> The exact list is up for debate, and currently undergoing change.

My strong impression is that even the roots of the tree are debated, with competing models that often change.

> The four-kingdom system should have died out decades ago

First, hopefully not! :) Second, I think it's used because it's the last stable model. Third, it's a model that the public can understand - theres no point in even trying to use "Archaeplastida, Excavata, SAR supergroup, Amoebozoa, and Opisthokonta" unless you are an expert in phylogenics or evolution. Who can understand and remember that?

Children can memorize all 50 US state capitals, they can memorize a handful of scientific names. If we really wanted to, we could teach them a much more accurate view of the tree of life. Also, I don't think the four-kingdom system has been taught in schools for a while? I went to high school in the late 90s and it wasn't taught then.

It's strange to see people promoting it online in 2025. If adults want to remain ignorant, so be it, but at least teach children the truth. Let them know that life is incredibly complicated, it's a mystery we're still solving, and they could be the ones to help figure it out. Don't overly simplify things for small minds, it creates a false picture and it kills the imagination.

I strongly disagree. It's necessary to teach oversimplified things to small minds, even oversimplified to the extent of being incorrect.

It's unlikely you understand relativistic mechanics unless you learn and practice Newtonian for a few years, then many people stop there and never go for relativism.

It's unlikely you understand Peano axioms without first spending years just working with numbers, completely disregarding the formal foundations. Then many people stop there and never study the formal math.

It's unlikely you understand electron configurations and orbitals without first imagining electrons orbiting the nucleus like earth is orbiting the sun. And even that part you won't understand until you master the false concepts of "sunrise" and "sunset".

You can't climb the ladder without stepping on the first step. I've been studying for many years, observing people around me, I also did a fair share of teaching myself. The purist approach that avoids oversimplifications inevitably leads to disaster. There are maybe 1-2 kids in the class who can "jump the ladder", the rest are left on the ground helpless and confused.

Another curious observation: when I found myself in that role of a kid jumping the ladder in a purist class, I did that by secretly building a false ladder of my own. When professor said "Banach space" I would imagine Euclidean or Hilbert spaces and would get correct intuition half the time. The other half I would remember and use it to understand the difference. Most of others suffered dearly, unable to grasp anything at all, seeing the glass bead game instead of vectors and functions. And we were 20 years old back then, not even that small.

To be fair, "functional analysis is infinite dimensional linear algebra" is a saying for a reason, that's an intuition a good professor should have given you. Mine gave me it so well, I still see no difference between R^n and a Hilbert space! (on the dangers of intuitions)

This reminds me of a short lived stretch in French mathematical education, the "Bourbaki years". For those unaware, Nicolas Bourbaki was "a dozen mathematicians in a trench coat" who, in the early 20th, reformed mathematics from the ground up, their work is notoriously opaque (to some, perhaps a revelation to others), if rigorous. It served as inspiration for ambitious mathematics education reforms in the 60s and 70s.

Some of the things my father had to contend with:

- naive set theory and non-10 basis arithmetic in primary school (age 7)

- set theory in early middle school (ages 10/11), maps over sets, so I imagine things like injectivity and bijections. "[...] a different approach of arithmetic, computations often replaced by a more abstract theoretical approach": I wonder how that went in the classroom

- general Algebra introduced at 15yo, groups, rings, fields, vector spaces; 16yo mostly linear algebra (vector spaces, linear mappings etc; in true French fashion I'll bet they didn't see many 2x2 or 3x3 matrices that year)

I'm quoting Wikipedia "Mathématiques modernes" here, my father only told me of the last point himself. Though I do have his notebooks from early higher ed, they had general topology before metric space topology, for example, in year 1 or 2 (probably 1, because how can you do anything before you know topology...). It was all like this, a theory that builds on itself and you can't skip any steps. A finite dimensional space is a particular case of an infinite dimensional one, so you start with the latter. Backwards from how things were constructed and are understood by people.

The fact these reforms survived about 10 years and have been completely reverted is testament that this approach probably doesn't work.

> To be fair, "functional analysis is infinite dimensional linear algebra" is a saying for a reason, that's an intuition a good professor should have given you. Mine gave me it so well, I still see no difference between R^n and a Hilbert space! (on the dangers of intuitions)

That's the thing: not only he didn't share this intuition, he actively prohibited people from bringing it up in the class because it can lead to mistakes.

The program was to start with most generic cases (Banach spaces, metric spaces) and prove whatever is provable there, then continue adding assumptions one by one and proving stronger and stronger theorems. I think we've reached Hilbert spaces by the end of the year and that was a gotcha moment for many students (wait, these vectors were functions the whole time?), but it was too late. Everyone failed miserably at proving or understanding all the preceding theorems because without the intuition it turns into a game of symbols with no structure or hope. The only recourse were those bootleg analogies from finite spaces and Fourier analysis that a few students knew or came up with.

The "New Math" you mention above gives a good frame of reference. A beautiful curriculum that's almost impossible to understand unless you already learned math the normal way -- a formally incorrect and inconsistent but reliable way.

I also made similar mistake myself when I tried to teach the C language to 12 y.o kids without saying the dreaded "just write it like that, you'll understand later". That experiment failed completely but I only understood why two years later when I myself was subjected to the functional analysis course. Or I think the complete realization came to me even later, with the C language experiment and the functional analysis story becoming pieces of the same puzzle.

A small note on Bourbaki:

Alan Sokal's famous and brilliant hoax Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity had a hilarious footnote that read (my highlighting):

> Miller (1977/78, especially pp. 24-25). This article has become quite influential in film theory: see e.g. Jameson (1982, 27-28) and the references cited there. As Strathausen (1994, 69) indicates, Miller's article is tough going for the reader not well versed in the mathematics of set theory. But it is well worth the effort. For a gentle introduction to set theory, see Bourbaki (1970).

I'm torn on this one, because there's no way I can accept "lies-to-children are for their own good", but on the other hand I'd hate to be overburdened with information about Peanut maximums or the Ophthalmic supergroup when all I wanted to know was how to do division or what kind of thing a mushroom is.

Once you accept that a model of reality is always somewhat incorrect you kind of stop seeing this as "lies". Reality is infinitely complex, a model however is finite and therefore understandable.

We value models for their simplicity, for their ability to disregard secondary and tertiary details to allow comprehension and prediction of primary effects.

Then the only question is: which level of the simplicity/correctness trade-off is appropriate in given circumstances? When teaching kids or even a non-professional adults, the appropriate level is often very heavy on the "simplicity" side. Adding more complexity results in less overall understanding, so a net-negative effect in the end.

I think the problem comes in when you have adults teaching kids a simplified model who don't actually understand that is what they are doing.

It is not always conveyed well that they are learning a simplified model, or using an analogy. That's when kids feel lied to.

There are very many pithy sayings to this effect, most famously "All models are wrong, but some are useful" (perhaps by George Box, but I can't find this exact phrase attributed to him)

Even Von Neumann said "truth is much too complicated to allow anything but approximations."

It's not hard. "It's sort of like that, but the details are complicated and you'll learn them later if you want" is a perfectly fine answer.

A big difference between a lie and a simplification is whether the other party knows it's a simplification. Communicating that is independent of specific simplification you use, and it's sometimes as easy as saying "is mostly like" / "sorta" instead of "is".

I was learned enough in school to know when teachers were “teaching” something oversimplified. They uniformly acknowledged that when asked, until one didn’t. That one didn’t care about the nuance and insisted I give the “expected” answer when asked and ruined my attitude in school for years (not the only event, but it didn’t help). Obviously I’ve never forgotten her.

One thing I adore about this community is the broad acceptance of “I don’t know” and “it depends” as the starting point for answers.

To bring that back into the tech/business world:

My personal rule for being an expert/consultant is to be very willing to say "I don't know, but I can find that out for you", and define that as my real expertise: know how to find out things.

Technology stacks, programming languages, all of those things come and go. The skill to pick up whatever is needed is long-term better.

It wouldn't be so nice if it was oversimplified and incorrect to the extent that the child realizes it doesn't add up.

Had this experience more than once, but the one that comes to mind:

In high school chemistry, the teacher was reviewing what we should remember from lower school about atoms & molecules (single bonds, double bonds, slots available for single atoms of different elements). I asked something like "If the model we were using treats the bonding sites on every atom of every element as equal, but says that some molecules are either rarer than others or not known to occur in nature, doesn't that mean the model is incomplete or incorrect?". She instantly shook her head with annoyance and said sternly "No.".

From my limited experience (being a child and raising one child) I would say that the problem is more that we (as adults) pretend that the simplified thing is the whole picture.

Every time someone told me: "this is a simplified version to give you a basic understanding and later you will be able to learn more accurate versions" that was tremendously helpful and sometimes it sparked my curiosity and motivated me to look stuff up myself.

I mean we should get ahead of the realisation that it doesn't add up.

When I moved to the US in 3rd grade, I was marked wrong for putting negative numbers as answers on a math test. The correct answer was "You can't subtract a larger number from a smaller number".

I had a similar experience, but was fortunate that the teacher took me aside and explained that I was right but they were teaching a simplified version. In hindsight that was really a helpful approach.

I got into an argument with my science teacher in 4th or 5th grade about whether rivers could flow north, because on a globe, north is up.

I suspect that the best approach would be not to "get ahead", but rather see this realisation develop naturally and help it along the way. It's hard to get critical thinking if everything is already criticized before you even come.

This can work with your kids though but I don't know if it can be effectively scaled to a school class. Maybe on a few dedicated play/discovery sessions, not on a regular basis.

Doing this would create a nice opportunity to teach the right and wrong ways to move the needle in scientific discourse (e.g. don't start by holding a press conference about cold fusion).

Graduation could mean an overthrowing of the known-wrong models. Congratulations, here are the next known-wrong models. Now prove these wrong.

Thankfully at very young ages where this is required, that level of critical thinking is very far off

I love your point that avoiding oversimplifications leads to disaster. It explains why I struggle to have a purist mindset while also unable to explain why things go poorly sometimes.

What's your point then?

All minds alike, big and small, benefit from simplification. I was replying to a comment that specifically referenced "small minds", that's all.

I'm a huge cladistics fan, but insisting that "animal" isn't a useful term is pretty out there, IMHO. Certainly we can (and do!) teach cladistics in high school biology, but does your ideal world have baby books titled with one of the mentioned names...?

More personally speaking: what am I missing out by using the four kingdoms? Like, how could that possibly ever backfire in a way that slightly impacts my life negatively, or impedes the scientists studying genetic lineages? There's basically infinite science to "remain ignorant" of, I don't see any justification for an elitist attitude on this nuance in particular.

I'm not arguing that animal isn't a useful term, but if you're dividing eukaryotes into the major groups, it's not one of them.

> More personally speaking: what am I missing out by using the four kingdoms? Like, how could that possibly ever backfire in a way that slightly impacts my life negatively, or impedes the scientists studying genetic lineages?

Sure, where does kelp fit in? How about slime molds?

Also, I'm not suggesting we teach children all the nuance of phylogeny. I'm suggesting we don't teach a version that we've proven to be objectively wrong.

Eventually, the four-kingdoms system will go away, and it will sit next to the "animal, vegetable, mineral" system in the annals of scientific history.

Interesting, thanks for elaborating! Still not sure I understand sadly, but maybe it’s just different worldviews on how to play language games. Like, you say we don’t need to teach nuance, and that animal is a useful term — but then what does it denote, if not a group of creatures?

To me, this discussion should center around utility — “objectively wrong” is assumed to apply to basically everything we ever say on some level (what are the chances we happen to live at the End of Science?) so I hesitate to adopt such a binary framework. In this light, taking a stand against “animal, plant, fungus”—which sums up an overwhelming majority of how laypeople interact with the world—seems of dubious value.

Re:examples, kelp are plants and slime molds are molds, and therefor fungi. Boom. Does that capture 100% of their characteristics on a genetic level? Presumably not (and TIL kelp are technically like flexible coral colonies, not vascular plants)! Is it more useful for 99.9% of usage than “they’re their own things, somewhat unlike anything else”? Definitely, yes.

P.s. animal vegetable mineral also seems to have held up okay…? It’s a culinary thing AFAIK, not an exhaustive list of all objects.

> animal vegetable mineral also seems to have held up okay…? It’s a culinary thing

Interesting - Linnaeus (and possibly contemporaries and predecessors) were maybe biased too look at the world through eating: The hunted, the grown, and the mined.

(Completely speculative, of course.)

Well in very practical terms, it gives you a way to name things you see in the forest, to figure out what is edible, and to understand what has a sentience of its own, similar to yours.

I don’t mean to be snarky, but it seems like you’re very removed from the reality of normal people and parents out there.

There is much more to figure out what is edible and what is not. Considering shrooms alone, it is much more "complicated", so much that there are specialists for that, even, but I agree, could be an useful skill, but not for people who do not even leave the city, I think.

However, they should know the basics such as "not eating potatoes (or its parts) that are green", and so forth, since that is something you run into even if you never leave the city. Food spoilage in general would be useful to teach, but that is the job of the parents, I would say. That said, my teachers in elementary school always used to tell me that they are our second parents. I can see where they were coming from.

I didn’t say there wasn’t. My point is that explaining to kids why they can pick a strawberry from the forest floor, but leave the fly agaric where it is, despite being the same color, is hard enough without going into the phylogenetic peculiarities.

Starting with animals (things that can think like you), plants (things that eat light), fungi (underground webs that bloom above ground), and bacteria (very small things that are sort-of alive, and can both be good for you or make you sick), makes things so much easier and is probably all you need to know for a while.

I agree.

The reality of normal people and parents is that a different basic classification is warranted:

- Humans are what they are;

- Animals are what they are;

- Plants and fungi of the kind you can gather in the forest, and anything else that is macro-scale but doesn't run or swim around, are just "plants";

- Bacteria, viruses, fungi of the other kind, archaea and even single-cellular organisms that could have negative impact on you, are all just "bacteria" or "microorganisms" or "pathogens";

- "Plants" breaks down into "trees", "grasses", "bushes", "shrooms", "flowers", and that's about it;

- "Animals" breaks down into "fish", "reptiles", "birds", "mammals";

That covers about all the biology regular people see, to the extent they care about.

Now, if you're teaching people the biological categorization, any one you will pick will be different from the daily experience of an ordinary person. Like, for practical reasons, whales and dolphins are fish (they look like every other fish and swim in water, and you hunt them with ships), and tomato is a vegetable (you don't put it into a fruit salad), and all that looks like grass is grass (despite genetics telling that some grasses are really just very tiny trees, or some trees are genetically just really big grass, etc.).

Point being, if you're going to teach them a biological categorization, that's already distinct from "normie everyday life" categorization, so you may just as well pick one that's current and useful in biology.

(And once again, this is another case of a non-issue that turns into issue only because people are unable to comprehend and teach the distinction between "is" and "can be thought of as"; the fact that categories are invented by people, are not facts of nature; that their only job is to be useful, and you can have many classification systems for the same thing, useful in different contexts.)

> That covers about all the biology regular people see, to the extent they care about.

Insects and spiders are feeling left out.

That insects and mammals are both Animalia can be nonintuitive for preschoolers.

Parazoa (e.g., sponges), radially-symmetrical creatures (jellyfish, corals, etc.), acoelomates (flatworms, I think), pseudocoelomates (nematode parasites, roundworms), echinodermata (sand dollars, sea urchins, etc), lophotrochozoans (molluscs, some worms, many more).

A 19th century breakdown by Cuvier, influential for a long time, was: Vertebrates, arthropods, molluscs, radiates. (I don't know where worms fit.)

> That insects and mammals are both Animalia can be nonintuitive for preschoolers.

Insects and mammals both walk around. Plants and shrooms don't. Can't get more obvious than that for a kid.

The four kingdoms system is taught because it is useful; not for science, but for everyday communication.

We use a similarly flawed model every day: fruit and vegetables. What's in one group or the other is based on vague similarities and is mostly arbitrary, but it's still useful to split the huge category of "edible plant parts" into more manageable chunks.

Anyone familiar with apples and pears will likely see an orange and say it's a fruit. Likewise anyone familiar with cats and dogs will see a boar and think "animal", not "plant" or "fungus". A genetics-based assessment would be more "correct", yes, but impossible on a walk or in the store.

Primary school teachers, from my experience, have a tendency to present things as "the truth" and accept no deviation from their own word. I think changing that would be a good step in fostering creativity in children, much more than skipping less-accurate models.

> We use a similarly flawed model every day: fruit and vegetables. What's in one group or the other is based on vague similarities and is mostly arbitrary, but it's still useful to split the huge category of "edible plant parts" into more manageable chunks.

This is completely wrong. Those categories aren't any smaller, in a practical sense, than the combined category "plants". The gain in manageability is zero.

The reason we divide the categories that way is that we put them to different purposes, not that they'd be too large if combined.

People gain understanding when we relate things to their frame of reference. Kids have very limited life experience and their frame of reference is very low. Introducing new concepts that are not relatable would create huge gaps in real understanding.

For example, explaining encryption as a lock to prevent thieves from stealing data is much more understandable to kids than going into actual definition of encryption. Lock is something concrete that they have seen, while encryption is an abstract concept hard to grasp.

Except encryption is nothing like a lock, and "stealing data" is a problematic term, as it's stretching the concept of theft way past its common meaning - it's using the term "stealing" in the exact same way people saying "software piracy is stealing" are. So that's already providing completely twisted mental model to kids. And it stems in big part from trying to pass one specific application as an answer to what the thing is.

(What is a car? It's like extra legs for your butt, that can run very fast and carry multiple butts.)

You can get much closer to the truth by explaining encryption as a trick to make words understandable only to those who know the trick. You can play a substitution game with your kids, explain how you and them could agree that when one says "snake" it means "I", etc. and so "snake eats green grass" means "I am very hungry", and that you'll understand them but no one else will, etc.

At any given age, kids are as likely to understand secrecy as they're to understand why locks exist, so it's really just a choice of not using a bad and confusing analogy.

Substitution is a new concept for kids. Not something they can readily understand. So you need to explain that in terms of a game. Kids know what secrets are. But from their point of view, why even talk about it if it is secret? Why can't we go to another place and talk secretly? Why do we need to talk secrets in public using substitution? Since they do not see obvious need for it in their daily life and there are workarounds for it, they do not get why there is a need for substitution.

By the time we explain all these to them, they would have already lost interest, or context and would easily forget the whole thing.

> Substitution is a new concept for kids.

Children learn substitution with language. Hand signs and words are substituted for the objects, feelings and actions they know inherently. It’s tempting to apply adult context on children but it’s a mistake.

Encryption might not even need much any explanation, just using familiar terms: kids come up with "secret languages" all the time between friends and siblings.

> Kids know what secrets are. But from their point of view, why even talk about it if it is secret? Why can't we go to another place and talk secretly? Why do we need to talk secrets in public using substitution?

Connect this to surprise gifts and birthday invites. Or another thing that resonates with them.

Explaining locks and their purpose ain't any easier. Just yesterday, my daughter asked me why I'm locking the extra set of doors we're normally keeping open, and when I told her about the just-issued warning about burglaries in our area, well, there's a lot of context to explain before a 5yo gets why locking the doors is the right thing to do in this scenario.

I mean, there's always a lot of explaining to do with kids anyway. So far, I've never had trouble giving them real explanations and letting them know when they're simplified.

> If adults want to remain ignorant, so be it, but at least teach children the truth. Let them know that life is incredibly complicated, it's a mystery we're still solving, and they could be the ones to help figure it out. Don't overly simplify things for small minds, it creates a false picture and it kills the imagination.

Yes we should have this firm stance and accept nothing less especially when it come to something fundamental such as the Theory of Evolution. It's a shame that some scientists are even promoting that human come from monkey while the fact that from Darwin own observation was that monkey and human probably share the same ancestor not human come from monkey and even that's debatable. They even create a false picture that now become a "universal truth" printed on people shirts and kind of accepted as truth as far as layman and kids are concerned [1]. But now even the one making the picture is regretting it but the damaged has already been done. Einstein once mentioned "Everything should be made as simple as possible, but not simpler". By making things simpler than simpler (pun intended), we are creating distortion and falsehood that can take years and perhaps centuries to be fixed, and just ask the "flat earth" crowd.

[1] On the Origins of “The March of Progress”:

https://sites.wustl.edu/prosper/on-the-origins-of-the-march-...

>>Don't overly simplify things for small minds, it creates a false picture and it kills the imagination.

I think we can all agree that in pedagogy and teaching, you have to start simplified; then it becomes a more productive discussion on what constitutes over simplifying, rather than a binary "do or do not over simplify". We can and absolutely should be open about complexity of the world, but at the same time be aware that average person goes through between 8 and 16 years of education (with important outliers on either side of the bell curve), and trying to fit all complexity and all the knowledge on day one generally does not lead to productive results.

The first lesson of the biology in this area I think is not so much "there are these and precisely these 4 or 7 or 9 fixed and immutable categories of life", but... "life can be categorized, and living creatures that look different actually have similarities". There's wonder, and insight, and enlightenment right there that's probably going to stick longer for vast vast vast majority of people, than the specifics of whether there were 4 or 7 or 9 categories. Heck, we changed number of planets and our understanding of "planet" remained the same :).

But... but... every cell has one spherical nucleus, one spherical chloroplast for plants or spherical mitochondria for animals, and a host of other features depicted in this helpful diagram that you're going to have to copy from memory.

Would you also propose we skip over the Bohr model of the atom and teach Schrödinger to ten year olds?

went to school till 2012, highly esteemed US high school, was still taught then

this was voted down, but the poster had expressed doubt that it had still been taught this way, and I was providing information that it was still taught thid eay even at a high end high school tenish years ago.

I thought it reasonable to share.

May as well add this to the above: https://en.wikipedia.org/wiki/Songline (large amounts of knowledge can be transferred just fine)

> it creates a false picture and it kills the imagination.

this reminds me of a certain voting population that think male and female are very simple XY and XX things and nothing else exists.

unfortunately a lot of people take dumbed down models and mistake the map for the terrain.

I'm not sure there's a cure for it - I have cousins who went through the same schooling and came out with very different abilities to generalise.

Yes I agree. 4 humors were enough for medieval europe, they're good enough for me!! Who can remember all this complicated 'germ theory of disease' liberal junk?! There must be hundreds of these supposed 'germs' out there! No sir, no thank you!

> Who can understand and remember that?

Anybody who is interested in it

At which point started to be important in science that “public can understand”? I think if something is a better explanation for the reality, we ahould go for it, even if it is difficult for the public.

Disclaimer: in this case I have absolutely no idea what is better. But the rationale seems wrong.

We can and, IMHO, should do both. Scientists explaining physical realities, such as gravity, don't use advanced mathematics - it would be pointless.

And then there are viruses, which don't show up on the tree of life at all because there's no consensus that they even constitute "life."

Pretty sure anyone who knows anything about viruses would say they are alive. Or at least as alive as parasitic nano archaea with genomes smaller than the viruses living right next to them... The philosophical way to look at it is humans aren't alive in the space between planets they live inside these little hard shells, then when they get to a planet they go wild using all the other resources around them made of biomass. Viruses are just this, their biome isn't the wider one you participate in instead they are sub-cellular life, in the same way you are sub-planetary life. Humans don't make the oxygen atmosphere on the planet themselves, they parasitize this feature of planets from other life. In the same way viruses use cellular machinery.

This guy agrees with you:

https://www.youtube.com/watch?v=mgS1Lwr8gq8

> Pretty sure anyone who knows anything about viruses would say they are alive

Whilst I don't doubt that, viruses don't abide by typical definitions of life that would include self-replication. Obviously, they do replicate, but not by themselves.

I thought "has a metabolism" (consumes food and produces waste) was the one viruses didn't fit with.

That as well. They also don't respond to their environment.

Men like me also don't replicate by ourselves. Does that mean that we are not alive?

Humans though, can create more humans, but viruses can't create more viruses without using the machinery within a cell that it compromises.

If humans create oxygen with a machine, is that parasitic?

I feel like what trips people up is the abstraction layer.

Viruses are abstracted on top of other living things in the same way that animals are abstracted on top of plants, in that they both require the lower layer of abstraction for their basic survival.

When classifying living beings, a single classification criterion is not good enough.

One classification criterion is descendance from a common ancestor, i.e. cladistic classification.

In many cases this is the most useful classification criterion, because the living beings grouped in a class defined by having a common ancestor share a lot of characteristics inherited from their common ancestor, so when using a name that is applied to that class of living beings, the name provides a lot of information about any member.

However there are at least 2 reasons which complicate such a cladistic classification.

One is that the graph of the evolution of living beings is not strictly a tree, because there are hybridization events that merge branches.

Sometimes the branches that are merged are closely related, e.g. between different species of felids, so they do not change the overall aspect of the tree. However there are also merges between extremely distant branches, like the symbiosis event between some blue-green alga (Cyanobacteria) and some unicellular eukaryote, which has created the ancestors of all eukaryotes that are oxygenic phototrophs, including the green plants.

Moreover, there have been additional symbiosis events that have merged additional eukaryote branches and which have created the ancestors of other eukaryote phototrophs, e.g. the ancestor of brown algae.

After any such hybridization event, there is the question how you should classify the descendants of the hybrid ancestor, as belonging to one branch or to the other branch that have been merged.

For some purposes it is more useful to classify all eukaryote phototrophs based on the branch that has provided the main nucleus of the hybrid cell, and this is the most frequently used classification.

For other purposes it is more useful to group together all the living beings that are oxygenic phototrophs, including various kinds of eukaryotes and also the blue-green algae, and divide them based on the evolution tree of their light-capturing organelles, i.e. the chloroplasts.

This is also a valid cladistic classification, because all oxygenic phototrophs, both eukaryotes and prokaryotes, are the descendants of a single common ancestor, some ancient phototrophic bacteria that has switched from oxidizing manganese using light energy, to oxidizing water, which releases free dioxygen.

Even when there are no branch merges due to hybridization, there remains the problem that in the set of descendants from a single ancestor there are some that are conservative, so they still resemble a lot with their ancestor, and some that are progressive, which may have changed a lot, so they no longer resemble with their ancestor.

In this case, using the name of the entire group provides very little information, because most characteristics that were valid for the ancestor may be completely inapplicable to the subgroups that have become different. In such a case, defining and using a name for the paraphiletic set of subgroups that remains after excluding the subgroups that have evolved divergently may be more useful in practice than using only names based on a cladistic classification. For instance the use of the word "fish" with its traditional paraphiletic meaning, i.e. "vertebrate that is not a tetrapod", is very useful and including tetrapods in "fishes" is stupid, because that would make "fish" and "vertebrate" synonymous and it would require the frequent use of the expression "fishes that are not tetrapods", whenever something is said that is correct only for vertebrates that are not tetrapods, or of the expression "bony fishes that are not tetrapods", for things valid for bony fishes, but not for tetrapods.

While in many contexts it is very useful to know that both fungi and animals are opisthokonts, and there are a few facts that apply to all opisthokonts, regardless whether they are fungi, animals or other opisthokonts more closely related to fungi or more closely related to animals, the number of cases when it is much more important to distinguish fungi from animals is much greater than the number of cases when their common ancestry is relevant.

Animals are multicellular eukaryotes that have retained the primitive lifestyle of the eukaryotes, i.e. feeding by ingesting other living beings, which is made possible by cell motility.

Fungi are multicellular eukaryotes that have abandoned the primitive lifestyle of the eukaryotes, and which have reverted to a lifestyle similar to that of heterotrophic bacteria, just with a different topology of the interface between cells and environment (i.e. with a branched multicellular mycelium instead of multiple small separate cells).

This change in lifestyle has been caused by the transition to a terrestrial life, which has been accomplished with a thick cell wall (of chitin) for avoiding dehydration, which has suppressed cell motility, making impossible the ingestion of other living beings, the same as for bacteria. Moreover the transition to a bacterial lifestyle has also been enabled by several lateral gene transfers from some bacteria, which have provided some additional metabolic pathways that enable fungi to survive when feeding with simpler substances than required by most eukaryotes, including animals.

So even from a cladistic point of view, fungi have some additional bacterial ancestors for their DNA, besides the common opisthokont ancestor that they share with the animals.

Animals are unique among eukaryotes, because all other multicellular eukaryotes have abandoned the primitive lifestyle of eukaryotes, by taking the lifestyles of either heterotrophic or phototrophic bacteria. However for both other kinds of lifestyle changes there are multiple examples, i.e. besides true fungi that are opisthokonts there are several other groups of fungous eukaryotes that are not opisthokonts, the best known being the Oomycetes. There are also bacteria with fungal lifestyle and topology, e.g. actinomycetes a.k.a. Actinobacteria.

If we will ever explore other planets with life, those living beings will not have a common ancestor with the living beings from our planet, but nevertheless it will still be possible to classify them based on their lifestyle in about a half of dozen groups that would be analogous to animals (multicellular living beings that feed by ingestion, so they must be mobile or they must have at least some mobile parts), fungi (multicellular beings that grow into their food, absorbing it after external digestion), oxygenic phototrophs, anoxygenic phototrophs, chemoautotrophs, unicellular equivalents of animals and fungi, like protozoa and heterotrophic bacteria, viruses.

These differences in lifestyles are more important in most contexts than the descendance from a common ancestor.

So while it is useful to have the name Opisthokonta for the contexts where fungi and animals and their close relatives must be included, it is much more frequent to need to speak separately about fungi and other fungous organisms on one hand, and animals on the other hand.

I agree that the term "kingdom" is obsolete when used in the context of a cladistic classification of the living beings.

Perhaps it should be retained for a non-cladistic classification of the living beings, based on the few fundamental lifestyles that are possible, and which would remain valid even for extraterrestrial living beings.

Glad to see diamond inheritance being a problem in other fields

It's not a problem, it's a feature.

Or rather, it's only a problem when you insist on rigid perspective that makes it a problem.

(The real problem is that so many people insist on viewing things as trees, when their natural shape is directed graph.)

They should rewrite biology in Rust.

Just to stay on topic, Rust Language was named after fungus. “over-engineered for survival”

I dunno you can mostly solve for this, look at the majority share of the genome in a compartment with a single membrane contained by the outer membrane (by definition for endosymbiogenesis), with the DNA molecules containing the highest quantity of coding gene content. That's the thing you do the cladistic descent on. Just because I'm carrying a load of bacterial symbionts that are better at digesting wheat doesn't make me a different species to humans who mostly eat rice. That I eventually carry those as an endosymbiont then eventually just a sack of genes doesn't really change who' was the boss in this situation, or who I'm able to reproduce with that entire time as a species either. Symbiogenesis is very much like this, look at Hatena arenicola if you want to see this emerging to see how it interacts with descent. This is really the difference between understanding reproductive relationships specifically, vs wider ecology. I agree that symbiogenesis is like this weird one where its both only going to happen through other ecological relationships and then reproduction. But there really is a clear cut time one turns into the other, with the fate of one of those organisms of the combination "winning" even though profoundly altered. Symbiodinium is probably another good example, it has loads of ecological partners and little remnants of all of those histories in its genetic material and organelle arrangement. But its still an obvious species, with all the other oddball dinoflagellates that act and look like it also appearing to have some common descent from something much simpler and eukaryotic.

As a programmer symbiogenesis is a mixin or interface not a class.

It is not that simple, because a large part of the genes that originally belonged to the mitochondria or to the chloroplasts have been transferred into the nucleus and they are now completely integrated into it, even if evolution trees will show that those genes have a different history than the remainder of the nucleus.

So even if you want to use only the DNA inside the nucleus for a cladistic classification, that does not produce a tree of evolution, but only a directed graph of genetic information flows, with many important hybridization events. While initially mitochondria and chloroplasts were just symbionts, like the useful bacteria in the human gut, eventually that symbiosis has become a full hybridization, with mixing and integration of the genetic information.

The official cladistic classification produces a tree from the directed graph of the evolution by cutting the branches that are considered to be less important.

Sometimes this is indeed the best choice, but there are contexts in which the genetic information brought through the minor branches is actually that which determines most of the importance of an organism in an ecosystem.

E.g. in many contexts the most important feature of a living being is whether it is an oxygenic phototroph due to inheriting genetic information from some blue-green algae, i.e. that it is a primary producer in the ecosystem, and not the features that depend on which is the exact eukaryotic group from which most of its nucleus has been inherited. For instance, it is more frequently useful to group together brown algae with red algae (whose chloroplasts share a common ancestor), than to group brown algae with some non-phototrophic stramenopiles (which share a common ancestor for most of the nuclear DNA), with which they share only inherited characters that need an electron microscope for detection.

As an unscientific layperson this was a riveting analysis, thanks for interesting reading.

From what I've gathered it's been pretty clear for a while now that archea is basal to eucarya, meaning humans are archea.

One of the great wonders of clustering algorithms is that no matter what k > n you choose, you can construct k clusters. Then we can argue about the clusters and about k. It is said that when Humanity discovers the One True K, the taxonomy will disappear and be replaced by a different one.