Special Pi Day Edition, by Carl Sagan

In his novel Contact, Carl Sagan described his character discovering a hidden message in the digits of pi:

"The Argus computer was so persistent and inventive in its attempts to contact Eleanor Arroway that it almost conveyed an urgent personal need to share the discovery.

The anomaly showed up most starkly in Base 11 arithmetic, where it could be written out entirely as zeroes and ones. Compared with what had been received from Vega, this could be at best a simple message, but its statistical significance was high.

The program reassembled the digits into a square raster, an equal number across and down. The final line was an uninterrupted file of zeros, left to right. The second line showed a single numeral one, exactly in the middle, with zeros to the borders, left and right. After a few more lines, an unmistakable arc had formed, composed of ones. The simple geometrical figure had been quickly constructed, line by line, self-reflexive, rich with promise. The last line of the figure emerged, all zeros except for a single centered one. The subsequent line would be zeros only, part of the frame.

Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts.

The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle — another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn’t matter what you look like, or what you‘re made of or where you came from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you’ll find it. It’s already here. It's inside everything. You don‘t have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great mark of art, there is, written small, the artist's signature. Standing over humans, gods, and demons, subsuming Caretaker: and Tunnel! Builders, there is an intelligence that antedates the universe.

The circle had closed.

She found what she had been searching for."

Zeno and the Fundamental Structure of the Universe

The universe is a weird place. I’m not the first person to notice this. A guy named Zeno also noticed it more than 2,000 years ago. Now, you wouldn't think there would have been a lot of people 2,000 years ago named Zeno, but it turns out there were. The Zeno I’m talking about is Zeno of Elea, a Greek philosopher.

We don’t know much about Zeno. Apparently, he’s mentioned, along with a buddy of his called Parmenides, in a book Plato wrote called Parmenides. That doesn’t help us much, because no copies of that book survive to our time. All we know about that book is what other people say about it when they refer to it in their own writing. People like Aristotle.

Anyway, Zeno and Parmenides had this idea about the universe, namely, that nothing changes. They didn’t just mean that you hit the exact same traffic every time you drive to Boston, or that the stories on TV all seem to be the same: they meant that NOTHING changes.

Ah, you might say, well, I took tuna for lunch today, and yesterday I took turkey, so that’s a change, which kind of refutes that whole theory, doesn’t it?

No, they’d say, that’s all an illusion. Really, nothing changes. And we can prove it, because the whole concept of change leads to logical contradictions. And if something leads to logical contradictions, it CAN’T be true.

Zeno is said to have concocted 40 of these demonstrations of how change leads to logical contradictions, which are called paradoxes. As I’ve said, we don’t have anything about him except from what others tell us, so we know of about 9 of these paradoxes, 5 of which are the most famous. These have to do with how the idea of motion—which is a change in position—leads to logical contradictions. Let me tell you about 2 of them.

The first one is called the Dichotomy. Suppose you want to walk up to a wall. To do this, you first have to move half the distance to the wall. Then you have to move half of the remaining distance. Then you have to move half of that remaining distance. Then half of that. And half of that. And so on, infinitely. In other words, before you can get to that wall, you have to do an infinite number of things first. And, of course, you will never finish that infinite number of things, so you will never get to the wall.

Ah, you might say, well, I’ve actually walked right up to walls with no trouble, so that’s not quite true, is it?

Exactly, Zeno would say. Logically, you cannot reach the wall. But you did actually reach the wall. That’s the logical contradiction I was talking about. Ergo, motion—and any other change—is actually impossible and is only an illusion.

These days, we can resolve paradoxes like this one using mathematics that was unknown in Zeno’s day. For example, we now know how to add up an infinite series like the one Zeno is presenting us with, namely ½ + ¼ + 1/8 + 1/16 + … You learn how to do this in calculus or pre-calculus. It turns out that this infinite series adds up to 1, so we don’t have to cover an infinite distance to get to the wall, just an ordinary finite distance.

Also, it doesn’t take us an infinite time to do it, either. We know that the time it takes to cover each of these distances is also an infinite series of the same kind, namely ½ + ¼ + 1/8 + 1/16 + … This also adds up to 1, so it doesn’t take us an infinite time to perform this infinite series of tasks, just an ordinary time.

Easy, right?

Well, the other paradox I want to tell you about is a little trickier. Spoiler alert: it turns out that the math for this one also explains it pretty easily. But the physics of it: that’s where the fun starts.

This other paradox is called “Achilles and the Tortoise”, and it has a little story attached to it. The Tortoise, slowest of all creatures, challenges Achilles, the mighty Greek hero of the Iliad, to a race. Achilles, a very speedy runner, agrees, and even graciously gives the Tortoise a generous head start. The race begins, and both racers start off, Achilles very fast and the Tortoise very slow. Achilles rapidly gets to where the Tortoise started from (call this location L₁). By the time Achilles gets there (L₁), however, the Tortoise has, of course, moved on a ways (to L₂). Achilles again gets to where the Tortoise was (L₂), but by the time he does so, the Tortoise has moved on a slight distance (to L₃). Again, Achilles catches up to where the Tortoise had been (L₃), but the Tortoise has again moved on (to L₄). This happens over and over. Indeed, instead of passing the Tortoise, Achilles can’t even catch up with him. Achilles stops to ponder this, as Greeks tend to do, and he takes so long pondering that the Tortoise crosses the finish line and wins the race.

What is going on here? We are surely all familiar with a faster racer overtaking a slower racer. It happens in every single race. But, the way Zeno tells it, that seems impossible. Every time fast Achilles gets to where the slow Tortoise was (L_n), the Tortoise has moved on a short distance (to L_n+1).

Now, as I said, this also has a fairly simple mathematical explanation. Let’s think about the times in this situation, rather than the distances. In the time it takes the Tortoise to move from location L_n to location L_n+1, Achilles is moving much further than the Tortoise is. Eventually, the distance that Achilles covers in this time is going to surpass the distance that the Tortoise covers, Achilles will pass him by, and win the race, just as we suspected all along.

Whew! Glad that’s straightened out!

But that was just the math part of it. What about the physics?

The physics of the situation is more complicated. As long as we can keep dividing the distance into tinier and tinier pieces to represent the Tortoise’s motion, there doesn’t seem to be a way for Achilles to catch up. Whenever he covers the tiny distance to where the Tortoise was (L_n), the Tortoise isn’t there anymore: he’s traveled the ever-tinier distance to L_n+1.

So, how can this paradox be resolved in physics?

One way is if that previous assumption isn’t really true: maybe we can’t really keep dividing the distance into tinier and tinier pieces. Maybe there’s some limit to how much you can divide distance.

Look at it this way. We’ve been thinking of this race as taking place on something like a wide open soccer field: no divisions, no limitations, nothing to suggest you CAN’T keep dividing the distance into tinier and tinier pieces.

But what if the race isn’t on a soccer field? What if it’s on a checkerboard, an enormous checkerboard, and Achilles and the Tortoise are checkers or chess pieces on the checkerboard? Achilles is a much faster kind of piece than the Tortoise is: he can move 10 squares to the Tortoise’s 1. But the thing about a checkerboard is this: the pieces can’t be just anywhere. They have to be in one square or another, not somewhere in between. In other words, on a checkerboard, you CAN’T keep dividing the distance into tinier and tinier pieces. Eventually, you come down to one single square, which cannot be divided any smaller.

How does running on a checkerboard affect the race between Achilles and the Tortoise? In this way: the Tortoise CAN’T keep moving tinier and tinier distances ahead. The Tortoise can either move 1 square ahead, as the tiniest move, or no squares at all. Either way, Achilles will eventually land on the square next to the Tortoise, and then pass the Tortoise in the next moment.

Think about what this means: this suggests that distance in the universe CAN’T be divided tinier and tinier. There is some lower limit to distance in the universe, some tiniest distance—like a square on a checkerboard—and there’s nothing smaller than that. The universe is granular, not continuous. You can be in square n or square n+1, but never in between the two.

Seems strange, doesn’t it?

And it gets worse.

We know, from Einstein’s theory of relativity, that time and distance are intimately related. In the equations, one can become the other. But if distance is granular, and there is a smallest distance like a square on a checkerboard, then time must be that way, too. There must be a smallest time, a shortest moment, and nothing smaller than that.

In this view of things, time isn’t a continuous flow of events. It’s more like a movie, which, despite the illusion of continuous flow, is actually many individual pictures running too fast for us to perceive the gaps in between. That’s what the universe is like.

Notice that this has nothing to do with quantum mechanics, which also suggests that space and time come in clumps, not continuously. This current discussion is deeper than quantum mechanics: you get to where we are so far using only classical physics, no quantum about it.

Well, so what? What does it matter if the universe is continuous or discontinuous? What’s the significance of this? The significance is that the phenomenon that most closely matches what we’ve been describing is: a computer game. The characters in a computer game don’t live in a world of continuous space and time either: their world is as granular as a pixel and as discontinuous as whatever small time-step the programmer has chosen. The illusion of computer games is very convincing: characters and places and objects and motion look continuous. But we know they aren’t.

Meaning what? Meaning this: our universe could actually be a constructed thing. Perhaps not a computer simulation, but something like that. Perhaps not “The Matrix”, but something like that. A place that was deliberately built. A place that exhibits this checkerboard kind of behavior.

“Could be.” Remember that, when we began our explanation of the “Achilles and the Tortoise” paradox, we said that this was one way to resolve the paradox. There are definitely others. But this is an interesting possibility, isn’t it?

That Zeno was pretty smart.

The Coincidence of the Moon

Just a quick one, today. And not even my own words.

Isaac Asimov, author of more than 500 books, and countless essays on science, had this to say about the Moon and its perfect fit over the Sun during a solar eclipse:

"What makes a total solar eclipse so remarkable is the sheer astronomical accident that the Moon fits so snugly over the Sun. The Moon is just large enough to cover the Sun completely (at times) so that a temporary night falls and the stars spring out. And it is just small enough so that during the Sun's obscuration, the corona, especially the brighter parts near the body of the Sun, is completely visible.

“The apparent size of the Sun and Moon depends upon both their actual size and their distance from us. The diameter of the Moon is 2160 miles while that of the Sun is 864,000 miles. The ratio of the diameter of the Sun to that of the Moon is 864,000/2160 or 400. In other words, if both were at the same distance from us, the Sun would appear to be 400 times as broad as the Moon.

“However, the Sun is farther away from us than the Moon is, and therefore appears smaller for its size than the Moon does. At great distances, such as those which characterize the Moon and the Sun, doubling the distance halves the apparent diameter. Remembering that, consider that the average distance of the Moon from us is 238,000 miles while that of the Sun is 93,000,000 miles. The ratio of the distance of the Sun to that of the Moon is 93,000,000/238,000 or 390. The Sun's apparent diameter is cut down in proportion.

“In other words, the two effects just about cancel. The Sun's greater distance makes up for its greater size and the result is that the Moon and the Sun appear to be equal in size. The apparent angular diameter of the Sun averages 32 minutes of arc, while that of the Moon averages 31 minutes of arc.

“These are average values because both Moon and Earth possess elliptical orbits. The Moon is closer to the Earth (and therefore appears larger) at some times than at others, while the Earth is closer to the Sun (which therefore appears larger) at some times than at others. This variation in apparent diameter is only 3 per cent for the Sun and about 5 per cent for the Moon, so that it goes unnoticed by the casual observer.

“There is no astronomical reason why Moon and Sun should fit so well. It is the sheerest of coincidence, and only the Earth among all the planets is blessed in this fashion. Indeed, if it is true, as astronomers suspect, that the Moon's distance from the Earth is gradually increasing as a result of tidal friction, then this excellent fit even here on Earth is only true of our own geologic era. The Moon was too large for an ideal total eclipse in the far past and will be too small for any total eclipse at all in the far future."

What’s significant about this is that it is by the observation of—and the explanation of—solar eclipses and similar phenomena that we came to create the science of astronomy, which led to the science of physics, science in general, engineering, and our modern civilization. Without that coincidence of the size of the moon and the sun, none of that would have happened as it did.

The Miracle of DNA

The Miracle of DNA

As evolutionary biologists tell us, life on Earth began more than three billion years ago with single-cell organisms. It’s amazing to consider that we are the direct lineal descendants of those single-cell organisms from billions of years ago. Despite our complex minds, our technological and artistic achievements, these are our original ancestors. We ingest, as they ingested; we excrete, as they excreted; we have DNA, as they had DNA; and we are constructed of much the same chemicals. Amazing.

In fact, the situation is more amazing than this. Not only are we humans the direct descendants of these single-cell organisms, but so are all the millions of other species of life on Earth. Every koala bear, palm tree, spider, hawk, swordfish, and snapping turtle in the world has the same common ancestor.

This means, of course, that we are related to every other species on Earth. They’re all our second cousins, once removed, although it might be more accurate to describe them as our 3,000^th cousins, 700 times removed. Still, our cousins. We have that common heritage, that common connection of chemistry and DNA together.

Some people take this kinship more to heart, trying to never harm any other living thing. It’s a challenging goal, since we must eat to survive, and the most easily obtained food comes from other living things. Even if one avoids this extreme, though, it makes sense to feel a connection to the other living things that share our ancestry, and to treat them with a family respect.

Yet, the situation is even more amazing than this. Consider that single-cell organism from more than three billion years ago. Its DNA eventually became our human DNA, and the DNA of every other species on earth. In other words, before there was ever a fish in the ocean, the possibility of that fish was contained in that DNA. Before there was ever a bird in the sky, the potential for that bird lay in that DNA. And before any human took a step on two feet, picked up a tool with a hand, spoke with a voice, or reasoned with a mind, that human was made possible by that single-celled organism’s DNA.

Isn’t it remarkable that such a flexible and capable molecule as DNA should have been present in that single-cell organism? After all, it didn’t need to provide for the possible arrival of more-complex descendants. Wouldn’t some far simpler mechanism for producing other single-cell organisms have been more efficient and appropriate? Why were all the astonishing capabilities of DNA necessary at that point more than three billion years ago? It’s as if the first tool devised by humans had been a Swiss Army knife rather than a stick. Somehow, DNA, for a single-cell organism, feels like overkill.

In fact, this is one of those situations that seem awfully suspicious to me. That single-cell organisms should have the ability, the potential, to produce such a vast variety of other life forms seems unnecessary and arbitrary.

I can think of a couple of explanations for the presence of such all-purpose DNA in an – at that time – simple organism.

One possibility is that the single-cell organisms on Earth didn’t originate on Earth. They originated somewhere else, the product of lots of evolution that produced such all-purpose DNA. And they got here … well, who knows how. Possibly accidentally, by some natural process, one that can convey living cells across space. Possibly deliberately. Scientists have figured out that the most efficient way to explore other planets is not to go ourselves. Send robots. Maybe include living cells that could be “injected” onto the surface of possibly habitable planets. If they don’t take, fine. If they do take, well, then maybe you get a planet whose single-cell organisms evolve into a vast variety of living things, thanks to their all-purpose DNA.

The other possibility I can think of is that DNA might be kind of inevitable. Perhaps, if you have enough randomly-created amino acids sloshing around for long enough, you inevitably get DNA, with all its latent potential for creating life. But think what this means: we live in a universe where it is almost inevitable that life like us would develop. That can hardly be random. If this is what’s happening, our universe is almost certainly designed, a created thing, with the odds skewed heavily in favor of life.

Pi and the Hydrogen Atom

     This is an example of something that I feel suggests that the universe is either designed, or has some underlying special structure that we are not aware of yet. Let me describe what was discovered, and what I think it means.

     Carl Hagen, a physics professor at the University of Rochester, was teaching his graduate-level physics students how to perform a particular calculation of the energy states of the hydrogen atom. This is not an unusual thing. When I was a physics grad student, I probably had to do something similar. One aside in the current situation is that Professor Hagen happens to be one of the co-discoverers of the Higgs mechanism, which has gotten so much press the last few years. This has nothing to do with that, though.

     Anyway, Hagen did the calculation himself and noticed that it was turning out oddly. He enlisted one of his students, Tamar Friedmann, to help him sort it all out. What they eventually found was that the formula they were using to calculate the energy states of the hydrogen atom also happens to be a formula for the irrational number pi.

     There are many formulas that you can use to produce the number pi. This particular one was devised by an English mathematician named John Wallis in 1655. The formula is in the form of the limit of an infinite sequence of ratios.

     In other words, what Friedmann and Hagen have found is a hitherto unknown connection between the actual physical world of atoms and the abstract world of mathematics.

     It's important to note that this connection between pi -- which has to do with circles, of course -- and the hydrogen atom has nothing to do with the fact that the simplest orbits of electrons around the atom are circles. That is completely beside the point. There are plenty of physical situations that deal with motion in circles, but whose formulas have nothing whatever to do with the number pi. This formula does, though, and that's what makes its discovery so amazing.

     Now, there seem to three different ways of looking at this discovery: "Of course", "Whatever", and "Holy crap!".

     Of course: This point of view says, Well, of course they found a connection between the physical world and the mathematical world. This happens all the time. If you pick up a rock and then pick up another rock, guess what: you've just found a physical-world example of the mathematical concept 1+1=2. This particular discovery is just a more complicated example of exactly the same thing. This is to be expected. There's nothing special to see here. Move along, citizen.

     Whatever: This point of view says, Well, okay, this is interesting, and, yeah, I guess nobody over noticed this before about the two formulas, so, sure, you can squeeze a paper out of it, I guess. But it certainly doesn't have any special meaning. It's just one of those strange things you come across now and then.

     Holy Crap!: This point of view says, Holy crap! These are two entirely unrelated areas that somehow are resulting in exactly the same thing. The laws of physics are about physics. They describe the behavior of the universe. Although they're certainly expressed using mathematics, they have nothing to do with mathematics. You would never expect to get a particular answer to a physics problem just because it was mathematically an interesting number. That a calculation of something so fundamental as the energy states of the simplest atom -- hydrogen -- would lead to the number pi is not only totally unexpected, but also, somehow, extremely significant.

     As to what the actual significance might be? I have two thoughts.

     One is that, if the universe is a designed and created thing, this is a clue from the designers of the universe. They're saying, See what we did there? In Douglas Adams's science fantasy book The Hitchhiker's Guide to the Galaxy, it turns out that the Earth was designed and built for a specific purpose. At one point in the story, one of the characters travels to Norway, and observes the signature that one of the designers of the Earth hid underneath a glacier. This discovery is something like that: a suggestion that the universe was created, and that the creators left their signature in places like this.

     The other possible significance is that the universe is NOT a designed and created thing, but that there is a deep underlying structure to the universe that we are not yet aware of. This structure means that the value of the ratio of the circumference of a circle to its diameter has something to do with the energy levels of the hydrogen atom, a connection that we don't see, to put it mildly.

     I, personally, am solidly in the Holy Crap! camp. This discovery is so unexpected, so suggestive, so inexplicable that it has to have a special meaning.

     What that meaning might be?

     Well ...

    

     Here is Friedmann and Hagen's actual paper on the subject (don't worry: it's only 4 pages long):

     http://arxiv.org/pdf/1510.07813v2.pdf

     Here are some links that describe Friedmann and Hagen's discovery in ordinary language:

     https://www.aip.org/publishing/journal-highlights/new-derivation-pi-links-quantum-physics-and-pure-math

     http://www.futurity.org/pi-quantum-mechanics-1046522-2/

     http://motls.blogspot.com/2015/11/pi-found-in-hydrogen-atom.html

     http://www.csmonitor.com/Science/2015/1111/Scientists-look-into-hydrogen-atom-find-old-recipe-for-pi

     http://www.gizmodo.com.au/2015/11/theres-a-hidden-connection-between-pi-and-quantum-mechanics/

    

    

     

The Extinction of Physical Law

The Extinction of Physical Law

In the universe, the structure of the physical laws, and the values of certain fundamental physical constants, appear to be “tuned.” That is, they appear to have values within a range that permit certain types of phenomena, including the existence of life. This could simply be happenstance. However, it is also possible that there is some process that has caused the selection of these particular physical laws and these particular fundamental constants.

If such an apparently “tuned” feature were to arise in a biological system, we would immediately hypothesize that it must be the result of the process of evolution. That is, some process of variation has caused the emergence of such a feature, and permitted its survival by the elimination of alternative features. This suggests the possibility that physical laws themselves might have evolved, and that this evolution of physical law is the cause of the observed features. This would further suggest that, in the original universe, there might have been a multiplicity of physical laws, but that only a certain few of these laws persisted. Moreover, the laws that persisted did so in such a way as to produce the observed values of fundamental constants.

Here’s one possible mechanism for the extinction of a physical law. Consider a force modeled on the Coulomb force of static electricity, namely, opposite charges attract and like charges repel. Particles that are subject to this hypothetical force would have some positive and negative property. Then, particles with like properties would repel each other while particles with opposite properties would attract each other.

Suppose further that it was possible to cancel out the positive and negative property, possibly by the particles coming into contact with each other. Suppose that all the particles in the universe possessing this property did cancel out their property, as far as was possible. There would then be two cases: either the number of particles with the positive property exactly equaled the number of particles with the negative property, or the numbers were different.

In the first case, this property of particles would cease to exist. There would be no particles to feel this hypothetical force any longer. The force would still exist, in a sense, but it would have no practical effect in the universe. Particles that formerly possessed this property would now only interact with each other, and with other matter, by other forces, such as gravitation. The hypothetical force would become extinct.

In the second case, after as much cancellation of the property was possible, a number of uncancelled particles would remain, all with the same sign. All of these particles would repel each other, and distribute themselves as far apart as possible throughout the universe.

In this way, this hypothetical force would become effectively extinct. In the first case, it would play no role at all in the universe. In the second case, it would serve only to distribute the remaining uncancelled particles at random, far from each other, throughout the universe. All the cancelled particles would then only interact with each other, and with ordinary matter, by other forces, such as gravitation.

There are indications that some such process of extinction of forces might already have occurred.

As one example, scientists have recently discovered the existence of so-called “dark matter”. Dark matter is called “dark” because it apparently doesn’t participate in any of the electromagnetic forces that produce radiation such as heat or light. We can’t see dark matter, because it’s dark in this way. We can only infer its existence because of the gravitational effects that it has on matter that we can see.

It could be that dark matter once experienced some type of force with other dark matter. In some way, that force might have become extinct, perhaps as hypothesized above. Now, all dark matter can do is interact with ordinary matter through a force that both types of matter feel: gravitation.

As another example, the theory of cosmological inflation postulates that the early universe went through an extremely rapid exponential expansion, to achieve the smoothness of distribution of matter that we now observe. However, there is no currently known force that could have caused this inflation.

It could be that there once was such a force, sufficient to cause the hypothesized cosmological inflation. But, since that inflation occurred – indeed, possibly as a result of that inflation – this force might have become extinct. It no longer operates in any meaningful way in the universe.

Thus, the extinction of physical law could be one way by which the nature of the universe changes, and features become "tuned".

Welcome to The Goldilocks Variations

We humans live in a universe that is remarkably well-suited to our existence. In fact, it's suspiciously well-suited to us. Consider the following:

* Life depends on specific environmental conditions on Earth, especially with regard to the prevalence and properties of water.

* The Earth is just the right distance from the Sun to make life possible.

* The Earth is the right size to permit the existence of life.

* A small change in any of the fundamental physical constants would make the Universe radically different.

* If, for example, the strong nuclear force were 2% stronger than it is, this would drastically alter the physics of stars, and presumably preclude the existence of life on Earth.

* If the ratio of the strength of electromagnetism to the strength of gravity for a pair of protons were significantly smaller, only a small and short-lived universe could exist.

* If the strength of the force binding nucleons into nuclei were slightly smaller, only hydrogen could exist, and complex chemistry would be impossible. If it were slightly larger, no hydrogen would exist.

* If gravity were too strong compared with dark energy and the initial metric expansion, the universe would have collapsed before life could have evolved. On the other side, if gravity were too weak, no stars would have formed.

* If the cosmological constant was not extremely small, stars and other astronomical structures would not be able to form.

* If the ratio of the gravitational energy required to pull a large galaxy apart to the energy equivalent of its mass were too small, no stars could form. If it were too large, no stars could survive.

* If the number of spatial dimensions were 2 or 4, life could not exist.

* If the third-lowest energy state of the carbon-12 nucleus, were slightly lower or slightly larger, insufficient carbon would exist to support life.

Such conditions are called "Goldilocks" conditions. The name comes from the fairy tale of Goldilocks and the Three Bears, where Goldilocks's porridge was "just right" between the extremes of "too hot" and "too cold" and Goldilocks's bed was "just right" between the extremes of "too hard" and "too soft".  Similarly, in the universe, the conditions must be "just right" between two often-close extremes for human beings to exist.

There are various explanations for the Goldilocks conditions in the universe:

* This is all pure coincidence.

* There are multiple universes, each with different characteristics. We happen to live in the one that has all the right conditions.

* Somehow, the eventual existence of humans retroactively influences the features of the universe to make the existence of humans possible. This is called the strong anthropic principle.

* This is all backwards: life has evolved to survive under the conditions of the universe.

* It's all backwards another way: if we humans didn't exist at all, we would not observe that the conditions weren't such to make us possible.

* There is some process that causes random values to converge to the values they have.

* We are part of a complex and convincing simulation.

* The universe was designed and created by some being or beings.

Here are my observations on these possibilities:

* Pure coincidence: In other words, this isn't suspicious at all. Nothing to see here. Move along, citizen. Sorry, but it is precisely by considering such highly suspicious situations that science advances.

* Multiple universes: There is no evidence for this. I'm not sure how it's even possible to have evidence for this.

* Humans make the universe happen this way: This makes no sense to me.

* Life has evolved under the conditions of the universe: Of course, but the conditions would still have to be there.

* No humans, no issue: Well, we do exist, so ...

* The universe is a simulation: Fooled me.

* Some process causes the values to converge: I think this is possible for some of these "coincidences", but we have no idea of what this meta-process might be. Also, there are many to explain.

* Designed and created universe: This seems obvious to me: it looks designed and acts designed, so, hey, maybe it's designed.

This blog will be devoted to research and developments in this area.

The title is a pun on the Goldberg Variations by Johann Sebastian Bach, because I expect there to be a number of variations on the theme that the universe is a designed and created thing.