Reality Straight Up!

Thoughts & Observations of a Free Range Astrophysicist

Entropy’s Rainbow

The statistically likely path to complexity

Entropy is often maligned as the enemy of order. In truth, without the inexorable march of entropy, the universe would be a very boring place.

This article originally appeared in my Astronomy Magazine column, For Your Consideration.


The early universe was remarkably uniform. Today’s universe is anything but. What gives? The details of how we got from there to here form one of the grand themes of science. But viewed from 30,000 feet, the transformation can be summed up in one word — entropy.

“Hold on a minute,” you say. “Entropy doesn’t build stuff. Entropy tears stuff down!” That is certainly the common impression people have about the Second Law of Thermodynamics. It’s also dead wrong.

Boltzmann's grave bears his formula for entropy.

Ludwig Boltzmann (1844-1906) is responsible both for his brilliant insight into the nature of entropy, as well as forever muddling its understanding by equating it with disorder. His grave in Vienna bears his formula relating entropy, S, with the number of indistinguishable microstates of a system, W.

Rewind the clock to the middle of the 19th century. In one of the all-time greatest advances in the history of science, Ludwig Boltzmann has just used the statistics of how molecules move to explain why heat always flows from hot things to cold things. It is a beautiful, elegant piece of work. It is also counterintuitive to a generation of scientists who are only beginning to get used to the atomic theory of matter.

“Entropy means disorder:” A misunderstanding that just won’t die.

Boltzmann has trouble explaining what he is on about, until he starts talking about entropy as “disorder.” A low entropy state, says Boltzmann, is more ordered. A high entropy state is more disordered. It’s easier to jumble things up than to go the other direction, which is why entropy always increases. It is a simple, visually compelling explanation that people can sink their teeth into. The idea of entropy as disorder sticks. And sticks. And sticks . . .

“The Second Law of Thermodynamics says that disorder increases with time.” To this very day, that statement remains de rigueur in classrooms (and blogs) any time the subject crops up. But it is an oversimplification that does more harm than good.

Identifying entropy with “disorder” is a lot like equating energy with “bombast.” It may well be that adding energy often makes things more bombastic. Talking about bombastic events might even help someone visualize what can happen when lots of energy is dissipated at one time. But there is no such thing as “conservation of bombast.” Trying to apply such a notion to the physical world would lead to all sorts of absurdity.

Random processes that increase entropy can build some pretty astounding stuff.

Rather than “disorder increases,” what the Second Law of Thermodynamics actually says is that random changes tend to move things toward statistically more likely configurations. What happens along the way can be really amazing.

Imagine watching a giant cloud of interstellar gas as it starts to collapse under its own weight. As the cloud gets smaller, it sure looks like things are getting more “ordered,” so perhaps you complain about the seeming violation of the Second Law.

What you don’t see is that the collapsing cloud is also getting hotter, meaning that the molecules in the gas have the energy to move faster. The wider range of velocities (more correctly momentum states) that molecules can take on more than makes up for the decrease in places the molecules can be. Entropy increases as it must.

But that hot molecular gas gives off radiation, which takes energy away from the molecules, reducing the available momentum states. OK, surely this is a violation of the Second Law!

Nope. The molecules are indeed more localized in both space and momentum, so their entropy is clearly lower than it started out. But what about the photons that were radiated away? There are all sorts of possible ways for those photons to be arranged, meaning that there are lots and lots of possible configurations for the system as a whole. The increased entropy of the photons is more than enough to make up for the decreased entropy of the cloud itself.

As energy (and entropy) is radiated away, the cloud loses pressure support and collapses further. Eventually that collapsing cloud settles into a disk. Stuff in the disk clumps up. The gas at the center gets so hot and dense that a fusion reaction kicks in. Where once there was a big, spread out, “disordered” clump of interstellar gas, now there is a young star surrounded by planets. So much for tearing things down!

As it goes with the formation of a planetary system from an interstellar cloud, so it goes for everything beginning with that early uniform universe, right up to you sitting there reading this article. The glorious, complex, awe-inspiring structure that surrounds us is a byproduct of increasing entropy, the blind, unguided, inexorable march of the universe toward ever-more statistically likely states.

Entropy’s Rainbow ^ The statistically likely path to complexity  © Dr. Jeff Hester
Content may not be copied to other sites. All Rights Reserved.

Reality Straight Up!

  • Great Deceiverism 101  Explanation or Theory? Therein lies the rub.Posted in For Your ConsiderationUnreasonable Faith
  • One Step at a Time  The  not-so-mysterious origin of lifePosted in For Your ConsiderationUnreasonable Faith
  • The Mind’s Siren Call  Being certain is a primrose pathPosted in For Your ConsiderationUnreasonable Faith
  • Constrained Hallucinations  How the brain uses science to perceive the worldPosted in For Your ConsiderationUnreasonable Faith
  • Entropy Redux  Why our universe isn’t boringPosted in For Your ConsiderationUnreasonable Faith
  • Entropy’s Rainbow  The statistically likely path to complexityPosted in For Your ConsiderationUnreasonable Faith
  • Cassandra Smiling  Science, politics and a march in the rainPosted in For Your ConsiderationUnreasonable Faith
  • EPA Rehash  A suddenly partisan NASA faces its futurePosted in Thoughts
  • The Hermeneutics of  Bunk  Alan Sokal and postmodernism’s black eyePosted in For Your ConsiderationUnreasonable Faith
  • A Dunning-Kruger Universe  Everyone, it seems, has a “theory”Posted in For Your ConsiderationUnreasonable Faith
  • Our Need to Know  We crave certainty, even when it is only an illusionPosted in CoachingThoughtsUnreasonable Faith
  • A Saguaro’s universe  Building a cactus starts with the Big BangPosted in For Your Consideration
  • Great Deceiverism 101
    Explanation or Theory? Therein lies the rub.

    If someone can’t tell you how they would know that they are wrong, they don’t have a clue whether they are right.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

    Read Article

  • One Step at a Time
    The not-so-mysterious origin of life

    Once seemingly incomprehensible, the origin of life no longer seems such a mystery. Most of what once appeared as roadblocks are turning out to be superhighways.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

    Read Article

  • The Mind’s Siren Call
    Being certain is a primrose path

    Being certain lights up our brains like a junkie’s next hit. Literally. Unfortunately, being certain and being right are two very, very different things.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

    Read Article

  • Constrained Hallucinations
    How the brain uses science to perceive the world

    The unique worlds we each consciously inhabit – the only worlds we will ever experience – are constrained hallucinations, products of hypothesis testing by our predictive brains.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

    Read Article

  • Entropy Redux
    Why our universe isn’t boring

    A month’s worth of sunlight could pay the entropy bill for a billion years of biological evolution. Entropy is evolution’s best friend.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

    Read Article

  • Entropy’s Rainbow
    The statistically likely path to complexity

    Entropy is often maligned as the enemy of order. In truth, without the inexorable march of entropy, the universe would be a very boring place.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

    Read Article

  • Cassandra Smiling
    Science, politics and a march in the rain

    On a cold day in April, 2017 scientists gathered in Washington DC and cities around the world for the March for Science. Their message was a single powerful idea. Truth is not a political expediency. Reality cannot be ignored. In the year that has followed the vital importance of that message has only grown.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

    Read Article

  • EPA Rehash
    A suddenly partisan NASA faces its future

    When I look at NASA’s new Administrator, Jim Bridenstine, it is his fellow Oklahoman Scott Pruitt’s EPA that jumps to mind. As politically uncomfortable science is pushed aside, NASA’s history of nonpartisanship appears headed for an abrupt end. Will a strongly partisan NASA have a target on its back?

    Read Article

  • The Hermeneutics of Bunk
    Alan Sokal and postmodernism’s black eye

    Some years ago, NYU physicist Alan Sokal wondered whether anti-science postmodernists could recognize politically-correct-sounding nonsense even if he rubbed their noses in it. The unwitting subjects of the Sokal Hoax jumped at the bait.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

    Read Article

  • A Dunning-Kruger Universe
    Everyone, it seems, has a “theory”

    Some people are sure they know more than the experts, but it can take a lot of knowledge to realize just how wrong an idea is.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

    Read Article

  • Our Need to Know
    We crave certainty, even when it is only an illusion

    The human brain craves the sensation of knowing like a drug addict craves the next fix. If real knowledge is uncomfortable or not at hand, we are quite content to just make something up, then convince ourselves it’s real. In a world where knowledge matters, that’s dangerous.

    Read Article

  • A Saguaro’s universe
    Building a cactus starts with the Big Bang

    The iconic saguaro cactus gives the desert an otherwordly beauty. That beauty does not exist in isolation. It embodies the fascinating and awe-inspiring processes that have shaped the universe, going all the way back to the Big Bang itself.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

    Read Article

Click on thumbnail to select post:

  • Great Deceiverism 101  Explanation or Theory? Therein lies the rub.Posted in For Your ConsiderationUnreasonable Faith
  • One Step at a Time  The  not-so-mysterious origin of lifePosted in For Your ConsiderationUnreasonable Faith
  • The Mind’s Siren Call  Being certain is a primrose pathPosted in For Your ConsiderationUnreasonable Faith
  • Constrained Hallucinations  How the brain uses science to perceive the worldPosted in For Your ConsiderationUnreasonable Faith
  • Entropy Redux  Why our universe isn’t boringPosted in For Your ConsiderationUnreasonable Faith
  • Entropy’s Rainbow  The statistically likely path to complexityPosted in For Your ConsiderationUnreasonable Faith
  • Cassandra Smiling  Science, politics and a march in the rainPosted in For Your ConsiderationUnreasonable Faith
  • EPA Rehash  A suddenly partisan NASA faces its futurePosted in Thoughts
  • The Hermeneutics of  Bunk  Alan Sokal and postmodernism’s black eyePosted in For Your ConsiderationUnreasonable Faith
  • A Dunning-Kruger Universe  Everyone, it seems, has a “theory”Posted in For Your ConsiderationUnreasonable Faith
  • Our Need to Know  We crave certainty, even when it is only an illusionPosted in CoachingThoughtsUnreasonable Faith
  • A Saguaro’s universe  Building a cactus starts with the Big BangPosted in For Your Consideration
  • If someone can’t tell you how they would know that they are wrong, they don’t have a clue whether they are right.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

  • Once seemingly incomprehensible, the origin of life no longer seems such a mystery. Most of what once appeared as roadblocks are turning out to be superhighways.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

  • Being certain lights up our brains like a junkie’s next hit. Literally. Unfortunately, being certain and being right are two very, very different things.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

  • The unique worlds we each consciously inhabit – the only worlds we will ever experience – are constrained hallucinations, products of hypothesis testing by our predictive brains.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

  • A month’s worth of sunlight could pay the entropy bill for a billion years of biological evolution. Entropy is evolution’s best friend.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

  • Entropy is often maligned as the enemy of order. In truth, without the inexorable march of entropy, the universe would be a very boring place.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

  • On a cold day in April, 2017 scientists gathered in Washington DC and cities around the world for the March for Science. Their message was a single powerful idea. Truth is not a political expediency. Reality cannot be ignored. In the year that has followed the vital importance of that message has only grown.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

  • When I look at NASA’s new Administrator, Jim Bridenstine, it is his fellow Oklahoman Scott Pruitt’s EPA that jumps to mind. As politically uncomfortable science is pushed aside, NASA’s history of nonpartisanship appears headed for an abrupt end. Will a strongly partisan NASA have a target on its back?

  • Some years ago, NYU physicist Alan Sokal wondered whether anti-science postmodernists could recognize politically-correct-sounding nonsense even if he rubbed their noses in it. The unwitting subjects of the Sokal Hoax jumped at the bait.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

  • Some people are sure they know more than the experts, but it can take a lot of knowledge to realize just how wrong an idea is.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

  • The human brain craves the sensation of knowing like a drug addict craves the next fix. If real knowledge is uncomfortable or not at hand, we are quite content to just make something up, then convince ourselves it’s real. In a world where knowledge matters, that’s dangerous.

  • The iconic saguaro cactus gives the desert an otherwordly beauty. That beauty does not exist in isolation. It embodies the fascinating and awe-inspiring processes that have shaped the universe, going all the way back to the Big Bang itself.

    This article originally appeared in my Astronomy Magazine column, For Your Consideration.

Over his 30 year career as an internationally known astrophysicist, Dr. Jeff Hester was a key member of the team that repaired the Hubble Space Telescope. With one foot always on the frontiers of knowledge, he has been mentor, coach, team leader, award-winning teacher, administrator and speaker, to name a few of the hats he has worn. His Hubble image, the Pillars of Creation, was chosen by Time Magazine as among the 100 most influential photographs in history.
©Dr. Jeff Hester LLC, 5301 S. Superstition Mountain Dr., Suite 104 #171, Gold Canyon, AZ 85118