萬物皆數——諾貝爾物理獎得主探索宇宙深層設計之美

by Frank Wilczek, 周念縈 (Translator)

物理世界體現了美麗。
物理世界充滿了痛苦、紛亂與壓抑。
無論如何，我們都不該忘記另一面的存在。——維爾澤克

2004年諾貝爾物理獎得主維爾澤克，從研究自然界的最小組成單位而獲獎，繼而轉身朝向廣袤的世界，不禁提出大哉問：宇宙萬物的結構是否體現了「美」的設計？

《萬物皆數》是一位諾獎大物理學家在自然哲學領地裡思辨的成果。他以一種詩意的語言來寫作，雄心勃勃地追求「物理之美」與「藝術之美」的和諧。
——陳瑞麟（國立中正大學哲學系系主任）

本書重點：

作者帶領我們綜覽西方古典物理史上的孜孜矻矻，更進一步引領我們看見物理學中的純粹概念，從理想一步步逼近真實，每一次關於真實的發現，我們對世界的了解更趨完美，也從中體會科學背後深刻的哲學基礎與觀點。

「上帝的偉大與榮耀在他所有的作品中奇妙閃耀，尤其是可從天空那本打開的書中讀到……」——伽利略

畢達哥拉斯導出「畢氏定理」，「世界」第一次與「數字」產生連結——畢氏企圖推演萬物與數字的關係，認定萬物存在理想而優美的設計。柏拉圖的洞穴寓言與正多面體同樣傳達出「真實」應是美好理想的構成與投影。從畢氏與柏拉圖開始，世界的組成即與心智中的理想串連起來……

「我們不得不這麼覺得，這些數學公式獨立存在，並具有自己的智慧，比我們還聰明，甚至比發明者還聰明；人類得到的總是超過原先放進去的。」——赫茲

牛頓是古典物理的創始人，以精確度量與嚴謹的宇宙觀。取代以主觀好惡判斷日常。而寫出電磁方程組的馬克士威，更帶來全新的視野與方法：因為對稱性而補全的電磁方程組，不僅統一電與磁，並解釋光的存在，直至今天成為電磁學的穩固基礎。原來方程式如同一般物體具有對稱性！大自然基本法則的無數方程式，更充滿大量的對稱性！

「宇宙最不能理解之處，在於它可以被理解。」——愛因斯坦
「物質告訴時空如何彎曲，時空告訴物質如何移動。」——惠勒

從波耳原子模型中看見駐波；從愛因斯坦相對論中看見伽利略不變性；從量子色動力學中又再度看見馬克士威。原來世界不只是可以用物理法則詮釋，乍看不同的法則彼此之間彷若鏡面裡外，相互輝映。看完此書，你將會發現，自然的基礎是如此精簡至極，極度對稱的方程式可將其特性表露無遺。 而物體構成的世界又是如此廣大無邊，變化無窮無盡。

書末收入作者精心編纂的《物理小辭典》，凡是涉及內文的重要的名詞與概念都加以定義與說明，以饗喜歡知識卻不見得是科學專家的讀者；或配合內文延伸閱讀，或當成獨立的科學小辭典。為方便查閱，中文版特別採取英文排序，由封底開卷。

國內外專業書評及推薦

＊人類自古就對世間事物的美投以主觀的眼光。然而，大自然亦自有其一套審美標準。不同的是，自然定律永恆不變。作為物理學家，法蘭克・維爾澤克一生致力在科學道路之上尋找大自然對美的定義。這本書，可以說是維爾澤克的一個總結：對稱性和經濟性。

我有時會問自己：一本好的科學普及書籍，應該如何寫？我漸漸發現，好的普及讀物不應單向傳達知識，那是教科書的任務。一部好的普及讀物，應該與讀者產生共鳴。維爾澤克以科學家為主軸，把兩千五百年物理史娓娓道來，解構科學與人類的闗係。

Genres: Science, Nonfiction, Physics, Philosophy, History, Nature, Popular Science

480 pages, Hardcover

First published July 14, 2015

About the author

Frank Anthony Wilczek, born May 15, 1951 is an American theoretical physicist, mathematician and a Nobel laureate. He is currently the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology (MIT), Founding Director of T. D. Lee Institute and Chief Scientist at the Wilczek Quantum Center, Shanghai Jiao Tong University (SJTU), Distinguished Professor at Arizona State University (ASU) and full Professor at Stockholm University.

Wilczek, along with David Gross and H. David Politzer, was awarded the Nobel Prize in Physics in 2004 "for the discovery of asymptotic freedom in the theory of the strong interaction.

Reviews

[David Rubenstein · Rating 5 out of 5]

The beautiful question is, whether the laws of physics are based on beauty; are they simple, symmetric, proportioned and economical. Wilczek is a Nobel-Prize winner in physics. Regardless of whether physics is based on beauty, Wilczek has written a beautiful book. His style of writing is excellent, and the book is graced with plenty of engrossing diagrams and color illustrations.

The earliest astronomers tried to make the orbits of the planets simpler than they actually are. They tried to make their orbits fit into the so-called Platonic solids. Then they tried to make their orbits fit into circles. When observations did not fit this idea, they made circles upon circles, and unnecessary complicated the orbits. It wasn't until Newton saw that gravity affects both objects on Earth as well as the planets, that the orbits could be determined from a simple physical law. The law states that gravitation is proportional to the masses of the objects and inversely proportional to the square of their distance.

Wilczek traces the idea of symmetry into all of the realms of physics; special and general relativity, electro-magnetism, and quantum mechanics. He shows how Maxwell completed his famous set of equations by assuming a degree of symmetry, and correctly found that electromagnetic waves travel at the speed of light. To this day, Maxwell's equations serve as the basic laws of electricity and magnetism.

My favorite chapter is about Emmy Noether, a mathematician with deep insights into physics. She was discriminated against because she was a woman, so she worked without pay. As the Nazis came to power, she emigrated to the United States. She proved a remarkable theorem; each law of conservation in physics can be derived from a basic concept of symmetry. So, for example, she showed why there are a basic laws of conservation of energy and momentum; she showed that it these laws are equivalent to stating that the laws of physics are invariant in time and space. Wilczek calls this the most profound idea in all of physics. And many prominent mathematicians and physicists have said that Noether was the most important of all women mathematicians.

Toward the end of the book, Wilczek describes the alphabet soup of fundamental particles. He shows the symmetries in their existence and properties, in certain respects. However, many of the particles do not really abide by symmetries, though this may simply be because of our present-day lack of full understanding.

[Mark Hebwood · Rating 4 out of 5]

Fighting it...

Oh wow. Reading this book was quite an experience. For one thing, to a person with no grounding in particle physics beyond what was included in a school curriculum (that person is me, and there was very little), reading speed is best described by reference to a log-scale: I read the first batch in a day, the second in 2 days, the third in 4, the fourth ... . But more fundamentally than that, I struggled with the book on a deeper level. I fought against some of Frank's ideas, and did not find it easy to get myself to a position from which I could see the outlines of his thoughts in sharper focus. Other ideas I could not accept wholly, but needed to refine and modify for my own purpose. I struggled with his style, which at first I found a little bit too sanctimonious, and I felt the need to shield myself against what I saw as Frank's spiritualism.

And was it worth it? Yes. Absolutely. Either I got used to his style, or Frank narrated more pragmatically as his account developed, but after a while I made my peace with the way he talked about his subject. Having gained this confidence, I allowed myself to 'let in' more of the spiritualistic aspects of the book, and found the experience worth-while and enriching.

I kept on struggling, and fighting, and Frank kept on persuading, and explaining, and I understood more of what he might mean, and successfully reconciled some of my own views with his. It was hard work, it was exhausting yet exhilarating, painful yet mind-expanding.

Looking back on my reading experience, I had a great time with this book. Nothing worth having seems to come easily, and I feel I did have to work for some of the fresh insights I now have. In the end, it is this struggle that leaves me satisfied, it is the fight that makes me feel that I earned it.

Is it really beauty we are talking about?

This question is the essence of my struggle. For a while now, I have been interested in the relationship between 'beauty' and 'truth', or to put it less esoterically, in the idea that there may be a connection between the aesthetic appeal of a scientific theory and its resilience to falsification.

But what is 'beauty'? How can we define the aesthetic appeal of a scientific theory? This is what I struggled with, and I struggled against Frank, at least in the beginning. 'Beauty', to me, is too wide a concept to be meaningful in the context of this topic. 'Beauty' can mean a lot, and it can mean different things to different people. Frank defines what he means by 'beauty' on page 11; it is symmetry as a "love of harmony, balance, and proportion", and economy as the ability to produce "an abundance of effects from ... limited means".

This is fine. As far as it goes. But this definition does not incorporate all that human beings tend to describe as 'in proportion'. Oddly, it is a mathematically well-defined relationship that governs the opposite of symmetry that lies at the root of the human sense for harmony. This is the Fibonacci series, or rather the value of 1/2*[1+sqrt(5)] on which ratios between two consecutive numbers in the series converge. The Golden Ratio divides a line roughly in the proportions 1:2 and is therefore not strictly speaking symmetrical.

Still. "Symmetrical" may be defined, perhaps, as "periodically recurrant", and my definition of a 1:1 proportion may be unnecessarily restrictive. Indeed, the F-sequence (which Frank never mentions in the book) appears to embody Frank's second principle, 'economy', as I can construct spirals from it, and even reconstruct patterns I find in nature.

Fractals, as a self-repeating pattern that displays at every scale, no matter how often I magnify a local area, are another example of 'economy' and 'symmetry'. And these do feature in Frank's book, even though only in passing. On page 113, Frank refers to a fractal as "a strikingly beautiful work of abstract art". And this is where I would contradict Frank. First of all, it is not "abstract art". Abstract art is not even asymmetrical, it is an expression of the artist's thought that takes on an entirely new, and individual, interpretation in the beholder. And second, a fractal is not colorful, as Frank's plate M suggests. A fractal is a repeated application of a replacement operation, and we define the colour of a specific point in the iterations in accordance to chosen criteria of how it behaves (does it go off to infinity, does it stay confined in a particular area). In other words, there is no natural beauty beyond the extraordinary self-similarity of a fractal that would make it colourful, and hence a "striking work of art". I think in this instance, Frank confused man-made artifice with fundamental harmony.

However, as Frank developed his account, I think he changed his mind about what he thinks 'beauty' means. He never gives up the (in my opinion, meaningful) twin categories of symmetry and economy, but his thoughts mature into defining a relationship between Platonic Ideals and Reals. Frank associates the world of pure intellect with the Ideals and the world of empirical, experimental evidence with the Reals.

The Frankomarkian model of beauty

And as Frank's account started to develop along these lines, our two, quite distinct, ways to think about 'beauty' became unified. It is not really 'beauty' we are discussing here. It is a concept of fundamental harmony between a conscious mind (the human mind) and the patterns it finds 'outside' of itself. Once I understood this dynamic, I was even happy to call it 'beauty'. I mean, why not?

From that moment on, I stopped fighting his ideas and was able to follow him into a fascinating world. And what an enriching, and deeply satisfying world it was. Maxwell unified the electric and magnetic forces in theory before electromagnetic waves could be observed experimentally - and the speed of light came out in the wash! Frank's own work on QCD, and his idea of asymptotic freedom, impressively explains the strong force - and what an odd, "a-newtonian" force it is. Peter Higgs postulated a new, "mass-giving" boson with its associated field (Frank calls it 'fluid') 70 years before it was found in one of the last runs of the LHC pre-upgrade. Supersymmetry, although speculative, allows the unification of all non-gravitational forces, and probably gravity, too!

So did I like the book?

Well. I still do not follow Frank into his (moderately) spiritual world. I do not think it is amazing that carbon orbitals seek contact with four neighbouring carbon nuclei and thereby define the vertices of a regular tetrahedron, one of the five Platonic solids. I am not silenced in awe by the fact that zero-dimensional buckyballs reduce to a dodacahedron, the quintessential Platonic solid, once somebody removes the hexagonal surface areas that keep the pentagons apart. I hear Frank (and Nils Bohr) when he observes the similarity between the Eastern philosophy of Yin and Yang and the dualism between substance- and force particles, but I am not really inclined to see more than a metaphorical equivalence between the two.

But I loved the book beyond measure. I loved the struggle it offered me, and the engagement with Frank in the early chapters. I love the insight I now have in the dynamics of particle physics, its history and its potential future. I love the possibility that I might be wrong, and that the human sense of harmony and its apparent reflection in nature may be more than merely a metaphor, that it may highlight a deeper similarity between the particles that enable our thoughts and the particles we think about. But above all I love the fact - let us pause here and savour this certainty: the fact - that the human intellect is capable to understand the world as it is before experimental evidence confirms its findings.

And yes, I know that I am going to get into trouble with the philosophers for saying this. But I do not think my last point is epistemologically naive. We certainly have not reached the end of the journey. We may never get there. But whether we do, or don't, is irrelevant. What is relevant is that we are able to take the next step, and the next step after that.

The history of insights in particle physics has impressively shown that we are able to take the next step. And the human urge to take the next step may be the most fundamental thing that makes us human. If this is so, I'd rather continue travelling than arriving. If we ever arrived, we'd have nowhere left to go.

I can only recommend this book. Do read it.

[Max · Rating 5 out of 5]

Wilczek shows the correspondence between physics and art focusing on their use of symmetry. He explains that symmetry lies at the heart of the relationship between numbers and form and even perception. He reviews the importance of symmetry in the history of physics. Wilczek uses analogies, pictures and diagrams rather than equations to explain concepts. But make no mistake this is a serious physics book. Wilczek is a Nobel Prize winning physicist who has strong beliefs about the importance of symmetry to physics research. He prefers to build beautiful symmetric equations and look for evidence that validates them than to work from assembled observations and try to turn them into meaningful equations. Below are my notes.

Wilczek begins with the ancients. Starting with Pythagoras and his eponymous theorem we see that numerical relationships are also geometric ones. Digging into Pythagoras’s musical interest we see how numerical relationships define musical ones such as chords even telling us which ones would be pleasing to our ears. Wilczek details the transfer of frequency or pitch from mechanical to electrical impulse tracing it from string to air to ear to neuron. Turning to Plato we see his focus on symmetry in the five platonic solids. Plato held four of them to be the atoms of his elements. Fire was the tetrahedron, water the icosahedron, earth the cube, and air the octahedron. The fifth, the dodecahedron was the shape of the universe. Plato realized structure is determined by symmetry just as physicists do today. So even though Plato was way off on the universe’s building blocks he was right on this foundational concept of modern physics. Wilczek also recounts Plato’s metaphor of the people chained in a cave who can only see shadows. Plato understood that there is much more to the world than what our senses can detect.

Next Wilczek discusses projective geometry. Brunelleschi pioneered techniques to achieve realistic perspective in painting. His Renaissance counterparts quickly adopted his methods to accurately depict three dimensions in two dimensions. The idea of perspective leads to fundamental concepts of modern physics: relativity (the essence of perspective), symmetry (maintaining the same state when rotated, moved, or other types of transformations), invariance (maintaining the same state from any perspective) and complementarity (looking not only different from a different perspective but to the exclusion of the other perspective).

Wilczek moves on to the scientific revolution. Newton changed the way physics was conducted. Famous for explaining gravity and motion, his greatest contribution may have been simply to demand quantitative precision. Qualitative assessments were no longer relevant. Maxwell, the author’s favorite physicist, ushered in truly modern physics with his equations that explained light as an electromagnetic wave. His symmetrical equations helped establish the importance of symmetry in physics. Maxwell’s equations paved the way for the twentieth century discoveries of relativity and quantum mechanics. Maxwell used observations made in Faraday’s experiments to build his equations. Wilczek favors the reverse approach. Formulate symmetrical equations and look for phenomena where they apply.

The early twentieth century was notable for many great physicists: Rutherford, Planck, Einstein, Bohr, and many more. One often overlooked who should be included in such lists was the great mathematician, Emily Noether. She saw the connection between mathematical formulations of physical laws and physical quantities that were invariant. Noether’s theorem holds that symmetries of physical laws yield quantities that are conserved. Time translation symmetry tells us that the laws of physics that applied in the past will do so in the future. The quantity that does not change with time is said to be conserved. In the case of time translation symmetry the conserved quantity is energy. It is invariant with respect to time. Spatial translation symmetry yields momentum as a conserved quantity. Rotational symmetry yields angular momentum as a conserved quantity. Einstein employed Galilean symmetry in deriving special relativity. Galileo in a thought experiment described being below decks in the closed compartment of a ship. Changes in the ships motion at a constant velocity did not change the laws of physics in the compartment. Einstein showed that even with Galilean transformation the speed of light remained constant. Einstein was inspired by Maxwell’s equations that showed the speed of light was a constant.

Wilczsek presents his version of the Standard Model; a name he feels belies its importance, calling his version Core Theory. The Standard Model excludes gravity, Core Theory includes it. Wilczek believes the conflict many see between quantum mechanics and general relativity is overstated. He does admit Core Theory has problems such as not explaining dark matter, dark energy or singularities. He describes the interplay between the four forces (electromagnetic, gravity, strong and weak) and the four respective properties of matter (electric charge, energy-momentum, strong charge and weak charge) that are described by the theory. In the case of gravity it is the density of energy and momentum that curves space-time or looking at it from a different perspective Wilczeck says energy-momentum density tells matter which way is straight. He employs the concept of property space. Populating space with values depicting distances between nearby points form a metric that maps the effect of energy-momentum on space time. Thus the metric of space-time determines the movement of energy-momentum objects, but energy-momentum objects determine the shape of the metric field. The concept of property fields and this same logic applies to the other three forces and their counterparts: charge and electromagnetic waves, as well as the strong and weak forces and their objects. From Wilczek’s point of view the fundamental forces and the respective properties of matter in essence are yin and yang, a receptive component and a driving component in a constant tug of war.

The carriers of the four forces are the photon, graviton, color gluon and weakon. They are the quanta of the electromagnetic, metric, strong and weak fields. These force mediating particles Wilczek describes as avatars of local symmetries. Local symmetries are key to Wilczek. Local symmetries allow changes in quantities within equations without changing the results of the equations. They are local because the symmetry does not have to apply everywhere or all the time. It is out of these symmetries that the force carrying particles arise.

What exactly are protons and neutrons (together called nucleons)? They carry most of the universe’s mass. They consist of quarks that are tightly contained by gluons but when close to each other quarks can be randomly arranged. This feature of the strong force that increases with the distance between quarks and is negligible when they are close together is called asymptotic freedom. One thing that stood out to me is that the mass of the quarks is tiny. Wilczek concludes, “almost all of the nucleon’s mass, and thus almost all of the mass of ordinary matter in the Universe, arises from pure energy”. The kinetic energy of the quarks and the field energy of the gluon fields supply, “Mass Without Mass, emerging directly from the purely conceptual, symmetry rooted equations of QCD.” QCD, quantum chromodynamics, is the theory of the strong force.

Quarks, in addition to electrical charge, carry one of three different color charges which embody the strong force. The term color here is completely unrelated to spectral color. Unlike electrical charge, each color charge is three dimensional defining a place in its property space. So if a quark changes from one color to another it can be considered to be in two different places in property space. Gluons mediate color charge and interact with quarks. In this complicated dynamic there are eight types of gluons and six types of quarks. Moreover unlike photons, gluons interact with one another and can change the color of other gluons. Also gluons take their positions based on that of the quark so in QCD we have another example of yin and yang between color charged particles and color property space.

In the end, it seems that Supersymmetry (SUSY) is where Wilczek is taking us. He is a strong advocate having bet that by 2020 evidence of SUSY will be found. SUSY posits that there are quantum dimensions in which particles transform from one type to another. He points out that, “what can depend on where. The same entity, located in different positions within a property space, often manifests itself as several different particles.” The theory holds that substance particles (fermions) can change into force particles (bosons) and vice versa when entering quantum dimensions. Thus substance and force particles cannot exist without each other. “Both are the same thing, seen from different perspectives.” So here we have it, the ultimate symmetry, the ultimate Yin and Yang and the ultimate beauty in Wiczek’s eyes.

This book starts out easy and gets increasingly complicated. Of great help is an excellent glossary with detailed explanations of terms used in the text. The index is also well done and I used it much trying to reconcile concepts. Still, without prior familiarity with the topics I would have been completely lost by the end. Wilczek’s presentation is refreshing and unique. It is connected by a theme, the evolution of the concept of symmetry. I selected this book to better understand symmetry which is at the forefront of physics today. For those with similar interests I highly recommend, A Beautiful Question.

[Jimmy Ele · Rating 5 out of 5]

I loved this book. It truly made me appreciate Pythagoras, Plato, Newton, Maxwell, and Einstein's insights a lot more. It is very easy to comprehend and comes replete with great pictures that help the reader visualize the beautiful ideas that are embodied in Nature's Deep Design (ElectroMagnetism, Gravity, Weak and Strong Force, Light, Sound, Geometry etc.) One of my favorite chapters was the chapter on the physics behind light and the color spectrum. I thought I knew what colors were, but quickly realized that I only had a surface understanding. After reading this book I am seeing all of the colors around me more deeply i.e. with an increased clarity. I appreciate the creation more and thus am increased in my admiration for the great Creator and Artisan's artistry, power, force, intelligence, and mercy. I am in shock that this book did not make it into the Good Reads Science Picks for this year. I don't think that it is very often that we get a Nobel Prize winning physicist to give us a physics history and art lesson. Frank Wilczek ends the book brilliantly by explaining to us with great depth of understanding the modern endeavor to unify all of the forces (by using supersymmetry as well as other concepts such as property space).

I recommend this book for anyone who is on the same quest for truth and beauty that Pythagoras, Plato, Newton, Maxwell, and Einstein were on.

[Mansoor · Rating 4 out of 5]

Masterfully written and structured.

[Beauregard Bottomley · Rating 5 out of 5]

I had stopped reading popular science books because most of the new ones had nothing to say or they ended up in the land of woo. This book does neither.

This book can work for any audience. The artist will appreciate the beauty that the universe gives to us through its harmony of concordance, the obsessive reader of science books (as I used to be) will love the fact that the author takes one way beyond what they thought they knew and the PhD in physics will learn things he didn't know about the coherence of the universe.

In the beginning of the book he shows how the early Greeks established the comprehension of the world through numbers by first explaining music, and how the perfect Platonic forms relate to the real. At the heart of our understanding (and beauty) is the symmetry we use to understand the world around us. Every reader will end up absorbing his definition of symmetry: that which brings change without change.

He'll show how the first real jump in human understanding is when Pope Leo X ask Copernicus to fix that calendar so that Easter doesn't change relative to the seasons. Copernicus asked a question as a thought experiment "what if I were on the sun, how would that effect how I perceive the year on Earth".

The author takes the John Wheeler quote, "matter tells spacetime how to curve, and spacetime tells space how to move". He'll show how that same phenomenon can be applied to all the fundamental forces of nature. Each of the forces of nature have a law of conservation associated with them. He'll go in detail on Emmy Noether and how she shows that (I like any book that gives Emmy Noether her rightful place in history). This is when the book starts to go way beyond all the other pop science books I've read over the years and never talks down to the listener.

He dissects Maxwell's equations and shows how they came to be and what they really mean. Ultimately, he explains Einstein's General Theory with the rule of relative perspective (Copernicus and Galileo) to the constant for the speed of light that pops up in Maxwell's equations. Once again the book is taking me places other science books fear to tread.

He'll go through the particle zoo and tell you what the Higgs Field really means and how the photon itself is modeled in an accelerator as if it did have weight. He'll tell the listener the problems with the standard model and how the extra dimensions needed for SUZY (string theory) allows for the solution to a host of standard model problems and how we are very close with the current levels of energy at the LHC in finding confirmations to this.

A couple of things. This book can be a difficult read. I would definitely recommend listening to it rather than reading it. Because, I if I had read it, I would have spent days on the up, down, charm quarks and how they go into the building the protons that build the universe. By listening to the book, I got the gist of the points and didn't overly dwell on the minutia. Another thing, this book is very comparable to Steven Weinburg's "To Explain the World". If you think this book is too difficult for you (that is you didn't follow what I wrote in this review), get his book instead. I recommend both books because they actually have a different philosophy on how they see the world. Wilczek would say from the fundamental models that describe the world emerge reality (e.g. atoms are an emergent property of our models). Weinburg would say that our understanding changes with our constricts we have There are differences in how each construct the structures underlying our universe ontologically. Each understand more than I ever will, I'm just fortunate that audible has made both books available to me.

We live in exciting times. The author quotes Keats, "that truth is beauty and beauty is truth" this book will show the listener why that is more true today than ever before.

[emily · Rating 4 out of 5]

‘Electrons are described by space-filling fields—their wave functions—which prefer to vary smoothly and gently. They settle into specific standing wave patterns, or “orbitals,” that find an optimal compromise between the attraction of nuclei and their natural wanderlust. I like to imagine electrons explaining themselves to nuclei this way:
“I find you attractive, but I need my space.”’

It is not as ‘meaty’ (in terms of the ‘science’/mathematical bits) as I would have liked/preferred, but it is surely a highly entertaining book; very engaging writing, for sure. Or as readers who prefer light-er reading of pop. science books would say, highly 'readable' (I cringe a little at the term, but it is so fitting). I’ve heard/read that his more recent publication, Fundamentals: Ten Keys to Reality is quite ‘good’ too. And having read this, I don’t doubt the rave reviews.

‘—Salvador Dalí used dodecahedral symbolism to express a cosmic connection that might otherwise be hard to put on canvas. We’ve also found a dodecahedron lurking within every one of the infinite variety of buckminsterfullerenes, where its twelve pentagons serve as enablers, allowing the hexagons of graphene to close up into a surface—The dodecahedron is a thing of beauty, and by now it’s become a familiar friend.’

‘To me, Caravaggio’s rendering conveys two profound messages that go beyond the words of the gospel’s text—Those who believe without seeing are blessed with the joy of certainty. But it is a fragile certainty, and a hollow joy—Those whose faith is not passive, but engages reality, will receive a second, more fulfilling blessing in the harmony of belief and experience. Blessed are those who believe what they see.’

‘Supersymmetry was (and is) a beautiful mathematical theory. The problem with applying supersymmetry is that it is too good for this world. It predicts new particles—lots of them. We have not seen, so far, the particles it predicts. We do not see, for example, particles with the same charge and mass as electrons, yet are bosons instead of fermions.’

‘Spontaneous symmetry breaking is a strategy for having our supersymmetric cake and eating it too. If we are successful, we can apply beautiful (supersymmetric) equations to describe a less beautiful (asymmetric—or should we say subsupersymmetric?) reality. Specifically, when an electron steps into the quantum dimension, its mass will change—At the frontiers of ignorance, applications of spontaneous symmetry breaking involve creative guesswork. You must guess a symmetry that isn’t visible in the world, put it into your equations, and show that the world—or, more realistically, some aspect of the world you’re trying to explain—pops out of its stable solutions.’

‘In beauty we trust, when making our theories, but their “cash value” depends on other factors. Truth is highly desirable, but it is not the only, or even the most important, criterion. Newton’s mechanics (centred on conservation of mass) and his theory of colours (centred on conservation of spectral types), for example, are not strictly true, yet they are hugely valuable theories. Fertility—a theory’s ability to predict new phenomena, and give us power over Nature—is also a big part of the equation.

Trust in beauty has often, in the past, paid off. Newton’s theory of gravity was challenged by the orbit of Uranus, which did not obey its predictions. Urbain Le Verrier, and also John Couch Adams, trusting in the beauty of the theory, were led to propose the existence of a new planet, not yet observed, whose influence might be responsible. Their calculations told astronomers where to look, and led to the discovery of Neptune.

Maxwell’s great synthesis, as we’ve seen, predicted new colours of light, invisible to our eyes, but also not yet observed. Trusting in the beauty of the theory, Hertz both produced and observed radio waves. In more recent times, Paul Dirac predicted, through a strange and beautiful equation, the existence of antiparticles, which had not yet been observed, but soon thereafter were. The Core, anchored in symmetry, gave us colour gluons, W and Z particles, the Higgs particle, the charmed quark, and the particles of the third family all as predictions prior to their observation.

But there have been failures too. Plato’s theory of atoms and Kepler’s model of the Solar System were beautiful theories that, as descriptions of Nature, utterly failed. Another was Kelvin’s theory of atoms, which proposed that they are knots of activity in the ether. (Knots come in different forms, and they are not easily undone, so they have, it might seem, the right stuff to make atoms.)

Those “failures” were not without fruit: Plato’s theory inspired deeper study of geometry and symmetry, Kepler’s model inspired his great career in astronomy, and Kelvin’s model inspired Peter Tait to develop the theory of mathematical knots, which remains a vibrant subject today—but as theories of the physical world they are hopelessly wrong.’

[Charlene · Rating 4 out of 5]

This book, at its core is about beauty in nature and the power of that beauty to serve as a criterion for determining if a theory is true. Can we use beauty as a guide to discover the laws of the universe? It's a great question. Wilczek points out the trouble the beauty criterion has caused from time to time, e.g. Kepler's beautiful, but wrong, theory about planetary orbits. In the end, Wilczek thinks beauty is a reliable indicator of reality.

The book reads like poetry and Wilczek is equally artists and physicist. He takes his reader back to the group of ancient thinkers, who are collectively known as Pythagoras and examines the symmetry and beauty in Pythagoras' Theorem. Looking at consonance and dissonance, he illustrates how the inner ear recognizes beauty as symmetry, e.g. we like a perfect fifths because our neurons like the beautiful math. Thus maybe math *is* beauty. Maybe the laws of nature *are* beauty.

Wilczek also describes the beauty of optics and of Newtonian physics in general. He provides a history of its shortcomings, which helps him usher in the beauty of Maxwell's equations, relativity, and quantum theory. His explanation of the standard model is wonderful and a good primer for those who are not familiar with the various particles.

Symmetry, and more importantly the breaking of symmetry -- from the Higgs nonzero field through the matter the Higgs creates, and onto the fractal nature of the many forms that matter takes -- seems to Wilczek to be fundamental to our universe. This is why the laws themselves would be expected to be beautiful in this way. I would have liked for him to talk more about networks, chaos, emergence, scaling and the like.

I would suggest readers who liked this book and wanted to keep thinking about these should read:

- Ian Stewart's Fearful Symmetry
- Lisa Randall's Warped Passages
- Geoffrey West's Scaling in Biology
- Albert-László Barabási's Linked
- John Kricher's Ecological Planet (One review called this basic. It is no longer basic when looked at through the lens of networks and complex emerging systems)
- Falkowski's Life's Engines
- Strogatz's Sync
- Scharf's Gravity's Engines
- Carroll's Particle at the End of the Universe
- Holmes' Secret Life of Dust
- Gleick's Chaos

[Patrick · Rating 2 out of 5]

(Disclaimer: I received this book through Goodreads First Reads.)

While the "question" Wilczek explores in this book is a compelling one, its pull is somewhat diminished by the foregone nature of the book's conclusion: Wilczek himself declares that quantum theory is a "definite answer 'yes'" just 8 pages in. With the drama of the hunt somewhat deflated by this bizarre spoiler, Beautiful Question goes from the advertised quest to something more like a meditation on the remarkable ability of scientists, from Pythagoras to Einstein, to uncover layer after layer of stunning structure and complex design. And that journey, moving less towards beauty than into it, is a hypnotic and illuminating one -- more than once I found myself meaning to polish off a chapter only to look up more than an hour later having gotten through hundreds of years of scientific progress.

That said, as a contemplation the book does often fail to live up to its promise. The prose is efficient but far from stunning, and too often seems wrapped up in its own satisfaction with possessing what it presents as "the answer." Many sections are frustratingly vague; the book seems stuck somehow between popular science and a legitimate exploration of the issues, often bringing up advanced topics I had never heard of (such as the "Platonic" structures of many algae and viruses) but only skimming the surface of actual explanation. On the other hand, I'm sure that I would have been lost or irritated had Wilczek gone too crazy with details that didn't interest me, and there are a few times (such as his exploration of Pythagorean acoustics) where he strikes just the right balance of economy and depth -- just the amount needed to appreciate the genuine structure of a given phenomenon, without too badly taxing the attention of a less-interested reader.

Overall, the book is a beautiful mess -- replete with joy, excitement, and yes, beauty, even as it ultimately fails as a narrative or an argument. Probably read best not as a single piece, but rather as a source of extended meditations on great realizations from the first geometry to the wildest dreams of modern physicists. As an ode to the (often-underrated) ways in which science can be good for the soul, it succeeds; it may not convince you that the universe is beautiful for any reason, but it should at least remind you that, yes, it's probably worth looking around once in a while.

[Alison · Rating 2 out of 5]

The question: does the world embody beauty? The answer: yes. The explanation: gluons and quarks and Schrodinger's equation and quantum energy and a bunch of other forces I vaguely understand. Overall, if the book is trying to be about beauty, which I thought it was, its explanations are kind of unsatisfying. But if it is trying to be about patterns and relationships as examples of "faces" of beauty, then I think it was interesting.

Mostly, I'd like to congratulate myself for actually finishing this book. One of my reading goals this year is to expand my knowledge base to include more scientific understandings of the material world. I suppose I inched toward that goal, but I'd probably have to read this book ten more times (not likely to happen) for anything of the knowledge to actually stick. The parts I understood the best were things that Nammy had previously explained to me, especially about light and color and fractals. Also the biographies of the famous mathematicians and scientists. In fact, I was completely enthralled by their life stories! Pythagoras has my heart, and I might give up beans out of solidarity. Outside of that, I didn't have enough inner understanding of atomic-this-or-that for the words I was reading to feel real or to connect them to meaningful life experiences. I couldn't get super into this book for the same reason that lots of people say they can't get into poetry: not enough access points.

Here's a little poem I wrote for my new love, Pythagoras:

ALL THINGS ARE NUMBER

Be weary
of telling people
you can hear
the Music
of the Spheres.
They will only
diagnose you
with tinnitus.

Be weary of
trying to count
what is not
thing. What happens
between the chord
and the ear
is an immortal
soul-secret.

[Clarissa · Rating 5 out of 5]

I do not come from a scientific background, and this is the first popular science book I read in the last 15 years, so it was definitely a challenge. I happened to come across this book in a book shop, and I fell in love with the premise. Naturally I was not able to understand everything Frank Wilczek wrote about, especially towards the end of the book, but did my best because I felt the book was worthwhile. I took copious notes and I learned a lot. For me this book was an adventure, and often the author's words moved me because his perspective of the physical world is so beautiful. I just feel sad I was not able to understand every single word in the book. I will probably try to read it again in the future.

[Gabby · Rating 5 out of 5]

A reread of my favorite science book. This book was so impactful, it lead me to change my major and career path. It’s one you have to really sit with to digest the concepts presented that show how the universe embodies beautiful ideas through the laws of physics, mathematics, and chemistry.

[Viola · Rating 4 out of 5]

Książka jest bardzo ciekawa, autor wykazuje się niezwykłą przenikliwością i zafascynowaniem otaczającego go świata. Opisuje ciekawe i dobrze dobrane aspekty piękna wszechświata, zachwalając przede wszystkim jego symetrię. Jako fizyk teoretyczny próbuje wprowadzić czytelnika do chaotyczniej dziedziny fizyki kwantowej. Od samego Arystotelesa do własnych badań prowadzi nas przez drogę odkrywania tajemnic rzeczywiści. Jednak, nawet pomimo obszernego "słowniczka" zamieszczonego na końcu książki niełatwym zadaniem było przeczytanie tekstu. Autor nie oszczędza nam skomplikowanych teorii i ich zawiłej treści. Nie jest to na pewno typ literatury dla takiego ignoranta fizyki jakim jestem ja, ale Wilczkowi udało się zachęcić mnie do własnych rozmyślań. W przyszłości z pewnością powrócę do tej opowieści, z nadzieją, że tym razem zrozumiem więcej.

[Peter Crofts]

Ho hum, guess I'm dumb. I couldn't finish this book, no matter how much I tried, though the major reason I wanted to finish it is simply so I can say I did read it, as opposed to actually understanding it.

I don't think I grasp what beauty has to do with symmetry, and it's a common misconception (I believe) and manner of evaluating aesthetic experience. Frankly, though Wilczek is clearly a man of astonishing intellectual capacity, that doesn't instantly translate into being able to effortlessly move from one discipline to another. I find his ideas on what the beautiful amounts to, as if it were an objective criteria, sterile and presumptuous.

[Christian · Rating 1 out of 5]

I found this book completely unreadable. I couldn’t make it three chapters in before giving up. This feels like a book that was a joy for him to write and probably fun to inspire academic debates amongst professors. But for anyone outside that group it’s fairly useless.

[Sandra · Rating 4 out of 5]

Es fascinante. Más por todo lo que no he entendido que por lo poco que he sido capaz de asimilar. Siempre que leo sobre las leyes del universo me siento superada y muy emocionada. Por eso sigo insistiendo. Por si algo queda en el fondo. Por cierto, que lo de los mesones y los bariones en español tiene su guasa.

No le pongo ni un pero al trabajo del Profesor Wilczek, otra vez más su entusiasmo es contagioso, pero sí a la edición digital: las láminas no están en color y aparecen todas juntas al final...

[Chris · Rating 5 out of 5]

I had a conversation with a friend, he just so happens to be an astrophysicist.

I felt like I was stepping all over my pud while talking with him. I didn't understand so much about so many things.

That's ok. To ask explore your ignorance is important to me, but the lovely thing is that I do t know enough to make assumptions- so my questions are thrilling. It's silly, but true!


This books explains graspable concepts like QCD theory, ideal to real, what = where, super symmetry, and wave functions in fluid dynamics. I also learned about Lee series, Grassman Numbers, and how exactly the four known forces in the universe work together. I was surprised at how much a role "color" plays.

It's similar to The Gene by Mukhergee in its exploration of Physics' and developments.

There is a lot to this one too... really important stuff here. Gonna have to go back on this one for actual notes.

[Hillary]

I received this book for free through Goodreads First Reads.

I have just received this book and I am looking forward to reading it. I have already started reading, but just looking through teh first part I can see that it will take me some time to read thoroughly enjoy and understand the given material.

I will update my review once I have had the opportunity to complete this book.

[Jane Cathleen · Rating 2 out of 5]

I was excited to read this book . However with my limited knowledge of physics and mathematics , I struggled through. The beginning was easy read however it got a little crazy the further I read into it. I would only recommend to someone who has more knowledge in the subject.

[Phil · Rating 3 out of 5]

learned alot but also felt very stupid. so hard to wrap my brain around how intelligent some people are...fascinating though

[SJ L · Rating 5 out of 5]

A Beautiful Question is a Damn Good Book

“We have learned to work from symmetry towards truth”

Isn’t it awesome when you discuss a topic with someone and they are knowledgeable and excited about the topic? There are few books, and few thinkers, who are able to combine different realms of knowledge into a cohesive package. Allow a grand simplification but books in the science camp are often dull and dry. Books in the liberal arts realm soft and nonconclusive. And we love to divide those into different sides of the aisle, but do we have to?
A Beautiful Question belongs in the rare category of books that is scientifically instructive, yet beautiful written, and comfortable to occasionally leave the static realm of “data” and visible reality to make a point. D and the scientific process are just one method of thinking, and to believe they are the only way to gain understanding is as much a leap of faith as believing in a deity – this is not a digression, it’s an important point to understand before digging into this book.
Wliczek combines aspects of traditional philosophy (including Plato and Chinese philosophy) with modern science in order to demonstrate two key points. 1. The universe is a beautiful place with a definition of what beautiful is (centered on symmetry and minimalism) 2. We are able to access this beauty through the intuitive appreciation of art, music, and equations that explain the divine.
There’s a saying that’s something to the effect of everything has been said, but not by everybody. I would say this is true about the majority of expressed thought and even writing. However, every once in a while you have a unique voice emerge and describe truth in a way that’s accessible and enlightening. This book is in that category.
The points are numerous, and I already know I will reread this book in order to understand them more deeply (I set this reminder in my calendar). This book is a meditation (the author’s own, brilliant phrase) on the divine in a way that the Mind of God by Paul Davies is. Here are some points I found most fascinating:
• We are programmed to appreciate symmetrical visual art as well as music (the way a gong sounds for instance, is soothing and uniform because of how the sound waves travel and how our ears are programmed to interpret the sound)
• Plato was a big influence on modern science because his notion of the ideal influencing the real (so not just in terms of excellence and philosophy, but his otherworldly dimensions and their influence on electromagnetism and quantum theories)
• Big thinkers tend to be drawn to the Divine
• It is possible to combine the “inward path where we examine concepts critically, and try to strip them of the dross of mere appearance, to reach their ideal” (philosophy and metaphysics) with “the outward path where we engage appearances critically, and try to strip them of their complications, to find their hidden essence” (science and physics). I’m reading a bit into this as he admits he favors the ladder, but he allows himself to be awed by art and beauty throughout the meditation, which falls into the former (if we insist on a dichotomy here).
• Gravity is an aspect of general relativity (the interaction between space-time and energy momentum

Quotes
Many creative spirits have found inspiration in the idea that the Creator might be, among other things, an artist whose aesthetic motivations we can appreciate and share – or even, in daring speculation, that the Creator is primarily a creative artist. Such spirits have engaged our Question, in varied and evolving forms, across many centuries. Thus inspired, they have produced deep philosophy, great science, compelling literature, and striking imagery. Some have produced works that combine several, or all, of those features. These works are a vein of gold running back through our civilization. 2
“The greatness and the glory of God shine forth marvelously in all His works, and is to be read above all in the open book of the heaves.” – Galileo
Our brains contain specialized molecules that allow us to construct, very quickly and without conscious effort, a dynamic worldview based on three-dimensional objects located in three dimensional space. We do this beginning from two two-dimensional images on the retinas of our eyes (which, in turn are the product of light rays emitted or reflected from the surfaces of external objects, which propagate to us in straight lines). To work back from the image we receive to the objects that cause them is a tricky problem in inverse projective geometry. In fact, as stated, it is an impossible problem…Nature has helpfully provided us, in our visual cortex, an excellent specialized processor...Like any good textbook [stars and the visual universe], it contains problems with varying degrees of difficulty. 13
Creatures that, like most mammals, perceive the world primarily through the sense of smell would have a much harder time getting to physics as we know it, even if they were highly intelligent in other ways…The world offers many possibilities for different sensory universes, which support very different interpretations of the world’s significance. In this way our so-called Universe is already a multiverse. 14
Symmetry and economy of means, therefore, are exactly the sorts of things we are apt to experience as beautiful. 15
If you listen to Pythagoras afresh, you realize he is saying something quite startling. It is telling you that the geometry of objects embodies hidden numerical relationships. 21
Now we’ve discussed three major Pythagorean discoveries: the Pythagorean theorem on right triangles, and two rules of musical consonance. Together, they link shape, size, weight, and harmony with the common threat being Number. For the Pythagoreans, that trinity of discoveries was more than enough to anchor a mystic worldview. 30
[How our brains process music] Neurons sensitive to fast and slow tones will then get a repetitive pattern that is predictable and easy to interpret. From previous experience, or perhaps by inborn instinct, those secondary neurons – or the later neurons that interpret their behavior – will “understand” the signal. 35
“I feel carried away and possessed by an unutterable rapture over the divine spectacle of the heavenly harmony. 50
*Deep truths: The great Danish physicist and philosopher Niels Bohr (1885 – 1962), a founding figure in quantum theory…was fond of a concept he called “deep truth.” It exemplifies Ludwig Wittgenstein’s proposal that all of philosophy can, and probably should, be conveyed in the form of jokes. According to Bohr, ordinary propositions are exhausted by their literal meaning, and ordinarily the opposite of a truth is a falsehood. Deep propositions, however, have meaning that goes beyond their surface. You can recognize a deep truth by the feature that its opposite is also a deep truth. In this sense, the sober conclusion “the world, alas, is not made according to mathematical principles in the way that Plato guessed” expresses a deep truth. As, of course, does its opposite: “The world is made according to mathematical principles, as Plato guessed.” 52
Allegory of the Cave.
Glaucon: “You have shown me a strange image, and they are strange prisoners.”
Plato: “Like ourselves.”
The point is simple and clear: The prisoners see a projection of reality, not reality itself. Because that projection is all they know, they take it for granted. It is their world. But we should not feel superior to those benighted prisoners because our own situation is no different, according to Socrates. The worlds “like ourselves” arrives with the force of a blow. The story of the Cave does not prove that point, of course – it’s only a story, after all. But it does persuade us to consider, as a logical possibility, that there’s more to reality than our senses detect. And this deeply subversive story issues challenges: Do not accept limitations. Struggle to attempt different ways of viewing things. Doubt your perceptions. Be suspicious of authority. 57
It is noteworthy that Plato (through Socrates) describes liberation as an active process, a process of learning and engagement. This is quite different from ideas that are more popular, though to me less inspiring, where salvation comes about through external grace, or through renunciation. 61
In his central intuition, Plato was quite correct – indeed, more profoundly correct than he possibly could have known. Our naturally given give of the world is but a shadowy projection of the world as it truly is. Our unaided senses take only paltry samples from the cornucopia of information the world puts on offer [microscopes revealing the small, optical telescopes the vast and hinting at dark matter and energy]…As for our senses, so for our minds. Without training and help, they cannot begin to do justice to the richness of reality we know, let alone what we don’t yet known – the unknown unknowns. We go to school, read books, tap into the Internet…those aids to sensation and imagination open the doors of perception, allowing us to escape from our Cave. 62
To Plato, as we’ve seen, what seemed overwhelmingly important is the human soul – its ascent to wisdom, purity, and a transcendent Ideal. Thus in building an account of planetary motion, what is most important is that the theory should be beautiful, not that it should be completely accurate. [We tend to scoff at that now, but it’s actually a fascinating insight that guides a lot of scientific thought. Truth is often pure and simple. Think e=mc2. Think Hemmingway’s six word short story.] 65
Through disciplined imagination, we transcend the Cave of ignorant sensation. 72
The strong form of complementarity, which takes it beyond relativity, is this: There are many equally valid views of your subject – perspectives, in the general sense of the word – but they are mutually exclusive. 75
Take ordinary two- (of three-) dimensional space, and pretend that it’s space time! In that way ordinary geometric curves get reinterpreted as dynamical trajectories. Or, to put it another way, we consider them as motions of a point through space. Newton developed that basic thought in great depth. For him, it was the conceptual essence of what today we call calculus. 108
“The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling along the lifeline of my body, does a section of this world come to life as fleeting images in space which continually change over time.” –Hermann Weyl 116
“And now we might add something concerning a certain most subtle Spirit. Which pervades and lies hid in all gross bodies…But these are things that cannot be explained in a few word, nor are we furnished with that sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic Spirit operates.” -Newton 120
[The benefit of diverse types of thinkers] Michael Faraday was born in England as the third child in a poor family of unorthodox Christians. His father was a blacksmith. He had little formal schooling. During the seven teenage years that Faraday was apprenticed to a London bookbinder, he became fascinated by some of the books that passed his way, especially those on self-improvement and science…He never got far in mathematics. He knew some algebra and a bit of trigonometry, no more. Unprepared to grasp the existing (“Newtonian”) mathematical theories, he developed his own concepts and images. 121
[Faraday and James Maxwell were like a John and Paul collaboration model] “My design is to show how, by a strict application of the ideas and methods of Faraday, the connection of the very different orders of phenomenon he has discovered may be clearly placed before the mathematical mind.” Over the course of seventy-five pages of substantial work, Maxwell developed Faraday’s imaginative visions into precise geometrical concepts, and then into mathematical equations. 124
“The velocity of transverse undulation in our hypothetical medium…agrees so exactly with the velocity of light…that we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.” - Maxwell 127
*[Start with the pure and beautiful and build up from there] In modern physics we have taken this lesson to heart. We have learned to work from symmetry towards truth. Instead of using experiments to infer equations, and then finding (to our delight and astonishment) that the equations have a lot of symmetry, we propose equations with enormous symmetry and then check to see whether Nature uses them. It has been an amazingly successful strategy. 139
[There is a whole really awesome section on how we perceive color and how vision works, the author occasionally taking the time to ponder what science would look like if other animals were doing the thinking.] You can get a convincing perceptual white by mixing just three spectral colors, red, green, and blue. If you passed that “white” beam through a prism, you wouldn’t get a continuous rainbow, but just three lines. As a physical entity this beam is quite different from sunlight, but human vision perceives it as identical. 142
Ordinary space is a three-dimensional continuum, and so is the space of perceived colors. 146
Pure electromagnetic waves with wavelengths in a specific, narrow range – from about 370 to 740 nanometers, quantitatively – are the raw material for human vision. They correspond to the pure light revealed in Newton’s prismatic spectrum. In musical terms, the human visual range spans one octave (one doubling of wavelength). Each spectral color corresponds to a definite wavelength. 150
* And now let’s make a leap of imagination, ascending from the solid ground of “what,” “how” and “why,” into the dreamscape of “what if,” “how to,” and “why not?” 159 [That’s a hell of a sentence for innovative thinking, note you have to start with the foundations of what how and why before leaping into the dreamscape. Awesome!]
* “Happy is the man who can recognize in the work of today a connected portion of the work of life and an embodiment of the work of Eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity. He strenuously works out his daily enterprises because the present is given him for a possession. Thus ought man to be an impersonation of the divine process of nature, and to show forth the union of the infinite with the finite, not slighting his temporal existence, remembering that in it only is individual action possible, nor yet shutting out from his view that which is eternal, knowing that Time is a mystery which man cannot endure to contemplate until eternal Truth enlighten it. 164
Our Question asks us to discover beauty at the root of the physical world. To answer its challenge, we must be active on both sides. We must enlarge our sense of beauty, as we enlarge our understanding of reality. For the beauty of Nature’s deep design, we shall find, is as strange as its strangeness is beautiful. 166
[Much like the fascinating discourse on vision, get ready to understand how we process sound!] Gongs produce an evolving chord, gradually shedding complexity until it becomes a single tone, because there are several long-lived patterns that decay at greater rates…These patterns bear striking resemblance to the pattern of electron clouds. The resemblance between their governing equations is profound, and more striking still. 175
It is impossible, according to quantum theory, to answer both questions [velocity and location of an electron] at the same time. You can’t do it, even though each question on its own is perfectly legitimate and has an informative answer…it’s a lesson in humility that quantum theory forces to our attention. We have, for example, Heisenberg’s uncertainty principle: You can’t measure both the position and the momentum of particles at the same time. 185
*Many kinds of rewards are given to people for tangible services rendered. These rewards take the form of salaries, profits, social status, and so forth. But the accumulated wealth of basic science and art often derives from efforts whose ultimate value isn’t immediately obvious. Even in cases where some breakthrough is clearly important, it may be years before the work yields any economic benefit; or the benefit may be entirely cultural and never become economic in the useful sense. People who work towards increasing this special kind of wealth are devoting their careers to long-term investment in the improvement of life for humanity as a whole. And what hardheaded businessperson or consumer will pay for that? Yet history teaches us that such devotion to the long term, and to the common good, pays off handsomely. A wise society will cherish opportunities to foster such devotion. 191
The world does, in its deep design, embody some forms of beauty that have been highly prized for their own sake, and have been intuitively associated with the divine. 223
One of the few stories attaching to Euclid – most likely apocryphal- is his reply to his patron and king, Ptolemy I, when asked if there was an easier approach to geometry than the Elements. Euclid supposedly replied, “Sire, there is no royal road to geometry.” [If there is no struggle, there is no progress, as always.] 227
Matter tells space-time how to curve. Space-time tells matter how to move…Electric charge tells electromagnetic property space how to curve. Electromagnetic property space tells electric charge what straight is. 233
The Core is profoundly rooted in concepts of symmetry and geometry, as we have seen. And it works its will, in quantum theory, through music-like rules. Symmetry really does determine structure. A pure and perfect Music of the Spheres really does animate the soul of reality. Plato and Pythagoras: We salute you! 276
Sometimes the most important step in understanding something is to realize you shouldn’t worry about everything. It’s usually better to be (maybe) right about something than “not wrong” about everything. 315
* We humans are posed between Microcosm and Macrocosm, containing one, sensing the other, comprehending both. 323

[K.A. Ashcomb · Rating 4 out of 5]

The question is, does beauty exist in nature or more so in physics? Frank Wilczek sets to prove it by looking through mathematical, physical, and philosophical theories about the world, starting from Plato and Pythagoras and ending up with his and his colleagues’ postulations about supersymmetry. I’m not sure if to give you an answer or a tip on what beauty means (there, now all of you got it instantly,) as Wilczek gives away the plot in the first pages, but I guess for the sake of tension, I leave it for you to find out.

I have complex feelings about this book. While it clarifies so much and the writer’s arguments are eloquent, there are also places I get lost, and I suddenly have read several pages with no comprehension. There are two reasons for this: the concepts expressed differ in their complexity. First, when we get to the nitty-gritty of atomic level and quantum theories with their Creek symbols, the simplicity of the explanations is lost. Understandable. But to argue, there are places where Wilczek uses metaphors to explain the whole concept in one sentence, and you are like, “Yeah, I understand now.” This is especially true in the sections handling color, vibration, and photons and how music fits into the picture. Second, the language of the book varies greatly, making reading a confusing experience. You spend hundreds of pages with the writer removed as an actor, and suddenly, we jump into his children and marvel at the cosmos. This contradiction and jumping around happens inside the chapters as well, suddenly changing from physics to philosophy, forcing you to stop and ponder why the jump was made, sometimes without an obvious answer.

What I also found very confusing was that I thought I had formed a coherent idea of the quantum world and physics through simple reads like Carlo Rovelli’s Reality is Not What it Seems: The Journey to Quantum Gravity, and as I read this book, suddenly it was all gone, and I was back lost in this universe without comprehension of the physical reality which governs me. I’m not sure if it is just my brain that finds competing explanations with slight differences in how and what theories are stressed distributive? All this makes me feel stupid and as if someone had sneaked in to steal what I already knew and leave a note saying, “sorry, not compatible.” And then I think that maybe the scientists are not so out of Plato’s cave, and actually, I’m caught between competing explanations and no sides make that clear to the laymen like me, and in my case leaves me lot confused and believing someone indeed stole information out of my brain. Anyway, this has nothing to do with the book—just my ruminations about the failings of my mind and comprehending the book in its entirety.

Still, I love reading books about physics and the quantum world, as always some new aspect will reveal itself and stick with me. From this book, I take with me the image of atoms as musical instruments played by photons. 

[Aarthi Ramesh · Rating 5 out of 5]

Quick notes for myself -

In trying to answer if the world embodies beautiful concepts, the author has written a response so beautifully, especially the final chapters when everything comes together. He writes about new and integrated concepts in an easily approachable way to get a cursory understanding.

"Asymptotic freedom" is a concept I've heard for the first time. Apparently strong forces are stronger as dist increases but is weak at very close distances! What an unintuitive concept compared to electric charge or gravity, where the closer you are, the effect of the force is higher. This force confines the quarks and gluons but also allows them to have relatively high energy/freedom at shorter distances. Since protons are made of quarks and gluons, apparently most of the proton is empty space and the energy of the quarks/gluons? is what gives a proton it's mass! Mass without mass - as quarks/gluons have negligible mass. But the proton gets it's mass due to the energy of these particles. Think it's a cool concept in general, getting "closer" leading to more freedom than less.

Another really cool piece of info - integrating fermions and bosons as transformations of each other! (Theoretically so far I think) Fermions are the substance or MATTER particles whereas bosons are the animating or FORCE particles? I don't think I understand this fully, but it feels like fermions are like electrons, which need to follow paulis exclusion. And bosons are force particles like photons which are happy to do similar things as other photons. Unlike electrons. Frank Wilczek mentions how they found a way (supersymmetry?) to make the matter particles become the force particles and the force particles matter particles. This hasnt been proven yet if I understood that right. But would be cool if substance and the thing that acts on substance were interchangeable and part of the same thing! All of this was something I didn't know had been proven or that it could be written in a book that I could read 😂
Kinda dumb questions for myself - technically didn't the big bang happen "everywhere" at once? Why should the microwave radiation travel a "long distance". If so, where is it traveling from? The center of the bang?
If most of the equations we have are for the laws of nature but not initial conditions, can we figure out initial conditions? Are they needed if it's symmetric? Maybe if we view in different perspectives, it'll appear as though we have different initial conditions?

Initially I thought I would shed a tear for how difficult the book might be to read, but instead shed a tear for the reasons intended by the author! For how much unity/beauty is contained in the standard model? And maybe a tear or two for how I'll never be able to actually grasp/see this for myself

[Ondrej Urban · Rating 4 out of 5]

Beauty is symmetry and the world is symmetric. A Beautiful Question gives a high-level overview of modern particle physics, focusing, in part, on the theory we call Standard Model and in part describing how it all kind of pops up from a few mathematical and philosophical assumption. Frank Wilczek, even though a Nobel-awarded physicist, keeps on marveling how come that all of this works, and works so well. Frankly, I remember feeling the same - a feeling that I've kept ever since - when during my undergrad I learnt how a few simple mathematical and philosophical assumptions lead to powerful results, to use an euphemism. For example, digging into the assumption that the laws of physics are the same today as they were yesterday and will keep on staying so tomorrow, you can, thanks to the genius of Emmy Noether, prove the conservation of energy, a concept that gave us the industrial revolution.

The target audience for this book is, of course, everyone, but a particularly good fit would either be physicists - such as myself, in a way - that will enjoy looking at problems they've encountered a while ago through new metaphors, or pre-university physics enthusiasts, who will remember the words and then add a new layer of enjoyment later when the issues have been mathematically derived in front of them (this is what happened to me seeing the Kerr black holes derived during a General Relativity course).

The fours stars com from two facts. First of all, the text sometimes gets too convoluted to properly follow unless you've actually followed all the research and read all the papers. Additionally, even though it wants to be, this is not really an entry-level popular scientific book for me.

All that to the side, give it a go and find out how filling in tables with pluses and minuses, according to some pattern a kindergartner could do tells you in detail how the world works.

[Maverick D. Aece · Rating 4 out of 5]

The way that the author/scientists leads the reader from the question to the answer is meticulously well done. Apart from some rhetoric repetition of some of the history of science (which I'm sure was pivotal to what was to come later both in the world and the book, and which mostly was meant for the first time readers I hope) the book takes you on a journey of all the beautiful ideals of science and how they fit with the reality.
All in all I must say, this was a wonderful journey despite rough rhetorics though some of the insights from them were really good.

[eris · Rating 1 out of 5]

i was 100% not the intended audience for this book. the author sets out to determine the answer to “is the world a work of art?” with a specific idea of ‘work of art’, ‘beauty’, and ‘world’ in mind, closely (and solely) tied to western scientific ideas. i can pass by the analogies and metaphors used to make the science itself palatable to a broad audience, even though they often confused me more, having studied the science itself, but what really got to me was that we were just meant to take those ideas and run with them. i honestly find it a bit odd that someone writing this sort of book would not at least touch upon the impact the concepts they are putting forth have had historically and socially as if neither of those things made up 'the world'.

[Jeffrey Romine · Rating 5 out of 5]

Wilczek opens the book with two questions. Does the world embody beautiful ideas? Of course, the answer must be yes, and especially for those who understand equations involving symmetry. The second question follows: Is the world a work of art? This is when any God-fearing man sobers. Wow! As Proverb 33 declares, the inhabitants of the earth will stand in awe.

[Tom · Rating 4 out of 5]

A lot more theoretical particle physics than I was expecting so I only grasped the basics. It did help answer some of my questions about the theory of relativity.

[Chris Esposo · Rating 3 out of 5]

There needs to be some nuance about this review: 1. ⅗ stars is a compromise between my consumption of this book via two different mediums: audiobook and kindle. I felt the audiobook portion was just adequate, for several reasons I’ll outline shortly. The kindle (or written) version of the text is much better, somewhere between 4 or 5 stars. Normally, the experiences are correlated and complementary, and I have a fairly easy time rating the book after finishing either/or, but in this case I felt the audiobook-experience and kindle-book experience almost seemed anti-correlated, and thus, situated in the opposite sides of the quality-spectrum and so wanted to partition the review with that in mind.

First, for the audiobook what it gets right is it’s read by the author. His reading is fine, and although he’s not a professional reader, there’s something to be said on having your 12+ hour audiobook read by a Nobel Prize winner in physics. What it gets wrong has less to do with the reading itself but with the organization. First, the audiobook is cut into 2 - 6 min chunks, or chapters. Which would be fine if the chapters had some sense to them in that they delivered a closed-cohesive idea, but from my listening, that wasn’t the case often, and more egregiously, none of the chapters were labeled. Thus, when listening to the text, it is challenging to chunk the information to ideas without directly labelling the ‘mini-chapters’ yourself, and I often use the audio medium to engage in a more passive manner of information consumption.

Second, the book comes with generous appendices with defined terms and definitions. This is great, especially for readers coming outside of physics, this is what I need to get a concise understanding of what the sentences mean in a well-formed manner. However, the audiobook literally is read sequentially by the printed page, so what we have is Wilczek spending the last 3 - 4 hours of the reading rotely checking off definition after definition. Not so great. It would have been better for the appendices to be partitioned and distributed to the chapters that they were most relevant for, or in my opinion, be placed at the beginning of the text if that was not possible. Also, though 90% of the definitions were relevant, there were some who’s placement in this section verged on pedantry, like the term “ubiquitous”, which is a normal english word, and does not be defined as the use of it in the text is the ordinary english usage.

As for the content, this text shined on it’s own, and relative to other layman books covering a similar topic, such as “Atom Land” by Jon Butterworth, and also covers a bit on quantum field theory (QFT) and the particle zoo. The presentation here is a bit more drawn out, less to the point, and far more “abstract” or concept-driven vis-a-vis Butterworth. I appreciated Butterworth’s approach, which was to as efficiently as possible equip the reader with some understanding of QFT, how it informs the standard model, and how all those particles that result from the model relate to each. Butterworth connects the material to the “sense-experience” of the reader via his analogy of going on an extended-trip into “Atom Land”.

Wilzcek’s approach is different in that he starts his narrative deep in the history of philosophy, in the time of Aristotle and Euclid and seeks to draw the reader in by connecting the phenomena resulting from QM, specifically the phenomena of light and color, to the sense-experiences of sight and perspective. He accomplishes several things with this approach: 1. He makes a seemingly abstract thing, a bit more concrete, by demonstrating the relevance of it’s mechanics in everyday phenomena 2. He provides a cohesive historical thread to discuss the nuisances of the evolution of ‘theory’ and systems of knowledge, specifically, through discussions of how various theories from the geometry, the metaphysics, and finally classical & modern physics has sought to tease out, via sense-experiences, essential natures of objects via observations, in a sequence of increasingly rigorous refinements, with observations being replaced with experimentation, and metaphysics being replaced by both mathematical analysis and synthesis 3. Introduce topics like frequency, symmetry, and harmony that will become important in both quantum mechanics and it’s field theories.

From my initial reading Wilczek is mostly successful, I found this book successful at many things, a history of scientific thought, a idiosyncratic overview of modern physics via historical lineage, and as a commentary on aesthetics, a unique combination for sure, and one that I’ve not yet found replicated even in part, by any other layman book I’ve read on this subject. The real challenging aspects of this text is that it touches upon so many materials, I found remembering or even recalling key portions of the book via audio challenging, and this is somewhat true even for the Kindle edition, though again, since visual reading is often a more involved activity, it’s less of an issue here, especially with active note taking.

As a book outlining the history of scientific thought, and the people who have engaged in that enterprise, I found two people outlined in the text of particular interest, Isaac Newton and Emmy Noether. Unfortunately, both Newton and Noether are often the lesser talked known luminaries in a subject so overwhelmed by one individual, Albert Einstein, though Newton less so than Noether. Newton is introduced relatively earlier on as the individual most responsible for turning meta-physics into a rigorous field, into the “natural philosophy” that became classical physics. As someone who has attempted a blind reading of the Principia via Heath’s translation, I can appreciate the awesomeness of his mind and contributions, if only through admiration of the complexity of the statements, and not so much a clear comprehension of the statements themselves (dedicated studies of the Conics of Appollonius and a mastery of the first 6 books of Euclid prior to the treatises on solids are probably required to really understand the constructions of the 1600s mathematicians -and this is not something I can claim to have mastered as of yet - though with Euclid one may get away with just a few ). I sense a similar awe from Wilczek from his overview of Newton.

Wilczek’s discussion of Newton is also apt because of Newton’s extensive work on optics and the nature of human vision, and color, which fits very well with the narrative he has sought to pursue at the beginning of his text. With Noether, I wish there was a bit more here. A conceptual discussion on her conservation laws is given, and some biography of the woman is made, but here I wish the scope of her work and its relevance was given more stature in this text. Noether is often referred to as “the mother of modern algebra” her name is found everywhere in the fundamentals of the field, and although she’s known for her study of “rings”, and not “groups”, the algebraic structure most associated with the notion of symmetry in mathematics, it must be the case that she was involved in work that was highly relevant to both symmetry and isometries, which are highly relevant to both the quantum mechanics and the field theories to my understanding. Though this is mostly conjecture on my part.

Overall, the book as a read, and not an audio artifact, is stellar. One other thing that the Kindle does great is reproduce high resolution fascicles of the many excellent visualizations in the text (something you are entirely missing in the audible experience). Not all are functional, but just seeing fascilimes of Newton’s notebooks or diagrams from Maxwell is not only inspiring, but helps one remember the material around those artifacts. This book is littered with many dozens of these images.

In conclusion, this book is very much a “meta-commentary” on the nature of physics, as a theory and set of ideas. Numerous times Wilzcek commentates on say the scope of Noether’s theorems to certain characterizations of mechanics, say those that are Lagrangian, and that it’s unclear to him if it is a “if and only if” with respect to the set of systems in mechanics and this set of mechanics that can be characterized as a Lagrangian (and maybe more broadly, a Hamiltonian?) i.e. are there relevant mechanics that cannot be characterized by the Lagrangian framework, and what does that imply about the scope of Noether’s conservation (caveat here: I’ve not studied a lick of physics, so this is my ‘interpretation’/comprehension on reading p.285 of his text -could be wrong). He comments on the necessity of putting certain statements as axioms, and others not, not only from the mathematical construction, but from an aesthetic purview. As an aside, this is very important I think from a pedagogical sense since often times modern students will only know a subject, say "graduate physics" or "modern physics" in it's axiomatic form, say 'the Hilbert Formalism of mechanics', and in many cases, students will take this form as canonical, but what they will miss is the historical development which could imbibe in them more of the intuition that motivated the structure of that form. In this sense, what you treat axiom, is less a matter of absolute truth, and more of an aesthetic choice on what you wish and do not wish to defend, and which complexity you wish to shave away by taking it as given. Very unique in a layman text, and I wonder how much of these ‘little’ comments the average reader really picks up on. Still, this book is definitely useful to a more technically minded person. I suspect a more general reader might be better with taking on something like “Atom Land” first, but they too could benefit from this reading, if only as a text on the history of scientific thought. Recommended (in kindle, only get the audible as supplement).

[Nestor · Rating 3 out of 5]

I rate books, not for their content but for the ideas that sparkle. This gave me two ideas that I presented below. They show the connection of physics to other areas of life. Though I found the book a little bit boring and I found the Plates at the end of the book cumbersome, exasperating, and irritating, having to flip pages is not something of the 21st century.

The Idea that I developed from reading the book:
Breaking Free from 19th-Century HR Mindsets
In the world of high-energy physics, collisions between particles can yield astonishing results, producing a multitude of new entities whose combined mass far exceeds the initial inputs. This phenomenon serves as a powerful analogy for the potential of diverse ideas and backgrounds in the corporate landscape. However, many organizations remain stuck in outdated mentalities akin to 19th-century practices, stifling innovation and growth.
The Stagnation of Traditional HR Models
Many HR departments still operate under principles reminiscent of the industrial era—mechanistic structures, Taylorism, and discriminatory practices based on race, gender, and age. This retrograde mentality not only hinders employee potential but also undermines the very fabric of organizational success. When HR, managers, and team leaders cling to these outdated paradigms, they limit their ability to harness the full spectrum of talent available in the workforce.
The Power of Diverse Perspectives
Just as the collision of particles generates new mass, the convergence of diverse backgrounds and perspectives within a company creates greater value. When individuals from various races, genders, and age groups collaborate, they bring unique insights that drive innovation and problem-solving. This diversity is not merely a checkbox to tick; it is a strategic advantage that organizations must embrace to thrive in today’s competitive landscape.
The Dangers of Autocratic Leadership
The current corporate model often sees managers and team leaders making unilateral decisions without democratic input from their teams. This "Sliwinsky-Corbelleri-Giordano Syndrome" reflects a toxic environment fueled by personal agendas, excessive ambition, and a relentless pursuit of prestige at the expense of others. Such a leadership style, called "SCG Syndrome", fosters an atmosphere of distrust and disengagement that ultimately erodes company value while promoting the waste culture of human potential, where valuable ideas and contributions from employees are ignored or suppressed. This not only leads to disengagement but also results in significant losses in creativity and productivity, ultimately eroding company value..
A Call for Democratic Practices
To break free from these shackles, organizations must adopt more democratic practices that empower employees at all levels. By fostering an inclusive environment where diverse voices are not just heard but actively sought out, companies can unlock the creative potential that lies within their teams. This shift requires a commitment to dismantling discriminatory practices and embracing a culture of equity and inclusion.
Conclusion: Embracing the Future
To truly succeed in the 21st century, we must confront the outdated mindsets that hinder our progress. The Sliwinsky-Corbelleri-Giordano Syndrome represents a critical barrier to innovation and growth, emphasizing the need for a paradigm shift in how we approach leadership and collaboration. By embracing diversity and democratic practices, organizations can create a vibrant ecosystem where ideas collide and flourish, ultimately leading to unprecedented success.
Let us commit to breaking free from the constraints of the past and harnessing the power of collective knowledge. In doing so, we can transform our workplaces into thriving environments that not only drive value but also reflect the rich diversity of our society. The future of business depends on it.


Navigating the Curved Landscape of Modern HR: Embracing Adaptability in a Liquid World
In today’s rapidly changing work environment, the principles of physics can provide valuable insights into how we navigate the complexities of Human Resources (HR). The notions of curved space-time and geodesics offer a compelling metaphor for understanding the need for adaptability in modern organizations. Just as matter influences the curvature of space-time, shaping how entities move within it, HR must adapt to the ever-evolving realities of the workplace.
The Curvature of Organizational Dynamics
Organizations are dynamic entities influenced by various factors—technological advancements, market shifts, and evolving employee expectations. Much like how mass and energy curve space-time, these elements shape the organizational landscape. For HR professionals, this means recognizing that traditional approaches may not suffice in navigating this curvature. Instead, we must embrace flexibility and responsiveness, rethinking our strategies to align with the current environment.
Adapting to New Realities
In the realm of HR, adaptability is paramount. The concept of geodesics—optimal paths connecting points in a curved space—serves as a powerful analogy. In HR, these optimal paths can be understood as the most effective strategies for talent management, employee engagement, and organizational development. By analyzing data, gathering feedback, and fostering a culture of continuous learning, HR can identify best practices that resonate with the current workforce.
Fluidity in Modern Liquid Workplaces
The idea of "liquid modernity," proposed by sociologist Zygmunt Bauman, emphasizes the fluidity of societal norms and structures. In this context, HR must embrace a similar fluidity, remaining open to new ideas, processes, and technologies. This approach requires regularly revisiting policies and practices to ensure they align with the shifting organizational climate.
Dynamic Workforce Strategies
A key aspect of adapting to a liquid modern workplace is implementing dynamic workforce strategies. This involves flexibility in roles, remote work options, and varying team structures that can respond effectively to changing circumstances. By fostering an environment that encourages adaptability, organizations can navigate the complexities of the modern workforce much like particles traveling along geodesics in curved space-time.
Strengthening Collaboration and Communication
As we embrace these principles, it’s essential to recognize the interconnectedness of teams and departments within an organization. Just as space-time connects various points in a continuum, strong communication and collaboration foster a holistic approach to problem-solving. Establishing feedback mechanisms can help HR stay attuned to employee needs and organizational shifts, acting as measurements of curvature that guide informed decision-making.
Cultivating a Culture of Continuous Learning
At the heart of adaptability lies a commitment to continuous learning. HR should encourage employees to embrace new skills and knowledge, equipping them to tackle unfamiliar challenges. This culture mirrors the concept of following a geodesic, where past experiences and current conditions inform our paths forward. By investing in employee development, organizations can create a more resilient workforce capable of thriving in uncertainty.
Embracing Technological Integration
Incorporating technology into HR practices is another vital aspect of navigating the modern landscape. Advanced HR tools and analytics can provide insights into employee engagement, performance, and overall organizational health. By leveraging these technologies, HR can make data-driven decisions that enhance adaptability and responsiveness.
Conclusion: The Path Forward
As we reflect on the interplay between matter and space-time, we can draw valuable lessons for HR in the modern workplace. The need for adaptability is not merely a response to external pressures; it is a fundamental aspect of organizational survival and growth. By embracing the principles of curved space-time, HR professionals can navigate the complexities of the modern workforce with agility and purpose.
In conclusion, the journey of HR in a liquid world requires us to continuously adapt, learn, and collaborate. By fostering a culture that embraces change and encourages innovation, organizations can not only survive but thrive in the face of uncertainty. Let us commit to following the geodesics of our organizational landscape, finding the most effective paths forward in this ever-evolving environment.