The Universe and the Teacup: The Mathematics of Truth and Beauty

by K.C. Cole

Filled with “a thousand fascinating facts and shrewd observations (Martin Gardner, Los Angeles Times), this “beguiling and lucid book” (San Francisco Chronicle) demonstrates how the truth and beauty of everything, from relativity to rainbows, is all in the numbers. Line drawings.

Genres: Science, Nonfiction, Mathematics, Philosophy, Physics, Popular Science, Stem

214 pages, Hardcover

First published January 1, 1998

About the author

For the past ten years, K.C. Cole has been a science writer and columnist for the Los Angeles Times; she has also written for The New York Times, The New Yorker, The Smithsonian, Discover, Newsweek, Newsday, Esquire, Ms., People and many other publications. Her articles were featured in The Best American Science Writing 2004 and 2005 and The Best American Science and Nature Writing 2002. She has also been an editor at Discover and Newsday.

Cole is the author of several nonfiction books, including Mind Over Matter: Conversations with the Cosmos; The Hole in the Universe: How Scientists Peered Over the Edge of Emptiness and Found Everything; and The Universe and the Teacup, the Mathematics of Truth and Beauty.

Reviews

[Will Byrnes · Rating 4 out of 5]

This is a popular science book that offers a very accessible look at how math figures in our lives, well beyond the obvious. What I found most interesting was the conclusion that math is not the bottom line hard truth we might think it to be. Everything, even math, depends on context and probability. There are many interesting notions considered here.

Chapter 5 goes into detail on how a difference in scale can also represent a difference in kind. Cole relates how scale would make it impossible for a sixty foot man to hold himself up with a body anything like the 6 foot variety. Height increases only in one dimension, area in two, volume in three. If you doubled the height of a man, the cross section, or thickness, of muscle that supports him against gravity would quadruple (two times two) and his volume and therefore weight would increase by a factor of eight. To bear such weight would require stout, thick legs. Think elephant or rhino. It called to mind a bit of personal experience. I grew up in the West Bronx, where lived the then tallest man in the world, Eddie Carmel, who measured about 8 foot 9 inches. Poor Mister Carmel was beset by a body that was incapable of comfortably carrying his mass. He walked with a cane, stooped over, and did not live anywhere close to three score and ten years, a sad example of math in action. Fleas form the opposite end of this spectrum. While their muscles are many orders of magnitude weaker than ours, the mass they have to push around is so much smaller that it makes each ant and flea into a superbeing. Leaping over tall buildings does not pose a problem.


K.C. Cole

A chapter titled Voting: Lani Guinier was Right holds a fascinating discussion of democratic methods and structures, and Chapter 11, The Mathematics of Kindness: Math Proves the Golden Rule, are both enlightening. I have a different take on the latter than the author, parallel, not contrary, but both chapters are thought-provoking.

Probability comes in for some heavy, and interesting inspection as well. I would expect the odds are better than even that if you have any interest at all in how things work, enjoy learning new things, or just like accumulating interesting bites of info about life at large, you will enjoy this very easy-to-read book.

=============================EXTRA STUFF

Links to the author’s personal, Twitter and FB pages

[Tim Kim · Rating 2 out of 5]

I couldn't find anything interesting about this book. All topics are superficial. The author keeps jumping from point to point, hardly addresses any topic with depth. If you have read many science books don't read this. I am sure you already now all the facts and relationships that she tries to cover.

[Russell · Rating 2 out of 5]

Meh. The author brings up a lot interesting points, but the connections are weak or odd at best. I mean, comparing the 'tipping point' to failing social programs? Odd.

No math is actually involved, no formulas were allowed here, thankyouverymuch. It makes sense, she is aiming for the lay person and trying to get them engaged with the concepts, but it makes for a weak math book.

There were a few factual errors that I noticed, like in chapter two. She leads in with "The Milky Way galaxy contains 200 billion stars..." but a couple of pages later she states: "Fifteen billion is also more or less the number of stars in the galaxy."

Um. 200 billion is quite a bit more than 15 billion. Not a huge deal, but this was indicative of the book, a few errors here and there.

Another thing that annoyed me is she spent a chapter discussing how broken the US election system is, but not once does she mention the Electoral College. Will Hively in 1996 discussed how the Electoral College does, in fact, work in his article "Math Against Tyranny". There are copies out in the intraweb, I recommend looking one up.

Anyway, there are better books out there, give this one a pass.

[Michael · Rating 2 out of 5]

A science book dumbed-down for the lay person. Cool, thank you, though there was no actual math in the book. No formulas to prove a point or hypothesis—which I thought the book was going to be about and why I was interested in reading it. Apparently, my expectations were either false or too high (or both), as math only applied tangentially to the various topics the author discussed. And when math was invoked, the connections between it and, say, prediction or kindness (and a host of other topics that would have been fascinating had math played an actual, provable role) were extraordinarily weak and insufficient.

Again, perhaps my expectations were too high. Though this book has now put me on a hunt for finding another title that actually does show, through numbers/equations/formulas, how math influences more than we thought it did.

[Sarah · Rating 2 out of 5]

A book that probably didn't need to be written. It was an OK read, but I didn't find anything new that she had to say. And the chapter on Emmy Noether and Albert Einstein (the reason I bought the book in the first place) was bland and disappointing.

[ManOfLaBook.com · Rating 4 out of 5]

I bought this book in 1999 and recently found it in a closet.

Even though the cover says this is a math book, I didn't find it to be so. Yes, there is some math in it but Ms. Cole is more of an observer. As a "non-scientist" I did not feel totally lost within the book, I felt as if I was being introduced to new concepts at a very high level, with some delving into details.

The book contains five parts which touch on mathematics, social issues and how they relate to one another. Some parts, in my case, needed to be re-read to understand - but that's the nature of many books especially on this subject.

Ms. Cole tries to keep the imagery of her examples clear and informal using current events (of 1999) as a stage. I think that the effort put forth in the book to explain complex thoughts in simple terms is commendable and admirable - even though sometimes it just doesn't "click".

This book is not meant for the mathematician, but for us layman who want to understand physics using an informal style while getting an insight of how those ideas affect us and our society in our daily lives.

[Othman · Rating 4 out of 5]

Interesting stuff

[Sangwon Hyun · Rating 4 out of 5]

Several eloquent essays about math and statistics/probability and physics, in the context of the real, real world we live in, observe and wonder about.

[Nico Perez · Rating 4 out of 5]

I was in the waiting area of the Dehradun airport waiting to board a plane heading to Mumbai. To pass the time, I was reading Freedom from the Known by J. Krishnamurti when a guy walked past and noticed I was reading a book. He ducked down to see what book I was reading and gave me a thumbs up. A couple of minutes later, the same guy passed by and gave me The Universe and the Teacup. He said he was glad to see me reading Krishnamurti, and he thought that I might like this book about math. I was so confused but so happy at the same time.

I didn't end up reading the book until a month later. I read it because one day I woke up with the urge to read it after not having thought about the book in a while. I ended up liking the book!. Just as it says in the description of the book, it taught me that math doesn't have to be so frightening.

I didn't like math before reading this book. Now after reading this book, I don't love it, but I like it.

[Jonas Tranchet · Rating 1 out of 5]

This book should have been titled "An Enumeration of Remotely Mathematical Things You Already Knew About".

It lacks both structure and depth. As others have pointed out, I wouldn't call it a book about mathematics. Instead of writing about mathematical applications, Cole makes strange and far-fetched comparisons between psychology and something she calls maths.
She doesn't bring anything new either. For example, there's a whole chapter about how humans assess their risks. The author's point is clearly "We're not good at it, because we're not so rational as we think", but in the end it's just an enumeration of anecdotes we've all heard about before, leading to conclusions we are already familiar with. Sometimes, she even makes false statements trying to prove her point.

At rare times when things do get interesting, Cole just jumps to the next item. The depth in this book is non-existent. Either you get what she's saying because you already know, or you don't because she doesn't explain it very well. Don't worry though: within the next five lines she'll mention something else which you do understand.

Advice: don't read this book.

[Yi · Rating 5 out of 5]

This book is really worth reading. Although I put it in the math shelf and it's title also suggests so, it is not a math book. It talks about many aspects in daily life, covering general math and science maybe even psychology. The book talks a lot about scales, reference frames, and point of view, and the book itself serves very well as a different point of view on the world we live in. Is it true? Or is it not true? Do we really know if it's true or not true? How well do we know what we think we know? And how well do we know how well we know what we think we know?

This book was recommended or referenced by one of youtube channels or the blogs I follow and subscribe, including but limited to ASAP Science, CGP Grey, MinuteEarth, minutephysics, SmarterEveryDay, Veritasium, Vsauce, WonderWhy, Matrix67(blog).
This one was probably referenced by Vsauce.

[David Thornley · Rating 2 out of 5]

This is pop mathematics, with assorted discussion of the math of various topics supported by an occasional handwave. I realize that this is necessary to get people other than me to read it, but there was no way to follow up anything to check anything dubious-looking or interesting. I found it overly fluffy and to say things I didn't think quite right.

[Jim · Rating 2 out of 5]

Disappointing. Readable but lacking in depth and clarity. A slapdash survey of mathematical concepts and applications to science as well as to everyday life, presented in a "newspaper reporter" style. Adequate in getting one's feet wet, like wading in the kiddie pool.

[Paul · Rating 4 out of 5]

Even though I enjoy reading about mathematics, this book delivered due to the way it delved into topics that were interesting but not typically associated with math at the level that the author managed.

[Alfia · Rating 2 out of 5]

Unfortunately, the author doesn't actually define key concepts that are later discussed, mostly through quotes from secondary materials. There is a lot of bouncing around, some of which is illogical. Don't bother.

[Jeff · Rating 2 out of 5]

A snoozer, not for scientists. The book jumps from topic to topic with little depth.

[James · Rating 4 out of 5]

A pretty good book, though it's not necessarily as math-oriented as the title suggests. It's more a guide to understanding thr World from the points of view of science, logic and rationality.

[Quail · Rating 2 out of 5]

DNF. sort of an out of date freakonomics. way too broad of a definition of math to be informative.

[Colle Owino · Rating 4 out of 5]

Would have given it five stars but that one chapter symmetry ruined it for me. Has to be the most approachable and beautiful math book I have ever come across.

[J.D. Steens · Rating 1 out of 5]

I couldn't get into this book. Not interesting. From some areas I do know something about, I think she hops on the bandwagon with some popular topics and gives mathematics (and scientific authorities) unwarranted credit for solving this and that problem.

She says some Nobel prize winner proved mathematically that "no democratic voting system could ever be completely fair." Not sure why that's a revelatory accomplishment. Quoting a researcher, Cole writes that unfair "'inevitably means different things to different people. When my kids say something's unfair,..what they really mean is, they didn't get what they want."' Disagreement on outcomes goes with Democracy, where people have different points of view. But of course, fairness on outcomes is different than voting systems that are set up to determine policy outcomes. If we disagree on policy outcomes, we still might regard the voting process by which we get those outcomes as being fair. That's the way it used to be in the pre-Trump era, but that's not where Cole is at when she writes that "The one thing that most parties do agree on is that the current system is the worst."
Before that conclusion though, she writes that "In the end, deciding which voting system is the fairest of them all comes down to, well, voting." So....the current system is the worst, but it's also the fairest? And isn't this the way Democracy works? Voters make the decision about how to conduct elections?

Cole gets into the rational "social choice theory" that applies mathematics to allocate societal benefits fairly ("Fair Division"). Not sure here why mathematics gets the credit which is built into our biological being, as Darwin observed in 1870's and as others with common sense have known all along. Group life is essential to survival and well being. We are bred to merge with the group, and to do that we must walk the line between our own self-interest and the interests of others within the group. That means we are disposed to, and impelled by, a wide array of social instincts to give up some of our own self-interest on behalf of the good of the group (a collection of self interests).

In a separate chapter, Cole gives mathematics credit for the golden rule. That rule, in all its variant forms, appears in a wide variety of cultures for a reason. It, and reciprocity, is necessary for group life to cohere. She touts the Axelrod book on the evolution of cooperation as if that feature of group life is a mathematical creation when it, with reciprocity and the golden rule, is built into our biology. It's necessary for our self-interest.

In her discussion of game theory, Cole notes that mathematical models prove that self-interested behavior doesn't work - because predators run out of prey - relative to cooperation. Pull in Darwin though, and you get a different picture. Within any group are those that seek the benefits of group life without any of the responsibilities that go with it. In other words, they go through the motions to hide self-interested imperatives. They manipulate and lie; they smile and screw people over. They dominate when they can get away with it. And, regarding game theory, it's the same. Cole writes that "Clearly, if one party cooperates while the other cheats, the cooperator is a sucker. But if both cheat, no one gets anything." She is setting aside common sense here. Other-regarding people who intend to get to yes in any dispute resolution process will be suckers if the others are not playing by the same rues.

Cole touts Lynn Margulis's excellent book that shows our bodies are made by cooperators. But, then, Cole doesn't note that our bodies have to fend off self-interested viruses and bacteria that have only their own interests in "mind." That sleight-of-hand business extends to her comments that, while the connection between smoking and cancer is proven statistically, "smoking caused by any particular case of cancer is near impossible to demonstrate." Really?

Cole's big thing here is that causality, taking from the quantum world, is in the end probabilistic: it applies generally, but not to individual cases. She notes that Einstein refused to go there - and we're familiar with the debates he had with the quantum theorists in this regard, but then she writes this: "Unpredictably, argued Born, does not mean that subatomic behavior does not have causes; it only means that it has causes too subtle and complex for us to untangle." While she calls Einstein's debate with Born "delicious," I am not sure what to make of this Born quote as it seems to substantiate Einstein's perspective, though I think she's making a point about causality in a probabilistic sense. Just because we cannot (inherently, because the act of observing via light influences what we see) know what's going on at the subatomic level, this doesn't mean that causality does not exist at an individual particle level.

[Ankush Agarwal · Rating 4 out of 5]

Providing the beauty of the universe in a teacup of mathematics, this book reveals the truths, the symmetry, and the alleged truths of the universe, as well as all the contradictions therein. My experience with this book was that it wasn't heavy (no equations, except 'the one') and that even the complex concepts were dealt with in a very readable way despite the complexity. This easy-to-read nature of the book is both its strength and its greatest shortcoming at the same time. The ideas presented in this book are easy to read and understand, however, I did not gain a deeper understanding of any of the topics covered, even though I enjoyed it.

Cole begins by explaining what mathematics has to do with all this, and though the relationship between mathematics and the universe is, on the whole, an interesting one, it is sometimes left to the sidelines. This is not the case in the later chapters of the book as math is not used as the link to bind the story together. There is no reason to think, however, that these chapters are any less readable or enjoyable for that matter.

Cole connects the mathematics of risk with the universe, and how we tend to (mis)count the risks. He talks about the limits of measurement, human’s (in)capacity to cope with the scale, whether it’s a minute or a thousand. How do we find and isolate the signals, like looking for a needle in a haystack? He analyzes the various voting methods and their pros and cons. (I loved his example; it’s so easy to remember and relate.)

Cole connects kindness to mathematics, though I wish he’d dig a little deeper. He finishes by talking about the truth itself. I’d recommend this as a light book on a very complex subject, especially for someone who isn’t an expert but wants to build interest in the subject.

[Carlito De]

O Universo em uma Xícara de Chá, da jornalista científica K.C. Cole, é uma das obras mais encantadoras da divulgação científica moderna. Combinando rigor e sensibilidade, a autora transforma conceitos que poderiam parecer áridos — como buracos negros, partículas subatômicas ou a expansão do universo — em imagens que cabem dentro do cotidiano, como a simples metáfora de uma xícara de chá.

O grande mérito do livro está em sua linguagem: clara, envolvente e, ao mesmo tempo, poética. K.C. Cole não escreve apenas para informar, mas para fazer o leitor sentir o assombro que a ciência carrega. Ler suas páginas é redescobrir o mundo com olhos curiosos, como se a realidade tivesse camadas ocultas reveladas pouco a pouco.

É verdade que leitores mais experientes em física podem achar o conteúdo simplificado, mas essa é justamente a intenção da autora: criar pontes entre o conhecimento científico e o público leigo, sem fórmulas complicadas e sem perder a magia do mistério.

Quando li este livro, anos atrás, lembro de como ele despertou em mim um entusiasmo genuíno. Hoje, mesmo sem recordar todos os detalhes, o que permanece é a sensação de maravilhamento — a certeza de que somos parte de um universo vasto e misterioso, e que a ciência é uma forma de poesia capaz de revelar essa beleza.

Recomendo a todos os que desejam compreender melhor o cosmos, não apenas pela ótica fria dos números, mas pela emoção de quem vê grandeza no simples, infinito no cotidiano.

[Pablo María Fernández · Rating 2 out of 5]

Tenía un mejor recuerdo. Releyéndolo me doy cuenta que es un artículo promedio inflado: mucho del contenido refrita clásicos como Matemáticas e imaginación de Newman y Kasner, repite una y otra vez las mismas ideas con distintas variantes y abunda en generalidades sin profundizar en nada en particular. Me siguen interesando los autores que hacen accesible campos complejos para los no especialistas como yo, pero el abordaje de este libro lo aleja de la ciencia y lo acerca a lo banal. Gran contraste con cualquier libro de Isaac Asimov por ejemplo que, sin ser deslumbrante, tiene una densidad de información, una narrativa para hilar el contenido y una rigurosidad y precisión que debería ser lo esperable de este tipo de libros.

En cuanto a la estructura tiene cuatro partes: las dos primeras acerca de lo exponencial, los riesgos y el mundo físico son lo que más se salva, y luego sobre el mundo social y la verdad que corren ya con peor suerte. Me llama la atención que lo haya leído entero porque solo releyendo mis marcas (lo que consideré más interesante en su momento) se me hizo tedioso e insustancial.

Más sobre esta reseña y otras en:
https://pablomariafernandez.substack....

[Julie Ruch · Rating 5 out of 5]

NonFiction Brilliant

I read this years ago and if math can be life-changing, this is the book that will do it.

I believe this book would appeal to a wide range of readers. In other words, you don't have to be a brainiac or a math genius to enjoy it.

A fascinating book that held my attention to the very end. It uses math to solve practical problems that we all run into in life, such as how to divide up everything in a parent's estate.

Highly recommended!

[Sirah · Rating 5 out of 5]

Sometimes, you just need a reminder that mathematics is good for something, and this book is it. While there's a lot of theoretical content, this book shows the ways that statistics, averages, probability, symmetry, and other mathematical concepts affect how we think and perceive the world. I keep coming back to quotes from this book in my daily conversations, and I'm eager to read a few of the works cited, as I like that feeling of understanding that books like this give me.

[William Guerrant · Rating 4 out of 5]

A fascinating collection of facts and observations, worthwhile for that reason alone. There are some maddening flaws--category errors, misleading and biased characterizations, inadequate attention to the philosophy of science and mathematics--but these seem mostly attributable to a desire to appeal to a popular audience and are outweighed by the overall merit of the book.

[Ayush · Rating 3 out of 5]

It’s a decent book. It tries its best to explain concepts in a very dumbed down manner.

So, if you are a math & physics scholar/ someone who has studied math or physics, this book isn’t for you.

But, if you are just a regular person who wants to know more about Math - give it a read, it’s not a bad book!

[Joe Mama · Rating 2 out of 5]

Interesting topics, but not enough detail to make it worth reading. It's pop science, and I didn't gain much, as a person who has had contact with several types of mathematics, throughout my education.

[Midnights · Rating 4 out of 5]

Boring. Mildly edge with muh feminism. Really basic.
All in all I should have expected as much from a journalist. I wanted something educational and I got something dated and political.

[Lisa · Rating 5 out of 5]

Absolutely brilliant. Couldn't recommend it more. Especially for those that have a problematic relationship with math, and experience math anxiety.