Specifically, it is the "entropy." Mathematically, the uncertainty of a message. If you know for certain what the genome of an individual will be, then the information in that genome is zero. If there are two possible alleles for a given gene then the information is greater than zero.
Genomes are containers of biological information, which direct the cell functions and the evolution of organisms. Combinatorial, probabilistic, and informational aspects are fundamental ingredients of any mathematical investigation of genomes aimed at providing mathematical principles for extracting the information that they contain.
Infogenomics The Informational Analysis of Genomes
Vincenzo Manca, Vincenzo Bonnici
You’re right that entropy, in Shannon’s sense, measures uncertainty. If you already know exactly which allele someone has, then there’s no uncertainty left, so Shannon information is zero. If there are two possible alleles, uncertainty goes up, and Shannon’s number goes up too. That part is correct.
Where the confusion starts is what that number actually tells us.
Shannon entropy tells us how unpredictable something is — not how useful or meaningful it is. A shuffled deck of cards has high entropy because you don’t know the order, but it doesn’t do anything. A computer program, on the other hand, has very low randomness but can do something amazing, like run a game or control a rocket.
Genomes really are information containers, but they are more like instruction manuals than random messages. The DNA sequence has to be very specific so the cell can build the right proteins at the right time. Most random changes increase uncertainty but break the instructions.
Here’s a simple example:
If you randomly change letters in a recipe, the uncertainty goes up. But the cake is ruined. So even though entropy increased, useful information was lost.
When biologists say genomes contain information, they usually mean functional instructions, not just uncertainty. Shannon entropy can help study patterns in DNA, but it does not measure whether a gene works, folds properly, or helps the organism survive.
So the key idea is:
Entropy = how unpredictable something is
Biological information = instructions that actually work
They are related, but they are not the same thing.
Dr Hall's bacteria disagree with you The first steps in the evolution of that enzyme system featured a very ineffective enzyme that was hardly better than a generic saccharase. But a series of mutations gradually produced much better enzymes. From low to very precise arrangements.
Dr. Hall’s bacteria don’t actually disagree with what I’m saying — they illustrate it.
In that experiment, the bacteria already had:
DNA
proteins that could fold
enzymes that already worked a little
a working cell with metabolism and regulation
The starting enzyme wasn’t random junk. It was a generic enzyme that already had the right shape and chemistry to do something similar. Natural selection could then improve it step by step, making it more precise over time.
That’s an important point: selection can improve something that already works, even if it works poorly at first. No one is denying that.
What this does not show is how a completely new enzyme system appears from nothing. The experiment didn’t start with random DNA and end with a working enzyme. It started with an existing enzyme scaffold and refined it.
So yes:
The enzyme went from “not very good” to “much better”
Precision increased over time
That would be real evolution
But the experiment presupposes the very things under discussion:
functional proteins
folding rules
catalytic chemistry
cellular machinery
But if you go from "2 cups of flour to 2.3 cups of flour" it still works. I got up early today, and made biscuits. I got a bag of soft flour recently and knowing it would produce flakier biscuits, I changed the flour amount by guestimate. Turned out very well. I suppose that if I had put sand in it, things wouldn't have gone as well. Natural selection handles that kind of thing.
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Your biscuit did not work out well due to natural selection. It seems your "biscuit" remained steadfastly a biscuit, resisting any evolutionary pressures toward becoming a ciabatta roll.
You've stumbled onto another of Darwin's discoveries. A well-adapted recipe will not change much so long as the environment remains the same. But even then, there might be open niches where random variation might work out. Suppose I'm making a chocolate cake with a cake mix. But I'm not paying much attention this morning and forget the water, add oil instead of butter, and put in one less egg than I should. And the result is ... brownies. BTW, this actually works to produce pretty good brownies.
You are fighting a strawman again. We were discussing the origins of complex biological systems which can't be explined through natural selection.
Random variation produces a novel result. Granted, most such goofs would result in something inedible or at least disgusting. But there you are.
Random variation
can produce something new — that part is true — but “new” does not automatically mean “useful” or “informative” in the biological sense.
Think about cooking. If you randomly change ingredients in a recipe, you’ll almost always get something inedible. Once in a while, you might stumble onto something interesting. But even then, that “new” dish only works because you already had a recipe structure, cooking tools, and ingredients that were compatible. You didn’t invent cooking itself by accident.
In biology, random mutations are like random recipe changes. Most make things worse or break them. Very rarely, one improves an existing function. Natural selection can then keep that improvement and build on it. That’s real evolution, and it’s well documented.
But this only works because the system already exists. The cell already knows how to read DNA, fold proteins, and run metabolism. Random variation doesn’t explain where those instructions and systems came from in the first place — it only explains how they can be tweaked once they’re there.
So yes, random variation can lead to something new now and then. But
novel results depend on a pre-existing framework, and that framework is exactly what’s being questioned.
You've lost focus again. This isn't about the origin of life. God says the earth brought forth life. Sounds good to me. If you have a different opinion, it doesn't matter at all to evolution.
No, I have not lost focus. We have been having two seperate conversations. You defending evolution and I discussing the conundrum of the formation of complex biological systems.
My question is still on the table. What step between prokaryotes and vertebrates do you think was impossible to have evolved? And if you can't find one, what makes you think there is one?
Although this is off topic, I will answer it for you even though I am not attacking evolution perse in this thread. Among the many transitions between prokaryotes and vertebrates, the most widely recognized challenge for evolutionary theory is the origin of the eukaryotic cell. Prokaryotes are relatively simple cells without nuclei or complex internal organization, while eukaryotic cells possess nuclei, mitochondria, elaborate membrane systems, and tightly coordinated gene regulation. Endosymbiosis provides a strong explanation for the origin of mitochondria and chloroplasts, but it does not fully account for how the nucleus arose, how multiple genomes became integrated into a single regulatory system, or how complex intracellular architecture and timing emerged together. Because all animals and plants are eukaryotic, this transition is foundational, and its rarity in the history of life highlights its difficulty.
A second major challenge is the origin of complex multicellularity with differentiated cell types. While simple multicellular organisms exist, complex multicellularity requires cells to cooperate, specialize, communicate, and sometimes undergo programmed death for the benefit of the organism. This runs counter to the usual expectation of selection acting at the individual cell level. The fact that complex multicellularity evolved only a few times suggests that it is not an easy or inevitable outcome of evolution.
Closely related to this is the emergence of developmental programs that guide embryological growth. Vertebrate development depends on precise genetic instructions that establish body axes, organ placement, and timing. Genes such as Hox genes play central roles, but they function only within highly coordinated regulatory networks. Partial or poorly tuned developmental systems often result in severe defects, raising questions about how such programs could evolve gradually when intermediate stages may not be viable.
Another significant hurdle is the origin of nervous systems, especially centralized brains. Neurons must transmit electrical signals and form accurate connections to specific targets. A poorly wired nervous system is often worse than none at all. This raises the challenge of explaining how intermediate stages could provide a selectable advantage rather than harm the organism.
The emergence of uniquely vertebrate features also presents difficulties. Vertebrates possess internal skeletons, complex immune systems, advanced sensory organs, and neural crest cells. Neural crest cells are particularly challenging because they migrate throughout the developing embryo and give rise to diverse tissues, all under precise genetic control. Errors in this system are often lethal, indicating a high level of interdependence among its components.
Your concern seems to be with the origin of life, rather than evolution. But there is considerable evidence that God has it right in saying that the earth brought forth live. It's noteworthy that the the one absolutely essential organelle for cellular life is also the simplest one. Would you like to talk about that?
The origin of life requires comlex systems.
