It Must Be Beautiful: Great Equations of Modern Science by Graham Farmelo (PDF)

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It Must Be Beautiful is a collection of 12 essays on the power and beauty of modern scientific equations by some of the world’s foremost scientists and historians. Contributors include Steven Weinberg, Peter Galison, John Maynard Smith, and Frank Wilczek.

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Reviews from Amazon users which were colected at the time this book was published on the website:

⭐An enjoyable book on “equations,” which contains some deep and profound writing and well worth reading.I am going to discuss the “The Drake Equation” article contained in the book.After all of the discussion in the article about extraterrestrial life it fails to discuss the most important thing about the development of life on Earth- Earth’s Moon.From my review of the book “30-Second Theories.”On page 110 we have the “Rare Earth Hypothesis,” which should be read by everyone.This entry shows that it is Earth’s Moon that is “special,” not the Earth itself. Why?”Earth’s huge moon is important too- it stabilizes the axis of the Earth and stops it wobbling like a spinning top (see Mars). The Moon- powered tidal forces inside the Earth keep it hot, and sustain the magnetic field that shields us from harmful cosmic rays. The same forces drive the ocean tides, which played a role in the migration of life onto land. The Moon is believed to be a chunk of Earth’s crust knocked into orbit by an immense impact in the early days of the Solar System. That impact also thinned the Earth’s crust, making plate tectonics possible, shifting the continents to and fro, allowing life on Earth to diversify in splendid isolation.”Here are two reasons the Earth is not “typical.” It is not the Earth, but the Earth’s moon.1. The Moon. We would not be here if the Moon was not there.The Mars sized planet that slammed obliquely into the Earth which created the Moon could be the unique circumstance of our plant Earth. It is not the Earth that is unique, but the Moon. If the Moon were not there the rotation of the Earth’s North Pole would vary so much over periods of about 100’s of millions of years that the relatively stable weather on the Earth would not have allowed the “weather stability” in “deep time” necessary for sentient, conscious life to emerge on Earth over billions of years. Its kind of like a top that as it starts to lose it spin and it’s north pole begins to oscillate wildly. The Moon keeps this from happening to the Earth and this fact allowed intelligent, sentient and conscious life to emerge over a period of billions of years on planet Earth. Life might have emerged on Earth if the Moon were not there, but not sentient, conscious life.2. Earth’s iron core. Also due to the Mars sized impact that created the Moon, the Earth has 1-1/4 to 1-1/3 the normal iron core for a planet this size. (Part of the iron core of the Mars size planet joined Earth’s iron core after the impact) This increases the magnetic bow wave shield that protects the Earth from the harmful rays of the sun. This may have facilitated the development of “life” on Earth and allowed the formation of sentient, conscious life on Earth over a period of billions of years.So the unique thing about the Earth is not the Earth, but Earth’s Moon.There is also a discussion in this article on interstellar travel using the Voyager and Pioneer spaceprobes as an example, however at the speed they are traveling through space it would take about 80,000 years to reach the nearest star:From my review of the Pioneer plaque:”… the 21-centimetre line of neutral hydrogen is used as a Rosetta Stone. The 21 centimeter line provides a standard of both length and time and is illustrated by a hydrogen atom that is shown rotating. It is possible to check the standard of length since the probe itself is drawn to this scale on the plaque. The spider-like mark and the lines radiating from it give the directions of the principal pulsars as seen from the Earth, and knowing the scale of time, their periods also.”Any civilization with the ability to find the probe in interstellar space would know the pulsars well and would certainly have included them in detailed charts of the Galaxy. This intelligence would then realize that there is only one point in space and time within our Galaxy that corresponds to the spider. Having thus located the Sun, members of this civilization would recognize the planets that surround it and find the one from which the probe was sent (the third, as indicated at the bottom of the diagram). What they would probably find most difficult to comprehend are the drawings of a man and woman – especially if they themselves resemble the spider in the center!” (NASA)Having said that, the speed of the Voyager space probes (not the Pioneer discussed above) is about 35,000 miles per hour, or about 51,000 feet per second. We will use this as an example for the Pioneer probes, see below. About 51,000 feet per second is much, much “faster than a speeding bullet,” which can range from about 800 feet per second to about 2,000+ feet per second.The nearest stars to Earth are Alpha Centauri (a binary star) and Proxima Centauri, which are about 4.2 light years away. At the speed of the Voyager space probes it would take about 80,000 years to reach Alpha Centauri (From “The Cambridge Atlas of Astronomy,” Third Edition, 1994, page 416-417, chapter called “The extraterrestrial life debate.) (Note: the wikipedia.org entry for Pioneer 10 has different information: “At its current speed, 26,900 m.p.h., it will be more distant than the red dwarf Proxima Centauri in 26,118 years.” I can not understand this huge difference in projected times between the “The Cambridge Atlas of Astronomy” page 417and this wikipedia entry.)This gives you some idea how large our Galaxy, the Milky Way is. The Milky Way, contains between 100 to 300 billion stars and is about 100,000 light years across. There are about 100 billion galaxies in our Universe. The point is there are many, many stars and a lot of “space” out there and the distances are “astronomical.”For reference, the speed of light is about 186,000 miles per second.See also “Beautiful Equations,” (2107), Mike Goldsmith, et. al., which is like an encyclopedia of equations, 365 of them, which sets the table for searching for further research and understanding of these equations. Buy this book now, currently listed at just over $11 bucks! One flaw: no index.

⭐It Must be Beautiful:Great Equations of Modern ScienceEdited by Graham FarmeloEleven scientists share their work supposedly about a “beautiful” mathematical equation. Variety and variability result. Ten of the authors can learn from Robert May’s clear presentation of biology and chaos theory without baggage, politics, religion or crap although, in a contrasting approach, Roger Penrose invites the reader into the convolutions of his own thinking. Aisling Irwin is apologetic about chemistry and the Ozone Layer perhaps because he cites a chemical equation. Frank Wilczek writes on the Dirac Equation (“My equation is smarter than I am”) while Peter Galison writes on the “Sextant Equation” (which, on Googling, only regurgitates a copy of the chapter – he seems to have rechristened Einstein’s E = mc2).Twenty four gushing accolades are quoted from book reviews such as “Many popular books shun equations, but here is one that relishes them, that celebrates their power and beauty, and that still manages to explain rather than baffle”. Not so. The equations are quickly mentioned then lost in a maze of politics and religion, plus poetry, music, and art erroneously introduced to please the editor’s “It must be beautiful” theme. Science without mathematics is nothing … a lack of diagrams is another burden.Styles vary amusingly. Robert May would describe a situation as “Jack & Jill went up the hill …”. Whereas Roger Penrose would caveat it as “Jack & Jill went up the hill, although Peter & Wendy are known to have tackled the hill years earlier getting about half-way, and Oscar definitely went three-quarters of the way even earlier albeit on his own and, even so, Jack and Jill, or Jack in particular, do not seem to have recognized the significance of their reaching the summit. Overall, in my opinion, on balance, we can accept that Jack & Jill did go up the hill.”Graham Farmelo sees scientific achievement as “A Revolution without Revolutionaries” – why? – and lauds Max Planck’s theory but criticizes him for living in Germany during World War 2 and invokes his religion “If Planck was Moses … Einstein was his Joshua”. He is critical of Planck for missing the vital step to Quantum Mechanics but states that “As strange as it may seem” Planck was excited by the units of Planck Length, Planck Mass, and Planck Time (without attribute) which to quote Max Planck in 1899 are: “Units for length, mass, time … which being independent of specific bodies or substances, retain their meaning for all times and all cultures, even non-terrestrial and non-human ones”. Clearly both exciting and revolutionary.The theme of the book is that the mathematics of science must be beautiful. The theme is best tackled by Frank Wilczek appealing to the “accumulation of tension between important, well-developed themes, which is then resolved in a surprising and convincing way. One feature which can make a work … beautiful is symmetry – balance of proportions, intricacy towards a purpose. The Dirac equation possesses both these features to the highest degree … and taken a life of its own”.The question is part of how science progresses. Three statements Quoted from my ‘Mathematics the Truth’ are:1) Richard Feynman claimed one needed (a) an intuitive idea of how something works, (b) then equations to quantitatively express the idea, (c) then calculations to verify and predict something new, (d) then an experiment to test the prediction, which if right, yields a theory or a principle.2) Paul Dirac looked for beautiful equations – if beautiful enough it is right. In his own words: “Physical laws should have mathematical beauty.”“It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty … You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it.”3) Albert Einstein looked for principles that collide, where we cannot conceive of either principle being false but taken together seem to lead to a contradiction. Physics makes the greatest conceptual advances when the conflicts are resolved.Wilczek goes further with a theme of “experimental logic”. “If a line of investigation has some success and is fruitful, it should not be abandoned on account of its inconsistency or its approximate nature. Rather we should look for a way to make it true … Creative mathematics and physics rely not on perfect logic, but rather on experimental logic. Experimental logic involves noticing patterns, playing with them, making assumptions to explain them, and – especially – recognizing beauty.”Perhaps it is time for publishers, authors and readers to agree that readers of biographies of scientists are after understanding and insight into the subject’s scientific achievement. Mathematical physics is nothing without the mathematics so do not avoid it. To quote Roger Penrose “… without the meaning that lies behind these symbols there is neither beauty nor physical significance … (but) … spare the equation a glance, and then press onwards … then do not be afraid to leave an equation behind”.Finally, reading “It Must be Beautiful” shows that mathematics forces scientists to stay logical while writing prose often does not.Malcolm Cameron16 July 2017

⭐Great book; profound in places yet easy to read. Good spread of themes; makes you want to read more of the same.

⭐Getting these “specialist” books is vital and this was as I hoped. I will be using this again and again. Thanks

⭐beautiful book, I read it avidly in the gym. I’m a nerd, deal with it

⭐Being a potential physics student for uni (with an offer from Oxford Uni) this year, I decided to continue to expand my knowledge of science.Given that this book is a compilation of essays based of specific equations which ‘shaped modern science’The essays give generally gives a brief history of the equations development and allbut some of the just don’t give the ideas in enough detail and give you vague ideas of how these equations are used in modern science.the authors of the essays assumes you would know certain things but the truth of the matter is that the average person wouldn’t have a clue what they’re talking about. Like i stated earlier, i am a potential physics undergraduate, so i must be studying A level phyiscs, yet the explanations still leave me baffled and frustrated with the content.yes they do give you the general idea what the equations are used for and what is so important about thembut personally i have read better books and have learnt a lot more from other booksI would say the book has a lot of words but doesn’t teach you in enough detail, you can force yourself through the book (like i did) and i dont think you’d be satisfied unless you’ve already learnt these topics in degree level detail and want to refresh your mind of the content.maybe its just mebut I found it pretty dry and dull which made it hard to go though AND I barely learnt anything

⭐Equations and their stories. Never thought that this could be a subject of such a beautiful book. Just read it and you will see it yourself

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