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Alex Through the Looking Glass: How Life Reflects Numbers, and Numbers Reflect Life by Alex Bellos
sil3nos's review against another edition
4.0
This is the best math book I've read to date. But that is only because there was finally something in here that I didn't know of.
Many of the chapters weren't that interesting (although I found the small anecdotes really enjoyable), but the second and the last one were exceptional. I thought the book couldn't get more interesting than when Benford's Law was introduced, but the last chapter introduced a possible reason why our universe exists, so... I guess that was interesting.XD
Many of the chapters weren't that interesting (although I found the small anecdotes really enjoyable), but the second and the last one were exceptional. I thought the book couldn't get more interesting than when Benford's Law was introduced, but the last chapter introduced a possible reason why our universe exists, so... I guess that was interesting.XD
ashrafulla's review against another edition
3.0
This is meant to be a fun book about some of the more whimsical parts of mathematics. The problem for me is that it's too trivial. It's enough to look at the chapter on logarithms. Every three paragraphs ends with "isn't this neat!?" like it's a TV show. That doesn't belong in a book. Books are active engagement mediums, I'm already interested, sentences like those interrupt what is being told. It's the equivalent of breaking the fourth wall.
I'm ok with the higher level descriptions and I believe laypeople can pick up the math. I just dislike the presentation and as a result the book.
I'm ok with the higher level descriptions and I believe laypeople can pick up the math. I just dislike the presentation and as a result the book.
eroston's review against another edition
4.0
I read a bunch of these pop math survey books, and this one is somehow better. Great e examples, and playful language. I haven't read his first, Here's Looking at Euclid, but look forward to it as the title is a five-star pun.
aminowrimo's review against another edition
5.0
Similarly to the first book in the series (loosely termed so), this is a look at everyday mathematics. I enjoyed it as much as the first one.
sometimesdazai's review against another edition
4.0
Every number tells a story.
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Sering dengar kan, dengan perkataan bahwa sebagian kecil orang terkaya menguasai sebagian besar kekayaan dunia? Pernah tau juga nggak, kalo dalam hampir setiap buku yang ditulis, sebagian kecil kata menyusun sebagian besar tulisan? Tapi siapa sangka kalo keduanya dihubungkan oleh konstanta yang sama?
.
Pernah dengar synaesthesia, yang salah satu kondisinya adalah kemampuan melihat angka sebagai warna, atau mendengar nada juga sebagai warna? Angka-angka ternyata membangkitkan bermacam persepsi pada manusia; seperti angka 7 yang diasosiasikan sebagai angka keberuntungan, kekuatan, kedigdayaan; atau seperti angka 4 dan 13 yang dianggap sial. Label harga 199 memberi kesan murah sedangkan 200 terasa mewah. Bilangan ganjil, misalnya, dipersepsikan maskulin sedangkan bilangan genap dianggap feminin.
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Kita hidup di dunia di mana matematika adalah bahasa universalnya. Sebagian kita mungkin mempelajari kalkulus dan menemui natural logarithmic di bangku kuliah saja, padahal sebenarnya, semua itu lebih dekat dari yang selama ini kita duga. Kita hanya...belum mencari tahu.
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Buku ini menjabarkan berbagai pola matematis dan kaitannya dengan kehidupan, mencakup sejarah, takhayul, psikologis manusia, bahasa dan sastra, hingga aplikasinya pada perkembangan sains dan teknologi.
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Hingga klimaksnya adalah, bahwa ternyata telinga kita merupakan pengejawantahan paling dekat, dari transformasi Fourier yang mengkodekan gelombang suara dalam domain waktu menjadi sebuah fungsi gelombang dalam domain frekuensi melalui folikel-folikel koklea; serupa dengan bagaimana MRI mengakuisisi data sinyal listrik dalam domain fase dan frekuensi kemudian mentransformasikannya menjadi domain spasial berbentuk citra. Dan, proses yang begitu rumit dan kompleks ini telah ada puluhan bahkan ratusan ribu tahun lalu sejak “telinga” pertama ada. Lantas, alasan apa lagi yang membuatmu menafikan bahwa ciptaan Tuhan itu sungguhlah amat sangat keren sekali?
.
Sering dengar kan, dengan perkataan bahwa sebagian kecil orang terkaya menguasai sebagian besar kekayaan dunia? Pernah tau juga nggak, kalo dalam hampir setiap buku yang ditulis, sebagian kecil kata menyusun sebagian besar tulisan? Tapi siapa sangka kalo keduanya dihubungkan oleh konstanta yang sama?
.
Pernah dengar synaesthesia, yang salah satu kondisinya adalah kemampuan melihat angka sebagai warna, atau mendengar nada juga sebagai warna? Angka-angka ternyata membangkitkan bermacam persepsi pada manusia; seperti angka 7 yang diasosiasikan sebagai angka keberuntungan, kekuatan, kedigdayaan; atau seperti angka 4 dan 13 yang dianggap sial. Label harga 199 memberi kesan murah sedangkan 200 terasa mewah. Bilangan ganjil, misalnya, dipersepsikan maskulin sedangkan bilangan genap dianggap feminin.
.
Kita hidup di dunia di mana matematika adalah bahasa universalnya. Sebagian kita mungkin mempelajari kalkulus dan menemui natural logarithmic di bangku kuliah saja, padahal sebenarnya, semua itu lebih dekat dari yang selama ini kita duga. Kita hanya...belum mencari tahu.
.
Buku ini menjabarkan berbagai pola matematis dan kaitannya dengan kehidupan, mencakup sejarah, takhayul, psikologis manusia, bahasa dan sastra, hingga aplikasinya pada perkembangan sains dan teknologi.
.
Hingga klimaksnya adalah, bahwa ternyata telinga kita merupakan pengejawantahan paling dekat, dari transformasi Fourier yang mengkodekan gelombang suara dalam domain waktu menjadi sebuah fungsi gelombang dalam domain frekuensi melalui folikel-folikel koklea; serupa dengan bagaimana MRI mengakuisisi data sinyal listrik dalam domain fase dan frekuensi kemudian mentransformasikannya menjadi domain spasial berbentuk citra. Dan, proses yang begitu rumit dan kompleks ini telah ada puluhan bahkan ratusan ribu tahun lalu sejak “telinga” pertama ada. Lantas, alasan apa lagi yang membuatmu menafikan bahwa ciptaan Tuhan itu sungguhlah amat sangat keren sekali?
strangeeigenfunction's review against another edition
informative
2.5
Could have been an average general audience math book but it's quietly sexist and I am not a fan of exactly how it treats ~psychology of numbers. I also just didn't like the treatment of some concepts as well as I have other people's treatments of the same or similar concepts.
Content Warnings
Moderate: Sexism
The chapter on exponential growth involves a speaker who forecasts ecological doom.rlse's review against another edition
2.0
Man, I thought I would love this, but just find myself skimming. Might try again later.
deepakchecks's review against another edition
5.0
A treat for the lovers of mathematics. In each chapter, Alex picks up a mathematical topic explains it thoroughly, going through its definition, history, uses and current relevance and gives the reader a good education. Except for the last chapter 'Cell Mates', which was tough for me to follow, the others were very informative.
In Every number tells a story , a lot of trivia around numbers and its appearance are mentioned. For instance, how people, including pythogarus interpreted odd and even numbers. Odd is considered male and strong; reasons for this include the odd number not getting divided by even numbers and also when an even is added to odd it remains odd, thus depicting a master/male behavior, while even numbers are vulnerable to split and are thus weak and benign.
In East Asia, number 4 means death and hence there would be no floors, seats in aeroplane with this number. Another TIL moment is the realization why sale items are depicted one less than the round numbers (for ex, 399, 499 etc. instead of 400, 500). Non-round large numbers causes us to see these numbers smaller, for ex. when read from left to right 799 appears smaller than 800 and it has also been identified experimentally that people subconsciously associate numbers ending with 9 with bargains.
The The long tail of the law describes a mathematically property known as Benford's law and Power law. Benford's law is an observation of the frequency distribution of leading digits in many real-life sets of numerical data and is used in fraud detection. Power law describes functional relationship between two quantities, and there most prominent example of this law is the animal size proportionality.
In Love Triangle , the importance of triangles, including the revolutionary trigonometric functions sine, cosine tan are explained along with its extended uses such as in prosthaphaeris (the use of add/subtract instead of multiply) and Napiers log. This has revolutionized cartography, one big example is the Great trigonometric survey of India conducted under the command of George Everest, who found that Everest was the highest peak, before which that title was accorded to Chimborazo in Ecuador.
In Cone heads , the properties of ellipse and how it came about to define planetary motion is explained, while parabola and its ability to focus, have been used in microscope techniques of spies, TV sound engineers and birdwatchers. Also before advent of electronic calculators, nomograms (using geometrics and graphs for problem solving) were used for calculating.
Bring on the Revolution is about circles and waves. Did you know how pi = 3.14 came about ? In every circle, circumference / diameter = 3.14. The fourier series was an important discovery, that simplifies sound and makes it theoretically possible to play a Beethoven in tuning fork, that is indistinguishable to orchestra. Switching sound wave from time domain to frequency domain makes it easy to capture and thus came the mp3s. In fact, Dolby software turns sound waves to sinusoids and thus help make the necessary edits and enhancements.
In the event of exponential growth, the 'doubling time' is identified using the rule of 72 (72/x). Plotting the exponential growth chart, the mathematical measure of steepness (change in height/change in distance), also known as gradient is an important factor. There is a constant value 'e', where the gradient and the height is always equal and has the value 2.718 and this is referred to as the exponential constant. In All about e , this is the number that is discussed. There are lot of equations and situations that use 'e', some of them are :
* Calculating the exponential decay y = 1/e^x (gradient is negative of height)
* Catenary - correct geometry of a string hanging from 2 points. When upside down, most stable shape for free standing arch - e^(ax) + e^(-ax) / 2 - used in architecture
* Secretary or Marriage problem - maximize your chances of choosing best match is to interview /date, 36.8% (1/e) candidates.
Negative numbers are discussed in The power of negative thinking . Another TIL moment is realizing that negative * negative = positive servers only to make the arithmetic coherent, but has no meaning beyond the system. An interesting proof proving this is as below:
- 3 * -2 = -6
(4-1)* -2 =-6
-8 * (-1 * -2) = -6
(-1 * -2) = 2
A historical trivia: Algebra (from al-jabr, meaning restoration) and algorithm were derived by/from Muhama ibn Musa al-Khwarizmi
One mathematical item that flummoxes pretty much all Indian students is the Calculus. In Professor Calculus , this property is explored. Although it was Newton who initially identified the use of Calculus, he used the flexions, but Leibniz defined it more clearly and used the term calculus integralis which stuck. In short, Integration for calculating area while differentiation is for calculating gradient (infinitesimal small change). Another TIL, is the fact that the initial roller coaster models caused head and neck injuries, because the correct shape/speed to be used while moving from straight to a curved track was not identified. Later the shape Clothoid was introduced to roller coasters, using Stenger's principles, in the 1970s that helped avert such injuries.
In The titl of this chapter contains three Erors , the author describes the various principles, including the use of theorems and proofs, initially used by Euclid and how it has become a standard system to prove mathematical concepts. With technological assistance today, proof assistant are used in computers to verify proof.
In Every number tells a story , a lot of trivia around numbers and its appearance are mentioned. For instance, how people, including pythogarus interpreted odd and even numbers. Odd is considered male and strong; reasons for this include the odd number not getting divided by even numbers and also when an even is added to odd it remains odd, thus depicting a master/male behavior, while even numbers are vulnerable to split and are thus weak and benign.
In East Asia, number 4 means death and hence there would be no floors, seats in aeroplane with this number. Another TIL moment is the realization why sale items are depicted one less than the round numbers (for ex, 399, 499 etc. instead of 400, 500). Non-round large numbers causes us to see these numbers smaller, for ex. when read from left to right 799 appears smaller than 800 and it has also been identified experimentally that people subconsciously associate numbers ending with 9 with bargains.
The The long tail of the law describes a mathematically property known as Benford's law and Power law. Benford's law is an observation of the frequency distribution of leading digits in many real-life sets of numerical data and is used in fraud detection. Power law describes functional relationship between two quantities, and there most prominent example of this law is the animal size proportionality.
In Love Triangle , the importance of triangles, including the revolutionary trigonometric functions sine, cosine tan are explained along with its extended uses such as in prosthaphaeris (the use of add/subtract instead of multiply) and Napiers log. This has revolutionized cartography, one big example is the Great trigonometric survey of India conducted under the command of George Everest, who found that Everest was the highest peak, before which that title was accorded to Chimborazo in Ecuador.
In Cone heads , the properties of ellipse and how it came about to define planetary motion is explained, while parabola and its ability to focus, have been used in microscope techniques of spies, TV sound engineers and birdwatchers. Also before advent of electronic calculators, nomograms (using geometrics and graphs for problem solving) were used for calculating.
Bring on the Revolution is about circles and waves. Did you know how pi = 3.14 came about ? In every circle, circumference / diameter = 3.14. The fourier series was an important discovery, that simplifies sound and makes it theoretically possible to play a Beethoven in tuning fork, that is indistinguishable to orchestra. Switching sound wave from time domain to frequency domain makes it easy to capture and thus came the mp3s. In fact, Dolby software turns sound waves to sinusoids and thus help make the necessary edits and enhancements.
In the event of exponential growth, the 'doubling time' is identified using the rule of 72 (72/x). Plotting the exponential growth chart, the mathematical measure of steepness (change in height/change in distance), also known as gradient is an important factor. There is a constant value 'e', where the gradient and the height is always equal and has the value 2.718 and this is referred to as the exponential constant. In All about e , this is the number that is discussed. There are lot of equations and situations that use 'e', some of them are :
* Calculating the exponential decay y = 1/e^x (gradient is negative of height)
* Catenary - correct geometry of a string hanging from 2 points. When upside down, most stable shape for free standing arch - e^(ax) + e^(-ax) / 2 - used in architecture
* Secretary or Marriage problem - maximize your chances of choosing best match is to interview /date, 36.8% (1/e) candidates.
Negative numbers are discussed in The power of negative thinking . Another TIL moment is realizing that negative * negative = positive servers only to make the arithmetic coherent, but has no meaning beyond the system. An interesting proof proving this is as below:
- 3 * -2 = -6
(4-1)* -2 =-6
-8 * (-1 * -2) = -6
(-1 * -2) = 2
A historical trivia: Algebra (from al-jabr, meaning restoration) and algorithm were derived by/from Muhama ibn Musa al-Khwarizmi
One mathematical item that flummoxes pretty much all Indian students is the Calculus. In Professor Calculus , this property is explored. Although it was Newton who initially identified the use of Calculus, he used the flexions, but Leibniz defined it more clearly and used the term calculus integralis which stuck. In short, Integration for calculating area while differentiation is for calculating gradient (infinitesimal small change). Another TIL, is the fact that the initial roller coaster models caused head and neck injuries, because the correct shape/speed to be used while moving from straight to a curved track was not identified. Later the shape Clothoid was introduced to roller coasters, using Stenger's principles, in the 1970s that helped avert such injuries.
In The titl of this chapter contains three Erors , the author describes the various principles, including the use of theorems and proofs, initially used by Euclid and how it has become a standard system to prove mathematical concepts. With technological assistance today, proof assistant are used in computers to verify proof.