Infinite Powers to explain

This post continues a series of post were I provide my thoughts on books that I deem worth reading.

This time it is the Infinite Powers book by Steven Strogatz that takes the reader into a realm of taming infinity to grasp nature’s secrets. The title of the book ambiguously plays on a method of using power series to approximate curves and powers which such a method, when exercised skillfully, brought to humankind. The book artfully describes how deferential and integral calculus was developed from Archimedes efforts to measure quadrature of curves through Descartes and Fermat, culminating in calculus invented by Isaac Newton in England and Gottfried Wilhelm Leibniz in Germany working independently. Lots of examples are provided showing how calculus is essential in many of inventions that are an important part of the modern civilization, be it GPS navigation, microwave ovens or the development of effective treatments to viruses induced diseases.

The power of insight

What I liked about the book is how the author is capable of explaining mathematical concepts, that usually require a solid mathematical background, mostly using analogies and down to earth explanations. Though, what I also liked that a mathematically inclined readers were not ignored, since what could, possibly, explained using proper mathematical notation was described as such. It is difficult to appreciate the beauty of calculus without using the mathematical symbols standing for derivative (differentials) and integral, that are so familiar to many people. I should say any person who studied at school should be familiar with them, and if not, the book provides a gentle and very intuitive explanation of what derivative stands for and why it is required, the same goes for integral.

As an example of a good explanation, I want to emphasize a Pizza Proof that is used to find an area of a circle. Since I recalled the formula for it being A = pi * R2, it was very interesting to see how the Pizza Proof showed clearly that A = R*C/2, where R is a radius of a circle and C its length. I think since school time I was curious where the power of two came in the area formula that I remembered. So, using the Pizza Proof result and substituting the C in it with the known formula for the length of the circle which is C = pi * 2R (which derivation was also explained in the book ) we get A = pi * R2. It was a nice insight, first one of many that the book provided.

I also liked how the method used by Fermat to find the maximum value of a curve, using a smart approach of double intersection, provides a correct result similar to what using derivatives would give. Another example, that was also insightful showed how the concept of derivative and curve interpolation could be used to find patterns in the seasonal changes of day length compared to the rate of change of day length, which both could be approximated by a sinusoidal function with a quarter cycle shift (pi/4 phase shift).

One can’t explain math without using it

Importantly, the concept of derivative was developed and shown very clearly using proper mathematical notation which should be clear even to readers coming from non-mathematical background, since the explanations gradually and systematically build up from simple to more advanced, as a reader progresses through the book (which means that the book should be read continuously). Then the concept of integral is shown quite remarkably well and the two concepts combined to showcase the Fundamental Theorem of Calculus about the duality of derivatives and integrals.

As I always mention, this book passes the test of providing references to other resources on the subject, like original papers of Newton or The Archimedes Palimpsest, which I was unaware of before reading the book.

Summary

It could be that reading Infinite Powers would provide your with appreciation of how calculus is essential in our day to day life and understanding of the world around us. And, maybe, show why mathematics could be beautiful in its own way and also applicable and useful, which could be an unexpected revelation to some.

Other resources

Universal organizers

source: Freepik

In this post I want to briefly outline what the next posts will be about. As we know from our day to day life and also from psychology and neuroscience research that we are very good at classifying, organizing things around us, and we have a naturally inclination to do this, since this is how our brain works. Our brain tends to build a hierarchically organized picture of the world, organizing things into groups, sub-groups etc.

Why I mention all of this? Well, I also tend to organize things and the most I like to organize is data that I think could be of interest to me. I do it by using Google Chrome Bookmarks functionality where I have bookmarks folders stand for various categories and nested sub-folders as sub-categories etc. Surely, it is possible to do it in many different ways, for example using an old-fashioned way of card-index, or a more modern approach of using Excel spreadsheets, OneNote application or Google Sheets etc.

It turns out that well known and less known scientists, writers, artists did similar things to organize their own work and most of them, if not all of them, did this following similar kind of “algorithm”. They methodically organized, categorized things that mattered to what interested them the most. For example, the renowned science fiction write Jules Verne had an extensive and well organized card-index about different topics that allowed him to write his novels without him actually visiting places he wrote about. Another example was Wilson Bentley who meticulously photographed various kinds of snowflakes to be able to understand their formation. And there are ample other examples of this kind.

The main point is, that for us to be able to make sense of the surrounding world there is a need in systematical classification of various topics, objects, ideas for their later analysis and then synthesis of new insights. For how is it possible to understand anything that you’ve got when you do not know where to find it?

So, what I want to write in the next few posts in the blog is a well organized and categorized listing of the books I read end-to-end that could be potentially useful to other readers. I want to augment the listings of these books with short commentaries about an author or content of the book. That’s it.

The topics that I want to cover are aviation, space exploration (manned and unmanned), popular science (including math, physics, neuroscience), applied mathematics, creative thinking and TRIZ. Let’s take, for example, the category of aviation and its breakdown with regard to books.

  • Aviation
    • Civil Aviation
      • Biographies of plane engineers
        • 747 by Joe Sutter
      • Biographies of jet engine engineers
        • The Power to Fly: An Engineer’s Life by Brian H. Rowe
        • Herman the German: Just Lucky I Guess by Gerhard Neumann
    • Military Aviation
      • Jet Fighter Planes
        • Hornet: The inside Story of The F/A-18 by Orr Kelly
      • Biographies of military jet planes engineers
        • Kelly: More Than My Share of It All by Kelly Johnson
      • Low Observable Technology aka Stealth
      • Stealth Planes
        • SR-71
        • F-117
        • Tacit blue
        • B-2
        • F-22

The books’ stack is changing

And so it continues…

This is a quick update on the status of the stack of the books I am reading. I am glad that it’s changing and worrying that its size remains the same overtime. The issue is, as I already mentioned in other posts, good books reference other good books and here we go. This time the culprit was Mind and the Cosmic Order book by Charles Pinter that mentioned the Selfish Gene and the ‘meme’ term created by Richard Dawkins. I have to say that I’ve heard about this book a long time ago, but never thought it was worth reading. But since a number of authors respected by me mentioned it I could no longer skip reading in. I should also mention that David Deutsch mentioned the meme term, coined by Dawkins, in his The Beginning of Infinity book. So did Jeff Hawkins in his recent A Thousand Brains book.

By the way, did you know that the preface to Jeff Hawkins’ book was written by Richard Dawkins?

The books that were on the stack physically or virtually since the last time

  • Mind and the Cosmic Order by Charles Pinter (A Book of Abstract Algebra brought me here)
  • The Right Kind Of Crazy by Adam Steltzner (well, have you heard about Curiosity and Perseverance?)
  • The Interstellar Age : Inside the Forty-Year Voyager Mission by Jim Bell (courtesy of watching a documentary on YouTube)
  • A Thousand Brains: A New Theory of Intelligence by Jeff Hawkins (following him since 2004)
  • Extraterrestrial: The First Sign of Intelligent Life Beyond Earth by Avi Loeb (a Google suggestion)
  • Unknown Quantity by John Derbyshire (I read the Prime Obsession so it was a natural continuation)
  • All Things Being Equal by John Mighton (was referenced by Anders Ericsson in his book on expertise )

Currently in progress

Infinite Powers by Steven Strogatz (well his text book on dynamic systems is a culprit). With regard to Steven Strogatz I want to mention his article he wrote for the Notices of the American Mathematical Society in 2014. In this article he descried tips on successful popular-science writing.

Writing about Math for the Perplexed and the Traumatized

Next to be popped from the stack

Selfish Gene by Richard Dawkins (mentioned by David Deutsch, Jeff Hawkins, Charles Pinter and others)

Rest of the stack

  • A Book of Abstract Algebra by Charles Pinter (Unknown Quantity sparked an interested in abstract algebra in me)
  • Number-Crunching by Paul Nahin (Paul Nahin’s book about Oliver Heaviside brought me here)
  • Discreet Mathematics by Lovasz, Pelikan and Vesztergombi (bought as a used book in 2014 while roaming in US, New Hampshire)
  • Applied mathematics by J. David Logan (who can resists math?)
  • Mathematical Modeling by Mark M. Meerschaert (the same as above)
  • The Mathematical Experience by Davis Hersh ( bought as a used book in 2014 while roaming in US, New Hampshire )

Think twice before you post a link

Abstract

This post is about time. It states that time is a scarce and valuable resource we have, and to be able to accomplish any goals in life a person should consider carefully managing it.

Who is this post for?

The information in this post could be applicable to general public, but the more intended audience is people who already have a professional occupation, have family and kids, but still want to allocate some time to think about our place in universe, who we are, where we came from and where we are heading.

Definitions

Before proceeding any further that us define a terminology to be able to use it later.

A content producer is a person or an algorithm that produces useful or useless content on the Internet.

A goal is a thoroughly defined objective with a plan of how to achieve it.

A valuable time is a time that’s left at your own disposal, except for time spent on work, chores and time with friends and family.

An intellectual activity is an activity that is a goal oriented toward thinking about questions of who we are, where we came from and where we are heading etc. and is done during a valuable time.

A disciplined approach is an approach to intellectual activity where it is carried out in a focused and mindful manner.

How goals affect the value of time

To say whether time is valuable or scarce depends on an attitude of a person towards it, namely a person who has no goals in life may think about time as a thing that’s in abundance and doesn’t care how it’s used. On the other hand, a person with defined goals think of a valuable time as a precise resource that should be accounted and measured.

On the total time management side is an example of a Russian biologist Aleksandr Lubischev who accounted all his time, and not only a valuable time. This type of time management is at the very extreme and, apparently, isn’t suitable for most of the people who still want to have a time for the family and friends and other hobbies.

On the opposite side, is a complete carelessness about time and the best example of this behavior is an objectiveless browsing on various kinds of social media, like Facebook, Twitter, LinkedIn, Instagram etc. and watching of endless TV series on streaming platforms and YouTube. This type of “time management” is familiar to most of us and I am guilty of this too.

Some practical advice

Note

As I mentioned, this advice could be potentially helpful only to a person with goals, who wants to get most out of available valuable time by applying a disciplined approach toward intellectual activity.

Consider eliminating all social media producers that tend to take all you valuable time.
  • This type of time waste is not only distracting and disorganizing, but it also tends to create a kind of addiction to it that is harmful in its own way.
    • This can be done by completely deleting all non required accounts in social media
    • Or if you have to have them it is possible to unfollow everyone, except for a carefully considered number of contacts who are valuable and do not take your valuable time by sharing useless content.
Consider unsubscribing from all streaming content providers, like Netflix, Prime Video, Disney and YouTube etc.
  • In a similar way to social media, streaming content is addictive and could waste months if not years1 of your valuable time without you noticing this happening.
    • If you have to have watch something to relax, at least you can try watching things related to your favorable intellectual activity topics
Think twice before posting any content on social media platforms
  • Since, most of what other content producers post on social media is useless and waste your valuable time, do not post anything that could potentially waste time of other people, even if they don’t care, and do not value their own time.

To summarize

Time could be a valuable or not depending on what your attitude toward it is, and whether you have defined goals you want to achieve in life. Social media and streaming platforms are the main source of useless and distracting content producers. Be mindful when posting content on social media and think twice does it have any value or not.

Endnotes

  1. Let’s have a quick back of the envelop calculation of how much time could be wasted by a person who watches say, four 45 minutes episodes a day, of a 5 season series that has 20 episodes a season, and he watches 20 such series in his life time.

Then,

Twasted = (4 hours a day x 45 minutes x 20 episodes x 5 seasons x 20 series) / 60 minutes / 24 hours = 250 days which is more than 2/3 of a year spent on watching!

This calculation is a conservative one and the waste could be a year or even more.

Books that make you think… differently

This post isn’t about the book by Adam Steltzner, I promised to write, but on an entirely different topic altogether. And this time it’s a book that is a unique and one of a kind.

There are books that you may find interesting, there are books that are easy to read and there are books that make you think… differently. I think I’ve read only a couple of books that caused me to think deeply about the reality and perception. One of them was On Intelligence by Jeff Hawkins, the other was Sapiens: A Brief History of Humankind by Yuval Noah Harari, but the last one that was most impressive, in my opinion, was Mind and the Cosmic Order by Charles Pinter Professor of Mathematics, Emeritus at Bucknell University.

What do I mean by the books that cause you rethink a world we live in, are books that try to answer deep questions about how the brains might work, how we function as a society, how we came to be in this Universe and more. Usually, these books require mindful reading, attention and are not that easy or fun to read. I should say these books require working with them, working through them. The more you think about the content of such books, the more you play with the concepts they describe, the more you get out of them. One additional thing that such books provide a reader is references to other useful books that could help to understand information better.

Mind and the Cosmic Order is exactly such a book I described above. This book contains a number of very well thought ideas that are systematically elaborated to convey a very peculiar point of view on how what we call as a perception emerges in a mind, be it humans or animals one. The books makes use of the evolutionary approach to animals behavior that emphasizes that evolution provided animals with such a system for perception that fits the animals environment and most efficient for animals survival. Based on this assumption, the author then introduces the concept of Gestalt perception

The essence of a Gestalt is that it’s “different from the sum of its parts.”

Pinter, Charles. Mind and the Cosmic Order. Springer Nature, 2020.

which is defined as a perception of an outside world as a coherent whole, which is what suits us humans from the evolutionary point of view, and makes us active agents in this world.

One of the interesting points that I haven’t thought previously was that the mind not only don’t get sensory input directly from the senses, but it also projects the internal world-model that it creates, outside making us, essentially, feel that we see a world outside, which feels perfectly real, but being a construct of the mind. Further elaborating on this point, the author explains that our whole perception is Gestalt based and is the only way we perceive outside world.

Additional point was, that outside world has no form and structure, which are creations of the outside observer, in our case the perceiving mind. The structure and the form of objects we think are outside there are only for us to be able to function in the world efficiently. They occur only for us, but are not required by the world outside and, are not inherent in the physics of the outside world.

The main and the most interesting point in the book that builds upon previous ones is that Quantum Mechanics paradoxes, namely, The Measurement Problem, can be resolved easily if we accept previous points, that human mind is incapable of sensing outside world directly, it has a bespoke world-model that serves a mind carrier survival and that an observer could only make conclusion based on an explanation of the world-model inferred from senses. In essence, what Charles Pinter proposes is an inversion of what the Copenhagen interpretation of quantum mechanics states. This means, that there is no wave function collapse during the measurement, instead it is the perception of the observer that is changing, while the world outside remains in quantum superposition. What is interesting in this explanation that is radically different from the multiverse point of view, where an observer is split with each measurement along with the universe where this measurements happen.

All in all, Mind and the Cosmic order provides you with many ideas to think about, It’s an interesting, but not an easy read. It requires your attention, it requires you to think and work through what is explained. In addition, the author mentions great many books and papers that worth reading to get a wider picture of what is mind, how it emerges and creates a world that we are so used to think of as being the only real one possible.

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These are the voyages of Voyager 1 and 2

Space, the final frontier. These are the voyages of the Starship Enterprise...

Probably, most of you can recall these opening lines from the Star Trek sci-fi franchise. But in this post I want to write about real space voyagers which are Voyager 1 and Voyager 2 that where launched in 1977.

Not long ago friends visited us at home and while having a lovely conversation we talked about space exploration. Eventually, we mentioned the Voyager 1 and 2 robotic spacecrafts. When our friends left I was curious to check what YouTube had with regard to interesting documentaries about Voyagers space mission. As you might guess, there were a lot on the YouTube, but one particular documentary called The Farthest produced by HHMI Tangled Bank Studios I liked the most. This documentary has a reasonable coverage of Voyagers mission from its inception until present and it features interviews with key scientists who were responsible for making Voyagers a successful endeavor.

As usually happens to me, while watching this documentary I’ve noticed that one of the people who was interviewed for this documentary was Jim Bell, a professor of Astronomy who wrote a book called The Interstellar Age : Inside the Forty-Year Voyager Mission which was the basis for the documentary. Again, as usual, I bought that same book and, boy, wasn’t I disappointed. The book was also very interesting and it covered robotic space program including early Mariner missions, but mostly focused on Voyager 1 and Voyager 2 journeys beginning in 1977 and until these days when they plow interstellar space continuing ad infinitum and, some may say, beyond. The books mentions interesting discoveries that where made by each Voyager in their encounters with giant planets following on a Grand Tour of Planets. It also covers what will be the fait of the Voyagers when we as a civilization will be long gone. I particularly, liked when Jim Bell described how the Golden Record was prepared to be carried by the Voyagers and also it was interesting to know that some moons of Jupiter and Saturn could be potential harbors of life besides Earth.

All in all, I recommend you to check out the documentary and if you like it you also may consider reading the book. The next book that I have in queue is The Right Kind Of Crazy by Adam Steltzner, the chief engineer of Curiosity and Perseverance Mars rovers, but this and more in my next post.