Strange attractors

A couple of months ago, I read Paul J. Steinhardt's wonderful book The Second Kind of Impossible, about his (and others') search for quasicrystals -- a bizarre form of matter that is crystalline but aperiodic (meaning it fills the entire space in a regular fashion, but doesn't have translational symmetry).  Here's an artificial quasicrystal made of aluminum, palladium, and manganese:

[Image is in the Public Domain courtesy of the United States Department of Energy]

As the above photograph shows, they can be created in the lab, but Steinhardt believed they could occur naturally -- and he finally proved it, in a meteorite sample he and his team found in a remote region of Siberia.

I was immediately reminded of Steinhardt's aperiodic crystals when I read a paper in Chaos: An Interdisciplinary Journal of Nonlinear Science, by Francesca Bertacchini, Pietro Pantano, and Eleanora Bilotta, of the University of Calabria, who were experimenting with another nonrandom but chaotic shape -- a "strange attractor."

A strange attractor is a concept from fractals and chaos theory, and represents a value toward which a perturbed system tends to evolve.  Chaos theory has been around for a while, but came to most people's attention from Jurassic Park, when the character Ian Malcolm (portrayed in memorable fashion by Jeff Goldblum) is explaining the unpredictability of complex systems using the direction a drop of water rolls on a relatively (but not perfectly) flat surface, in this case, the back of someone's hand.  Systems like that one tend to rush far out of equilibrium -- once the drop starts to move, it keeps going -- but some systems settle into a set of loops or spirals, as if something in the middle was drawing them in.

Thus the name strange attractor.

These systems, when mapped out, create some beautiful patterns -- like Steinhardt's quasicrystals, with the superficial appearance of regularity, but without any repeats or obvious symmetries.  Bertacchini et al. used the mathematical functions describing the system to drive a 3-D printer and actually create models of what strange attractors look like.  The team was struck with how beautiful the shapes were, and had a goldsmith fashion them as jewelry.  Here are a few of their creations:

They look a little like Spirograph patterns gone off the rails, but they have a striking, almost-but-not-quite-symmetrical shape that keeps drawing the eye back.

The authors write:

[We used] a chaotic design approach used to develop jewels from chaotic design.  After presenting some of the most important physical systems that generate chaotic attractors, we introduced the basic steps of this approach.  This approach exploits a number of fundamental characteristics of chaotic systems.  In particular, the parametric design approach exploits the concept of extreme sensitivity to the initial data that leads to evolutionary transformations of dynamic systems, not only along the traditional routes to chaos and through qualitative changes in the starting chaotic system, but also through changes in the basic parameters of the system, which create infinite chaotic forms.  Such phase spaces, therefore, represent an enormous potential to be exploited in the design of artistic objects, whether they are jewelry pieces or other objects of abstract art. In the computational approach used, each shape is unique and it is identified by a set of parameters that almost constitute its precise value.  This leads to the creation of unique artistic forms and, thus, to the customization of products in the case of jewelry pieces, which exploits chaotic design as a methodology.

The whole thing brings up for me the mysterious question of what we find beautiful -- and how so often, it's a balance between predictability and unpredictability, between symmetry and randomness.  It reminds me of the quote from the brilliant electronic music pioneer Wendy Carlos: "What is full of redundancy is predictable and boring.  What is free from all structure is random and boring.  In between lies art."

****************************************

Patterns and meaning

I remember a couple of years ago noticing something odd.  While eating breakfast on work days, I'd finish, and always give a quick glance up at the digital clock that sits on the counter.  Three times in a row, the clock said 6:19.

I know there's a perfectly rational explanation; I'm a total creature of habit, and I did the same series of actions in the same order every single work morning, so the fact that I finished breakfast three days in a row at exactly the same time only points up the fact that I need to relax a little.  But once I noticed the (seeming) pattern, I kept checking each morning.  And there were other days when I finished at exactly 6:19.  After a few weeks of this, it was becoming a bit of an obsession.

[Image licensed under the Creative Commons Mk2010, LED digital wall clock (Seiko), CC BY-SA 3.0]

So being a rationalist, as well as needing a hobby, I started to keep track.  And very quickly a few things became obvious:

• I almost always finished breakfast (and checked the clock) between 6:16 and 6:22.
• 6:19 is the exact middle of that range, so it would be understandable if that time occurred more often.
• Even considering #2, 6:19 turned out to be no more likely than other times.  The distribution was, within that six minute range, fairly random.

So I had fallen for dart-thrower's bias, the perfectly natural human tendency to notice the unusual, and to give it more weight in our attention and memory.  The point is, once you start noticing this stuff, you're more likely to notice it again, and to overestimate the number of times such coincidences occur.

The whole thing comes up because of a link sent to me by a loyal reader of Skeptophilia called, "Angel Numbers Guide: Why You Keep Seeing Angel Number Sequences."  I'm not going to recommend your going to the site, because it's pretty obviously clickbait, but I thought the content was interesting from the standpoint of our determination that the patterns we notice mean something.

The site is an attempt to convince us that when we see certain numbers over and over, it's an angel attempting to give us a message.  If you notice the number 1212, for example, this is an angel encouraging us to "release our fears and apprehensions, and get on with pursuing our passions and purpose... [asking you to] stay on a positive path and to use your natural skills, talents, and abilities to their utmost for the benefit of yourself and others."

Which is good advice without all of the woo-woo trappings.

Some numbers apparently appeal not only to our desire for meaningful patterns, but for being special.  If you see 999 everywhere, "you are amongst an elite few... 999 is sometimes confrontative, and literally means, 'Get to work on your priorities.  Now.  No more procrastinating, no more excuses or worries.  Get to work now."

Since a lot of the "angel numbers" involve repeated digits, I had to check to see what 666 means.  I was hoping it would say something like, "If you see 666, you are about to be dragged screaming into the maw of hell."

But no. 666 apparently is "a sign from the angels that it's time to wake up to your higher spiritual truth."  Which is not only boring, but sounds like it could come from a talk by Deepak Chopra.

So the whole thing turns out to be interesting mostly from the standpoint of our desperation to impose some sense on the chaos of life.  Because face it; a lot of what does happen is simply random noise, a conclusion that is a bit of a downer.  I suspect that many religions give solace precisely because they ascribe meaning to everything; the Bible, after all, says that even a sparrow doesn't fall from the sky without the hand of God being involved.

Me, I think it's more likely that a lot of stuff (including birds dying) happens for no particularly identifiable or relevant reason.  Science can explain at least some of the proximal causes, but as far as ultimate causes?  I think we're thrown back on the not very satisfying non-explanation of the universe simply being a chaotic place.  I understand the appeal of it all having meaning and purpose, but it seems to me that most of what occurs is no more interesting than my finishing breakfast at 6:19.

*************************************

I've always had a fascination with how our brains work, part of which comes from the fact that we've only begun to understand it.  My dear friend and mentor, Dr. Rita Calvo, professor emeritus of human genetics at Cornell University, put it this way.  "If I were going into biology now, I'd study neuroscience.  We're at the point in neuroscience now that we were in genetics in 1900 -- we know it works, we can see some of how it works, but we know very little in detail and almost nothing about the underlying mechanisms involved.  The twentieth century was the century of the gene; the twenty-first will be the century of the brain."

We've made some progress in recent years toward comprehending the inner workings of the organ that allows us to comprehend anything at all.  And if, like me, you are captivated by the idea, you have to read this week's Skeptophilia book recommendation: neuroscientist Lisa Feldman Barrett's brilliant Seven and a Half Lessons About the Brain.

In laypersons' terms, Barrett explains what we currently know about how we think, feel, remember, learn, and experience the world.  It's a wonderful, surprising, and sometimes funny exploration of our own inner workings, and is sure to interest anyone who would like to know more about the mysterious, wonderful blob between our ears.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

The grand plan

When I'm teaching the unit on evolution in my biology classes, one of the hardest ideas to expunge from my students' brains is that evolution is goal-oriented.

Take, for example, the worn-out example, used in every seventh-grade life science textbook, about giraffes' long necks.  Why do they have these outlandish proportions?

So they can reach food higher up in trees, of course.

The subtle error here is that it implies that a bunch of short-necked giraffes were standing around on the African savanna, looking longingly up at the tempting foliage higher up, and one said, "Dude.  It'd be nice if we could reach higher, don't you think?"  And another said, "Well, we're kinda screwed, because we're short.  But if we had longer-necked kids, that'd be cool, yeah?"

The other giraffes agreed, and lo, they had long-necked kids.

[Image licensed under the Creative Commons Universalwin1222, Lamarckian inheritance- Giraffes, CC BY-SA 4.0]

Okay, I'm oversimplifying, here, but the gist is correct.  The assumption of goal-orientation puts the cart before the horse; that there was some sort of end product evolution had in mind, so organisms headed that way.  Of course, the truth is both simpler and more complex.  What Darwin actually said was that organisms vary from some other cause (being pre-Mendel, he didn't know about genes and mutations), and the environment selects the ones that work the best.  The others die off, taking their deleterious genes with them.

No goal necessary.

The ultimate in goal-orientation, of course, is strict creationism, which posits a designer who created everything as it currently is.  The immediate problem with this -- besides the fact that there's no evidence for it whatsoever -- is that there are a lot of things that seem, well, poorly designed.  The creationists are fond of trotting out some examples of complex structures that work pretty well (such as the eye) and conveniently ignore some examples of seriously poor design (such as the male urinary/reproductive system, which routes the urethra through the prostate gland, making a lot of older guys seriously unhappy).

All of this goal-orientation is known to philosophers as "teleological thinking" -- the attribution of a final cause or goal in natural processes.  And just last week, a paper came out of some research in France that suggests teleological thinking as a commonality between creationism... and conspiracy theories.

The study, done by Pascal Wagner-Egger, Sylvain Delouvée, Nicolas Gauvrit, and Sebastian Dieguez, found an interesting set of correspondences:

Although teleological thinking has long been banned from scientific reasoning, it persists in childhood cognition, as well as in adult intuitions and beliefs.  Noting similarities between creationism (the belief that life on Earth was purposefully created by a supernatural agent) and conspiracism, we sought to investigate whether teleological thinking could underlie and associate both types of beliefs. First, we sought to establish whether teleological thinking, classically associated with creationism, was also related to conspiracist beliefs. College students filled a questionnaire including teleological claims and conspiracist statements, as well as measures of analytical thinking, esoteric and magical beliefs, and a randomness perception task.  Promiscuous teleology — the tendency to ascribe function and a final cause to nonintentional natural facts and events — was significantly... correlated with conspiracist beliefs scales.  In addition, teleological thinking was negatively related to analytical thinking, and positively to esoteric beliefs, which in turn were both related to acceptance of conspiracist beliefs.

The results are perhaps not terribly surprising, although I don't know if anyone previously has linked them this way.  Both creationism and conspiracy theories imply a belief in a Grand Plan -- benevolent in the case of creationism, malevolent in the case of conspiracy theories.  Adherents to either tend to be repelled by the idea of chaos, that things just happen because they happen.  (Thus "even when bad things happen, God has a plan" from the former, and the steadfast refusal by the latter to believe that any unpleasant event might just be random bad luck.)

I'd add one more piece to this, however, and that's the determination by both to avoid or explain away facts that contradict their favorite model of how the universe works.  Of course, that unites them with some other groups that aren't necessarily thinking teleologically, such as the anti-vaxxers.

Although the anti-vaxxers tend to believe that there's a huge coverup by "Big Pharma" of the horrific side effects of vaccination, so maybe there's some overlap there, too.

Anyhow, I thought the whole thing was interesting.  And it does bear mention that the students who are the most repelled by evolution for non-religious reasons tend to be the ones who hate the idea that so much of the world could be the result of randomness.  How can the biodiversity on the Earth, with all of its "endless forms most beautiful and most wonderful" (to quote Darwin), be produced by chance mutations?

Of course, the universe is not compelled to be organized in such a way that it makes you comfortable.  The evidence is very much in favor of the idea that mutations plus selection have generated all of the life forms you see around you.  And since selection is a "whatever works" sort of process, it's unsurprising that sometimes it creates designs of dubious logic -- such as the urethra/prostate situation I mentioned above, which a friend of mine calls "routing a sewer pipe through a playground."

********************************

This week's Skeptophilia book recommendation is a classic, and especially for you pet owners: Konrad Lorenz's Man Meets Dog.  In this short book, the famous Austrian behavioral scientist looks at how domestic dogs interact, both with each other and with their human owners.  Some of his conjectures about dog ancestry have been superseded by recent DNA studies, but his behavioral analyses are spot-on -- and will leaving you thinking more than once, "Wow.  I've seen Rex do that, and always wondered why."

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]

Patterns and meaning

I remember a couple of years ago noticing something odd.  While eating breakfast on work days, I'd finish, and always give a quick glance up at the digital clock that sits on the counter.  Three times in a row, the clock said 6:19.

I know there's a perfectly rational explanation; I'm a complete creature of habit, and I do the same series of actions in the same order every single work morning, so the fact that I finished breakfast three days in a row at exactly the same time only points up the fact that I need to relax a little.  But once I noticed the (seeming) pattern, I kept checking each morning.  And there were other days when I finished at exactly 6:19.  After a few weeks of this, it was becoming a bit of an obsession.

[image courtesy of the Wikimedia Commons]

So being a rationalist, as well as needing a hobby, I started to keep track.  And very quickly a few things became obvious:

1. I almost always finish breakfast (and check the clock) between 6:16 and 6:22.
2. 6:19 is the exact middle of that range, so it would be understandable if that time occurred more often.
3. Even considering #2, 6:19 turned out to be no more likely than other times.  The distribution was, within that six minute range, fairly random.

So I had fallen for dart-thrower's bias, the perfectly natural human tendency to notice the unusual, and to give it more weight in our attention and memory.  The point is, once you start noticing this stuff, you're more likely to notice it again, and to overestimate the number of times such coincidences occur.

The whole thing comes up because of a link sent to me by a loyal reader of Skeptophilia called, "Every Time This Happens, an Angel Reveals Itself!"  I'm not going to recommend your going to the site, because it's pretty obviously clickbait, but I thought the content was interesting from the standpoint of our determination that the patterns we notice mean something.

The site is an attempt to convince us that when we see certain numbers over and over, it's an angel attempting to give us a message.  If you notice the number 1212, for example, this is an angel encouraging us to "release our fears and apprehensions, and get on with pursuing our passions and purpose... [asking you to] stay on a positive path and to use your natural skills, talents, and abilities to their utmost for the benefit of yourself and others."

Which is good advice without all of the woo-woo trappings.

Some numbers apparently appeal not only to our desire for meaningful patterns, but for being special.  If you see 999 everywhere, "you are amongst an elite few... 999 is sometimes confrontative, and literally means, 'Get to work on your priorities.  Now.  No more procrastinating, no more excuses or worries.  Get to work now."

Since a lot of the "angel numbers" involve repeated digits, I had to check to see what 666 means.  I was hoping it would say something like, "If you see 666, you are about to be dragged screaming into the maw of hell."

But no.  666 apparently is "a sign from the angels that it's time to wake up to your higher spiritual truth."  Which is not only boring, but sounds like it could come from a talk by Deepak Chopra.

So the whole thing turns out to be interesting mostly from the standpoint of our desperation to impose some sense on the chaos of life.  Because face it; a lot of what does happen is simply random noise, a conclusion that is a bit of a downer.  I suspect that many religions give solace precisely because they ascribe meaning to everything; the bible, after all, says that even a sparrow doesn't fall from the sky without the hand of god being involved.

Me, I think it's more likely that a lot of stuff (including birds dying) happens for no particularly identifiable or relevant reason.  Science can explain at least some of the proximal causes, but as far as ultimate causes?  I think we're thrown back on the not very satisfying non-explanation of the universe simply being a chaotic place.  I understand the appeal of it all having meaning and purpose, but it seems to me that most of what occurs is no more interesting than my finishing breakfast at 6:19.