Biology, Cosmology and the Direction of Time

 1. Introduction

Why does biological evolution move "forward" in time, despite the fact that the fundamental laws of nature seem to be more or less time-symmetrical? Why are we born before we die, and not after?

Physicists and philosophers often seem to assume that all, or almost all time-asymmetrical (or, irreversible) processes can be reduced to, or explained by, the Second Law of Thermodynamics. In this essay, I will argue that, the biological arrow of time may not be reducible in any straightforward manner to the thermodynamic arrow of time, and that we may need a new cosmological/thermodynamic explanatory framework.

2. The Limits of Thermodynamics

Evolution enables the emergence of more complex beings over time, which, in and of themselves, have relatively low entropy. This doesn't violate the second law, because "mother nature" pays for the reduced local entropy by compensating for it in other ways, like infrared radiation.

That explains how forward evolution is possible despite the second law. That's a far cry from invoking the second law to explain why backwards evolution is impossible!

For evolution to go "forward" in time, it would seem that it needs to go thermodynamically "uphill". Wouldn't it be easier to go downhill? If it was going downhill, then, in principle, it wouldn't need to bother with the infrared radiation, because there would be nothing to compensate for.

3. Niwrad's Universe

Let me introduce you to Niwrad's universe, which I just made up: the universe in which everything else is the same as ours, except biological evolution runs in the opposite time direction. In Niwrad's universe, human beings assemble themselves over a period of years, say, in the ground, and, when they're ready, they're raised from their graves, taken somewhere to come to life, and walk away. Then they get younger until they turn into babies, and the doctors put them into their mothers' wombs.

Something seems wrong with that picture -- but what, really, is the problem? Is the second law of thermodynamics somehow being violated? Let's focus on reverse-decomposition, which is equivalent to spontaneous assembly. Does it violate the second law? No, it doesn't, for the simple reason that, although spontaneous assembly decreases local entropy, mother nature is compensating for it elsewhere. How does mother nature do it? Who knows, that's beside the point. The second law certainly doesn't care. All you have to do to placate the Entropy Police is to pay for the entropy you use. There are no requirements on how you pay.

In fact, the local entropy loss generated by spontaneous assembly is approximately the same entropy loss that happens when a man and a woman have a child (in our universe) -- and mother nature pays for it. How? The second law doesn't care.

So let's put the second law aside for a moment. (Put the second law aside? How could we? That's against the rules! You can't put the second law aside, even for a moment! The second law explains everything! Or maybe it doesn't?) This process still seems astronomically improbable. It should never happen in a million years. And in Niwrad's universe it's happening all over the world all the time.

Does that explain what's wrong with Niwrad's Universe? It certainly seems like it should, but that's just because of our forward-centric bias. After all, look at our own universe.

4. Darwin's Universe

In our own universe, we tend to think that spontaneous assembly doesn't happen, but it all depends on your point of view. If you look at our universe from the other direction of time, "backwards", then spontaneous assembly is happening all over the world, all the time. That's not fair! Why is it OK for astronomically improbable events to happen if you look at our world backwards, but not if you look at our world forwards? Can this somehow be reduced to the second law of thermodynamics? (Hint: it can't.)

We could generalize by saying that in forward-directed time, improbable things rarely happen, and astronomically improbable things approximately never happen, whereas in backwards-directed time, improbable things happen all the time. And this is *not* reducible to the second law of thermodynamics. With apologies to all the real physicists, I'm going call this the first law of chronodynamics, just so that I'll be able to refer to it later.

So we established that, in the backwards direction of time, astronomically improbable things are happening all the time. But not just any random astronomically improbable things. More specifically, in backwards time, astronomically improbable things happen *only if* they *are* probable in the forwards direction. Let's call that the second law of chronodynamics.

Both of these laws seem to be true in our universe. But why? What is really going on?

5. Did the Big Bang Really Have Low Entropy?

The consensus among physicists seems to be that the early universe had (improbably) low entropy. This would seem to be an inescapable consequence of the second law of thermodynamics. After all, if entropy rises with time, then the universe in the past must have had lower entropy than the universe of today -- there's no getting around that. And almost by definition, low entropy is improbable, certainly more improbable than high entropy.

However, I believe that the early universe actually had high entropy -- so high that it was actually at equilibrium. How is that possible? Because the early universe was smaller than the current universe -- not just a bit smaller but way, way smaller. A smaller universe means fewer places particles can be -- smaller positional "phase space", if I'm using the term correctly.

The argument can be found here: https://mccomplete.blogspot.com/2025/03/did-big-bang-really-have-low-entropy.html

6. Macrostate Transitions and Explanation

Take a snapshot of the universe (our universe) at some moment of time, T -- say, 1 billion years ago, with life already flourishing on Earth. This macrostate is far from equilibrium — full of complex structures, gradients, and processes like evolution and metabolism.

If you take the forward-looking view, the macrostate at time T follows -- is caused by -- the macrostate at T - 1. The macrostate transition from T - 1 to T is a "probable" transition, whereas the macrostate transition from T to T - 1 is an improbable transition.

The macrostate transition from T - 1 to T is a "probable" transition, even though neither T - 1 is or T is a probable macrostate. Both T and T - 1 are not at thermodynamic equilibrium -- maximum entropy -- far from it, and therefore, they are both improbable, in and of themselves.

The macrostate at T is an "improbable" macrostate -- unless you *explain* it by invoking the macrostate at T - 1. But that kind of explanation just "begs the question". It pushes the "question" back to T - 1.

But the improbability of T - 1 can be "explained" by invoking T - 2. And so on, back to the big bang.

That's where the high entropy big bang comes in. According to my argument referenced above, the big bang *was* at equilibrium. It was a *probable* macrostate, so it needs no explanation. (What does need explanation is the cosmological arrow of time, the expanding universe.)

7. Conclusion

I have argued that the biological arrow of time is traceable to a boundary condition in the past, but contrary to the standard view, it is traceable to a high entropy -- in fact, equilibrium -- boundary condition, not a low entropy boundary condition. 

Due to the fact that the big bang was at equilibrium, relative to its small size, it was able to "kick off" a chain of moments where each moment explains the next -- but only in the forward direction of time.

Did the Big Bang Really Have Low Entropy?

 1. Introduction

We’re often told that the early universe was in a state of "inexplicably low entropy." This idea appears everywhere from textbooks to pop science: it’s the puzzle behind the arrow of time. If entropy always increases, and the future is higher-entropy than the past, then the early universe must have started in a low-entropy state. And low entropy states are highly ordered states, right? Why would the universe have started in a highly ordered state?

2. What is Entropy?

Entropy is often misunderstood as "disorder," but more precisely, it’s a count of how many microscopic states are compatible with the macroscopic conditions of a system. More possible configurations = more entropy.

In a box of gas, high entropy means the particles are spread out randomly, not clustered in a corner. As time passes, the gas tends to spread — not because it’s trying to "disorder" itself, but because there are vastly more ways to be spread out than to be concentrated. Entropy increases not by intention, but by statistics.

3. Why was the Big Bang Hot?

In statistical mechanics, high temperature corresponds to high entropy. If you have a lot of energy in a small volume — as in the early universe — the most probable, highest-entropy state is a hot (smooth?) radiation bath. The energy gets distributed among many short-wavelength, high-energy particles. That’s what high entropy looks like in a small universe.

In other words: the early universe was hot because it was high entropy. In fact, I believe that one could argue that the early universe was at equilibrium -- it had maximum entropy for its size.

4. Then Why Does Entropy Keep Increasing?

Because the universe didn’t stay small. As space expands, it creates more room — not just in a literal sense, but in "phase space", the abstract space of all possible configurations. More volume means more ways particles can be arranged, more available microstates, and thus a higher maximum entropy.

So even if the early universe started with the highest entropy available to it, the expansion of space allowed entropy to keep rising. The second law of thermodynamics doesn’t demand that the early universe was "low" entropy — only that entropy increases from whatever value it started with. And that’s exactly what happened, because space itself was growing.

The growth of "max entropy" due to expansion of space far outpaced the growth of actual entropy, even though both were growing. That gave the universe thermodynamic "elbow room" to undergo processes that unfolded by leveraging the gap -- such as gravitational clumping.

5. Do Clumps Really Have High Entropy?

It’s often said that the early universe was "too smooth," and that a clumpier configuration — with stars and planets already formed — would’ve had higher entropy. But there would seem to be a problem with that idea. In the hot early universe, clumps wouldn’t have lasted. They would have instantly disintegrated under the enormous pressure and thermal motion. Smoothness wasn’t a fragile, special arrangement — it was the stable, high-entropy state under those conditions.

Later, as the universe cooled and expansion made clumping possible, gravitational structures emerged. But that was a change in what kinds of configurations were entropically favored — not a sign that the early universe had been low entropy to begin with. And that change itself was a direct result of the expansion of the universe.

6. Do Black Holes Really Have High Entropy?

The current consensus among physicists today would seem to be that black holes are very highly entropic objects. If that's true, then it would be a mystery why the universe didn't start out as one big black hole, or maybe a collection of smaller black holes.

It could be that the universe was too small at the big bang to mathematically support black holes, or it could be that the universe did start out with black holes but they evaporated -- small black holes evaporate more quickly, and if there were black holes at the big bang, they would have to have been extremely small.

But I think we should be a bit skeptical of the claim that black holes are highly entropic, for reasons I've outlined here: https://mccomplete.blogspot.com/2025/03/do-black-holes-really-have-high-entropy.html

7. The Arrow(s) of Time

Instead of saying "the past is when entropy was lower," maybe we should say something deeper: The past is when space was smaller. The future is when space will be larger. Entropy increases because there’s more room to grow.

First of all, this reduces the "early universe low entropy" problem to the "expanding universe" problem -- a problem we already had. Second of all, it takes two arrows of time -- the thermodynamic arrow and the cosmological arrow -- and unifies them, and argues that the cosmological arrow is more fundamental. In a sense, it reinterprets thermodynamics as geometry.

8. Conclusion

The early universe wasn’t cold and clumpy. It was hot and smooth, and — it would seem to me — typical for a small, newly born universe. As space expanded, entropy increased. The universe of the past was not improbably ordered -- it was just kind of small.

Do Black Holes Really Have High Entropy?

1. Introduction

The idea that black holes are highly entropic objects originates in the Bekenstein-Hawking entropy formula:

S = (k_B * c^3 * A) / (4 * G * ħ)

where A is the area of the event horizon. This formula has been deeply influential, leading to the development of black hole thermodynamics. However, it relies on an analogy between Hawking temperature and classical temperature that is difficult, if not impossible, to test empirically. In this post, I question the assumption that black hole entropy must be as high as the Bekenstein-Hawking formula suggests.

2. Gravitational Collapse and the Asymptotic Horizon

From the frame of a distant observer, a collapsing star never crosses its Schwarzschild radius in finite time. Due to extreme gravitational time dilation, the surface of the star appears to freeze ever closer to the would-be event horizon, asymptotically approaching it.

There seems to be no reason that the entropy of the object should suddenly jump, or, as was assumed before Bekenstein, suddenly drop. Instead, the entropy of the object should evolve continuously as more matter collapses or falls in. It would seem that the entropy of the object should be traceable to its matter content and configuration, much as in any other thermodynamic system.

3. Rethinking Bekenstein's Argument

Bekenstein originally introduced black hole entropy to resolve apparent violations of the second law of thermodynamics. His concern was that objects with entropy could fall into a black hole, causing the total entropy of the universe to decrease unless the black hole itself was assigned an entropy. However, Bekenstein was largely concerned with avoiding the conclusion that black holes had zero entropy.

From the perspective of a distant observer, collapsing matter retains its identity outside the horizon for all time. Assigning it its original entropy—without invoking an area law—is sufficient to satisfy the second law in this frame.

4. Hawking Radiation and Thermodynamic Analogies

Hawking's conclusion that black hole entropy is extraordinarily large -- proportional to the area of the event horizon -- relies on the formal analogy between the surface gravity of a black hole and the temperature of a classical thermodynamic system. This analogy, while elegant, is still a conjecture. It is not derived from a statistical mechanics account of microstates, but from a semi-classical field theory calculation. The identification of entropy as proportional to the area is not a necessity of the theory but an interpretive leap.

5. Relevance to the Information Paradox

The question of whether black holes are highly entropic is often linked to the black hole information paradox. However, this link may be overstated. It is generally accepted that even asymptotically collapsing black holes emit Hawking radiation and can evaporate, regardless of whether a true event horizon forms. The existence of Hawking radiation and black hole evaporation depends on quantum field behavior in curved spacetime, not on entropy accounting.

Therefore, the claim that black holes must be highly entropic is not essential for understanding or resolving the information paradox. Even if the entropy remains equivalent to that of the infalling matter in the frame of a distant observer, the mechanisms for evaporation and information retention (or loss) remain intact. The paradox should be addressed on its own terms, without assuming a horizon-based entropy law.

6. Observational Considerations

It remains unclear whether any empirical observation could definitively distinguish between the standard claim that black holes have an enormous entropy proportional to horizon area and the alternative proposal that their entropy corresponds to the infalling matter. Both perspectives make the same predictions for external observers in terms of Hawking radiation and gravitational dynamics. As a result, the entropy-area law may be more a theoretical convention than an empirically testable fact.

7. Conclusion

I have presented a conceptual argument for skepticism about the claim that black holes are intrinsically highly entropic. From the frame of a distant observer, where an event horizon is never fully realized, there is no compelling reason to assume that black hole entropy must obey the area law. Instead, it may be more natural to assign entropy based on the matter content that is collapsing, without invoking an enormous entropy jump.

That's What I Call a Compliment: A Hasidic Parable by MC Complete

 There once was a commoner transporting a lot of heavy packs on his donkey. Suddendly the donkey stumbled and all the packs fell off. Oh no, thought the commoner. It will take forever to reload this donkey. Just then, he saw his friend running over to help him. Together, they were able to reload the donkey in half the time. The commoner was so grateful to his friend. "You're the king," he said.

The next day, the commoner went to a show where a musician was playing the harp. The music was so beautiful and so skillfully played that it almost brought the commoner to tears. After the show, the commoner ran up to the musician. "You're the king!" he said.

The next day, the commoner went to pick up a shirt from the tailor. He couldn't believe his eyes. It looked as good as new. "You're the king!" he said to the tailor.

The next day, the palace guards grabbed him and dragged him to the throne room. "What did I do?" he asked the king.

"Nothing," said the king. "I just want you to sing my praises."

"But I can't sing," said the commoner.

The king rolled his eyes. "You don't need to sing," said the king. "Just say something nice about me."

"You're the king!" said the commoner.

"Excuse me?" said the king.

"I said, you're the king."

"Off with his head," said the king.

"What?" said the commoner. "What did I do?"

"Obviously I'm the king," said the king. "That's not a compliment, that's just stating a fact."

The executioner was summoned. The guards put the commoner's neck on the chopping block. The executioner raised his axe. "Wait, wait!" said the king.

"What now?" said the executioner.

"This idiot deserves to die," said the king. "But I'm going to let him go home."

"Home?" said the executioner. "You're not even going to like throw him in the dungeon or something?"

"You heard me," said the king.

The executioner shrugged. "You're the king," he said.

The commoner fell to his knees and bowed. "Thank you, thank you, thank you!" he said. "You truly are a merciful king!"

The king smiled. "Now that's what I call a compliment," he said.

Promises

In Pirkei Avos 1:15, Shammai Hazaken says, "say little and do much."

Devarim 23:23 says, "if you don't make vows, you won't end up doing sins." (Meaning, you won't end up doing the sin of breaking your vow.)

We learn from this that keeping promises is good, and making promises is bad.

A Plague of Sound

 Why didn't the dogs bark on the night of the Exodus?

I never thought about it much until recently. I'd usually assumed that what the Torah really means by saying that the dogs didn't bark was that the Egyptians didn't protest when the Jews sacrificed lambs. Earlier, Moses had predicted that if the Jews were to sacrifice lambs in Egypt, then the Egyptians would stone them, because the lamb was considered a god (Shmos 8:26). So I'd thought that the Torah was using a kind of hyperbole: when the Jews actually did sacrifice lambs, not only did they not get stoned, the Egyptians didn't even raise their voices in protest, and even the dogs didn't bark.

It also reminded me of the trope that often appears in ghost stories, that humans can't see ghosts, but dogs can (and the dogs usually bark at the ghosts). During the plague of the firstborn, the angel of death came to Egypt, so you might have thought that the dogs would have barked at him, but they didn't.

When you read the pasuk in context, however, a different explanation suggests itself. (It's Shmos 11:6-7.) The previous pasuk talks about the screaming and wailing that will take place in Egypt when the firstborn die. The lack of dogs barking seems to describe the silence (peace and quiet) that will prevail among the Jews. As if the plague of the firstborn is not only a plague of death, but also a plague of sound.

This makes an interesting juxtaposition to the previous plague, which was a plague of darkness, so in a sense, a plague of light, or lack thereof: "For all of the children of Israel, their was light in their dwelling places." (Shmos 10:23)

The Artscroll commentary on the Chumash says basically the same thing: "In sharp contrast to the grief and death that will engulf the Egyptians, the Jews will enjoy complete tranquility; not even a dog will bark or how against them."

Why Did Moshe Hit the Rock?

Moshe dies right before the Israelites invade the land of Canaan. The Torah makes it clear that this is not an accident; it's a punishment. What is it a punishment for? There are actually two versions in the Torah. The less familar one, stated in parshas Devarim, is that Moshe is being punished along with the generation of the desert for the sin of the spies. The one most of us are more familiar with is the sin of Mei Meriva, when Moshe hit the rock.

What exactly did Moshe do wrong in the story of Mei Meriva? There are actually multiple opinions about this, and the Torah does not say explicitly. Most of us assume that Moshe's sin was hitting the rock after Hashem had told him to speak to the rock; presumably the reason that this theory is so common is that it is endorsed by Rashi.

In this case, I find Rashi's position compelling. So let's assume that Rashi is right. Hashem told Moshe to talk to the rock, and Moshe disobeyed a direct order and hit the rock instead.

That raises a big question. What was Moshe's motive? Why didn't he just talk to the rock?

Another question -- not so big, but still a question -- why does Hashem say that Moshe (and Aharon) didn't believe in Him, and desecrated His name? I can understand how disobeying a direct order would lead to the punishment of not going into the land -- it's arguably not such a big punishment, Moshe lived 120 years -- but why would hitting the rock constitute 1. a desecration of Hashem's name and 2. a lack of faith?

To find out why Moshe might have hit the rock instead of talking to it, let's take a look at what he says to the Israelites right before he hits the rock. "Listen you rebels, from this rock, shall we bring forth water?"

Grammatically, this is a question. But what kind of question is it? It doesn't seem to be the kind of question where Moshe is actually asking for information. It sounds like a rhetorical question. Right?

Whenever there is a rhetorical question, there is an implied answer. What is the implied answer here?

One possibility is that Moshe is implicitly asking whether the Israelites want him to draw water from the rock. Maybe it could be rephrased as "Hey guys, want me to draw water from this rock?" in which case the implied answer would be "yes" -- Moshe knows that the Israelites want water, they've made that painfully clear.

But there's another possibility. Imagine that there's a natural disaster today that creates a water shortage in some area of the world. There's no running water, no water in the stores. Imagine a family where all the kids are whining and complaining to the father (or the mother) that they're thirsty and they want water. In a fit of frustration, the father picks up a broom and says, "What do you want from me? Do you think I can just hit the wall with a broom and water's gonna come out?" Maybe Moshe was saying something like that. "What do you want from me? Do you think I can just hit a rock and make water flow?"

The big difference between the story I just told and the story of Mei Meriva is that the father in the story has no magical powers and has no reason to believe that a miracle will happen. Moshe, on the other hand, was told by Hashem that if he talks to the rock, the rock will indeed bring forth water.

Which would explain why Moshe hit the rock and didn't talk to it -- he didn't want the rock to bring forth the water.

Which begs the question, of course -- why not? Why didn't he want the rock to bring forth the water?

In the story of Mei Meriva, the Israelites were asking for water. That's a reasonable request -- a very reasonable request. Water is one of our most basic needs. Without water, they might all have died. However, they didn't ask very nicely. They said "why did you take us out of Egypt" and other not-so-nice things. They started a riot. Without divine intervention, Moshe himself might have been killed.

This probably bothered Moshe very much. But somehow, it didn't seem to bother Hashem at all. Hashem didn't even condemn the Israelites' behavior. He just said "give them water" and He told Moshe how. At that point, maybe Moshe snapped. He didn't think they deserved water, at least not without a good talking-to.

If this interpretation is correct, it makes perfect sense that Hashem would say to Moshe (and Aharon, who was apparently in on Moshe's plan, though the Torah is coy on those details) that he failed to sanctify Hashem's name. In this instance, Hashem -- for whatever reason -- was focusing on performing the miracle of producing the water, which would be a spectacular show of power. Moshe tried -- and ultimately failed -- to get in the way of that.