Frick & Frack(tal)

Press photo of skating duo, Frick & Frack

     Press photo of skating duo, Frick & Frack

      Don't worry, I am no good on the ice, nor am I a mathematician or scientist capable of explaining what a fractal is.  There are already plenty of people and algorithms working away to find the "perfect" shape, something partially credited earlier to Buckminster Fuller (think geodesic domes).  But fractals are quite different, but similar (what??).  Here's a quick explanation (and the only one I'll foist upon you) from Scientific American: Fractals are geometric figures.  They are difficult to define formally but their features and beauty make them accessible and intriguing.  One feature is self-similarity, which describes how fractals have patterns that recur at different scales.  In other words, when you zoom in, you will find a smaller version of a pattern you had seen initially.  When you zoom in some more, you will find an even smaller version of that pattern, and so on.  This seems to go on infinitely.  Added Florence Williams in her book The Nature Fix (mentioned in the previous post): Benoit Mandelbrot first coined the term "fractal" in 1975, discovering that simple mathematic rules apply to a vast array pf things that looked visually complex or chaotic.  As he proved, fractal patterns were often found in nature's roughness -- in clouds, coastlines, plant leaves, ocean waves, the rise and fall of the Nile River, and in the clustering of galaxies...When I look at the equations describing these relationships, my eyeballs spin, but to a mathematician they are clear, consistent and beautiful.  Arthur C. Clarke described the Mandelbrot set (a beetlelike drawing that illustrates these equations) as being "one of the most astonishing discoveries in the entire history of mathematics.  

      So why would I bring any of this up at all?  Because author Williams adds that our vision and how we see things is likely based on the same principle: In addition to lungs, capillaries and neurons, another human system is branched into fractals, the movement of the eye's retina.  When Taylor [physicist Richard Taylor] and Hägerhäll [environmental psychologist Caroline Hägerhäll]used an eye-tracking machine to measure precisely where people's pupils were looking on projected images, he saw that the pupils used a search pattern that was itself fractal.  The eyes first scanned the big elements in the scene and then made micro passes in smaller versions of the big scene...Interestingly, if you draw a line over the tracks animals make to forage food such as albatrosses surveying the ocean, you also get this fractal pattern of search trajectories...This is a critical task; we need to assess quickly what's friendly and what's dangerous, among other things.  If a scene is too complicated, like a city intersection, we can't easily take it all in, and that in turn leads to some discomfort, even if unconsciously.  It makes sense that our visual cortex would feel most at home among the common natural features we evolved alongside, like raindrops falling on a lake.

Europe-centered map: Dreamtime

     We all tend to search for patterns, even in our relationships.  Sometimes people head to therapists for another set of eyes to help us break us free of whatever we feel has held (or is holding) us back or making us feel inferior.  A family history, a series of bad partners, some poor financial or job choices?  A quick scan of book or online magazine titles and podcasts will reveal that this is a huge market, as in nearing $100 billion by the time self-help, self-esteem, and cosmetic surgery trends are added together (men accounted for 1.6 million of those "improvement" surgeries in 2024, reported the American Society of Plastic Surgeons ).  Or consider the patterns we imagine are there when gambling, hoping that after so many spins of the wheel or rolls of the dice or lottery picks that it will finally be our time to win (alas, most modern day slot machines have sophisticated randomizer chips which work to truly make each spin "random;" and as for the odds favoring the house, Scientific American had an article on playing the lottery --on a $20 million jackpot, the odds of your single dollar winning was a negative ten cents-- but added : Even though all sequences of six lottery numbers are equally likely to win, many people handpick their numbers, and they tend to choose sequences that mean something to them, such as birthdays or anniversaries [which results in many numbers under 31].  People also seem to prefer odd numbers and numbers that aren’t multiples of 10, perhaps because they seem more random.)

US-centered map: World History Atlas

US-centered map: World History Atlas

     But what the heck does any of this have to do with these maps you're seeing?  Like many of you, I always accepted the "typical" map on the above left, one which showed the Atlantic Ocean as the defining ocean, never thinking that all of what I had been taught in school was Danish-European based.  Wrote Nicos Hadjicostis in his book Destination Earth: It was the European explorers who made all the modern discoveries and created our modern maps, so they placed Europe (themselves) in the center of the world...up until the discovery of the Americas in the fifteenth century, the Atlantic Ocean was considered the end of the world...The Pacific Ocean is actually the single most important natural feature of our planet.  First of all, it comprises 32 percent of the Earth's surface -- it is actually three times larger than Asia, our largest continent, and larger than all of the Earth's land area combined.  When one takes into account the fact that 70 percent of the Earth's surface is covered by water, the Pacific may be said to be not just the symbol of the Earth itself, but actually it's defining feature.  It is because of the Pacific that our "blue planet" looks blue from space.  By looking at second map, the larger size of the Pacific Ocean becomes strikingly clear.  But the second map also shows something else, how Greenland is much smaller than the continent of Africa....as in 14 times smaller, something readily visible when viewed through the third map below (author Hadjicostis also pointed out that Mexico is 5x larger than Germany [Japan is also larger than Germany], Antarctica is half the size of Africa, and Brazil is larger than Europe, if you take away Russia and Greenland).

Greenland vs. Africa,Pierce Quincuncial Map: Future Maps

      How could so many of us have missed this (actually, maps cater to all sort of parameters and many, including Buckminster Fuller, tried to find a way to flatten our 3-dimensional world into a 2-dimensional map).  Part of this jumps back to fractals and how we break things down into smaller segments (the Mercator projection map added those longitude/latitude lines to help us pinpoint and navigate the globe, but in turn stretched land masses out of proportion when placed onto a globe, wrote Wikipedia).  So that brought up another projection, that of peoples.  When I picked up the new book by Daniel Krauss, I was attracted by its premise of WW I soldiers finding a fallen angel, as in an angel from the sky.  Despite the story having more than a few holes (for one, there are no wounds or wings on the virtually non-speaking angel), the premise was that boys will be boys and avarice, lust and greed rather quickly takes over each of their war-weary heads.  But it was difficult reading because (and here I stereotype) it was written in a Gen-Z format*, that is, no capital letters (other than for naming a character), and no punctuation other than a zillion commas, and the book becomes a seemingly endless series of paragraphs and they go on and on and at times appear that they won't end, and still you tend to read more because you want to see if this angel has powers, and yet there is no magic waving of the hand, and the war continues unabated, and yet the men do not wish for the war to stop, and why does one of them feel obligated to simply follow orders, and would women have acted differently and would you and why if you were hungry and cold and tired of fighting and why were you fighting anyway and who made that other guy an enemy and my how the chapters seemed unnecessary and so did the capital letters and so did the commas and this was growing easier and easier to read and why did you not notice that the commas had stopped and was this just a lazy way of writing and why did this 50 year old author write this way and was he just experimenting and did he need to do so since he already has so many film and book credits and why in heavens name would he do that anyway and why was his interview so different from his book and how did you make it this far and would you read another book written like this and how on earth did you eyes and mind begin to sort this out and on and on and on and on and and and and.  Phew, we seem to like fractals when we read...or do we?

     It all made me think of how we view the world and what is happening with it.  We know that Earth is an anomaly in space, and that this blue planet is our home, and that we may be affecting its climate and resources because there are so many of us.  But not that many, we think, since we continue to ignore so many peoples and places such as the doctors trying to help in Gaza who are now also beginning to starve, wrote The Independent.  And while we fill up our trash cans and fill up our cars at the gas station; we ask where exactly are those military people with guns on our sidewalks since everyone else (especially Congress) seems to tell us that all is normal and it's nothing to worry about.  Just go about your day.  Besides, it's not your Congressman/woman that is sheepishly bowing down to Trump with his disruptive actions (unless that person is a Republican then it sort of is, since the voting is unanimous and along party lines). So fractals.  Perhaps all that is happening IS too much to take in all at once because how can this be when you don't really see it happening in front of you?  Sure, it feels hotter and drier, but then other places are flooding.  And sure those masked gun-toting vest-wearing mercenary contractors are throwing surprised people in vans and telling others to step back or also face "arrest," but none of that is happening where you are...is it?  And sure the lawsuits and court hearings are piling up and laws are being broken by those in Washington but no one seems to think it's that bad, at least not those of you at the restaurant where you're shrugging it all off since you're here to not think about that stuff and really only wondering if you should order another glass of wine.  Can we talk about something else?

     Sometimes I hear a voice in my head, nothing angelic or that of a distant ancestor, just a neutral voice asking a question, or making a statement...nothing negative or positive, sort of that gut feeling "voice" that tells you not to go down that dark deserted path.  This doesn't happen often, perhaps once or twice a year, nothing that would label me as ready for a Hannibal Lecter jacket.  But they do come unexpectedly and at random times, such as the other day when I was watering the flowers on my deck.  "Do you appreciate this," the voice asked, perhaps because I did and I didn't; because of our hot summer I had rarely sat out on the deck, even as I steadily watered and pruned those flowers and took care of my cacti.  But appreciate them?  Hmm, it was more like they were just there, beautiful, cared for, but not really appreciated.  Then the voice moved to my house and time, and grudgingly I found that I had the same answer.  Then the voice moved to my wife.  Do you appreciate her?  Dang, who was this speaking and now making me feel uncomfortable?  Could it have been because of just reading that book Presence, and the author's brain injury? (her TED video has been watched over 75 million times)

     Long ago, author Amy Cuddy was just one of three students sharing the long 13+ hour drive from Montana to Boulder, Colorado.  The drive would be divided into thirds, where one would drive, one would stay awake as a passenger, and one would cat nap in the back.  Amy did her shift as both driver and passenger and was now snuggling into the folded-flat back seat for a quick nap as they drove the midnight hours through desolate Wyoming.  Sound asleep, Amy has no recollection of the car deviating, then swerving, then flipping several times as she was ejected from the car in her sleeping bag.  The right side of her head hit the highway hard, leaving her with a diffuse atonal injury, a DAI where the brain shifts and rotates and bangs against the skull (her skull fractured upon hitting the highway).  She wrote: The brain is meant to exist in a safe place, protected by the skull and cushioned by several thin membranes, called meninges, and cerebrospinal fluid.  The skull is the brain's friend, but the two are never intended to touch.  The shearing forces of a severe head injury tear and stretch neurons and their fibers, called axons, throughout the brain.  Like electrical wires, axons are insulated by a protective coating, or buffer, called the myelin sheath.  Even if an axon isn't severed, damage to the myelin sheath can significantly slow the speed at which information travels from neuron to neuron...A head injury makes you feel confused, anxious and frustrated.  When your doctors tell you they don't know what you should expect, and your friends tell you that you're different, it certainly amplifies all that confusion, anxiety, and frustration...Our way of thinking, our intellect, our affect, our personality -- these aren't things we expect will ever change.  We take them for granted.  We fear having an accident that will make us paralyzed, change our ability to move around, or cause us to lose our hearing or sight.  But we don't think about having an accident that will cause us to lose ourselves... How you think, how you feel, how you express yourself, respond, interact -- all of these dimensions are affected.  

     Our brain may also break things down into fractals, giving us what we can or cannot handle or deal with; and those few who can view things in groupings or as a whole we may tend to view as an anomaly (such as autistic people, or people hyper-focused as depicted in A Beautiful Mind and Prime Target).  My own "voice" did that early one morning, asking me to briefly go over my life in 10-year brackets.  Age 0-10, it asked; and I thought of a few highlights, not many, but a few, and the voice said, "okay, let's jump to 10-20."  And once again, a few bright spots came out but basically just a whirlwind of school days, first loves, that sort of thing.  Then 20-30...and on it went.  In the end, my life was far from a 250-page memoir but more of an obituary, a summation.  When I asked a few friends to do the same exercise, they told me that it wasn't a fair question, that when pressed it was difficult to remember all the small moments, the details, the things that often came out as you speak with others, or laugh with friends at a gathering.  But I think the voice (my subconscious?) was trying to show me that each moment now is important, and whether you remember it later or not, that moment is something to treasure now.  Appreciate the whole and not the minutiae...

     History, wrote French historian Fernand Braudel, has three cycles -- what moves rapidly, what moves slowly, and what appears to not move at all.  Added the Bloomberg commentary: Right now, events are moving almost too fast to track, and the slow-moving Pax-Americana is heading rapidly toward the dustbin of history.  If global temperatures rise much further or machines start thinking for themselves, there will be movement even in the cycle that appears not to move at all.  As The Waterboys sung: Now November is here with its carpet of leaves, and the songs of the dead fill my ears.  All the champions are fallen, all the heroes are deceived, and the world they made has disappeared.  So let's tell it like is, man, let's nail it on the line; let's be clean with our tongues from here on in.  For we're deep in the heart of the enemy's design just waiting for the breakout to begin.  In my time on this earth I will speak the secret.  In my time on earth I will tell what is true.  In my time on earth I will say what the heart knows.  In my time on earth I will say I am you.

     Coming back to Earth and our maps, author Nicos Hadjicostis pointed out in his book that if maps showed our oceans as land, and our land as oceans, that we might look at our planet differently.  But he went further, writing that we view travel incorrectly, that we should view our entire world as a place to visit because we "own" it: In some strange sense, the things we supposedly own are "less owned" by us than is the nearby lake.  For we have to serve them in order to own them.  We need to repair our vehicle or our home, take care of our lawn, water the flowers in our garden in order to enjoy them  Yet, the ownerless lake that belongs to nobody, paradoxically, belongs to all.  It will take care of itself for as long as we live and will allow us to enjoy it without servicing it.  The idea of ownership, beginning as it does from the illusion of size and proceeding to the artificial and mistaken division of things into "mine" and "not mine," ends up being one of the great shackles of mankind.  But all of us can break these shackles and begin to see the world and everything it contains from a completely new perspective.  Travel is one of the great destroyers of the conventional idea of ownership.  We may even go as far as saying that another definition of travel is repossessing the world.  Each of us owns the planet...I know there are a few spaces scattered around the world with surrounding fences and a humorous inconspicuous sign saying "Private Property."  I leave all these confining pieces of land to all those who choose to be imprisoned within them.  I am the owner of the world.  That's more than enough.  As Ibn Battuta** proved, there's still a lot of world to see...

Reversed map highlighting oceans: Frans Blok/Kottke

*Gen-Z (and the new Gen-Z Beta)...how presumptuous for me to presume that I could identify or point out their differences or traits, and the short answer is, I can't.  The "definitions" of sorts came from a piece in The Washington Post which was written by, and featured interviews by, a few people from that time group (born 1997-2012).  Phone calls, bar tabs, uppercase letters...adios.  Wait, do Gen-Z'ers use that term?

**Who the heck is Ibn Battuta?  Back in 1300s, this Arab explorer traveled over 75,000 miles along the African coast, the Middle East, and on into India and China, 40 countries in total.  In the 1300s!  His journals, which were dictated only from memory upon his return, are credited by historians as helping to detail much of the Muslim world of the time...those recited writings remained unrecognized for over 600 years ad only came to light in the early 1900s.