New Caelifera

New Caelifera

modern methow cabin

Book: Proofs and Refutations, The Logic of Mathematical Discovery


Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos

The flow is a mental state in which you are totally immersed in what you are doing. It’s been a long time since I got into the flow while reading a book, but this book did it for me. Written as a socratic dialogue it is a discussion between a teacher and many students who work on proving Euler’s polyhedron formula. The great thing about this book is that the proof (really plural proofs) here are easily comprehensible to someone with only a small mathematical background, but the way in which the story unfolds is both dramatic and insightful. Or at least it was for me.

The best book I’ve read in a few years, I highly recommend this to anyone who is interested in how mathematics and mathematicians work, and in general to anyone who wonders about how discovery and newness appear in the world.

I’d give you mine, but Imma dog ate it (apparently she had some disagreements with Gamma):

admin February 5, 2017 Leave A Comment Permalink

Book: The Quantum Handshake, Entanglement, Nonlocality and Transactions by John Cramer

The Quantum Handshake: Entanglement, Nonlocality and Transactions by John Cramer.

The transactional interpretation of quantum theory is probably the most neglected interpretation of quantum theory (I know, you would have thought all interpretations of quantum theory would be fodder for gossip mags and the glitterati!)  Invented by John Cramer it was inspired by the Wheeler-Feynman absorber theory of electromagnetism.  In this later theory Wheeler and Feynman examine the consequences of taking both advanced and retarded solutions of electromagnetism seriously.  You may recall from your hours spent reading Jackson (I will not link to the blasphemous third edition) that when solving Maxwell’s equations of electromagnetism you end up in the tricky situation of having solutions to the equations that seem to go the wrong way in time.  When you wiggle (accelerate) a charge there are solutions to the electromagnetic fields which are waves propagating away from the charge into the future (called retarded waves).  But there are also solutions that have waves essentially propagating backwards into the past (called advanced waves).  Of course this should make you head hurt, and so the normal thing to do is disregard the advanced waves.  What Wheeler and Feynman attempted to do was to not make a theory of electromagnetism without this kludge of disregarding advanced waves.  They were in a sense successful, able to show that in essence they could recover the retarded only electromagnetism via an assumption that all emissions must result in absorption.

What Cramer’s transactional interpretation does is to attempt to use advanced (backwards in time) solutions to the relevant quantum mechanical equations to help us overcome our difficulties understanding quantum theory.  Roughly this works as follows, an emitter at some time emits and “offer” wave.  In nonrelativistic quantum theory this is just the normal wave function for Schrodigner’s equation.   At some later time an absorber interacts with this offer wave.  In particular the absorber sends a wave backwards in time to the emitter, in nonrelativistic quantum theory this is the solution to the complex conjugate of Schrodinger’s equation.  The emitter then receives this “confirmation” wave.  Now, interestingly, if one thinks about the amplitude of the wave function at the emitter, it will be the norm squared of the wave function at the absorber.  An emitter can receive many “confirmation” waves from future absorbers.  In order to change this into reality, a “transaction” must be established: a choice is made so that only one of the confirmation wave “survives”.   Because the emitter has access to the amplitudes, we can see that this choice could be made so as to follow Born’s probability law, at least in so much as the information necessary to get the correct probability law is at the emitter.  Supporters of the transactional interpretation like to say that the interpretation “derives” Born’s law, though I find this slightly wanting in this area since I still wonder how probabilities arise here, why is a field norm squared turned into the probability that a transaction is chosen?

The nice thing about the transactional interpretation is that it can help one attempt to reason about seemingly paradoxical setups in quantum theory.  For example in a Bell experiment, one can reason about the probabilities that violate local realistic theories, by imagining backwards in time propagation of measurement directions to an original emitter, who because they receive confirmation offers from spacelike separated detectors in the future, can make the same probabilities arise as those in quantum theory.  The thing I most like about the interpretation is that it attempts to keep locality of information propagation intact, at the price of these backwards propagating solutions.

“The Quantum Handshake: Entanglement, Nonlocality and Transaction” is a gentle introduction to the transactional interpretation. I begins with a description of the history of quantum theory and conceptual problems that arose. It then introduces the transactional interpretation. And then comes my favorite part of the book, which is where Cramer applies the interpretation to just about every paradoxical quantum experiment ever proposed. In my view this is the best part of the book, an amazing collection of these different issues and what led people to get confused. In each Cramer attempts to show how the transactional interpretation would deal with these issues. But it is a seriously good list of the experiments that makes this book worth picking up, even if you are not likely to be converted to Cramer’s view of the world. The book also includes a bit on an objection to the transactional interpretation due to Maudlin. This involves, Cramer’s approach, an additional assumption about the hierarchy of transactions, which is interesting to ponder.

Recommended for quantum theory buffs and anyone who want’s to beat their head up against understanding quantum theory.

admin February 5, 2017 Leave A Comment Permalink

Books of 2016

Arranged roughly according to my own personal ranking.

Nonfiction

Fiction

(*) = recommended

admin January 1, 2017 Leave A Comment Permalink

Books: Fleet of Worlds Books 1, 2, and 5


Fleet of Worlds by Larry Niven and Edward M. Lerner
Juggler of Worlds by Larry Niven and Edward M. Lerner
Fate of Worlds by Larry Niven and Edward M. Lerner

Summary: As a physics loving kid growing up in rural Northern California my sources for physics were few and far between. Mostly there was the county library. I learned calculus from a textbook in the library (when I went back a decade later, my checkout date was still stamped on the circulation slip, only ten people or so had checked it out after me over the course of a decade.) The first edition of Spacetime Physics by Taylor and Wheeler taught me hyperbolic trigonometry before normal trigonometry. But there was no physics text book. Instead I turned to the vast archive of Scientific American magazines, the pop-sci physics books, and eventually, for Christmas one year, I got a college physics textbook.

In addition to this, of course, there was also the science fiction section. Hard science fiction in particular was something I ate up. In this mode I first encountered Larry Niven. His Ringworld is a wonderful novel, but more importantly Niven did try to bring in valid theoretical physics to his novels. So, when November of 2016 hit, and I found myself in need of withdrawal from news, I decided reading some Niven would be my comfort food. It was this that led me to pick up book 5 of the Fleet of Worlds pentalogy. Oops, wrong order. So then I read book 1. And discovered that I head read it years before. So then I read book 2. Book 1 is the story of the revolt of captured humans from Puppateers. Book 2 is the other side of a bunch of “known space” stories from the perspective of paranoid detective Sigmund Ausfaller. Book 5 is the final cleaning up.

Rating: Book 2 is very disjointed if you haven’t read much other work set in Niven’s “known space”. Book 1 and 5 are both big plot focused, there is still a bit of the hard science fiction in both that I enjoyed. I’ve never read Niven for his characterization, but I did enjoy the attempt in these books to show events from different alien perspectives. If your a known space junky these books are a good read, otherwise, I’d recommend other Niven material like Ringworld or the Mote in Gods Eye.

admin December 31, 2016 Leave A Comment Permalink

Book: Death’s End

Death’s End by Cixin Liu translated by Ken Liu.

Summary: The third and final book in The Remembrance of Earth’s Past trilogy (best known for its first book, “The Three-Body Problem”). To say that this is an epic conclusion is an understatement to what the word epic means. The story is manifold but primarily focuses on Cheng Xin, an aerospace engineer of the 21st century, and picks up after the defeat of the Trisolarans via the dark forest deterrence. The novel then swings a wide arc into the future, with some very interesting physics ideas spaced in along the way.

Rating: I’m inclined to put this one at about the same level as the first novel, I think I enjoyed the second the most (though I suspect that I like Ken Liu as a translator better. I can’t attest to how the translation compares to the original but there were less points in his translations that I knew I was reading a translation). I highly recommend the entire trilogy, especially if you like hard science fiction.

Speculation: Would give away too much! This is speculative hard sci fi at its best.

admin December 21, 2016 Leave A Comment Permalink

Book: Rebel Genius, Warren S. McCulloch’s Transdisciplinary Life in Science


Rebel Genius: Warren S. McCulloch’s Transdisciplinary Life in Science by Tara Abraham

Summary: In “A Logical Calculus of the Ideas Immanent in Nervous Activity” Warren McCulloch and Walter Pitts presented one of the first mathematical/logical models of a neuron. The model is at once naive and also incredibly insightful: it certainly is not fully realistic, and yet it is an attempt to reduce the complexity of the brain and intelligence down to a simple model amenable to logic and mathematics. In many ways the model is a founding paper for the connectionist approach to understanding the mind, though one can see through its connections to boolean algebra the thread of computationalist ideas as well. This book is a very academic biography of one of the authors of this important paper, Warren McCulloch.

Rating: This is the sort of book you get assigned to read in a history of sciences course. The strength of the book is in its examination of the challenge of transdisciplinary work, here defined not just as a mingling of disciplines, but as one discipline being used as a stronger tool in another (here logic and math being applied across the divide into neuroscience). I found the sections discussing how McCulloch’s work was perceived of across the disciplines interesting. Unfortunately the book is very light on a detailing of the actual contributions of McCulloch. I left the book having some idea of who McCulloch was, and the events that transpired to put him where he sits in the pantheon of early neuroscientists, but didn’t come away with a deep understanding of the details of his work, or how it compared and contrasted with that of other early AI pioneers (like Hebbs and Weiner).

Speculation: Mappings from one field into another often bring about great change in the target field. Consider these mappings as reductions in the computational complexity sense. In computational complexity reductions lead to complexity classes and the realization that for some of these classes there are complete problems: every problem in the class can be reduced to these complete problems. One wonders if there are similar notions across the disciplines. And what the complete problems we should seek out when at first delving into a new field?

admin December 20, 2016 Leave A Comment Permalink

Book: Children of the New World

Children of the New World: Stories by Alexander Weinstein

Summary: A collection of short stories about technology and the possible futures it might give rise to. You need only look at the screen upon which you are reading this to understand how profoundly technology has changed our lives. In these short stories Weinstein projects many of our current trends to endpoints that are sometimes inspiring, but more often disturbing and dark.

Rating: This is cyberpunk with a human heart. If you like Black Mirror, you’ll like these stories.

Speculation: Someday machines will use these stories in the classes they teach about how humans spent a lot of time thinking about the emotional impact of machines. They will puzzle.

admin November 20, 2016 Leave A Comment Permalink

Book: To Engineer Is Human

To Engineer Is Human: The Role of Failure in Successful Design by Henry Petroski

Summary: Nearly every day I drive across one of the bridges that spans the ship canal connecting the Puget Sound and Lake Washington. It’s easy to not notice that the bridge that I drive on is an engineering feat. The interesting thing, as well described in this book, is how the building of such structures like these bridges was the culmination of a series of failures, each one pushing the others into uncharted territory. Primarily concerned with civil engineering the book hammers home that progress in engineering is tightly coupled to failure, essentially because building differently inevitably leads to issues which even the best theory and planning cannot anticipate.

Rating: A good summary of what it’s like to build into the unknown.

Speculation: I’m always struck by the description of books about innovation or building new things how much these remind me of solving instances of NP-complete problems. In general we don’t know good methods to try to push our systems into newness, but when we get there we can often see why were able to get there. In the old days this was limited by our own brains, but these days, computation helps us define these limits. It is as if the whole universe was set up to help explore the region of intractable problems.

admin November 20, 2016 Leave A Comment Permalink

Book: Hedge Fund Market Wizards


Hedge Fund Market Wizards by Jack D. Schwager.

Summary: The first rule of about traders is never to believe anything that a trader says. If there exist methodologies that can ‘beat a market’ then in divulging this info is not in the best interests of those who are profiting. Hedge Fund Market Wizards is the latest in a series of market wizard books and consists of a series of interviews with hedge fund managers who have been identified as successful. The criteria for success is high returns relative to risk. So, depending on your view of markets, this is either an interesting group to interview, or an interview of a bunch of guys who have won more than their share of large number of coin tosses.

Rating: I like books that interview ‘experts’ in fields as they give one a feel for the culture of the field. Coders at Work by Peter Seibel, for example, is the one book I read before becoming a software engineer that really gave me an idea about what coders thought about. Similar this book’s biggest virtue is that it provides a cultural guide to the what hedge fund managers think about. There is a diversity of different hedge fund styles that are discussed. Schwager does a good job pulling out people’s views, but as the first sentence of this post says, the traders themselves divulge a varying amount about their actual techniques. Still one gets a sense for how they think, and their approach to the world of markets. I particularly like the interviews of Jaffray Woodriff and Edward Thorp (the later invented card counting in blackjack). Likely the portions of the interview that were most interesting were those discussing risk control, with a majority of managers taking on fairly strong stoping methodologies for trading. Another interesting part was the stress associated with managing others money. Recommended if you want to get a glimpse into the culture of hedge funds.

Speculation: LOL, yep. Also I have deleted my own speculation, as if it is correct, then…well…you know 😉

admin August 31, 2016 Leave A Comment Permalink

Book: The Pentagon’s Brain


The Pentagon’s Brain: An Uncensored History of DARPA, America’s Top-Secret Military Research Agency by Annie Jacobsen.

Summary DARPA nee ARPA is a U.S agency in the Department of Defense responsible for emerging technologies. If you’ve heard of it, it’s likely because you know that the internet started in part from one of ARPAs projects, a packet switching network called the ARPANET. This book details the history of DARPA, initially created after the launch of Sputnik and the realization that future technology superiority was a key military goal. The book starts with details of the connections between the JASONs, a group of elite scientists and DARPA, and then hits the highlights of much of the research that was funded by DARPA. Sadly my own DARPA funded research (from my previous life) on self-correcting quantum computer was not mentioned 😉

Rating The book shines mostly in the detailed motivations of the agency and it’s relationship with the JASONs. One the technological front I found it a bit frustrating in lack of details (OK so some of this is likely because it is still classified, but others were at a fairly superficial level), and would have likely even more color on the people who ran DARPA. But it’s a good book to get a broad understanding of the agency, where it came from, and what it’s had its hands in.

Speculation One of the most interesting concepts in the book is the idea that the type of research DARPA focused on needed to be “pre-requirements”:

“There is a kind of chicken-and-egg problem in other words, in requirements and technology,” Rechtin explained. “The difficulty is that it is hard to write formal requirements if you do not have the technology with which to solve them, but you cannot do the the technology unless you have the requirements.” The agency’s dilemma, said Rechtin, was this: if you can’t do the research before a need arises, by the time the need is there, it’s clear that the research should already have been done.

Would that it were the funders who want 3 month reports on milestones have this sentence read to them daily!

Technologies that don’t exist do have one specification, that they are not currently specified. If one wanted to work formally in this area, wouldn’t it be cool if we had a formal specification of what we know. A map of the totality of our technological knowledge. If we could then dice this into different views we could, potentially, see where our gaps are, the places where in the totality of all the formal specification, we are missing knowledge. And use this to discover technologies.

admin August 22, 2016 1 Comment Permalink