#Weapons_of_Math_Destruction - Cathy_O'Neil - #Review

There is no mathematics, though, rather it is all Statistics and the apprehension associated with Big Data when it comes to application either through AI or ML. Most of the time we may agree with almost all of the author’s views but there is no algorithm anywhere as the title suggests, and instead O'Neil takes us on a tour of a collection of business and public policy malpractices, stating that the solution is to "encode values into our algorithms.". This might really be useful for some. With a few real stuff inside I think it would be an excellent book for those with skills and interest in social justice to take to an interview with Big Data firms.

    Still, I am inclined to think this book is best targeted to thoughtful high schoolers and college-aged students who are thinking about planning their careers, who have a penchant for mathematical and computer modeling. You may be able to conclude the effect of:

 # Targeted advertising, especially the way it allows predatory advertisers

# Predictive policing, with equality before the law replaced by an algorithm that sends different degrees of law enforcement into different communities.

# Automated algorithms sorting and rejecting job applications, with indirect consequences of discrimination against classes of people.

# Poorly thought-out algorithms for evaluating teachers, sometimes driving excellent teachers from their jobs.

# Algorithms that score credit, determine access to mortgages and to insurance, often with the effect of making sure that those deemed losers stay that way.

 Some of these are broken down chapter wise:

        After teaching math at Barnard College for several years, O’Neil left Academia for a new “laboratory”—the global economy. As a “quant” (quantitative analyst) for D.E. Shaw, a major hedge fund, she was amazed by how the operations she and her team performed each day translated into “trillions of dollars sloshing” between accounts. But in the fall of 2008, everything changed and the financial crisis brought the economy to a halt.

     The Big Data economy emerged as mathematicians began calculating human potential (as students, workers, lovers, criminals), but its math-powered algorithms were encoded with their creators' human prejudices and biases. Despite deepening the global wealth divide, Big Data seemed unimpeachable. Author O'Neil calls these harmful models "Weapons of Math Destruction." While baseball statisticians also use complex, game-defining models, those models are transparent, offering everyone access to the statistics that rule the sport.

    Human beings carry models in their heads all day—as an example, O’Neil uses the “informal model” of how she decides what to cook for her large family each night. She has data (each person’s likes and dislikes), and she has new information concerning that data all the time: fluctuating grocery prices, changing tastes, and anomalies like special meals for special occasions.

     Prosecutors in Harris County are three times more likely to seek the death penalty for Black people. And sentences imposed on Black men (who comprise only 13% of the U.S. population yet make up 40% of the U.S.’s prison population) are 20% longer than those for white people.  The three elements of a WMD, according to O’Neil, are opacity, scale, and damage.

     To illustrate the scale of a Weapon of Math Destruction (WMD), O'Neil asks readers to imagine the "caveman diet" becoming a mandatory national standard for all 330 million Americans, creating a distorted economic climate. This large-scale distortion is what happened to higher education when the U.S. News & World Report, in 1983, began ranking approximately 1,800 colleges based initially on opinion surveys. The rankings, which attempted to statistically measure "educational excellence," created a "rat race" in U.S. academia.

     Big tech platforms like Google and Facebook allow for-profit universities to segment and target vulnerable populations with ads based on A/B testing, similar to massive credit card mailings. These ads often use fake job postings or misleading promises (like routes to food stamps/Medical aid) to gather user information and send it to recruiters. Separately, after police force cuts in 2013, Pennsylvania's police chief invested in PredPol, a Big Data crime prediction software. This system used historical data to forecast crime hotspots, and within a year, burglaries in vulnerable areas were down by over 20 percent.

     While human programs like stop and frisk (a program in which NYPD offers were given the go-ahead to stop, search, and frisk anyone who seemed suspicious anywhere at any time) have created friction and danger in vulnerable communities, mathematical models now dominate law enforcement. The author suggests justice system data scientists must understand the realities inside prisons (like solitary confinement, rape, and malnutrition) and instead study how improvements—such as better food, sunlight, and educational programs—could impact recidivism rates. Similarly, Human Resources departments rely on automated processes to screen resumes, forcing jobseekers to adapt their writing to the algorithms' prioritized buzzwords. The overall issue is that WMDs (Weapons of Math Destruction) often serve unfair objectives instead of helping people.

     American workers have coined a new idea: “clopening” -closing and opening, and refers to when an employee works late closing one night and comes in early, sometimes just a few hours later, to open up shop the next morning. U.S. government data shows that over two-thirds of food service workers and over half of retail workers find out about scheduling changes with less than a week’s notice.

     Modern-day scheduling technology is rooted in the discipline of applied mathematics called “operations research” (OR). Mathematicians used OR to help farmers plan crop plantings. During World War II, OR was used to help the U.S. and British militaries optimize their resources. After the war, OR was used in manufacturing and supply chain logistics, and now it underpins huge companies like Amazon, FedEx, and UPS. But these models exploit workers, bending their lives to unfair schedules. Optimization programs are everywhere now, and they’ve contributed to the creation of what O’Neil calls a “captive workforce.”

    Local bankers, who knew their neighbors and their backgrounds, previously controlled lending with a human, intelligent judgment. Now, companies like Neustar use metrics like location and internet history to assign "e-scores," creating destructive and biased feedback loops that move society away from fairness. Instead of slowing down to allow for greater human oversight, the tech world is doubling down on predictive models. For example, Facebook has patented a credit rating system based on social networks that can unfairly privilege a person (e.g., a white, connected college graduate with no credit) while penalizing a hardworking person (e.g., a Black or Latino housecleaner) whose social network may include unemployed or incarcerated friends.

     In 1896, a German statistician named Frederick Hoffman, who worked for the Prudential Life Insurance Company created a WMD. He published a 330-page report claiming that the lives of Black Americans were so precarious that “the entire race was uninsurable.” It was he who first correlated smoking with cancer! However, like many other WMDs, Hoffman’s analysis was statistically flawed, racist, and unfortunately widespread.

     In 2015, Swift Transportation, the largest U.S. trucking company, installed dual-facing cameras in long-haul trucks to reduce accidents and insurance costs. This also allowed them to gather data to optimize profits and compare drivers. Now, insurance companies offer regular drivers discounts if they share data via a small, in-car telemetric unit. Similarly, companies like Michelin and CVS have implemented wellness programs that charge employees extra for failing to meet goals (like glucose or cholesterol targets) or for refusing to report their health data. Finally, the author notes that posting a petition for tougher WMD regulations on Facebook means the site's algorithm controls who sees it, based on its existing data about one's friends.

     During the 2010 and 2012 U.S. elections, Facebook created experiments to hone a tool called the “voter megaphone” that would allow people to spread the word about voting. Facebook was encouraging over 61 million American users to get out and vote by leveraging peer pressure against them. Because the profits of companies like Facebook, Google, Apple, Microsoft, Amazon, and Verizon are heavily regulated by government policies, these companies often spend a lot of money lobbying and donating to the political system. Now, they can influence Americans’ political behavior and, as a result, the shape of American government.

     Rayid Ghani, one of the campaign’s data scientists, when Obama was presidential candidate had previously worked on projects for a consulting that analyzed grocery stores’ consumer data. This information was used to create customized shopping plans for many kinds of shoppers: coupon-clippers, brand loyalists, foodies, and so on. Now, Ghani was trying to see if similar calculations would work on swing voters. The shoppers who switched brands to save a few cents often behaved like swing voters.

     The main difference between the WMDs of the present and the prejudiced human error of the past is simple: humans can evolve, learn, and adapt. But automated systems are stuck in time—engineers have to change them as society progresses. So essentially, “Big Data processes codify the past” rather than inventing the future. Only humans have the “moral imagination” needed to create a better world. 

 

#Quantum_Physics_Made_me_do_it - Jeremie_Harris - Review

There have been so far relevant guides to the most paradoxical notions proposed around quantum world throughout the last century. Some cut out the unnecessarily complex way of explaining concepts, and this one really hits its mark in terms of being the perfect introduction to quantum mechanics and the questions that arise from it for complete novices or for those looking for a light-hearted science reader. The book happens to be packed with science and excellent discussions on the repercussions for humanity if certain theories are in fact correct but fails midway when the author switches over to criticizing other writers. Here is the brief break-up as we move through the books.

    The author explains that the most scientists have misunderstood how nature works. To begin with the author, Harris, starts with Youngs double slit experiment giving due credit to Max Planck on Quanta and then goes over to Schrodinger and Heisenberg’s theories.

    The use of Kats has always been confusing when describing quantum states. Using illustrations and simple points like, | ¶ > | ↑ > + | ↓ >, Harris goes on to explain the probabilities that are confusing the scientific minds and ends up with Schrodinger’s cat experiment on collapsing that forms the ultimate basis of quantum mechanics.

    That Einstein did not like randomness formed part of debate with Bohr and if we really looked hard enough we would actually discover that random experimental outcomes are controlled by variables we aren’t aware of! Thus, consciousness-based QM was born and the author, therefore, illustrates that Multiverse exist and vanish (with Kats, of course).

Here are some extracts from the chapters:

    When consciousness collapses the physics around should also. Ancient Egyptians used to treat tooth aches by killing rats, grinding them and applying them over the affected place.  What mouse paste is to dentistry is to invention was before brush. Using microscope of observation in kats is discussed - shouldn’t microscope also exist at various states

Neumann showed that there is no cut off between big and small.

    Science treats world as it if it is made of up of inanimate objects but consciousness is s subjective thing. Deepak Chopra with almost 80 books and over 80 million copies sold is fully criticized because his receipt includes gimmicks using Quantum age physics that works with new age meditation stuff for gullible audience. Quite similarly another author, Amit Goswami, who said electron does not exist before it was observed, is also denounced. Kets again with observer and light!

There is nothing wrong with being wrong.

Schrodinger and big bang would look alike!

Free will and do we have it?

    Goswami again - consciousness becomes the source of all your decisions and make those decision by selecting possible timelines to collapse into existence

    Collapse without consciousness - Kat diagram on spontaneous collapse. Free will and the law of quantum world. Brain cells – signals are made of tiny quantum particles so they can exist at many places at once and collapse into one location. If deontology won’t do, then what are your other options?

    Quantum Multiverse and Dunning Kruger effects – people tend to overestimate themselves. About 65% of Americans think that they are more intelligent than average.  If you can calculate the time for a 30 g ball to fall to the ground from a height of 1.5 m, you can develop superiority complex!

    Kat again! On climbing Mount Everest, but ever thinking about zombie cat? Dead and live cat - enter academic politics - Bose idea. A world of small things which can exist at many places at the same time and big things which can’t. This was Einstein versus Bose dialogue.

     Why do I have to empty water bottle on this stupid flight? 10 octillion cells come together to make your body. Its presence in the universe. Universe is probability from physics to biology and vice versa. It talks about Femi paradox, which says aliens do exist of Multiverse in a particular religion story. You probably believe in it to the exclusion of others and all others or false.

Kats on quantum suicide! We can’t experience being dead is a state. We experience life as a series of digital moments, and in each moment, we feel complete existence in a particular moment. The Mandela effect is unrelated to his death, but it is about winning a lottery after surviving three lightning strikes!

    About chemistry on atoms, if they existed to figure out electrons in the orbital refinement, clarity and confidence go together. General discussion on nuclear weapon program leaves, MAGA theory and Saddam Hussain in relativity.

Bohemian mechanics again, double slit experiment in a duet discussion.

 A little philosophy is a dangerous thing, fatalism

    Physics has any kind of explanation for emergence of consciousness. Plants consciousness, feature of consciousness.  AI needs data processing power and model and use this to learn calculus in the era of AIGPTx. We are offloading more and more of our thinking to machines. Who is to blame when something goes wrong? The free will has to be informed, at least by quantum physics doing physics.

 If you can make out the connections between the lines given above, then the book is a good read!

 

#Humble_Pi: A comedy of Maths Errors - #Matt_Parker - Review

    This is certainly the first book I have ever read in which page numbers start from higher to lowest. And it has been done to justify the title (a comedy of maths errors). The book is filled with informative and relentlessly entertaining matter right from the beginning and has illustrations that are related to real-time incidents. The author explores the series of glitches, near-misses, mathematical mishaps leading to severe bugs over the PCs or internet, chunks in big data, logic in street signs, the chances over winning lotteries and bizarre ways the maths can equip or trip us. The book is well organized so that similar themes are framed together into chapters, but each incident is only a few pages long so that it never gives a feeling of bogged down or boring.

     

    There are surprises with some punchlines that are explained in a way that they would actually be only one of the things that would be needed to go wrong for the whole thing to come crashing down. The author explains that sometimes stuff ups are necessary, rather than just tragic accidents. Progress in science and engineering often involves someone needing to go beyond the cutting edge, on to the bleeding edge. The mistakes were thus costlier that would have been avoided if there was no complacency in making decisions.

 Here is the brief break-up of the book, chapter-wise:

    The number 4,294,967,295 was the most attractive one the author mentions in the first chapter, more so because for a few pages it was kept suspense before revealing to us that this happens to be the 32-digit '1's full capacity (in binary form), attaining which, any system would restart. Quite similar to BSOD, the dumping of memory and the micro-second timed restart of the PC went unnoticed in California’s airport, leading to loss of radio connections with almost 800 aeroplanes. Now that this memory has been replaced with 64-bit ones, it might take 584.9 million years for the system to restart upon reaching the maximum limit of that capacity by a memory device! 

The subtle account of Earth’s rotation around the sun has been considered for accuracy calculations of periods. The difference between sidereal and tropical year has been discussed thus. There is this mention about the Y2K38 bug that would make microprocessors stop working on 19^th January 2038 for the same reasons mentioned above. The info that February 1847 has 31 days did not prove to be true when the author asks the readers to check their iPhones for this ‘feature’. Probably it has been corrected.

    The next chapter is an elaborate account on Engineering mistakes with ample examples that I never thought would be the result of miscalculations. A building in Fenchurch London designed with a sweeping curve behaved like a massive concave mirror in a season such that it set fire to everything that came in its way of convergence.  A few suspension bridges in UK had matched severely with a frequency of 1 Hz leading to wobbling and collapsing. It was Boston tower that collapsed when 167^th person entered it, a threshold for the frequency mentioned as the bolts and nuts used had an individual capacity bearing (approx. 9280 kg, integrated). We are considered as approximation machines and maths can get us to correct values.

            That some English names have been making us go crazy is well known and Steve Null was a name whose entry was often non-existent wherever he tried to enter. So it was important that the names are well defined (reserved words). Similarly, the flaws in open spread sheets in excel is mentioned with some examples. A similar incident with data entry led to vanishing of war in Afghanistan!

    A wrong design of a road signal in UK was brought to notice legally by a person as he found that the football image over the signal light was not in tune with a regular one where one pentagon is surrounded by hexagons. The author goes on to describe the efficacy of bee-hive type structures.  The Apollo program’s space craft had a door that opened inside, finds a vital mention to prove the structural efficiency.  Similarly, the ‘Challenger’ disaster had a design flaw. Richard Feynman who was in the inquiry team demonstrated that the O-rings (rubber gasket), that separated two fuel tanks, failed to spring back when the temperature was cooled to ice’s. Though a simple one, the place it was used has a significant impact that was not rightly addressed. A brief discussion on gears and mechanism ensues till the end of this chapter.

    Someone going to gym was very particular about the number of days in a week. Though the concept is silly, but in a month as weeks get repeated working every alternate day would actually let you do so four times a week! A few pages are devoted to McDonald’s menu in which some combination of the menu legends did not mean breakfast or meal. The customer once chose such a combination on flavours and refused to pay on par with meal in the menu as prescribed by the outlet. The number of ways to arrange these eight menus are given as 8x7x6x5x4x3x2x1=81. 

The number of digits on zip codes is discussed with regard to USA. A game on M K Gandhi, who is revered in India, was responsible for losing the reputation merely because the game ‘Civilization’ treated a number 255 as aggressive. Downloaded and played by more than 33 million, a 1-2 subtraction was resulting in '255', which was a flaw in binary system. Remember 255 contacts as the limit in WhatsApp? (256 being the order of 8-bits). This 255-type problem was there with Swiss rail system as well. The author writes that this rail network was probably the only one which issued bureaucracy patch rather than software – 256 axles should not be engaged in the system. 

The 256- error was a life taking issue with Therac-25 a medical radiation device which was used to treat cancer patients with electron beam bursts. A setup required a routine check-up as class 3=0. A subroutine would slightly activate whenever the class was zero and the beam would fire the electrons. Unfortunately, it was 8-digit binary number which should roll back to zero after it had maxed out. Every 256^th time it would roll back 0.4% of time to skip running. This error led to continued bursts resulting in the death of a patient in 1987.

An interesting truncation error that was encountered during the first Gulf war. Every time a 'Scud' was fired 'Patriot' would destroy it before it reached the target. Due to a mathematical oversight in ‘Excel’ the fraction of 1/3^rd of a second was omitted leading to a lapse of about 500 meters. This accumulated calculation error misled the Patriot, and it could not fire on time. The software error was later located, patched up and imported from US for later use.

A large number of examples on probability can be found in this part of the book which is titled ‘probably wrong’. A woman was wrongly sentenced twice in UK due to statistical error. The work out was there but it did not evince any interest in me. Factors like these were also documented when using dice and lotteries. But the probability of error with regard to the Columbia shuttle drew my attention. When Feynman was inquiring into its disaster, he was told by over-confident engineers that the probability of errors was like 1 in 100000. Feynman put it as ‘it would mean a daily launch of the shuttle for 300 years with only one disaster', and which was probably improbable. That was just some data like 46087 road deaths were in USA in spite of them driving about 1838240000000 miles that year!

    Putting money where your mistakes is all about stock exchange and commerce related.  On 8 December 2005 the Japanese investment firm Mizuho Securities sent an order to the Tokyo Stock Exchange to sell a single share in the company J-COM Co. Ltd for ¥610,000 (around £3,000 at the time). Well, they thought they were selling one share for ¥610,000 but the person typing in the order accidentally swapped the numbers and put in an order to sell 610,000 shares for ¥1 each. They frantically tried to cancel it, but the Tokyo Stock Exchange was proving resistant. Other firms were snapping up the discount shares and, by the time trading was suspended the following day, Mizuho Securities were looking at a minimum of ¥27 billion in losses. It was described as a ‘fat fingers’ error. 

    The world’s most expensive book ‘The making of a fly’ was purchased by the author. What made it so expensive? Well, the seller used algorithm that raised the price of the book each day by 26.8% when the buyer visited the site.  It was a whopping 23,698,000 USD! After Stocks and Commerce, political issue finds a way into the book. The election in Schleswig Holstein where an MP can get seat only if he scores 5, got a breakthrough when his actual number 4.97 was rounded off to 5. Trump also gets a mention.

 Salami slicing is the term used when something is gradually removed one tiny un-noticeable piece at a time.

Because we had no accurate clock in the 1917 someone might have actually run faster than the present-day athlete whose clocks now show accurate times.  When the US switches all coal power to solar it would save 51999 lives - roughly 52000 lives, and each life matters. 13.8 million years do not mean 13,800,003 years when mentioned 3 years later. In view of all the above a round-about is always essential but with a caveat. R Sikdar of Kolkata actually calculated the tallest mountain, but GTS which was run by someone not aware of minute details about calculations, ignored the value and put forth the name of Everest so that this became the tallest mountain in the world!

Hubble Space Telescope was put into orbit in 1990, and its first images were blurred - out of focus due to mirrors’ wrong shape. The wrong paraboloid 1G to 0G lead to edges of 2.4 m mirror - about 2.2 µm longer. The correction was carried out in the repair mission.

Mecca of mistakes carries the photo of Mecca over a mobile phone having a compass app on play. The direction is not straight towards it, but rather tilted. Due to small uncorrected errors proper west is not thus shown. Similarly, a small error in a flight windshield bolts A211 had two almost similar notations - 7D and 8C. A lot of difference was there in size at the micro level. A BAC 1-11 jet liner of British Airways fixed wrong bolt and during the flight the wind screen exploded outward. The chronology of this event, right from checking to take off is mentioned in great detail showing the ignorance of the minute mathematical error leading to major accident when the pilot was flown out!

The conventional unit mistake, often quoted in many books, when in 1998 NASA’s Mars Climate Orbited flopped due to discrepancy in units, finds a mention.

The funny thing about British prime minister was a question “how long has Theresa been pm?” and the engine threw an answer 1.72 trillion pm! PM was for minister and the pm it mentions is ‘Pico-meter’!

Aircraft fuel is calculated in mass and not in volume. Flight T143 of Air Canada was wrongly fuelled but accident was avoided during a cross check. The two-way connection from the aircraft’s two wings over a common sensor circuit is discussed clearly and was a pleasure to read.

Defining average has always been a serious task, particularly in Australia. An average Australian meant a 37-year-old living with a spouse and two children and to fit this data a man at a place emerged from nowhere during a survey. There are often incidents of people appearing from nowhere, just like people disappearing. The concept of average gets a go all along this chapter. Fitting of clothes with average in mind is another example when dress makers carry out the region wise average assessment. Some statistical measurements have more than one formula to produce desired result and many examples are quoted in this chapter.

Sampling bias like conducting a survey about what people might think of modem tech but only accepting submission by fax, makes a lighter read of the bias. A negative result from a drug trial is twice as likely to remain unpublished as positive result (should be published).  In 1980 anti-arrythmias drug trial was conducted whereby out of 48 patients, 9 died but only 1 of the 47 given placebos died.  And it took 13 years for this fact to get published. It is in Maths that you can find any pattern you want as long as you are prepared to ignore enough data. 

Direct correlation between the number of mobile phone towers and number of births in UK was fun to read - with every tower 17.6 birth was recorded. Woolworth a chain shop went bankrupt, the GPS coordinates of 800 ex Woolworth was downloaded, and they revealed a kind of equilateral triangle between nearest locations, and it was illustrated for us to understand. The author mentions that everywhere the triangular pattern was found the Woolworth went bankrupt. Did Aliens help?

Totally Random: Netscape navigators id generation was random so was IBM’s randomness calculation about any id.  Chrome had to fix a random number generator because math.random, a java script they used was returning used numbers after few million tasks. It was then that the chrome download was shown as zero even though thousands downloaded it.

Three things are certain in life: death, taxes and people trying to cheat on taxes.

If you can write a short computer program to generate s sequence of numbers, then the sequence cannot be random – Kolmogorov complexity.

    ESA’s Ariane 5 in June 1996 went on self-destruction mode 40 seconds after launch. Inquiry revealed that the on-board computer tried to copy a 64-bit number into a 16-bit space. The space craft was using an old sensor meant for Ariane 4. This tracked the rocket based on inertia and as the space exceeded the available space, the SRI (Inertial Reference System) device which gets raw data to convert into meaningful one calculated that the trajectory was different, and it meant that rocket was going haywire. To avoid debris damage in the residential area the self-destruction mode, programmed inside, was invoked and it blasted the entire system over the sea. 

There was this case of University of North Carolina not able to send mail to far off places. it was a problem with sendmail.cf and is a classic case of a program trying to digest data that was not intended for it. More than 500 miles, an update set the things right.

So, the advice to the programmer is to recheck and reverify the code that is written. The metaphor the author uses at the end of the book is hot Swiss cheese, that is, there are always holes, you need to make sure that the holes in your defences don't all line up or rather line up when you want a get-through. If you are smart, the challenge is to create something that will be as close to fool proof as you can, rather than blaming people afterwards for not using it properly.

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#Infinite_Powers: The_Story_of_Calculus-The_ Language_of_ the_Universe - #Steven_Strogatz - Review

     Often, the public thinks that scientific breakthroughs happen when lone geniuses discover something new, but in reality, discoveries occur when people improve upon the work of others. In ‘Infinite Powers’ Strogatz traces the methods used by Archimedes and moves on to Newton and Leibniz, who refined the use of calculus. Along the way, with plenty of illustrations and interesting insights we get to know about contributions from Fermat, Galileo and Descartes. This apart the contributions of Indian, Arabic, and Chinese mathematicians is also included, and the 'Infinite Powers' continues on to Fourier, Katherine Johnson and Sophie Germain.

    We even get to see how calculus is being used today to treat HIV patients, to create microwaves, and help the 787 fly. The Infinity concepts start with Pizza proof – based on radius, if the one with larger radius is suitable for getting more of it (One 18-inch pizza or Two 12-inch, which is greater?). Well, the one 18-inch has more pizza! This is shown in the light of a curvy top having a length equal to half the circumference - C/2.  So, a parallelogram made of inverted cuts will be flatter if the number is more (infinite) Then A=R*C/2; 1/3=0.333 and the discussion on infinity thus continues.

In the following passages, important mentions of the book are listed in the order of chapters.

    Infinite polygons have flatter outcome – For a circle where the number of polygons take the denominator, like 6/0.1=60 or 6/0.01 is 600 (6 being constant) it would be indicative that smaller the number (polygons) bigger is the answer. As the denominator approaches zero the answer becomes bigger and bigger so that we cannot divide by zero any more to avoid a value going big!

    Likewise, Zeno’s paradox carries a similar concept. Every single step you need to talk would require a half of that step so that it can be expressed as: 1+0.1+0.01+0.001 +….=1.111 sec. This is equated with Achilles concept where it would take 10+t to catch-up a tortoise (t is time).  Zeno meets Planck’s length root h/C³ (10^-35m). If one takes a large possible distance – say diameter of the Universe - and divide by smallest possible distance (h), the most one would need to express becomes obvious.

    iPhone tracks the distance covered while walking using calculus – length of the stride multiplied by the height of the person is the distance travelled (in km). Similar idea is applied to calculate circumference of each step which is a fine straight line; pi=C/d.

    Many circle-ellipse-parabola drawings and segments are found in the third chapter of the book. For instance, the Quadratic parabola = 1+1/4+1/16+1/32, illustration was intuitive. An animation for facial surgery and Avtar’s (movie) face carry great level of polygonal details, and this became extravagant when this was the first instance to use polygon for creating faces. Use of rotating screw for propelling goes back to Archimedes.

    Laws of motion: Knowledge of what comes from a moment into existence and then perishes – Plato on objective geometry. The apparent position of the stars -parallax - finger shifting sideways when you view with an eye closed – Galileo, Copernicus, Aristotle and Ptolemy get due credits for using calculus in letting us know where we are weighed up in the Universe.

    Water clock invention was also based on calculus and the law of odd numbers gets a mention:1+3+5+7=16 which is 4 squares (4²) likewise, 1+3+5=9 which is 3 squares (3²). This concept is explained diagrammatically with good figures.

        Swings take same amount of time and only the speed varies! This was first checked by using Chandeliers in a Cathedral. This was later confirmed in the case of stars and our own Earth which has an elliptical orbit thus getting to roll speeder at the Perigees! Kepler who had damaged vision and hands due to smallpox, did works for establishing laws of planetary motions. Over elliptical orbits equal areas cover equal times, so planets have to move faster at places thus do not have constant speeds. The closer they get to the sun the faster they move.  T²/A³ is same for all planets – T is the time, and A is the average distance from the sun. Thus T²=A³ for Venus it is about T² 0.378 and A³=0.378.

Latitude can be ascertained by looking at the Sun or Stars, but longitudes have no counterpart. Galileo helped solve it and found that fifteen (15) degree longitude translates to 1000 miles at equator – Navigation by Huygens in creating a position of the pivotal point amidst a traverse used the concept of Calculus.  GPS uses at least 4 of the 24 satellites (orbiting at 12000 miles over head) for this purpose – Time received vs time transmitted in GPS would not be possible without calculus. Wireless or GPS to atomic clocks that use Cesium atoms use calculus. 

    Dawn of differential calculus discusses the aspect of Algebra meeting geometry. For instance: An XY plane expresses relationship between two parameters and a simple example includes number of slices taken vs calories consumed with a bread; thus Y=200X.  Through equations shapes are arrived at and Descartes and Fermat used this concept in studies leading to optimization of how to do things in the best possible way. This way designing of boxes to stuff as much gold as possible is described using a simple geometry in metric values:  10x10x25=45 (adding boxes) or 10x10x25 = 2500 (getting volume) but in the place of above if 15x15x15 size is used, it might give a volume of 3375 which is better room compared with 2500 (which means change is geometrical parameters for getting best volume).

    Fermat helped FBI which had millions of records of fingerprints storing and retrieving them through calculus - quite similar to JPG and MP3 formats retrieval using the algorithm. This chapter also includes the concept of bending of light that helped Snell arrive at his famous formula for refractive index.

    In Crossroads it was a pleasing aspect to see that a Function of function is power function.  And thus, an Exponential function would help one arrive at how bacteria multiply. Likewise, Logarithm is used for non-round numbers, and this enables us to write any positive number as powers of ten. Exponential growth and decay mechanism, similarly, use the same concept and is applied to reduce noise off a microphone when it picks up the sound of its own speaker. This is the same with nuclear chain reactions.

    In a further explanation on the Y and X factors the author clearly explains what dy/dx actually mean; for instance, it is (-velocity) that is rate of speed. Dy/dt is acceleration on a graph of distances and against time for a moving car the slope is indicative of a car’s speed – universal rate.  Area under the curve is important factor.  Linear function of the constant rates for instance in the case of slice, 400 calories/2 slices is 200 calories/slice. Many aren’t aware of using calculus dy\dx curves for velocity which can give distance covered. 

    Infinitesimal piece of curve as parabola helps us to understand a couple of caveats about derivatives. A curve with V shape is exampled with a sharp corner at one point and when we zoom into it, it will look like a corner. However, if it is a curve, it might not look like a corner.  Derivative as rates of change of day length help us to know how much extra sunlight a year can be obtained. Usain bolt Running style and slowing down near the end point leading to losing the first place is an example of this derivative application. 

    Leibnitz introduced the word calculus which means small stone. Incidentally, Newton and Leibnitz had these calculi (stones) in bladder and kidney, and it is written that the former died of this stone in bladder.  Integration is global operation instead of microscope we are using telescope and peering far off into the future (past?). The concept of pi gets a cue - 3.14 corresponds to 3+10⁰+1(1/10)¹ + 4(1/10)².   

    Mathematician from Kerala solved power series related to cosine and sine. Jyestadeva and Nilantha attributed the set to Madhava (1350-1425) in what is Kerala school of Mathematics and Astronomy today. Newtown had mashed up work of Greeks, Islamic Algebra and French geometry for arriving at infinity principle.

    Fictions of the mind: Infinitesimals supposed to be the tiniest number, smaller than everything but greater than nothing! For instance, 2³ is 8, but (2.001)³? Algebra has answers for that; x+dx may be used to get at (x+dx)³ or using Pascal’s triangle it can be arrived at 8+12 dx+6 dx² + dx³.

    Differentials can also be used to describe the fundamentals of the calculus; Upshot of dA=ydx=f(x) dx. Altimeter for measuring the altitude lot of number fractions illustrated with a grand sketch.  The author goes on to justify that finding HIV with assistance from calculus dV/V=-cdt was possible with greater accuracy based on the above principles. Similarly, estimation of virus mutation (at every genome) was also done using calculus.

    The calculus comes to aid in describing the Universe.  Planck, Einstein, Bohr, Dirac, and Heisenberg used calculus in all their calculations. With statistics initiating the estimation of gravity using F=ma, Moon’s acceleration was compared to the acceleration of the falling bodies on Earth and with that of Galileo’s experiment. It was differentiated by 60² according to the inverse law prediction. Moon was 60 times farther from the center of the Earth. Known as Two-body problem, the irregularities in the orbit of Uranus suggested an unknown planet (calculus) and using astronomy it was proved as ‘Neptune’.

    Katherin Johnson of NASA used calculus to predict the position of moving space crafts and to bring back John Glenn, the first American to orbit the Earth. NASA has a building named after her! 

    A bowl of soup is a discrete collection of molecules all bouncing erratically. Then, if you think the soup as continuum using x,y,z for the given point at temp T, partial differentiation makes ordinary differentiation equation a child’s play.  Pejorative is using art of differential equation that depend on just one variable.

        The final chapter has talks about the flights inspired from kites and birds. Dreamliner of Boeing applied Mathematics and Calculus to anticipate how the airplane’s wing would flex when working at 600 miles an hour - avoiding aeroelastic flutter, a nastier version of venetian blinds. Marking waves, standing, sinusoidal, Fourier series and String theory (vibration burst out of some of sine waves), and overtones, all get through this application of calculus.  Appearance of patient after facial surgery, flow of blood through artery, rumbling of ground after earthquake etc. all use the concept of calculus.

    A derivative of sine wave is another sine wave shifted by a quarter cycle (for other waves it gets distorted), so Sine wave is always efficient. Chaldini Patterns in guitar gets a mention too.

    Microwave ovens which used microwaves during world wars as Magnetron for detecting signals can be used to calculate the speed of light. ‘Frequency’ of vibrations (listed on the door frame of ovens) multiplied by ‘Wavelength’ can give that! (2.45 billion cy/sec into 12cm wavelength is close to the speed of light = 29.4 billion cm/sec). Percy Spencer had placed peanut cluster besides these Magnetrons, and he found later that it was like cooked one leading to the discovery of heating using MW. It was later tested with eggs.  Calculus provides the analysis in CT and brain imaging.

        The Future of calculus would be dealing with application to biology over writhing number of DNA. The diameter of typical nucleus is about 5 millionth of a meter and is 400,000 times smaller than DNA! That has to fit inside this smaller!! Not only this the alignment or arrangement is so neat that the DNA copy (multiplication) is flawless!!!

    Non-Linearity is a factor that is solved by Calculus. For instance, if you listen to your favourite songs again and again, the same pleasure is not doubled as cause and effect are proportional.

    Chaos over contour maps is discussed in detail followed by role of computers in getting Artificial Intelligence to the fore. But the eye-catching postulate of this book is when the author mentions Quantum Electron Dynamics. QED merges Maxwell’s theory of Electricity & Magnetism with Heisenberg’s & Schrodinger’s Quantum Theory and Einstein’s Special relativity, which turns out to be a pleasant aspect when you close the book and imagine how we all are enjoying this merger!