Category Archives: Science

Science

Glimpsing into the Future?

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I saw this blog posting on NPR about some recent experiments by Dr. Daryl Bem of Cornell that are so very weird and interesting that I just had to share.  The blog, by Robert Krulwich, delves into a recent paper by Dr. Bem in which he describes 9 experiments meant to probe extrasensory perception — ESP.  I haven’t read the paper myself, as it is quite long and I haven’t found the time, but if Krulwich’s understanding of the results is correct, it is fascinating stuff.

Krulwich describes two of Bem’s experiments in detail.  In the first, Bem had students sit in front of a computer, which showed two curtains on the screen.  Behind one was an image, behind the other nothing.  The computer randomly determined where the image would go.  The students’ job was to pick the curtain hiding the image.  As you might expect, this is a purely random process and, sure enough, in the first variant of the experiment, the students picked the curtain with the image 49.8% of the time, essentially random guessing.  However, when they were told that erotic images might be behind the curtain — porn if you will — they picked the curtain with the image 53.1% of the time.  Not a whole lot more, but statistically different than random.  Somehow, they were able to “see” where the image was without any more information, given the right motivation.

In the second, even more intriguing experiment (to me), Bem had the students again sit at a computer.  They were shown 64 words, one at a time for 3 seconds each, and asked to visualize the word for those 3 seconds.  So, if the word was tree, the students were supposed to visualize a tree.  After they went through all the words, they were given a quiz on what words they were shown — a memory quiz.  All fine so far.  After the quiz, they were shown 24 of the words, chosen at random, and again asked to visualize them.  That was the end of the experiment.  However, what Bem found is that the students did much better with those 24 words on the quiz than any other random selection of 24 words, even though they only saw those 24 words after the quiz.  That is, studying those words after the quiz somehow helped them during the quiz.  Studying after the fact improved their test score.

Bem is interpreting this as some kind of seeing into the future, or that time is fluid or porous.  And already it seems one paper has not been able to reproduce the results of one of his experiments (not either of these two described here).  And I would say it is way too early to speculate about what these results mean about the nature of time and seeing the future.  But, I have to say, these results are very strange, completely counter to anything we might have expected, and certainly very intriguing.  It certainly begs more study, and I’m sure an army of scientists are trying to reproduce Bem’s results as you read this.  I for one will definitely be following this story to see where this all leads.

Books, Science

The Calculus Wars by Jason Socrates Bardi

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People outside of science often have the impression that the practice of science is a sort of altruistic pursuit of knowledge with all scientists working towards the same goal: increasing our understanding of the universe.  And, in a very rough sense, this is true, if one looks at the development of science itself and ignores the personalities that are involved.  However, if you look at the details, egos and the realities of limited funding often get in the way and produce dramas that are every bit as melodramatic as any other human endeavor.

There is no better example of this than that described in The Calculus Wars by Jason Socrates Bardi.  The Calculus Wars describe the development of calculus, today accepted to be independently discovered by Sir Isaac Newton and Gottfried Leibniz.  In fact, while Newton tends to get more credit (he technically did discover it first, though Leibniz published first), our modern notation is due to Leibniz.  When Leibniz first published his version, there was no big outcry.  But, over the years, as Newton want to assert his primacy over the discovery, the fight between Newton and his people and Leibniz and his became downright nasty, culminating in assertions of plagiarism.  In the end, Newton essentially won, as we tend to attribute calculus to him.  But, to paraphrase Bardi, while the discovery of calculus illustrates the great heights the human mind can achieve, the war that develop between these two demonstrates the corresponding depths we can sink to.

To me, the most fascinating part of the story is the life of Leibniz.  Here is a true genius, a man with no formal training in math (he was a lawyer) who taught himself what he needed to know to eventually develop calculus.  He was a renaissance man befitting the word, with activities in mining, math, science, politics, law, and philosophy.  He was in some sense the first geologist.  He established the first scientific society in Germany.  For all of his accomplishments and his genius, he languished in his later years researching a history of the genealogy of his sponsoring noble, an effort that both distracted from pursuits more befitting such a great mind and kept him in the backwaters of the scientific world.  If Leibniz had the intellectual freedom that Newton did, one wonders what he might have achieved.

Overall, this was a highly entertaining account of two great intellectuals and their personal battle.  It certainly makes me want to learn more about Leibniz.  I highly recommend it to anyone who has even a casual interest in the history of math and science.  While it does highlight the lows of scientific endeavor, showing the all too human face, I still believe that the scientific method is the most powerful way of looking at the universe that humanity has devised.

Books, Science

Simplexity by Jeffrey Kluger

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kluger-simplexityA lot is made of complexity and complex systems. A prime example is the formation of materials from atoms. Atoms are, for the most part, relatively simple things. However, put them together, and very complex behavior emerges, from basic defects such as vacancies and dislocations to properties such as superconductivity and fast ion conduction. Another example is the complex behavior of even the simplest of ecosystems created by ants.

Understanding how complex systems arise from simple components — in essence simplifying them in a way that can be used to make predictions and design useful systems — has become a science in itself. In his book Simplexity, Jeffrey Kluger gives an overview of this new science. His approach is to describe many different examples of how complexity is hidden around us, how complexity emerges from simplicity, and how complex things can be understood via some simple rules. This connection, between complexity and simplicity, leads to the term simplexity. The framing thread is the work done at the Santa Fe Institute, founded to study exactly these kinds of issues.

The examples Kluger describes are definitely very interesting. They include the spread of disease (how such seemingly complex and random things such as the spread of disease can be traced to simple origins), the complexity of different types of jobs (driving a truck is more complex than being a middle level manager), and how hard it is for people to judge risk to themselves (illustrated by the behavior of people in the Towers on 9/11).

The examples do a good job of describing various aspects of complexity science, of showing how things we think are simple are really very complex and vice versa. And I did learn a number of things. For example, in evacuation routes in buildings, they purposely put false columns in the rooms to break the flow of people to emergency exits as that adds some “turbulance” that makes the overall flow of people smoother and less likely to jam at the doors. Also, in describing how our technology has become overly complex, so much so that most of us can’t really figure out our devices, at least not fully, he tells about research going on at the Media Lab at MIT on the “bar of soap“.  This sounds like an awesome device, something that would be awesome to see and the implications for technology in general and how we interact with it are really intriguing. And these are just a few of the things that I learned.

However, I was overall disappointed, because I don’t feel like I learned anything about the science of complexity. I learned about how things are complex, and how they can be simplified in some ways. And some of the specific examples were really interesting. But, I really didn’t learn about the science behind it, how complex systems are studied, how they are classified, or how they are characterized. What makes a complex system amenable to study? To simplification? What makes a collection of simple things complex? The book is a bit of a tour de force of examples from complexity science, but there isn’t any deeper probing behind any of it, nothing that gives any deeper insight.

Thus, as an introduction, of a teaser of the science, the book succeeds. However, as any real introduction to the science itself, it felt flat to me.

Books, Science

Professor Stewart’s Cabinet of Mathematical Curiosities by Ian Stewart

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I picked this up randomly at a bookstore in Santa Fe, intrigued by the thought of delving into a little bit of math.  And that is just what this is.  Professor Stewart’s Cabinet of Mathematical Curiosities, by Ian Stewart naturally, is a tour de force of many of the most interesting corners of math, both historical and modern, covering each just a little bit.  Each topic is never given more than a couple of pages, though some of the topics do join together.  He covers everything from regular polyhedra (Platonic solids) to Fibonacci numbers to the shape of oscillations on a drum head to complexity science.  He gives just enough to tantalize, to intrigue, to whet the appetite.  The history of math is also scattered throughout with brief mentions of many of the important mathematicians.  Finally, there are lots of exercises and puzzles for the interested reader which, I admit, I was not — after so many years of school, I’m hard pressed to do anything that appears like homework.  But, the solutions are in the back of the book and offer further insight into the mathematical topic at hand.

There were two concepts that particularly caught my attention, mostly because I hadn’t heard of them before and they are so interesting.  The first is Benford’s Law.  Imagine you are working at a company and you decide to cook the books a bit, creating false transactions.  You might think that the numbers associated with the transactions should essentially be random, that, for example, the number of transactions starting with 1 (like $10224) should be about the same as starting with 2 ($221) and so forth.  In reality, this isn’t true.  If you look at the distribution of house numbers in a city, or the size of islands in the Bahamas, or the GDP of the nations of the world, numbers starting with 1 are more common than 2 which are more common than 3, and so on.  This fact is Benford’s Law, and it is used today to catch embezzlers and others who don’t realize that the distribution of these numbers isn’t random, but follow this pattern.  Wikipedia, naturally, has a nice article about Benford’s Law.

Ok, the second example I’ve heard about but it is presented in a very nice way.  That example is Penrose tiles (here is the Wikipedia article about those).  If you think about tiling the plane, like say tiling your bathroom floor, there are three shapes you can use that will let you completely tile the floor: (equilateral) triangles, squares, and hexagons.  These, in turn, give you patterns that have 3, 4 or 6-fold symmetry (if you rotate your view direction by 120, 90, or 60 degrees, the pattern will look the same).  It was thought that 5-fold symmetries are impossible:  you can’t tile a floor with pentagons.  However, Roger Penrose showed that if you use two shapes, a kite and a dart, you can tile the floor and get a 5-fold symmetry.  What’s more, the resulting pattern is not completely periodic.  It has short range, but no long range order.  Why does this all matter?  Well, symmetries are crucial for understanding crystal structures:  atoms arrange themselves in patterns that are the three dimensional equivalent of these 2-D patterns.  Again, no one thought that 5-fold symmetry could exist, but on the surface of chemical compounds, “quasi-crystals” can form, which exhibit the same patterns that Penrose tiles do.  Very cool!

This book offered lots of glimpses into many unfamiliar corners of math, and as such was very interesting.  He describes each topic at a level that the basic idea can be gleaned by those who have little or no math background.  I highly recommend this book to anyone who has even a vague interest in math.

One final note: in the previous book I discussed, The Golden Ratio by Mario Livio, he claimed that the nautilus shell followed the logarithmic curve.  Stewart says that isn’t so:  the shell is wound tighter than a logarithmic curve would dictate.

Books, Science

The Golden Ratio and Understanding the Universe

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When you stop and think about it, it is truly astonishing how well we can describe the universe around us using mathematics.  That equations as simple as F=ma and E=mc^2 can describe so much of what we observe is really amazing.

The Golden Ratio by Mario Livio is essentially an examination of one of the most remarkable numbers to be discovered as a pretext for ultimately exploring the question why do mathematics work so well.  The golden ratio, known from the time of the ancient Greeks, is a pretty simple concept: take a line (defined by points A and B) and divide it (at point C) such that the length of the entire line over the length of the longer portion of the division is the same as the length of this longer portion over the shorter portion.  That is, if the longer portion is CB and the shorter is AC, then AB/CB=CB/AC.  A pretty simple concept and definition.  It turns out, this has many profound consequences.  This golden ratio, normally dubbed phi by mathematicians, is one of the first irrational numbers discovered and is, in some sense, the most irrational of all.  It shows up in many branches of math, especially geometry, and has been observed in nature in the patterns formed by petals on flowers, the seeds in sunflowers, the shape of certain seashells, and the shape of galaxies.  It is ubiquitous in nature.  Why should that be so?  That is the real point of Livio’s book.

Livio spends a lot of time on the history of phi, how it was discovered, how it was understood, and what it means to math and science.  When he is focusing on the role of phi in science, the book is wonderful.  There were many very interesting insights that I was unaware of that were real gems to discover.  Livio also spends a lot of time on the supposed role the golden ratio played in art, poetry, music, and architecture, including the constrution of the pyramids of Egypt.  His goal is to debunk those who claim that the golden ratio was an instrumental part in many such works, and he does so convincingly.  Unfortunately, I found this a huge distraction and very uninteresting.  I would much rather that he had filled those pages with more discussion of how the golden ratio is found in nature and science.  I understand that he felt a need to determine where the golden ratio is really to be found, but I felt it was over done.

Ultimately, the fact that the golden ratio, and by extension math as a whole, figures in so much of what we see around us leads Livio to examine why that is so.  He describes two alternative views.  First, that the universe is objectively Platonic; that humans are discovering the laws of the universe and those are written in the language of math.  Any civilization in the universe would uncover the same mathematical laws.  The second view is that math is a human language, a human construct, and we are using it to interpret our observations of the universe.  Civilizations with different formulations of mathematics would have a different view of how the universe works.  Livio falls somewhere in the middle, and, to be honest, I did not overly understand his reasoning for his position.

It is an interesting question.  I guess I would tend a bit more towards the Platonic view.  I think that it is just too striking that our math and physics can not only describe but predict what is happening around us so well.  I once had a chat with a fellow grad student at the UW physics department that was about this.  His point, as far as I could understand, is that maybe we create the reality around us via our investigations and our interpretations of our observations.  Essentially, that there is no objective reality, that reality is created by the observer.  Thus, as we develop our math, we view the universe through that math and thus shape it to conform to our math.  This “the observer shapes reality” perspective seems like an extreme view of the Copenhagen interpretation of quantum mechanics.  I definitely wouldn’t go so far as this.  But, it is an interesting question.