The Reticulum

On Abnormal Distributions, Psuedostatistics and Modern Management Fads

Dr. Frankenstein: “Would you mind telling me whose brain I did put in?”
Igor: “And you wont’ be angry?”
Dr. F: “I will NOT-be-angry.”
Igor: “Abby…someone.”
Dr. F : “Abby Someone..?”

Igor: [Nods with an enthusiastic positive manner while looking up as if he is recollecting]
Dr. F: “Abby Who?”
Igor: “Abby Normal”
Dr. F: “Abby Normal?”
Igor: “I’m almost sure that was the name.”
Dr. F: “Are you saying that I put an abnormal brain into an seven and a half foot long, 54 inch wide… GORILLA!? IS THAT WHAT YOU’RE TELLING ME!?”
— Dialogue from Young Frankenstein

As the movie Young Frankenstein demonstrates so hilariously, abnormal stuff just happens. We need to get better at dealing with it.

Abby Normal Data

A case in point occurred when analyzing a large dataset for a survey project. The findings were rich and interesting, but there was one small hitch: the responses we got for one of the more important questions was rather skewed in one direction. In other words, the data was distributed in a way that looked nothing like the conventional bell curve, or Gaussian distribution, that represents normality in statistics.

This kind of thing can give researchers a touch of heartburn. After all, inferential statistical theory usually boils down to deviations from normal bell-curve distributions. It’s all related to the so-called Central Limit Theorem, which states that the distribution of any statistics (e.g., size of snowflakes, heights of people, lifetimes of light bulbs) will, if you have enough data points, wind up in something pretty close to a bell-curve shape.

That normal shape is handy dandy because the mean (aka, average) of all the data is equivalent to the median (aka, midpoint) and the mode (aka, number that appears most often). If your data looks like it has a normal distribution, then standard deviations are a piece of cake and it’s easier to analyze using statistical techniques such as conventional regressions.

Empirical_Rule normal distribution — Visual representation of the Empirical (68-95-99.7) Rule based on the normal distribution, by Dan Kernler

Ways of Coping with Non-Normal Data

So, we had non-normal, or what I’ll call abnormal, distributions in one data set. It wasn’t really a serious problem, of course. There are lots of ways of coping. Maybe you can’t run a T-test but you can conduct a Mann-Whitney test. Maybe an ANOVA is no good, but you can drum up a Kruskal-Wallis Test. A conventional correlation may not work but a Spearman’s correlation just might. You get the idea (for more on this, see “Dealing with Non-normal Data“).

Over the years, statisticians have come up with quite a few methods for coping with abnormal data because, well, the world isn’t nearly as normal as we normally assume. That fact should not only be remembered by statisticians but by everyone who has been, consciously or not, sucked into the world of what could be called normal-distribution psuedostatistics.

One example of such psuedostatistics is so-called forced or stacked ranking, which is when companies adopt employee performance evaluation systems that require set percentages of employees to be ranked in specific categories. It’s controversial, in part because it can force managers to give unrealistically low evaluations to members of all-around strong teams.

Aside from the fact it can be a lousy system, it bugs me because it’s inspired by, if not based on, the notion that people, even pretty small and non-arbitrary selections of them, fall into normal distributions of talent and performance. In my book, that’s a dangerous form of psuedostatistics. The world is just too abby-normal, as Igor might say, to bet the professional lives of employees on such a shady notion.

On Psuedostatistics

There are plenty of other examples of psuedostatistics biting us in our bimodal rumps. The bell-curve meme messes with our heads all the time. For example, we are conditioned into wondering and worrying if, in any given area of our lives, we are, like the children of Lake Woebegone, above average. Or maybe far above above average, at the 95th percentile? The 99th?

And it’s not just ourselves we place somewhere along the bell curves of our imaginations. Men start assigning numbers to women walking by on the streets based on some creepy central limit theorem of beauty. Parents start worrying to which side of some infernal bell curve their kids’ grammar school test scores fall.

I could go on, coming up with hundreds of data points along this warped line of reasoning. And, I fear, so could you. That’s because we are victims as well as beneficiaries of our powerful statistical paradigms. And these paradigms that will only grow more powerful in our increasingly digitized, quantified, big-data world that encourages us to view everyone, including ourselves, as abstracted volumes of variables and vectors. So, amid the measurement mania, we should strive to remember that we are all, in the end, an abnormal sample of one. Vive la difference

Paretian Distributions

PS: Lately, there’s been another stats-related meme focusing on the idea that employee performance follows a Paretian (aka, Pareto or Power-Law) distribution rather than a normal distribution. Therefore, in theory, a sliver of the employee population is able to produce the majority of positive impact in an organization. The Pareto Principle has been around since management guru Joseph Juran coined the phrase, but, from what I can tell, the notion that this can legitimately explain employee skill and performance levels stems largely from a 2012 article in Personnel Psychology called “The Best and the Rest: Revisiting the Norm of Normality of Individual Performance.”

In it, the authors looked at factors such as citation reports in academic journals and awards given to entertainers. I’m sure the article is a legitimate attempt to shed light on the elusive subject of performance within professional fields. But the findings strike me as far from conclusive. The authors themselves, for example, allude to the Matthew effect. So, are the patterns to which they allude truly about elite performance, or are they more about network effects and preferential attachments?

Another way of stating this is, “Are perceived elite performers actually much better than others in their fields or are they just better connected and able to leverage a more polished public image?” These things are often tough to tease apart. Perhaps time will tell. In the meantime, I recommend maintaining a modicum of skepticism in the face of sweeping sociological assertions linked to simple statistical equations.. Human behavior is tricky stuff and seldom boils down to single lines, however curvy and lovely, of mathematical abstraction.

Featured image: Illustration by Theodor von Holst from the frontispiece of the 1831 edition

Note: I originally published this nearly 10 years ago in a previous incarnation of The Reticulum - mrv

The Universe of Seurat and Rovelli

I was once chastised by security guard at the Art Institute of Chicago for getting too close to A Sunday Afternoon on the Island of La Grande Jatte, the greatest work by the greatest of the pointillist painters, Georges Seurat. I remember blushing with embarrassment as other patrons flicked their attention to me to take in the barbarian careless enough to endanger one of the world’s most beautiful and important works of art.

I also felt an initial rush of outrage that anyone would think I would harm such a treasure. But then I realized that was indeed too close, that my foot was over the line of the designated safe distance to the masterpiece, that I was indeed the Philistine they took me for. But I was a curious Philistine, looking closely to tease out how he was able to pull off his technique.

Pointillism, Atomism and Digitization

The art movement known as pointillism¹ is the technique of applying small strokes or dots of paint so that from a distance so they visually blend together. Largely invented by Seurat, I think the technique visually demonstrates atomism, which Rovelli associates with certain Greek philosophers but was probably first described by the Vedic sage Aruni back in the 8th century BCE. Aruni proposed the idea that there were “particles too small to be seen [that] mass together into the substances and objects of experience.”

Seurat aesthetically anticipated not only the atomic and quantum theories but the digital age in which we find ourselves living today, an age in which so many people spend the majority of their waking hours looking at screens of pixels.² We are entranced by pointillism all day long.

In a sense, the idea of a pixelated universe is the topic of both Seurat’s work and Rovelli’s as laid out in Reality Is Not What It Seems: The Journey to Quantum Gravity? If you read the last post (or, better yet, the book itself) you should have at least a general notion of quantum gravity.

But what prospects does the theory have? How might it be supported by scientific evidence, and where might it lead us? Let’s discuss.

Vive la Révolution

Quantum physics was a revolution in physics, but what if Rovelli is right and all of spacetime is quantum? Well, then, the revolution is just beginning. Who really knows what knowledge it could bring us? Might quantum gravity help us better understand understand how to harness gravity itself? What new technologies could be created with it? Rovelli doesn’t discuss possible applications, but I can’t think of any major physics discoveries that didn’t also bring earth-shaking new technologies.

Testing Quantum Gravity

So, how can the theory be tested? One idea is to look for evidence of a “Big Bounce” as opposed to a “Big Bang” in the origins of the universe. According to Einstein’s view of the universe, all of spacetime could be squashed ad infinitum, ultimately leading to the Big Bang. But, that’s not what quantum gravity would predict. Rovelli notes that “if we take quantum mechanics into account, the universe cannot be indefinitely squashed.” And if that’s true, then we wouldn’t get a Big Bang but, rather, a gigantic rebound that he refers to as the Big Bounce.

So, how does one test that? Well, one can look at the statistical distribution of the fluctuations of cosmic radiation. That should provide evidence of the Big Bounce. In addition, according to Rovelli, “cosmic gravitational background radiation must also exist–older than the electromagnetic one, because gravitational waves are disturbed less by matter than electromagnetic ones and were able to travel undisturbed even when the universe was too dense to let electromagnetic waves pass.”

There’s also the prediction by the quantum gravity theory that black holes are not ultimately stable because the matter inside them cannot be squeezed into a single point of infinite density. Rather, at some point, the black hole explodes (like a miniature Big Bounce). If we can locate some exploding black holes in the universe, then we have more evidence of quantum gravity.

So, basically, if we find that super dense stuff is bouncing and rebounding in the universe, the quantum gravity folks might be right. If not, well, at least we’ll have evidence the theory is wrong and we can consider the other theories that have been, and surely will be, conjured up by the endlessly creative theoretical physicists.

If the quantum gravity champions do turn out to be right, then one of the side effects will be that the infinity goes away. Or, at least, physicists are a lot less likely to get infinity as the answer when they run certain calculations based on general relativity theory. The universe itself becomes “a wide sea, but a finite one.”

Bit by Bit, Information Becomes Reality

But don’t assume that, just because the universe might be finite, it doesn’t stay weird. In fact, it may start seeming weirder than ever if humanity succeeds in merging quantum mechanics information theory not only with the theory of relativity but with information theory.

First conceived by engineer and mathematician Claude Shannon in the mid-20th century, information theory assumes that information “is the measure of the number of possible alternatives for something.”

It was Shannon who popularized the word “bit” to mean a unit of information. He used it in his seminal 1948 paper “A Mathematical Theory of Communication,” and he attributed the origin to a Bell Labs memo written John W. Tukey, who used bit as an acronym of “binary information digit.”

Rovelli explains, “When I know at roulette that a red number has come up rather than a black, I have one ‘bit’ of information; when I know that a red even number has won, I have two bits of information…”

I won’t belabor this because information theory gets pretty complicated and Rovelli doesn’t go too deeply into it. To get a better but non-technical understanding, I recommend reading The Information: A History, a Theory, a Flood by James Gleick. I read it several years ago and hope to give it a second read over the next several months.

Anyway, it was John Wheeler, the father of quantum gravity, who was “the first to realize that the notion of information was fundamental to the understanding of quantum reality.” He coined the phrase “from it to bit,” meaning that the universe is ultimately made up of information.

Rovelli writes:

Information…is ubiquitous throughout the universe. I believe that in order to understand reality, we have to keep in mind that reality is this network of relations, of reciprocal information, that weaves the world. We slice up the reality surrounding into “objects.” But reality is not made up of discrete objects. It is a variable flux.

Although Rovelli has one more chapter on the scientific method, I think this is the better place to wrap up a post on a blog called The Reticulum. Let’s sum up: Reality is a network of relations among bits of information in a variable flux.³

I don’t know if that’s a true description of our underlying reality. But it does feel familiar: flux and foam, bits and bytes, indeterminacy and statistical spins. Even if quantum gravity doesn’t work out as epistemology, it still captures much of the essence of our baffling, vertiginous and often wondrous modern lives.

¹ The word pixel, by the way, is a portmanteau of "picture element," which is the smallest addressable and controllable element of a picture represented on a digital screen.

² As visionary as the technique was, the term "pointillism" was actually coined by art critics in the late 1880s to ridicule Seurat and the other members of the art movement. But the artists, as they so often do vis-a-vis critics, got the last laugh. Today, the term is regarded as describing one of the great movements of neo-impressionism.

³ Which makes me think, of course, of Doc Brown's famous "flux capacitor."

Feature image: A Sunday Afternoon on the Island of La Grande Jatte by George Seurat: https://commons.wikimedia.org/wiki/File:A_Sunday_on_La_Grande_Jatte,_Georges_Seurat,_1884.jpg

Falling for Quantum Gravity

We’ve gone through Chapters 1, 2, 3 and 4 of Reality Is Not What It Seems. The abstract groundwork has been laid, the rhetorical lumber all trucked in, and now it’s time to start building a brand-spanking-new theory of reality on quantum gravity!

Groovy. This particular post is my attempt to distill what I learned in Chapters 5, 6 and 7 of Rovelli’s treatise on quantum gravity.

Teeny Weenie Itsy Bitsy (and then Some)

As physicists started trying to make general relativity and quantum mechanics compatible with one another, they came up with a variety of ideas. One of them–the one Ravelli favors–is the idea of quantum gravity, an idea that hypothesizes that space itself can be be broken down into teeny, tiny basic components.

How tiny? Rovelli says they would be Planck length, which he describes as follows:

To give an idea of the smallness of the scale we are discussing: if we enlarged a walnut shell until it had become as big as the whole observable universe, we would still not see the Planck length.

So, “tiny” doesn’t even begin to cover it. This is almost the definition of infinitesimal, assuming it actually exists outside the confines of the minds of the quantum gravity theorists.

Space Is a Reticulum

Sometimes quantum gravity is called “loop quantum gravity” because some solutions to what’s known as the Wheeler-DeWitt equation–which is seminal to this school of thought–depends on closed lines in space, aka loops.

Remember Faraday lines from “May the Forces Be With You”? Well, the loops are Faraday lines of the gravitational field (as opposed the electronic fields that Faraday was discovering). These lines are not just in space, according to the theory, they are the stuff from which space itself is woven. How cool is that? I makes me think of the Great Norns of Norse mythology, spinning time and space and the fate of humankind.

In a sense, then, space is an enormous reticulum (or “graph”) in which the lines intersect. The intersections are “nodes” and the lines themselves are “links.” Those nodes are the quanta of space. This means, according to the loop theory, that space is not a continuum, as has long been assumed. It’s made up of those fantastically small atoms of space (though space itself is the gravitational field, according to this theory).

More Networks, This Time Spinning

So, if the gravitational field is woven of these quantum particles of space, then how do we talk about specific networks of them? Well, the lines between the nodes are viewed as half-integers, and those integers are called “spin” in the lingo of quantum physics. And so….Rovelli calls these little networks “spin networks.” The networks “represent a quantum state of the gravitational field.”

I don’t know how to properly conceive of spin networks, so for now I’m thinking of them as molecules. That is, atoms make up molecules and nodes make up spin networks. But this isn’t how Rovelli describes them so I’m probably way off.

One of the ways in which my molecule metaphor fails is that molecules actually exist as a thing (I think) whereas spin networks aren’t really entities at all. Rather, they are, like quantum particles, clouds of probabilities “over the whole range of all possible spin networks.”

But they look pretty simple when depicted on the page:

Source: https://en.wikipedia.org/wiki/File:Spin_network.svg

The image above is identified as a spin network but, unlike the version in Rovelli’s book, the lines are not represented by half integers, which I thought represented the quantum spin. Still, you get the idea.

Let’s allow Rovelli sum it up for us:

At extremely small scale, space is a fluctuating swarm of quanta of gravity that act upon one another, and together act upon things, manifesting themselves in these interactions as spin networks interrelated with one another.

This leaves me visualizing thick clouds of mosquitos down in the Everglades, which may not be quite what he intended. But, ready or not, it’s time to deal with time.

Got No Time

According to Rovelli’s ideas, time doesn’t exist apart from the gravitational field. (Side note: Do we really need to keep calling it the gravitational field? Seems kind of lame for something this essential. How about The Lattice of Existence? Maybe The Network of God, or even The One True Reticulum? As I said before, physicists are usually shit as namers and even shittier as marketers, though I’d admit that stealing “quarks” from James Joyce was kind of genius.)

Anyhow, time pops out of this Lattice of Existence (trademark!).

This may seem a bit nuts, but Einstein has already taught us that time is elastic, relative and linked to velocity and gravity. So Rovelli is just doing Weird Al one better. In a sense, time ceases to exist altogether or at least it does at the Planck scale. Time is only the measure of how the loops and nodes interact. It is emergent.

Spinfoaming at the Mouth

We already discussed spin networks. Now let’s graduate to spinfoam, which sounds a lot like the suds one sees in one’s washing machine as it gyrates noisily away. Here’s how Wikipedia defines it: a topological structure that “consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman’s path integral description of quantum gravity.”

Does that help you? No, me either.

Let’s start again. The “foam” metaphor comes from the foam that you and I are familiar with. I think the image below is a very cool portrayal of literal foam, maybe helping us better visualize the network-like quality of spinfoam.

Paul VanDerWerf from Brunswick, Maine, USA: https://commons.wikimedia.org/wiki/File:Soap_Bubbles_(41493399275).jpg

And the “spin” part, of course, comes from the quantum mechanical notion of spin, to which we alluded earlier.

Rovelli writes that spinfoam “is made of surfaces that meet on lines, which in turn meet on vertices, resembling foam soap bubbles.” My impression is that spinfoam is a tool that merges two calculation techniques used by quantum physicists: a Feynman diagram and a lattice approximation. Rovelli provides more information about these but I’d clearly need a lot more education to understand them to my satisfaction.

You can see a representation of spinfoam here. Spinfoam is apparently what happens when a spin network moves through time. The lines become planes and the nodes become lines. You know how you can draw a series of stick figures on a small pad of paper and then flip the pages real fast to produce the illusion of moving animation? Well, that’s kind of what spinfoam is: the animation of the spin network moving forwards (or backwards!) in time.

The Universe Dresses Up in Spacetime but Is Secretly …

Rovelli argues that if you sand the universe down to the very bottom layer, you don’t find a beautiful hardwood floor (or spacetime or even oodles of particles). You find — dun dun dun! —covariant quantum fields.

Hah, I bet you’re so surprised, thinking I was going to say “gravitational field”! But, no, now we have a new and equally wonky term that stumbles trippingly off the tongue: covariant quantum fields.

Sigh. More Star Trek jargon to be rattled off by Geordi La Forge on the bridge of the Enterprise.

As I said, physicists are shit at naming stuff.

On the other hand, they sure can weave a tale.

Nice job, Professor.

Featured Image: John Tenniel's illustration from The Nursery "Alice" (1889). See https://commons. wikimedia.org /wiki/File: Alice_drink_me.jpg

Now You See Me, Now You Don’t

Out of the Frying Pan

So far, we’ve covered ancient atoms, electromagnetism and the theory of relativity. In Chapter Four of Reality Is Not What It Seems: The Journey to Quantum Gravity, we finally enter the last and strangest realm of known physics: quantum mechanics (aka, quantum physics).

In my last post, I compared trying to some to terms with the implications of Einstein’s model of reality to taking the red pill in The Matrix, leaving behind our comfortable (though false) notions of stable time and space in order to live in the bizarre, uncomfortable and yet often beautiful and exciting realm of spacetime.

Live free, Neo!

But entering the realm of quantum mechanics is something else. Just as you’re coming to terms with spacetime, you’re told that, by the way, spacetime is also a kind of matrix. An even stranger and more mysterious one. A matrix that isn’t populated by Agents trying to keep the truth from you but rather by gaggles of egghead physicists doing their damnedest to explain it to you….between their extended bouts of arcane squabbling.

Want to go back to your comfy pre-relativity matrix? Too late, Neo.

Into the Fire

So, let’s get down to explaining this new realm. Rovelli specifies that our quantum reality has three primary characteristics: granularity, relationality and indeterminism.

Hey, Why Is My Reality All Pixelated?

Let’s start with granularity. The short version is that, for the sake of convenience, a guy name Max Planck assumed that the energy comes in bite-sized (okay, smaller than that, but finite nonetheless) packets when doing his calculations.

Not long after, Einstein said something like, “Hey, you know what, Max? Energy really is made up of packets. What do you know!” (And, so, yes, the original Weird Al is one of the fathers of quantum mechanics and not just relativity).

Einstein claimed that this granularity extended to light, a form of energy. Most of the other physicists said, “No way! James Clerk Maxwell says light is a wave and waves don’t come in convenient bite-sized packets.”

To which Einstein said something like, “I guess it’s both! Beats the hell out of me how that could be true but let’s just go with it and see where it leads.”

And, wow, those breadcrumbs led to some very strange places…

Wait, They Were Just Here a Second Ago!

Next up is relationality, which is a boring name for something utterly bizarre. Rovelli sums it up in just three short sentences: “Electrons don’t always exist. They exist when they interact. They materialize in place when they collide with something else.”

So, you’re asking, how can that possibly be? Aren’t electrons just a part of an atom, like your arms and legs, nose and mouth are part of you? It’s like saying a person’s left arm doesn’t exist unless they happen to bump into somebody else. How does that work? you ask. I haven’t a clue, but electrons are apparently just ghosts that appear during interactions with one another.

Even though it was his personal bread crumb trail, Albert Einstein thought this was all too strange to be true. But there’s this other physicist, Paul Dirac, who didn’t seem to have problems with it. Rovelli writes, “For him the world is not made of things; it’s constituted of an abstract mathematical structure that shows us how things appear, and they how behave when manifesting themselves.”

Speaking of the problems posed by Dirac, Einstein groused, “To maintain an equilibrium along this vertiginous course, between genius and madness, is a daunting enterprise.”

Rovelli indicates that objects (though what really constitutes an object?) can still have characteristics such as mass while they are not interacting with one another, but the object’s “position and velocity, its angular momentum and its electrical potential only acquire reality when it collides–interacts–with another object.”

Okay, can it get any weirder? Glad you asked!

I’ve Determined that I Can’t Determine

Last up is indeterminacy. Einstein hated this part. He famously said, “God does not play dice with the universe.”

What he objected to was the fundamental quantum physics idea that one cannot predict what any given particle is going to do. Rovelli wraps it up like this: “While Newton’s physics allows for the prediction of the future with exactitude, if we have sufficient information about the initial data and if we can make the calculations, quantum mechanics allows us to calculate only the probability of an event. This absence of determinism at a small scale is intrinsic to nature.”

“Intrinsic to nature” — let that one sink in. All you can do is give and get probabilities. It’s all a big dice game, as far anyone can tell.

Or maybe it’s a baseball pitcher with lousy ball control. For some reason, I think of the movie Bull Durham in which the rookie pitcher Nuke can throw hard but doesn’t know where any given pitch is going to go. “Hell if I know where the damn thing’s going…” Nuke’s catcher, Crash, tells a nervous batter. (And, yes, Bull Durham fans, I know it’s a ploy on Crash’s part but, hey, it’s just a metaphor).

Anyway, what Dirac’s equations can do is give you a range of the possibilities and then a calculation of the probabilities within that range (At least, I think that’s right, based on what I can determine. Get it? Determine. Indeterminacy? Ok, never mind).

We Cobbled Her Together But She Sure Does Run Good

Over the years, physicists “cobbled together” (Rovelli’s phrase) what we now call the Standard Model (physicists are crap at naming and marketing, it appears). He sums up:

The Standard Model is completed by the 1970s. There are approximately fifteen fields, whose quanta are the elementary particles (electrons, quarks, muons, neutrinos, Higgs, and little else), plus a few fields similar to the electromagnetic one, which describe electronmagnetic forces and the other forces operating at a nuclear scale, whose quanta are similar to the photons.

The thing is, this junky heap of particles, fields, equations and whatnot turn out to be extremely robust and fast around the corners. Experiments keep confirming it and engineers depend on it to build all our fancy electronic gadgets. In the end, it’s the model that everybody buys.

Now Comes the Hard Part

So, quantum mechanics works like a charm. But so does Einstein’s theory of relativity. The problem is that the two explanations don’t work well together. One works super well in the macro world and one works super well in the micro world, but nobody knows how to marry the two.

So, that’s where Rovelli and others come in. They want to settle these irreconcilable differences by building a house that both theories can comfortably fit in. Heck, they want more than that. They want our two theories spooning each other, finishing one another sentences, lovingly telling us stories of how their many zany antics and impassioned conflicts finally ended in a Harry-and-Sally-type romance that we can all laugh about now.

So, will they or won’t they? Stay tuned. Next week: Falling For Quantum Gravity

Feature image: Clara Ewald's portrait of Paul Dirac: From https://commons.wikimedia.org/wiki/File:Clara_Ewald_-_Paul_Dirac.jpg

Einstein and the Big Squid

Taking the Red Pill of Relativity

Now things get weird. In the first post about Rovelli’s Reality Is Not What It Seems, we focused on atoms. Despite the strange fact that medieval Christians tried to censor the concept of atoms, they do not score very high on my weird-shit-o-meter. I was brought up with them, so they seem as friendly as eating potato chips on a comfortable couch.

In the second post, we got into electromagnetism. But, considering that most of us live enmeshed in cocoons of wire and wifi, it’s hard to see that topic as outlandish, however much our forebears would have been astonished.

But in Rovelli’s third chapter, the topic of this post, we’re forced to choke down a red pill if we want to enter the spacetime reality of Albert Einstein’s mind, thereby exiting The Matrix of our comfortable everyday reality where time and velocity seem as easy to grasp as a digital readout.

You’d think that by now we’d be accustomed to the original Weird Al’s big brain. I mean, we’ve had a century or so to get acclimated to this stuff. But, speaking for myself, I’m still struggling to cope with the idea that the world is not what it seems.

Present But Not Accounted For

Rovelli tries. But, despite the cartoons, his section on the “extended present” is hard to swallow. How and why has the present moment been extended by the Special Theory of Relativity?

I assume it has to do with the speed of light and relative time, but you’ll need to take it on faith within the context of this chapter. Here’s an example:

[O]n the moon, the duration of the extended present is a few seconds, and on Mars a quarter of an hour. This means we can say that on Mars there are events that are yet to happen, but also a quarter-of-an-hour of events during which things occur that are neither in our past nor in our future.

I find this hard to wrap my brain around and wish Rovelli had gone to greater lengths of explain the details. I remember getting a deeper glimpse of time relativity when pondering the ideas in the book Why Does E=mc2 (And Why Should We Care?), but I’ve since lost it (the glimpse, not the book). And now I’m wondering if I’ll need to bear down on that text again in order to grasp Rovelli’s arguments. We’ll see.

Space Is a Monster Mollusk

Okay, let’s put the “extended present” into a box (perhaps along with Schrodinger’s cat) and come back later to see what happened. For now, I want to focus on another statement in Chapter Three:

What if Newton’s space was nothing more than the gravitational field? This extremely simple, beautiful, brilliant idea is the theory of general relativity…. Newton’s space is the gravitational field. Or vice versa, which amounts to saying the same thing: the gravitational field is space….We are not contained within an invisible, rigid scaffolding: we are immersed in a gigantic, flexible mollusk (the metaphor is Einstein’s).

Okay, despite the Cthulhu vibe, I understand this better than the concept of extended present. I get the whole spacetime-curved-by-big-hunks-of-matter idea. I get that everything’s moving and has speeds only relative to everything else and everything is in constant flux. I even kind of (though not really) get the idea that time flows faster at the top of a mountain rather than in a valley.

But spacetime is the same thing as the gravitational field? Was that originally part of the Theory of Relativity? Apparently I’m not the only one confused. I wonder if that’s part of scientific history or just a tenet of the quantum gravity hypothesis, which is the ultimate subject of the book.

A Universe Designed by Escher

The latter sections of Chapter Three are mostly focused on how the universe may be a humongous globe with an extra dimension stuck in there. Einstein conceived a way in which the universe might be finite while still having no discernable boundary. Rovelli uses the metaphor of a globe:

On the surface of the Earth, if I were to keep walking in a straight line, I would not advance ad infinitum: I would eventually get back to the point from which I started. Our universe could be made in the same way. I fly around the universe and eventually end up back on Earth. A three-dimensional space of this kind, finite but without boundary, is called a “3-sphere.”

Although he goes on for another 12 pages or so, for me the above is the essence of the discussion. And, I kind of get it, or at least think I do, because we all understand the metaphor of the globe. Whether I can can truly conceive the shape of the universe like this, however, is another matter. It’s something to work on.

It’s Networks All the Way Down

Boiling it all down, I take away two main insights from this chapter. First is the idea that space as we (or at least I) sometimes think of it doesn’t exist. There are no vast empty spaces in space. It is jam-packed with gravitational and electromagnetic fields light waves, radio waves, gamma rays, microwaves, etc. In fact, maybe space is nothing more nor less than an unthinkably immense gravitational field.

Whatever space is, however, it’s certainly not mostly empty. It is a packed and fluctuating landscape in its own right. Jupiter is a not a planet but a mountain, one that we can climb and look down at the curved and rippling real estate of our solar system, if we’re willing to see beyond the merely visible.

My second insight is that network describes the scene even better than landscape. In my mind’s eye, I see block-and-tackle pulleys everywhere, connecting everything in our solar system (and the greater universe, of course) in a constantly shifting network.

Some mythologies have it that the Earth is supported on the back of a giant World Turtle. But what does the turtle stand on? There’s the old joke that, well, it’s “turtles all the way down” in a kind of infinite regress.

Perhaps it’s less of a joke to say that the universe is a network of networks. What do the networks attach to? Well, other networks via gravitational forces. I guess we could say it’s networks all the way down.

Featured image: Artist's concept of the Interplanetary Transport Network. The green ribbon represents one possible path from among the infinite number possible within the larger bounding tube. Constricted areas represent locations of Lagrange points. Wikimedia Commons

May the Forces Be with You

Making Up with Plato and Aristotle

In the second chapter of Reality Is Not What It Seems, Rovelli takes us on another millennia-spanning tour of physics. He starts by making up with Plato and Aristotle, whom he had previously seemed to denigrate by comparison with the great and yet savagely censored Democritus (see previous post). Then he takes us on a whirlwind tour of the ideas of Galileo, Newton, Faraday and Maxwell.

Rovelli says that Aristotle, who invented the name of the physics discipline, deserves credit for describing the physical nature of the universe in a systematic if unquantified manner. He may not have understood the universe well by our standards, but what he wrote was coherent, rationale and served at as humanity’s best description of the physical universe for many centuries.

As for Plato, he championed mathematics (and, in particular, geometry) as a way of understanding the universe. Without mathematics, of course, we could not possibly have modern physics.

The Great Experimenter

Nonetheless, it took a long time before what we call experimental science emerged, according to Rovelli, who boldly states that “experimental science begins with Galileo” (aka, Galileo di Vincenzo Bonaiuti de’ Galilei, born February 15, 1564 and died January 8, 1642).

Once again, Rovelli seems to be simplifying in order to tell a clear, compelling and succinct story. I’m all in favor of that, but in reality there were probably a lot of experimenters before Galileo, even if they were not as systematic, brilliant and productive. For example, the Greek physicians Herophilos (335–280 BCE) and Erasistratus of Chios used experiments to further their medical research. Erasistratus repeatedly weighed a caged bird to determine its weight loss between feeding times.

But let’s go with Galileo as the first truly great experimenter. In a very small nutshell, he discovered that objects do not always fall at a constant speed and that, indeed, they pick up speed as they go: about 9.8 meters per second per second. This number comes up a little latter in history, speeding (so to speak) modern physics on its humanity-changing path. (By the way, the science fiction novel by Kim Stanley Robinson, Galileo’s Dream, goes into some detail about his experiments, insights and life; if you want to know more about Galileo without reading an actual biography, I’d recommend the book.)

Absurd Realities from Isaac

When Isaac Newton (born December 25, 1642 and died March 20, 1726) famously said, “If I have seen further it is by standing on the shoulders of giants,” he must have been thinking of Galileo as one of them.

Inspired by the moons of Jupiter (discovered by Galileo, of course), Newton conducted a thought experiment (a technique Einstein latter became especially famous for) in which he imagined a little moon orbiting the earth just above our highest mountain tops.

“Now,” writes Rovelli, “an object that orbits does not go straight: it continually changes direction, and a change of direction is an acceleration. The little moon accelerates toward the center of Earth. This acceleration is easy to compute. Newton makes the simple calculation and the result is … 9.8 meters per second per second! The same acceleration as in Galileo’s experiments for falling bodies on Earth.”

So Newton figures that the force that would cause the little moon to orbit around the Earth is the same one that Galileo measured for falling objects. In this way, he linked heavenly bodies with objects on Earth and came up with the modern idea of gravity, the first of the four basic forces so far identified by science.

But just because Newton came up with the idea and the math associated with it doesn’t mean he wasn’t baffled by it. Indeed, he thought the idea of one physical object (such as the Earth) acting on another physical object (such as the moon) via some distance and invisible thread of influence was “inconceivable” (even though he’d conceived it) and “is to me so great an Absurdity, that I believe no Man who has in physical Matters a competent Faculty of thinking, can ever fall into it.”

Except, of course, we all have “fallen” into it (did he recognize his pun?) for hundreds of years since. What’s more, we still don’t truly understand gravity, even if we have learned quite a bit more about it thanks to other great thinkers.

Mike and Jim’s Excellent Intellectual Adventure

Faraday the Astonishing Autodidact

Then, in the 1800s, two other British brainiacs came along and discovered another fundamental physical force that would change humanity, ultimately putting a powerful computer in the pockets of just about every angst-ridden teenager in the so-called developed world.

The two geniuses in question are Michael Faraday and James Clerk Maxwell, who are typically portrayed as the the original odd couple of electromagnetics. Faraday was an up-by-the-bootstraps scientist who grew up poor and not formally educated, yet he somehow sweet-talked his way into a lab assistant job with the Cornish chemist and inventor Humphry Davy. He was never trained in higher mathematics but, according to another of my favorite books on science history (Conquering the Electron: The Geniuses, Visionaries, Egomaniacs, and Scoundrels Who Built Our Electronic Age by Derek Cheung and Eric Brach), he had a “uncanny intuition and a superhuman ability to visualize abstract objects, concepts and shapes.”

It was Faraday (born September 22, 1791 and died August 25, 1867) who basically created the first electrical motor, discovering that electrical energy could be directly converted into the kind of energy (that is, kinetic) that makes stuff move. (So, in theory, if there’d been no Faraday, we’d still be driving steam engines around and who knows what Elon Musk would be doing these days).

But, he was more than just a fantastic tinkerer. He came to the conclusion, in Rovelli’s words, that “there exists an entity diffused throughout space that is modified by electric and magnetic bodies and that, in turn, acts upon (pushes and pulls) the bodies. He calls these ‘lines of force.'” So, in essence, Faraday discovered fields!

Faraday created a number of iron filing diagrams in 1851 to demonstrate magnetic lines of force. Source: Royal Institution

Maxwell the Scottish Aristocrat

I love the little I know about James Clerk Maxwell (born June 13, 1831 and died November 5, 1879) because he seems almost god-like in his ability to crystalize the baffling universe into just a few, elegant equations. He was the Einstein of his day. In fact, without him, Einstein may never have crafted his theories of relativity at all. After all, Einstein’s special theory of relativity is often seen as owing its origin principally to Maxwell’s theory of electromagnetic fields.

Here’s what Maxwell achieved. After working 11 laborious years, he was able to embody all the electrical and magnetic principles into just four seemingly simple equations” (okay, there were 20 at first but they were later distilled by yet another Brit, Oliver Heaviside, whose name seems to pop directly out of a Dicken’s novel).

Rovelli says of the equations: “They describe an amazing number and range of phenomena. Almost everything we witness taking place, with the exception of gravity and little else, is well described in Maxwell equations.”

Perhaps most amazingly, Maxwell’s equations suggested that there would be other types of hitherto undiscovered waves aside from those teased out of nature by Faraday. In fact, it wasn’t too long after Maxwell’s death that radio waves were discovered, harnessed and transmitted. Here’s how Wikipedia reports it:

Radio waves were first predicted by mathematical work done in 1867 by Scottish mathematical physicist James Clerk Maxwell. His mathematical theory, now called Maxwell’s equations, predicted that a coupled electric and magnetic field could travel through space as an “electromagnetic wave”. Maxwell proposed that light consisted of electromagnetic waves of very short wavelength. In 1887, German physicist Heinrich Hertz demonstrated the reality of Maxwell’s electromagnetic waves by experimentally generating radio waves in his laboratory, showing that they exhibited the same wave properties as light: standing waves, refraction, diffraction, and polarization. Italian inventor Guglielmo Marconi developed the first practical radio transmitters and receivers around 1894–1895. He received the 1909 Nobel Prize in physics for his radio work. Radio communication began to be used commercially around 1900.

Maxwell never got to see all this because he died of stomach cancer at only the age of 48. If he had lived to be as old as Galileo, he would have seen Hertz generate radio waves, Marconi develop the first practical radio transmitters and receivers, and Einstein publish his special theory of relativity.

I so wish that the young Einstein could have met the old Maxwell, just as the young Maxwell met, interviewed and learned from the old Faraday. Yet life isn’t always fair like that, even for the truly great ones.

Feel the Forces, Luke

At this point in our scientific story, Galileo and Newton have discovered and quantified gravity while Faraday and Maxwell have done the same for electromagnetism. (That last sentence is an oversimplication, but let’s go with it.) Regardless of the names, humanity has learned to better understand and increasingly harness these two forces, not to mention the strong and weak forces discovered later. The forces were already there, of course, but understanding how to manipulate them has brought power that would have been viewed as god-like to people in the past.

In this sense, we are all like Luke Skywalker in the Star Wars universe, except the Forces are genuine. With them have come wonders, of course, but also more dangers. As fun as they might be, I don’t think our cinematic space operas can hold a candle to the narrative in which Forces-wielding humanity finds itself.

The Rise of New Networks

A network is a group or system of interconnected people or things. Without networks of thinkers who communicate ideas over time, often via the written word, we would have have no real understanding of electromagnetism or the technologies based on that understanding.

These networks of ideas led to the rise of technologically mediated networks, which led to scientific ideas being spread across the world at the speed of light. This is where we are today, our radio waves not only spanning the globe but expanding well beyond it, perhaps one day washing up on alien shores light years away, maybe even reaching the stars of the Reticulum constellation itself.

The Reticulum Constellation. Author: IAU and Sky & Telescope magazine (Roger Sinnott & Rick Fienberg)

Featured image is VFPt dipoles electric from author Geek3. For more information, go to https://en.wikipedia.org/wiki/File:VFPt_dipoles_electric.svg

How Grainy Is Your Reality?

I’m in the process of reading the book Reality Is Not What It Seems: The Journey to Quantum Gravity by Carlo Rovelli. I figured I’d write a bit about each chapter as I go along. Maybe this will help me integrate the ideas a better than if I simply read it.

I’ll give it a try, anyway, even if am suffering from the horrors of the WordPress editor at the moment (BTW, what gives, WP? Why did you move from a relatively user-friendly UI to this exceptionally unfriendly block system that specializes in producing heartburn and headache in equal proportions? Just wondering.)

The Ancient Power of Democritus

The first chapter is called “Grains,” which I assume is a reference to two things: 1) the fact that we are starting with the seminal ideas of today’s physics going back to ancient Greece and 2) the fact that the topic is atoms, which are the grainy little building blocks that reportedly make up our reality.

Rovelli, a theoretical physicist and science writer, insists that our current best understanding of reality began around 450 BCE with a Greek named Leucippus, the teacher of Democritus. “Together,” writes Rovelli, “these two thinkers have built the majestic cathedral of ancient atomism. Leucippus was the teacher. Democritus, the great pupil who wrote dozens of works on every field of knowledge, was deeply venerated in antiquity, which was familiar with these works.”

Rescued from Obscurity by Latin Poetry?

Why don’t we know more about these two great philosophers? Because, according to Rovelli, the texts of these philosophers were systematically destroyed by Christians in accordance with their ideas about reality. “Plato and Aristotle, pagans who believed in the immortality of the soul or in the existence of a Prime Mover could be tolerated by a triumphant Christianity,” he writes. “Not Democritus.”

These losses are tragic, especially given the very long list of works by Democritus, who looks to have been just as prolific as Aristotle. The good news is that a little about the philosophy of atomism was preserved in a work by the Latin poet Lucretius: that is, De rerum natura, or The Nature of All Things.

The Catholic Church really had it out for atomism. In the 1500s, they even tried to ban the works Lucretius but failed. Lucretius was already in the bloodstream of European thinkers and they were not going to give him up. Rovelli describes the work as “an articulate and complex structure of thinking about reality, a new mode of thinking, radically different from what had been for centuries the mind-set of the Middle Ages.”

Einstein and Atomism

So atomism survived by the skin of its philosophical teeth. Would we have today’s understanding of the universe without it? Impossible to know, of course, but Rovelli seems to think not. What’s especially interesting is Einstein’s role in atomism, a role I’d never heard about before. Apparently Einstein knew of the experiments of the 19th century biology Robert Brown, who graphed the movement of small particles suspended in water. The particles, it turns out, do not fall straight down. They move around in a zigzag manner.

Why does this happen? Because, Einstein hypothesized, the molecules in the water are colliding with one another. He even figures out the the approximate size of these tiny particles: “From observations of granules drifting in fluids, from the measurement of how much these ‘drift’ — that is, move away from position — he calculates the dimensions of Democritus’s atoms, the elemental grans of which matter is made. He provides, after twenty-three hundred years, the proof of the accuracy of Democritus’s insight: matter is granular.”

A Suspiciously Specific Dawn

Do I buy all this? Sort of. My impression is that it’s seriously oversimplified, as good stories often are. But it sounds generally true. Yes, I’m skeptical that the “first dawn of scientific thought” occurred only at Miletus in the sixth century BCE. That seems overly specific to me. I imagine that scientific thought is more organic than that, having begun thousands of years before when prehistoric humans slowly uncovered the workings of the natural world.

I think about Ötzi the Iceman, for example, who lived about 5,000 years ago and how his hair was heavily contaminated with copper and arsenic, suggesting he was somehow associated with copper smelting. That is pretty serious technology for an age millennia before Democritus was born. After all, such technology requires considerable patience, insight and multi-generational knowledge. In short, I doubt metallurgy is possible without the kind of reasoning that may itself be considered part of an extended dawn of scientific thought.

But that’s just nitpicking. Even if he is simplifying and mythologizing a bit, Rovelli tells a good and insightful story, one that I’ll remember even if I ultimately get a little fuzzy about the dates and names.

Featured image:  "The Young Rembrandt as Democritus the Laughing Philosopher", a portrait study, half length oil on copper, bears monogram top left "HL?" and lengthy French hand written inscription verso, 23.75 × 17 cm’). Go to https://commons.wikimedia.org/wiki/File:Rembrandt_laughing_1628.jpg

Minding the Universe

I read an article about how a study finds similarities between the human brain and networks of galaxies in the universe. Maybe we should be minding the universe a bit more carefully if it truly is, as the playwright once said, the mind of God.

Camerae Ready

Surprising? I don’t know. It seems as if the universe uses a lot of its same basic structures over and over at different scales, and these structures often have mathematical counterparts. One of the more famous examples is the Fibonacci sequence, in which each number is the sum of the two preceding ones, starting from 0 and 1. That is, 0 + 1 = 1, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21, etc. So, the actual sequence looks like 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and on and on.

What’s interesting is that this pattern shows up with some frequency in nature. Perhaps the most robust and convincing example is the spiraling nautilus shell, which is composed of chambered sections called camerae. Each chamber is equal to the size of the two camerae before it, creating a logarithmic spiral.

But there are there other examples as well: tree branches, flower petals, the seeds in sunflowers. It may extend to much larger phenomena as well, such as hurricanes and spiral galaxies.

So, perhaps it should not be surprising to find that brains and the universe are largely defined by their networks (that is neurons and galaxies) made up of nodes connected by filaments. In short, both are kinds of reticula. To read the actual report, go here.

Assuming the authors have a legitimate point, what do we make of the similarities between the universe and the human brain? Are we supposed to consider the idea that the universe is itself a thinking organism of some sort, that we exist in the mind of God?

Panpsychism

That’s too great a logical leap for me to make, but maybe it does lend support to the pseudo-scientific notion that the universe is conscious. In his book Galileo’s Error: Foundations for a New Science of Consciousness, philosopher Philip Goff considers the idea that consciousness is not something special that the brain does but is instead a quality inherent to all matter, a theory known “panpsychism.” To read an interview in which he discusses the notion, go here:

Goff isn’t alone in wondering about the consciousness of the universe. Astrophysicist Ethan Siegel has discussed it in Forbes, and NBCNews highlights other thinkers in its article “Is the Universe Conscious?”

I don’t know what to think about all this. It feels a bit like the Gaia hypothesis (which is the idea that the interconnected biological systems of the Earth act as one, enormous organism), except extended to “infinity and beyond” (in the immortal words of Buzz Lightyear).

Our Town

Back in my college days, I was in a staging of the play Our Town, in which I played the character George. I don’t remember many of George’s lines but I do remember a scene in he was speaking with his sister Rebecca at the end of Act One:

REBECCA: I never told you about that letter Jane Crofut got from her minister when she was sick. He wrote Jane a letter and on the envelope the address was like this: It said: Jane Crofut; The Crofut Farm; Grover’s Corners; Sutton County; New Hampshire; United States of America.

GEORGE: What’s funny about that?

REBECCA: But listen, it’s not finished: the United States of America; Continent of North America; Western Hemisphere; the Earth; the Solar System; the Universe; the Mind of God–that’s what it said on the envelope.

GEORGE: What do you know!

REBECCA: And the postman brought it just the same.

GEORGE: What do you know!

I doubt Thornton Wilder was the first writer or mystic to envision the universe as the mind of God. But I do wonder what he’d think about the fact that here in the third decade of the 21st century, it has become an idea taken seriously by the likes of philosophers, physicists, and science journalists. What do you know!

Featured image from https://en.wikipedia.org/wiki/File:NautilusCutawayLogarithmicSpiral.jpg. Nautilus shell cut in half. Photo taken by Chris 73 | Talk 12:40, 5 May 2004 (UTC)