called "world-wide" philosophy books skip almost completely the philosophies of the East, and concentrate almost entirely on those of the West. While John Hands does devote attention to Eastern philosophies, he also spends much more time on Western ones.
This is not an entertaining book. There is not a trace of humor, and there is no effort taken to make it easy on the reader. However, the sheer scope of the book, and the intelligent unbiased descriptions of the science, history, and philosophy, make this a book deserving of one's attention. I recommend the book for people who are truly curious, and want an unbiased view of our understanding of human evolution....more
I wanted so much to love this book, but it was difficult. About half of the book is about Frenkel's life; and it was fascinating. The other half, inteI wanted so much to love this book, but it was difficult. About half of the book is about Frenkel's life; and it was fascinating. The other half, interleaved with his memoirs, are descriptions of Frenkel's mathematical work and discoveries. I had a great deal of trouble following the descriptions of the math. I am superficially familiar with many of the concepts, but it just gets more and more complex. Toward the end, especially, I became quite confused.
Frenkel grew up in a small town in the Soviet Union, a two-hour train ride from Moscow. Initially interested in physics, Frenkel's father introduced him to a mentor who showed him how modern physics, especially quantum mechanics, relies on some very modern concepts in mathematics. In that way, Frenkel got hooked on math.
When he was in high school, starting to think about college, Frenkel applied to the math department at Moscow State University. It was explained to him that he had no chance of being admitted. He had a Jewish last name, and anti-Semitism would prevent his admission. Frenkel applied for admission anyway, and he was grilled mercilessly during an oral entrance exam. The examiners found excuses to refuse him admission.
So, Frenkel went to undergraduate school at a different college, one that did not discriminate so much. Nevertheless, he attended lectures and seminars at Moscow State University. He didn't have a college ID, so he scaled the fence to get in! The Soviets put tight controls on photocopiers. While in undergraduate school, his research papers were secretly copied and smuggled out, and reached mathematicians around the world. One day, Frenkel received an invitation from the president of Harvard University to come to Harvard on a fellowship grant, and become an assistant professor. At that point in time, he didn't even have a PhD!
What I did get out of the math descriptions, is the inner beauty of math. Vastly different areas of math can be connected, through hidden connections, as if by magic. This attracted Frenkel to the Langlands Program, a grand unified theory of mathematics. Now a vast subject, the program tries to connect number theory, harmonic analysis, geometry, representation theory, and mathematical physics. Riemann geometry is the cornerstone of Einstein's Theory of General Relativity. It contains hidden connections with number theory. Frenkel's career goal is to establish connections between the dualities in physics and the dualities in mathematics.
In the last chapter, Frenkel spent a sabbatical in France, writing and producing a short film. He also co-stars in the film, titled Rites of Love and Math. The trailer is on a site on YouTube.com. In this allegorical film, a mathematician discovers a mathematical formula for love. He realizes the formula's importance, and that it could be used for good as well as for evil. He tattoos the formula on his lover's body. The film was screened at many film festivals to wide acclaim, but also received a lot of controversy.
You can read the book and skim or skip through the math. Frenkel does a good job of describing the hidden connections and beauty of math. But he leaves the average reader lost in the details....more
This book is an engaging, comprehensive guide to strategies, as applied to everyday life. The first part of the book focuses on standard game theory, This book is an engaging, comprehensive guide to strategies, as applied to everyday life. The first part of the book focuses on standard game theory, graphical notations for various problems, and applications of the prisoners' dilemma to everyday situations. The second part of the book concentrates more on everyday and business problems, and strategies to achieve optimal solutions. Game theory is not always applicable to all of these problems, but logic and rational problem-solving and a bit of mathematics are ever-present.
The book explores the voting issue in some detail. When two candidates are running against each other, the best strategy of course is to vote for your first choice. When three or more candidates are running, it is not always best to vote for your first choice, especially if you believe that your first choice has no chance of winning. For example, in the presidential election of 2000, there were three candidates, Bush, Gore, and Nader. If you preferred Nader to the others, you could vote for him, but your vote would be pretty much wasted, as he had little chance of winning. It would be best to vote for your second choice. But, what if the election was predicted to be much closer; what would the best strategy be then?
Furthermore, the book explores other voting systems that would allow you to list all of your voting preferences? For example, what if you could vote on all of the candidates, listing their names in preferential order. Various vote-tallying systems could take these preferences into account, and come up with a fairer assessment of the most-preferred candidate.
But here's the rub; there are numerous vote-tallying systems, each of them objective, but depending on which one is chosen, a different candidate could win. The book goes into some detail in considering the different outcomes of the 2002 presidential race, considering several of these systems.
The book also describes three different systems for auctions. Although the systems differ dramatically, the optimum strategy is the same for all of the systems.
The book describes various approaches for political negotiations. Examples include incentives and threats. But a threat is only good if it is credible. The book describes some historical approaches that have made threats credible. Another type of strategy is how a company can best compete with other companies, by setting prices that will maximize profitability.
The book has a set of exercises to try out your newly-gained understanding. One of the exercises is to consider how to make a good first impression on a first date. You are faced with two simultaneous problems; how to prove your sincerity and quality to your date, and how best to assess the sincerity and quality of your date. In other words, what is the best strategy for signaling and screening?
This book is best appreciated if you are not afraid of some simple algebra. However, many of the strategies are not at all mathematical, but simply rely on logic. I thoroughly enjoyed this book; some of the chapters were a bit repetitive, but not overly so. ...more
This is a wonderful book about mathematics and its application to everyday life. Jordan Ellenberg shows that the certainty that people associate with This is a wonderful book about mathematics and its application to everyday life. Jordan Ellenberg shows that the certainty that people associate with math is often misplaced; some areas of math are devoted to uncertainty, and that's where things get very interesting.
Ellenberg starts the book with a beautiful example of application of mathematics, logic, and thinking out of the box. During World War II, a group of mathematicians working for the Statistical Research Group were given a problem by some Air Force officers. Fighter planes returning from missions were analyzed for bullet holes. The number of bullet holes per square foot were counted. For example, there were 1.11 bullet holes per square foot in the vicinity of the engine, 1.73 in the fuselage, 1.55 in the fuel system, and 1.8 in the rest of the plane. The officers wanted to add some armor to the planes; the question was where? The planes could only support so much weight, and where would additional armor be most advantageous? The officers thought that since the fuselage had the greatest density of bullets, that would be the logical location for more armor. A mathematician named Abraham Wald said exactly the opposite; more armor is needed where the bullet holes aren't, namely, around the engines. Planes with lots of bullet holes in the engine did not return at all!
The book discusses the issue of statistical significance. Scientific experiment often use a 95% confidence threshold as an indicator of statistical significance. This means that if a truly random outcome were expected, a positive correlation would be seen only 5% of the time. Ellenberg includes an xkcd cartoon that shows how easy it would be to perform a set of experiments that could come up with statistically significant results like "Green jelly beans linked to acne! at the 95% confidence level.
Some of the section and chapter titles are hilarious. For example, in the chapter titled "Are you there, God? It's me, Bayesian Inference", Ellenberg brings up a scary example of the use of "big data". Based on a teen-age girl's purchases of unscented lotion, mineral supplements, and cotton balls, the retail store "Target" began sending her coupons for baby gear, because of the (correct) inference that she was pregnant. Another great section title is "One more thing about God, then I promise we're done."
Another interesting title is "The Cat in the Hat, the Cleanest man in school, and the creation of the universe", in which Ellenberg reviews some of the probabilistic arguments for and against the existence of god. And I love the famous quote by Richard Feynman:
You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW375. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!
I also love the chapter title, "If Gambling is exciting, you're doing it wrong". Ellenberg describes how several groups capitalized on several state lotteries. Due to some strange lottery rules, it is (was?) possible to reliably make a profit, given enough investment of resources. No illegal shenanigans--the states make money no matter what you do. You could make a profit by taking advantage of the rules, and of the people who buy lottery tickets without a coherent strategy. And, I did not realize that Voltaire made his fortune by taking advantage of state lotteries!
Ellenberg brings up the phenomenon of Nate Silver predicting the outcome of the Obama-vs.-Romney election. Silver predicted the probability of both candidates winning state by state, along with the margin of error. By adding up the probable errors, he estimated that he would be wrong by 2.83 states. Critics seemed to have ignored the fact that he was not wrong by this many states--in fact he correctly predicted the outcome in all 50 states!
I highly recommend this book to all people who are even vaguely interested in math, probability, logic, and the application to everyday life. This is an excellent book!...more
This book is a wonderful introduction to history of predicting stock prices using mathematics and concepts from physics. It is basically a history of This book is a wonderful introduction to history of predicting stock prices using mathematics and concepts from physics. It is basically a history of pricing models; from the earliest mathematical models to the most modern ones. Of course, the best ones are maintained in secret by some super-secretive investment companies, for good reason. The only way a pricing model can be profitable is it to be better than most others being used.
The author, James Weatherall, has a PhD in physics, and is presently an assistant professor of logic and philosophy of science at the University of California, Irvine. He writes with clarity and an engaging style. His narrative follows a logical path, and does not take big diversions along the way.
Now, many of the subjects of this book are not physics at all, but applied mathematics. For example, the so-called "black box" model does not use any physics, but use purely statistical associations that are discovered algorithmically. Their name stems from the fact that they are opaque; they may make accurate predictions, but they offer no insight into the reasons for their predictions. Hence, it is difficult to judge how much confidence should be given to their results. But, for example, a model that predicts an investment strategy that returns a hundred times the S&P 500 over a fifteen-year period is nothing to be sneezed at.
Some of the models are definitely an application of physics concepts, such as the gauge theory model. I find if fascinating that this arcane physics concept has some practical applications in economics and predictions.
Some people blame these computer models for the disastrous economic downturns and stock market volatility that occur from time to time. While Weatherall sympathizes with this attitude, he wholeheartedly endorses the models, as they are simply tools. Sometimes, the assumptions and limitations of these tools are ignored, with dire consequences....more
The first half of this book is a review of modern physics on the macro and micro scales. The second half of this book is a discussion of the author's The first half of this book is a review of modern physics on the macro and micro scales. The second half of this book is a discussion of the author's speculation, that the universe is a mathematical structure. Max Tegmark is quite clear--he is not saying that the universe is described by mathematics, but that the universe is mathematics. He calls this the "Mathematical Universe Hypothesis", or "MUH" for short.
Tegmark asserts that this idea is a testable, falsifiable hypothesis. I did not find the experimental test, but perhaps I simply missed it. To be perfectly frank, I don't even understand his reasoning.
The last chapter of the book switches gears entirely, and discusses the existential threats to human survival. Things like asteroid collisions, eventual expansion of the sun, and so on. Then the book describes the two most immediate threats to human existence. The first is a nuclear war. And the second is--are you sitting down for this?--the singularity, where artificial intelligence takes over the world.
I didn't read this book--I listened to the audiobook, read by Rob Shapiro. He did an excellent job, giving the narration an aura of authenticity. It's just too bad that the content of the book is not as good as the narration....more
This is a very good book about methods for computing probability puzzles. There are two types of methods discussed here: analytic solutions and computThis is a very good book about methods for computing probability puzzles. There are two types of methods discussed here: analytic solutions and computer simulations. The book is intended for readers with a strong mathematics background. Good algebra skills are essential, and calculus is also required to solve some of the puzzles analytically.
This book is divided into three parts. The first part is a description of 21 puzzles. The descriptions go into some detail, and provide hints. The second part contains the analytic solutions to the puzzles. The third part contains computer programs for simulating the solutions; the programs are written in Matlab, which for me is just perfect.
The puzzles have interesting names, for example, "How to Ask an Embarrassing Question", "When Idiots Duels", "Who Pays for the Coffee", "The Unsinkable Tub is Sinking!", "The Blind Spider and the Fly." The puzzles are all different; solving any one of them requires an approach different from any other. This is a well thought-out book, highly recommended for anybody with a need to try challenging puzzles that require some thought and mathematical skills....more
The Universe in Zero Words is a beautiful book, in all senses of the word. Dana Mackenzie devotes several pages to each of many equations that made a The Universe in Zero Words is a beautiful book, in all senses of the word. Dana Mackenzie devotes several pages to each of many equations that made a difference in the spheres of mathematics, science, and economics. The history of each equation is told superbly, as well as the meaning of each equation and its applications in the real world. The explanations are geared toward the layman--you don't have to be a mathematician to understand most of the explanations.
Dana Mackenzie is a mathematician, and his enthusiasm for the subject shines through his writing. He chose equations that have been important in the development of mathematics and science. I found his choice of equations to be quite good, and I learned a lot, even though I was already very familiar with the majority of the equations. A few, however, were quite new to me. The equation of quarternions is brand new for me, and Mackenzie tells why; the concept is rarely mentioned in modern-day physics textbooks. Also, the Black-Scholes equation is entirely new to me, as it is used by financial analysts and "quants".
The book is filled with beautiful illustrations and diagrams. In fact--I strongly urge interested readers to obtain a printed copy of the book, rather than an e-book version. The beauty of the printing, the layout, typography and illustrations add a considerable amount of charm to the reading experience. ...more
This is a fun book of puzzles of all types; mathematical, logical, algorithms, estimation, mind games and creativity. There is also lots of interview This is a fun book of puzzles of all types; mathematical, logical, algorithms, estimation, mind games and creativity. There is also lots of interview advice, when applying for a job. The advice is good not just for Google, but for many other companies as well.
It was fun trying to solve the puzzles. Lots of them are quite tricky. I was able to solve some, others I flubbed.
The book correctly points out that, even though lots of companies rely on such puzzles during interviews, they are not reliable predictors of eventual performance on the job. In fact, sometimes there is zero correlation between interview performance and job performance.
The book mentions the "20% project" at Google, where employees are allowed to work on any idea they may have, for one day a week. The book cites a list of highly-regarded products that came out of these 20% projects. I recently read that, unfortunately, this perk has been rescinded at Google.
The last half of the book supplies not just the answers to all the puzzles, but detailed explanations as well. The style of the writing has a light touch, and is often subtly humorous. I recommend the book for all those who like a diverse range of challenging puzzles....more
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