Shinichi Mochizuki and the impenetrable proof of the abc conjecture

Read The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof of the ABC Conjecture (Nature News & Comment)
A Japanese mathematician claims to have solved one of the most important problems in his field. The trouble is, hardly anyone can work out whether he's right.

The biggest mystery in mathematics

This article in Nature is just wonderful. Everyone will find it interesting, but those in the Algebraic Number Theory class this fall will be particularly interested in the topic – by the way, it’s not too late to join the class. After spending some time over the summer looking at Category Theory, I’m tempted to tackle Mochizuki’s proof as I’m intrigued at new methods in mathematical thinking (and explaining.)

The abc conjecture refers to numerical expressions of the type a + b = c. The statement, which comes in several slightly different versions, concerns the prime numbers that divide each of the quantities a, b and c. Every whole number, or integer, can be expressed in an essentially unique way as a product of prime numbers — those that cannot be further factored out into smaller whole numbers: for example, 15 = 3 × 5 or 84 = 2 × 2 × 3 × 7. In principle, the prime factors of a and b have no connection to those of their sum, c. But the abc conjecture links them together. It presumes, roughly, that if a lot of small primes divide a and b then only a few, large ones divide c.

Thanks to Rama for bringing this to my attention!

Book Review: A Fatal Family Secret by Samantha Marks

Read A Fatal Family Secret (The Morphosis.me Files, Book #1) by Samantha Marks
A Fatal Family Secret Book Cover A Fatal Family Secret
The Morphosis.me Files, Book
Samantha Marks
Young Adult, Sci-Fi/Fantasy
Samantha Marks
May 10, 2015
Paperback
264

What if, with a simple thought, you could change everything about yourself? On the first day of high school, Kayleigh wishes she could be taller, curvier, and cooler. But when she discovers she’s a morph--shape-shifters who can become anyone or anything--the boundaries around personality, sexuality, and gender identity are blurred. Suddenly, everything is fair game. But there are those who want to control Kayleigh and her gifts. Overnight, she becomes a target, and surviving the school year means defending herself against cyber-bullies, learning to control her newfound powers, and hiding from the ancient secret society that kidnapped her mother. Morphing has consequences, and Kayleigh begins to realize that being able to change into anything can mean losing herself in the process. After all, in a world full of morphs, rules are meant to be broken...

This is a well-paced young adult novel that mixes a dose of interesting fantasy in an otherwise all-too-real teenage world. In the vein of classics like Dracula and Frankenstein that take adolescence and turn them into great fiction as well as well-veiled morality plays, this novel, with a much better and modernized version of the “Teen Wolf” plot or perhaps in the vein of “X-Men: The Teenage Years”, takes things up three notches by adding a dose of thriller/suspense in what portends to be an awesome four book series.

Typical teenage protagonist Kayleigh comes home one day to find her father bleeding and injured in an apparent home invasion that ultimate reveals her mother has been either kidnapped or killed. Struggling with the psychological fallout of losing her mother under more than suspicious circumstances, she faces the turmoils of puberty, relationships, and fitting in as a teenager in high school. Making things worse, she discovers, that like her mother, she’s a “Morph” with the ability to change her appearance into almost anyone she can imagine to even animals. Facing post traumatic stress disorder amidst teenagerdom, her new-found ability just compounds things and gives her some hope that her mother may not only be alive but that she may be able to find her — if she can withstand constant bullying from classmate Emma and a very mysterious and potentially threatening online stalker who seems to know her every move.

I can’t wait to see the next installment in November 2015.

Reading Progress

👓 How our 1,000-year-old math curriculum cheats America’s kids | LA Times

Read How our 1,000-year-old math curriculum cheats America's kids – LA Times by Edward Frenkel (Los Angeles Times)
Imagine you had to take an art class in which you were taught how to paint a fence or a wall, but you were never shown the paintings of the great masters, and you weren't even told that such paintings existed. Pretty soon you'd be asking, why study art? That's absurd, of course, but it's surprisingly close to the way we teach children mathematics. In elementary and middle school and even into high school, we hide math's great masterpieces from students' view. The arithmetic, algebraic equations and geometric proofs we do teach are important, but they are to mathematics what whitewashing a fence is to Picasso — so reductive it's almost a lie. Most of us never get to see the real mathematics because our current math curriculum is more than 1,000 years old. For example, the formula for solutions of quadratic equations was in al-Khwarizmi's book published in 830, and Euclid laid the foundations of Euclidean geometry around 300 BC. If the same time warp were true in physics or biology, we wouldn't know about the solar system, the atom and DNA. This creates an extraordinary educational gap for our kids, schools and society.
An interesting train of thought to be sure. I should post in response to this, or at least think about how it could be structured. I definitely want to come back to write more about this topic.

University hiring: If you didn’t get your Ph.D. at an elite university, good luck finding an academic job

Read University hiring: If you didn't get your Ph.D. at an elite university, good luck finding an academic job. (Slate.com)
Read Vocabulary Study with Mnemosyne by Chris Francese (Dickinson College Commentaries)
Learning any language involves acquiring a large amount of vocabulary. For this reason, I think it is very useful for Latin and Greek students to put time and effort into systematic vocabulary study.
I’ve added a copy of the DCC Core Latin Vocabulary to the Anki platform for those interested in utilizing it there instead of on Mnemosyne. The cards can be found/downloaded at: https://ankiweb.net/shared/info/1342288910. My personal thanks to the DCC for posting and sharing the results of their research and work in this manner. This is a brilliant example of the concept of digital humanities.

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.

Book Review: The Man Who Loved China: The Fantastic Story of the Eccentric Scientist Who Unlocked the Mysteries of the Middle Kingdom by Simon Winchester

Read The Man Who Loved China: The Fantastic Story of the Eccentric Scientist Who Unlocked the Mysteries of the Middle Kingdom by Simon Winchester (Harper Perennial)
The Man Who Loved China: The Fantastic Story of the Eccentric Scientist Who Unlocked the Mysteries of the Middle Kingdom Book Cover The Man Who Loved China: The Fantastic Story of the Eccentric Scientist Who Unlocked the Mysteries of the Middle Kingdom
Simon Winchester
Biography & Autobiography
Harper Perennial
April 28, 2009
Paperback
352

In sumptuous and illuminating detail, Simon Winchester, bestselling author of The Professor and the Madman, brings to life the extraordinary story of Joseph Needham—the brilliant Cambridge scientist, freethinking intellectual, and practicing nudist who unlocked the most closely held secrets of China, once the world's most technologically advanced country.

Winchester really is a magnificent writer. Although I am a bigger fan of some of his other works, this certainly fits well into the rest of his life’s opus. Somehow he manages to cover bits of science, technology, philosophy, history, (his love) geology, archaeology, culture, politics and even uses his flair for travel writing with great ethos and pathos to tell an interesting story.

Aside from the breadth of topics he covers while telling the story of one man’s life’s work, he writes about and discusses topics which should be part of everyone’s personal cultural knowledge. As a small example, he makes mention of one of the real life archaeologists who served as a model for Indiana Jones – though sadly he only makes the direct connection in a footnote which many may not likely read.

Though I had originally picked up the book out of general curiosity (not to diminish the fact that I’m on a quest to read every word Winchester has written), I find that it also neatly fits into providing some spectacular background on the concept of “Big History” (see Maps of Time: An Introduction to Big History) as it relates to China’s place in the world. In particular “Needham’s question” (briefly: Why, given China’s illustrious past, did modern science not develop there after the 1500’s?) turned around becomes a interesting illustration on the course of human history and the rises and falls of cultures and societies since the Holocene.

For those who may miss the significance, I was particularly impressed with the overall literary power imbued to the book by the use of the book-ended contrasts of Needham’s Chongqing at the opening of the work and modern day Chongqing at the close. This is one of the few times that the mechanics behind how Winchester, the master of telling often non-linear stories, has been patently obvious to me. I hope one day to unravel all of his other secrets. I can only imagine that in his heavy research of his topics, he somehow internally sees the ultimately magical ways in which he will present the information.

I will note that, in contrast to some of his past works, this one had some better physical maps and photos to go along with the text, although I was highly disappointed in their unusable presentation in the e-book version of the book. (Higher dpi versions would have gone a long way, particularly with the ability to zoom in on them in most e-readers.) For those unfortunate enough to have the e-book copy, I commend picking up a physical copy of the book for better interpretations of the photos and maps included.

Finally, perhaps for Winchester’s benefit, I’ll note that typically I would give this book a full five stars in comparing it will all others, but I’m comparing it only with Winchester’s other works and, so it stands at four, and that only because there isn’t the ability to give tenths or hundredths.

Reading Progress
  • 12/17/09 marked as: want to read; “Purchased copy from Amazon.com.”
  • 12/27/09 Purchased copy from Amazon.com.
  • 02/05/10 started reading
  • 04/24/10 started reading again
  • 04/24/2010 8.81% done or on page 31 of 316; “Simon Winchester has such a lovely writing style and grasp of language. I’m depressed that I’ve finished reading most of his works.”
  • 12/03/12 started reading again from the beginning
  • 12/03/2012 09.0% done
  • 12/10/2012 20.0% done
  • 12/17/2012 30.0% done
  • 12/20/2012 40.0% done
  • 12/31/12 Finished book

Highlights, Quotes, & Marginalia

John Hay, America’s secretary of state at the turn of the twentieth century, remarked in 1899 that China was now the “storm center of the world,” and that whoever took the time and trouble to understand “this mighty empire” would have “a key to politics for the next five centuries.”

Highlight (blue) – Location XXX
China – storm center of the world;
Syndicated to: Amazon, Twitter
Guide to highlight colors

Yellow–general highlights and highlights which don’t fit under another category below
Orange–Vocabulary word; interesting and/or rare word
Green–Reference to read
Blue–Interesting Quote
Gray–Typography Problem
Red–Example to work through

Book Review: Charles Seife’s “Proofiness: The Dark Arts of Mathematical Deception”

Read Proofiness: The Dark Arts of Mathematical Deception (Penguin)
Proofiness: The Dark Arts of Mathematical Deception Book Cover Proofiness: The Dark Arts of Mathematical Deception
Charles Seife
Mathematics, Popular Science
Penguin
September 23, 2010
Hardcover
320

The bestselling author of Zero shows how mathematical misinformation pervades-and shapes-our daily lives. According to MSNBC, having a child makes you stupid. You actually lose IQ points. Good Morning America has announced that natural blondes will be extinct within two hundred years. Pundits estimated that there were more than a million demonstrators at a tea party rally in Washington, D.C., even though roughly sixty thousand were there. Numbers have peculiar powers-they can disarm skeptics, befuddle journalists, and hoodwink the public into believing almost anything. "Proofiness," as Charles Seife explains in this eye-opening book, is the art of using pure mathematics for impure ends, and he reminds readers that bad mathematics has a dark side. It is used to bring down beloved government officials and to appoint undeserving ones (both Democratic and Republican), to convict the innocent and acquit the guilty, to ruin our economy, and to fix the outcomes of future elections. This penetrating look at the intersection of math and society will appeal to readers of Freakonomics and the books of Malcolm Gladwell.

Charles Seife doesn’t prove that mathematics is essential for a democracy, but he certainly shows how the lack of proper use of mathematics can fray heavily at the edges!

Proofiness was a great book to have read over a long Fourth of July holiday. Though many people may realize some of the broad general concepts in the book, it’s great to have a better structure for talking about concepts like Potemkin numbers, disestimation, fruit packing, cherry picking, apple polishing, comparing apples to oranges, causuistry, randnumbness, regression to the moon, tragedy of the commons, and moral hazard among others. If you didn’t think mathematics was important to daily life or our democratic society, this book will certainly change your mind.

Seife covers everything from polls, voting, politics, economics, marketing, law, and even health to show how numbers are misused in a modern world that can ill-afford to ignore what is really going on around us.

This is a fantastic book for nearly everyone in the general public, but I’d highly recommend it for high school students while taking civics.

Original review posted on GoodReads.com on 7/9/12.

Reading Progress
  • 07/07/12 marked as: currently reading
  • 07/07/12 23.0% #
  • 07/09/12 52.0%
  • 07/09/12 Finished book

Christoph Adami: Finding Life We Can’t Imagine | TEDx

Watched Finding life we can't imagine by Christoph Adami from ted.com
How do we search for alien life if it's nothing like the life that we know? Christoph Adami shows how he uses his research into artificial life -- self-replicating computer programs -- to find a signature, a "biomarker," that is free of our preconceptions of what life is.
Adami’s work is along similar lines to some of my own research. This short video gives an intriguing look into some of the basics of how to define life so that one can recognize it when one sees it.

Entropy Is Universal Rule of Language | Wired Science

Read Entropy Is Universal Rule of Language by Lisa Grossman (Wired)
The amount of information carried in the arrangement of words is the same across all languages, even languages that aren't related to each other. This consistency could hint at a single common ancestral language, or universal features of how human brains process speech. "It doesn't matter what language or style you take," said systems biologist…
The research this article is based on is quite interesting for those doing language research.

Barnes & Noble Board Would Face Tough Choices in a Buyout Vote | Dealbook

Read Barnes & Noble Faces Tough Choices in a Buyout Vote by Steven Davidoff Solomon (DealBook)
If Leonard Riggio, Barnes & Noble's chairman, joins Liberty Media's proposed buyout of his company, the board needs to decide how to handle his 30 percent stake before shareholders vote on the deal.
This story from the New York Times’ Dealbook is a good quick read on some of the details and machinations of the Barnes & Noble buyout. Perhaps additional analysis on it from a game theoretical viewpoint would yield new insight?

The Science of Why We Don’t Believe Science | Mother Jones

Read The Science of Why We Don't Believe Science by Chris Mooney (Mother Jones)
How our brains fool us on climate, creationism, and the vaccine-autism link.
This is a fantastic article that everyone should read and take some serious time to absorb!

Bob Frankston on Communications

Watched Triangulation 4: Bob Frankston by Leo Laporte and Tom Merritt from TWiT Network
Computer pioneer who helped create the first spreadsheet, Bob Frankston, is this week's guest.
On a recent episode of Leo Laporte and Tom Merrit’s show Triangulation, they interviewed Bob Frankston of VisiCalc fame. They gave a great discussion of the current state of broadband in the U.S. and how it might be much better.  They get just a bit technical in places, but it’s a fantastic and very accessible discussion of the topic of communications that every American should be aware of.

The Adventures of Sherlock Holmes

The Adventures of Sherlock Holmes Book Cover The Adventures of Sherlock Holmes
Sherlock Holmes, #3
Arthur Conan Doyle
mystery, detective
The Strand Magazine
1892
Kindle e-book
Amazon

Comprising the series of short stories that made the fortunes of the Strand, the magazine in which they were first published, this volume won even more popularity for Sherlock Holmes and Dr. Watson. Holmes is at the height of his powers in many of his most famous cases, including The Red-Headed League, The Speckled Band, and The Blue Carbuncle.

The original “procedural”, but in fiction form and focusing on logic instead of high tech science.

Read between January 02 – May 09, 2011

Quotes and Highlights:

You may remember the old Persian saying, ‘There is danger for him who taketh the tiger cub, and danger also for whoso snatches a delusion from a woman.’ There is as much sense in Hafiz as in Horace, and as much knowledge of the world.

Singularity is almost invariably a clue. The more featureless and commonplace a crime is, the more difficult it is to bring it home.

Well, moonshine is a brighter thing than fog, …

…as I said then, that a man should keep his little brain-attic stocked with all the furniture that he is likely to use, and the rest he can put away in the lumber-room of his library, where he can get it if he wants it.

“My God! It’s Watson,” said he. He was in a pitiable state of reaction, with every nerve in a twitter.

41% Note: An interesting early use of @Twitter…

I should be very much obliged if you would slip your revolver into your pocket. An Eley’s No. 2 is an excellent argument with gentlemen who can twist steel pokers into knots. That and a tooth-brush are, I think, all that we need.

magnifying lens.

87% First reference to Holmes with a magnifying lens in print that I’ve seen.Like