Marsden and Weinstein’s Calculus Series

A friend tipped me off that Marsden and Weinstein’s entire Calculus series is available for free online now.

I remember using volume III in Dr. James Martino‘s class many moons ago and enjoying its style. I do however have to credit all my facility in the subject to Dr. Richard Joseph who taught it to me by means of the steepest gradient possible – that of electromagnetic theory.

Marsden & Weinstein's Calculus III textbook cover

Fundamental Difference Between Science and Politics

Nate Silver, statistician
in The Signal and the Noise: Why So Many Predictions Fail-but Some Don’t (Penguin Books, 2012)

 

The Signal and The Noise

Review of The Signal and the Noise: Why So Many Predictions Fail – But Some Don’t

Read The Signal and the Noise: Why So Many Predictions Fail - But Some Don't by Nate SilverNate Silver (Amazon.com)
The Signal and the Noise: Why So Many Predictions Fail, But Some Don't Book Cover The Signal and the Noise: Why So Many Predictions Fail, But Some Don't
Nate Silver
Business & Economics
Penguin Press HC
September 27, 2012
Hardcover
534
personal library

The founder of FiveThirtyEight.com challenges myths about predictions in subjects ranging from the financial market and weather to sports and politics, profiling the world of prediction to explain how readers can distinguish true signals from hype, in a report that also reveals the sources and societal costs of wrongful predictions.

Started Reading: May 25, 2013
Finished Reading: October 13, 2013

Given the technical nature of what Nate Silver does, and some of the early mentions of the book, I had higher hopes for the technical portions of the book. As usual for a popular text, I was left wanting a lot more. Again, the lack of any math left a lot to desire. I wish technical writers could get away with even a handful of equations, but wishing just won’t make it so.

The first few chapters were a bit more technical sounding, but eventually devolved into a more journalistic viewpoint of statistics, prediction, and forecasting in general within the areas of economics, political elections, weather forecasting, earthquakes, baseball, poker, chess, and terrorism. I have a feeling he lost a large part of his audience in the first few chapters by discussing the economic meltdown of 2008 first instead of baseball or poker and then getting into politics and economics.

While some of the discussion around each of these bigger topics are all intrinsically interesting and there were a few interesting tidbits I hadn’t heard or read about previously, on the whole it wasn’t really as novel as I had hoped it would be. I think it should be required reading for all politicians however, as I too often get the feeling that none of them think at this level.

There was some reasonably good philosophical discussion of Bayesian statistics versus Fisherian, but it was all too short and could have been fleshed out more significantly. I still prefer David Applebaum’s historical and philosophical discussion of probability in Probability and Information: An Integrated Approach though he surprisingly didn’t mention R.A. Fisher directly himself in his coverage.

It was interesting to run across additional mentions of power laws in the realms of earthquakes and terrorism after reading Melanie Mitchell’s Complexity: A Guided Tour (review here), but I’ll have to find some texts which describe the mathematics in full detail. There was surprisingly large amount of discussion skirting around the topics within complexity without delving into it in any substantive form.

For those with a pre-existing background in science and especially probability theory, I’d recommend skipping this and simply reading Daniel Kahneman’s book Thinking, Fast and Slow. Kahneman’s work is referenced several times and his book seems less intuitive than some of the material Silver presents here.

This is the kind of text which should be required reading in high school civics classes. Perhaps it might motivate more students to be interested in statistics and science related pursuits as these are almost always at the root of most political and policy related questions at the end of the day.

For me, I’d personally give this three stars, but the broader public should view it with at least four stars if not five as there is some truly great stuff here. Unfortunately a lot of it is old hat or retreaded material for me.

Book Review: “Complexity: A Guided Tour” by Melanie Mitchell

Read Complexity: A Guided Tour by Melanie MitchellMelanie Mitchell (amzn.to)
Complexity: A Guided Tour Book Cover Complexity: A Guided Tour
Melanie Mitchell
Popular Science
Oxford University Press
May 28, 2009
Hardcover
366

This book provides an intimate, highly readable tour of the sciences of complexity, which seek to explain how large-scale complex, organized, and adaptive behavior can emerge from simple interactions among myriad individuals. The author, a leading complex systems scientist, describes the history of ideas, current research, and future prospects in this vital scientific effort.

This is handily one of the best, most interesting, and (to me at least) the most useful popularly written science books I’ve yet to come across. Most popular science books usually bore me to tears and end up being only pedantic for their historical backgrounds, but this one is very succinct with some interesting viewpoints (some of which I agree with and some of which my intuition says are terribly wrong) on the overall structure presented.

For those interested in a general and easily readable high-level overview of some of the areas of research I’ve been interested in (information theory, thermodynamics, entropy, microbiology, evolution, genetics, along with computation, dynamics, chaos, complexity, genetic algorithms, cellular automata, etc.) for the past two decades, this is really a lovely and thought-provoking book.

At the start I was disappointed that there were almost no equations in the book to speak of – and perhaps this is why I had purchased it when it came out and it’s subsequently been sitting on my shelf for so long. The other factor that prevented me from reading it was the depth and breadth of other more technical material I’ve read which covers the majority of topics in the book. I ultimately found myself not minding so much that there weren’t any/many supporting equations aside from a few hidden in the notes at the end of the text in most part because Dr. Mitchell does a fantastic job of pointing out some great subtleties within the various subjects which comprise the broader concept of complexity which one generally would take several years to come to on one’s own and at far greater expense of their time. Here she provides a much stronger picture of the overall subjects covered and this far outweighed the lack of specificity. I honestly wished I had read the book when it was released and it may have helped me to me more specific in my own research. Fortunately she does bring up several areas I will need to delve more deeply into and raised several questions which will significantly inform my future work.

In general, I wish there were more references I hadn’t read or been aware of yet, but towards the end there were a handful of topics relating to fractals, chaos, computer science, and cellular automata which I have been either ignorant of or which are further down my reading lists and may need to move closer to the top. I look forward to delving into many of these shortly. As a simple example, I’ve seen Zipf’s law separately from the perspectives of information theory, linguistics, and even evolution, but this is the first time I’ve seen it related to power laws and fractals.

I definitely appreciated the fact that Dr. Mitchell took the time to point out her own personal feelings on several topics and more so that she explicitly pointed them out as her own gut instincts instead of mentioning them passingly as if they were provable science which is what far too many other authors would have likely done. There are many viewpoints she takes which I certainly don’t agree with, but I suspect that it’s because I’m coming at things from the viewpoint of an electrical engineer with a stronger background in information theory and microbiology while hers is closer to that of computer science. She does mention that her undergraduate background was in mathematics, but I’m curious what areas she specifically studied to have a better understanding of her specific viewpoints.

Her final chapter looking at some of the pros and cons of the topic(s) was very welcome, particularly in light of previous philosophic attempts like cybernetics and general systems theory which I (also) think failed because of their lack of specificity. These caveats certainly help to place the scientific philosophy of complexity into a much larger context. I will generally heartily agree with her viewpoint (and that of others) that there needs to be a more rigorous mathematical theory underpinning the overall effort. I’m sure we’re all wondering “Where is our Newton?” or to use her clever aphorism that we’re “waiting for Carnot.” (Sounds like it should be a Tom Stoppard play title, doesn’t it?)

I might question her brief inclusion of her own Ph.D. thesis work in the text, but it did actually provide a nice specific and self-contained example within the broader context and also helped to tie several of the chapters together.

My one slight criticism of the work would be the lack of better footnoting within the text. Though many feel that footnote numbers within the text or inclusion at the bottom of the pages detracts from the “flow” of the work, I found myself wishing that she had done so here, particularly as I’m one of the few who actually cares about the footnotes and wants to know the specific references as I read. I hope that Oxford eventually publishes an e-book version that includes cross-linked footnotes in the future for the benefit of others.

I can heartily recommend this book to any fan of science, but I would specifically recommend it to any undergraduate science or engineering major who is unsure of what they’d specifically like to study and might need some interesting areas to take a look at. I will mention that one of the tough parts of the concept of complexity is that it is so broad and general that it encompasses over a dozen other fields of study each of which one could get a Ph.D. in without completely knowing the full depth of just one of them much less the full depth of all of them. The book is so well written that I’d even recommend it to senior researchers in any of the above mentioned fields as it is certainly sure to provide not only some excellent overview history of each, but it is sure to bring up questions and thoughts that they’ll want to include in their future researches in their own specific sub-areas of expertise.

Starbucks Causes Cancer!?

Apparently Starbucks has learned well from big tobacco and they’re getting ahead of the whole cancer thing whether or not they really need to. This morning while picking up my morning tea (and apple fritter), I ran across a Prop 65 warning very prominently posted–ironically above the aspartame, though that wasn’t mentioned specifically in the notice–about the cancer risks of acrylamide.

Prop 65 Warning at Starbucks All the fine print boils down to saying that coffee might cause cancer.
Prop 65 Warning at Starbucks
All the fine print boils down to saying that coffee might cause cancer.

I’ve read a fair amount about acrylamide in the past two years following the news that just about anything cooked or fried has small trace amounts of the substance, so I know there’s not too much to be worried about. The biggest “scare” was apparently over french fries–particularly those served at fast food restaurants. Apparently after the scare blew over the general public – the subject just didn’t seem to catch any traction aside from a few snippets in the mainstream press–Starbucks has decided to get out ahead of this “non-issue” just in case. (I will admit that the State of California has actually sued and won against major corporations under the Safe Drinking Water and Toxic Enforcement Act of 1986, Health and Safety Code section 25249.6, also known as “Proposition 65,” that businesses must provide persons with a “clear and reasonable warning” before exposing individuals to these chemicals which includes acrylamide.)

As an aside, I will mention that placing the warning on the condiments counter which I visit only after I’ve made my purchase seems a bit after-the-fact – it would have done me more good in front of the cash register. For the ambulance chasers, this is probably great “grounds”–pun intended–for a major class action.

PROP 65 WARNING

Chemicals known to the State of California to cause cancer and reproductive toxicity, including acrylamide, are present in coffee, baked goods, and other foods or beverages sold here. Acrylamide is not added to our products, but results from cooking, such as when coffee beans are roasted or baked goods are baked.  As a result acrylamide is present in our brewed coffee, including coffe made at home or elsewhere from our beans, ground or instant coffee, baked goods or other foods sold here, in grocery stores or other retail locations.

Your personal cancer risk is affected by a wide variety of factors.  For more information regarding acrylamide, see www.fda.gov. For more information about acrylamide and Proposition 65, visit www.oehha.ca.gov/prop65/acrylamide.html.

As posted in Starbucks Coffee, Lake Avenue, Pasadena, CA

While I laud their savvy general counsel, do we really need this type of notice in our lives? Humankind has been living with acrylamide cancer risk since the dawn of the Holocene when man first learned to use fire to cook, is there any reason to worry about it now?

I’m reminded of Jared Diamond’s book The World Until Yesterday and some of the things that primitive societies simply learn to live with, but which our overly litigious society just can’t seem to deal with logically. Simple things didn’t fool primitive societies like: don’t sleep under trees that look like they are dead or possibly rotting–just in case the tree falls over and kills you in the night while you’re sleeping. Yet somehow some of us need additional warnings about our coffee from McDonald’s being served hot  or cautions not to operate our toasters in the bathtub.

Next I fear that we’ll discover we need signs telling us that pinecones might fall out of pine trees.

Photo of large pine tree with an inordinately large caution sign next to it stating "Caution: Falling Cones."
“Caution Falling Cones”
Photo taken about 20 miles from Jared Diamond’s home in Los Angeles.

I sure hope that Henny Penny copyrighted, registered, and patented everything about the concept of “The Sky is Falling” as I’m sure it’ll have made her the richest chicken in the world.

God Could Have Caused Birds to Fly With Their Bones Made of Solid Gold

Salviati’s (Galileo’s voice) response to Simplicio (Pope Urban VIII)
Galileo Galilei in Dialogue Concerning the Two Chief World Systems

 

Galileo's Dialogo Title Page
Title Page from Galileo’s Dialogo

Model of a cell in Jello with candy, 2013

Model of a cell in Jello with candy, 2013
Science project by some bright 7th grade girls from Wilson I ran into while having afternoon tea. (Model of a cell in Jello with candy, 2013)
Science project by some bright 7th grade girls from Wilson I ran into while having afternoon tea. (Model of a cell in Jello with candy, 2013)

Instagram filter used: X-Pro II

Beauty, Melody, and Entropy are an Equivalence Class

Sir Arthur Stanley Eddington, OM, FRS (1882-1944), a British astronomer, physicist, and mathematician
in The Nature of the Physical World, 1927

 

Sir Arthur Stanley Eddington

 

How to Sidestep Mathematical Equations in Popular Science Books

In the publishing industry there is a general rule-of-thumb that every mathematical equation included in a book will cut the audience of science books written for a popular audience in half – presumably in a geometric progression. This typically means that including even a handful of equations will give you an effective readership of zero – something no author and certainly no editor or publisher wants.

I suspect that there is a corollary to this that every picture included in the text will help to increase your readership, though possibly not by as proportionally a large amount.

In any case, while reading Melanie Mitchell’s text Complexity: A Guided Tour [Cambridge University Press, 2009] this weekend, I noticed that, in what appears to be a concerted effort to include an equation without technically writing it into the text and to simultaneously increase readership by including a picture, she cleverly used a picture of Boltzmann’s tombstone in Vienna! Most fans of thermodynamics will immediately recognize Boltzmann’s equation for entropy, S = k log W , which appears engraved on the tombstone over his bust.

Page 51 of Melanie Mitchell's book "Complexity: A Guided Tour"
Page 51 of Melanie Mitchell’s book “Complexity: A Guided Tour” featuring Boltzmann’s tombstone in Vienna.

I hope that future mathematicians, scientists, and engineers will keep this in mind and have their tombstones engraved with key formulae to assist future authors in doing the same – hopefully this will help to increase the amount of mathematics that is deemed “acceptable” by the general public.

Book Review: Gregory Chaitin’s “Proving Darwin: Making Biology Mathematical”

Gregory Chaitin’s book Proving Darwin: Making Biology Mathematical combining biology, microbiology, mathematics, evolution and even information theory is directly in my wheelhouse. I had delayed reading it following a few initial poor reviews, and sadly I must confirm that I’m ultimately disappointed in the direct effort shown here, though there is some very significant value buried within. Unfortunately the full value is buried so deeply that very few, if any, will actually make the concerted effort to find it.

proving

This effort does seem to make a more high-minded and noble attempt than what I would call the “Brian Greene method” in which an academic seemingly gives up on serious science to publish multiple texts on a popular topic to cash in on public interest in that topic through sales of books. In this respect Chaitin is closer to Neil deGrasse Tyson in his effort to expound an interesting theory to the broader public and improve the public discourse, though I would admit he’s probably a bit more (self-) interested in pushing his own theory and selling books (or giving him the benefit of the doubt, perhaps the publisher has pushed him to this).

Though there is a reasonable stab at providing some philosophical background to fit the topic into the broader fabric of science and theory in the later chapters, most of it is rather poorly motivated and is covered far better in other non-technical works. While it is nice to have some semblance of Chaitin’s philosophy and feelings, the inclusion of this type of material only tends to soften the blow of his theoretical work and makes the text read more like pseudo-science or simple base philosophy without any actual rigorous underpinning.

I’m assuming that his purpose in writing the book is to make the theories he’s come up with in his primary paper on the topic more accessible to the broader community of science as well as the public itself. It’s easy for a groundbreaking piece of work to be hidden in the broader scientific literature, but Chaitin seems to be taking his pedestal as a reasonably popular science writer to increase the visibility of his work here. He admittedly mentions that his effort stems from his hobby as his primary area is algorithmic information theory and computer science and not biology or evolution, though his meager references in the text do at least indicate some facility with some of the “right” sources in these latter areas.

Speaking from a broad public perspective, there is certainly interest in this general topic to warrant such a book, though based on the reviews of others via Amazon, Goodreads, etc. the book has sadly missed it’s mark. He unfortunately sticks too closely to the rule that inclusion of mathematical equations is detrimental to the sale of ones books. Sadly, his broader point is seemingly lost on the broader public as his ability to analogize his work isn’t as strong as that of Brian Greene with respect to theoretical physics (string theory).

From the a higher perspective of a researcher who does work in all of the relevant areas relating to the topic, I was even more underwhelmed with the present text aside from the single URL link to the original much more technical paper which Chaitin wrote in 2010. To me this was the most valuable part of the entire text though he did provide some small amount of reasonable detail in his appendix.

I can certainly appreciate Chaitin’s enthusiastic following of John von Neumann but I’m disappointed in his lack of acknowledgement of Norbert Weiner or Claude Shannon who all collaborated in the mid part of the 20th century. I’m sure Chaitin is more than well aware of the father of information theory, but I’ll be willing to bet that although he’s probably read his infamous master’s thesis and his highly influential Bell Labs article on “A/The Mathematical Theory of Communication”, he is, like most, shamefully and wholly unaware of Shannon’s MIT doctoral thesis.

Given Chaitin’s own personal aim to further the acceptance of his own theories and work and the goal of the publisher to sell more copies, I would mention a few recommendations for future potential editions:

The greater majority of his broader audience will have at least a passably reasonable understanding of biology and evolution, but very little, if any, understanding of algorithmic information theory. He would be better off expounding upon this subject to bring people up to speed to better understand his viewpoint and his subsequent proof. Though I understand the need to be relatively light in regard to the number of equations and technicalities included, Chaitin could follow some of his heroes of mathematical exposition and do a slightly better job of explaining what is going on here. He could also go a long way toward adding some significant material to the appendices to help the higher end general readers and the specifically the biologists understand more of the technicalities of algorithmic information theory to better follow his proof which should appear in intricate glory in the appendix as well. I might also recommend excising some of the more philosophical material which tends to undermine his scientific “weight.” Though I found it interesting that he gives a mathematical definition of “intelligent design”, I have a feeling its intricacies were lost on most of his readership — this point alone could go a long way towards solidifying the position of evolution amongst non-scientists, particularly in America, and win the support of heavyweights like Dawkins himself.

I’ll agree wholeheartedly with one reviewer who said that Chaitin tends to “state small ideas repeatedly, and every time at the same shallow level with astonishing amount of redundancy (mostly consisting of chit-chat and self congratulations)”. This certainly detracted from my enjoyment of the work. Chaitin also includes an awful lot of name dropping of significant scientific figures tangential to the subject at hand. This may have been more impressive if he included the results of his discussions with them about the subject, but I’m left with the impression that he simply said hello, shook their hands, and at best was simply inspired by his having met them. It’s nice that he’s had these experiences, but it doesn’t help me to believe or follow his own work.

For the technically interested reader, save yourself some time and simply skim through chapter five and a portion of the appendix relating to his proof and then move on to his actual paper. For the non-technical reader, I expect you’ll get more out of reading Richard Dawkins’ early work (The Selfish Gene) or possibly Werner R. Loewenstein’s The Touchstone of Life: Molecular Information, Cell Communication, and the Foundations of Life.

Though I would certainly agree that we could use a mathematical proof of evolution, and that Chaitin has made a reasonable theoretical stab, this book sadly wasn’t the best one to motivate broader interest in such an effort. I’ll give him five stars for effort, three for general content, but in the end, for most it will have to be at most a 2 star work overall.

This review was originally published on June 17, 2013.

Book Review: Jared Diamond’s “The World Until Yesterday: What Can We Learn from Traditional Societies?”

I’m honestly shocked that no one else has written a book similar to The World Until Yesterday: What Can We Learn from Traditional Societies prior to now. It’s certainly a wonderful synthesis and a fantastic resulting thesis based on an incredibly broad array of areas of study over a lifetime of work.

I personally don’t think that it is as significant as Guns, Germs, and Steel: The Fates of Human Societies was, though perhaps it should be just as (if not more) ground shaking for modern society. As a long-time student of evolutionary biology and other fields related to this work, I’m not as impressed with the effort as I might otherwise be since most of the overarching thesis is second nature to me. It does however have some superb anecdotes and broad reviews of large areas of literature to provide some excellent motivation that I might not otherwise have spent the time to find thus giving it some excellent value to me.

The World Until Yesterday by Jared Diamond (bookcover)

As for others in the general public, I highly recommend it for it’s simple and clear examples and the ultimate thesis which are exceptionally worth reading (and implementing) into one’s life as well as into broader areas of modern society. If nothing else, it points out how drastically life has changed for human societies even in the last 150 years, much less the last 10,000.

For those in the field or with an interest in Big History, this is certainly a must-read and possibly an excellent place to start for those without any background at all.

Based on my own personal background, I’d give this 3 stars (in terms of it’s direct value to me), but for the general public it’s easily a 5 star work. I do wish that it had been more traditionally and extensively footnoted, but for a broader audience I certainly understand Dr. Diamond’s reasons for publishing it as he did.