Christopher Sevin

Independent scientific educator, France.

Email: c-sevin (at) live (dot) fr

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Monster Hunter is a fantasy-themed video game franchise created by the Japanese company Capcom in 2004, with the first game Monster Hunter. The player embodies, in the third person, a hunter who accomplishes quests, assigned by an organization called the Guild, by killing or capturing creatures. Since then, twenty-seven other games have taken shape, developing the lore. Each game provides its new set of ecosystems, with items, maps, flora, and bestiary.

The world of Monster Hunter, although a fantasy universe, presents a scientific dimension. The games explore the concept of trophic chain, with prey, predator, and apex predator monsters. These creatures live in many different and complex ecosystems, from volcanic areas to desert plains, through tundra, tropical forests and grassy plains, each possessing its own climate, vegetation, and geology.

A form of taxonomy is also present in-game. Some monsters have subspecies generally defined by alternate skins and, sometimes, abilities. Monsters are also grouped in families, a superior clade based in the general overall aspect of creatures. Sometimes, evolutionary explanations are given to explain links between some of these taxa, like trophic partitioning, host-parasite coevolution, or allopatric speciation. All these arguments lead us to see the bestiary of this universe as a group of taxa, linked to one another by an evolutionary history.

Two books, Hunter’s Encyclopedia 4 (2015) and Monster Hunter Rise, Official Setting Document Collection – Rampage Disaster’s Secrets (2021) present a classification tree called “Ecological Tree Plots”. However, this tree doesn’t rely on a scientific approach. Phylogeny of Monster Hunter creatures is also a recurrent topic in the fan community, with many posts on Reddit, Discord and Steam, for example. These fan-made attempts rely more on an overall morphological similarity comparison and are not based on any scientific protocol.

This article is an attempt to reconstruct a speculative phylogenetic tree by using Cladistics, observing the external anatomy of monsters. The topology of the tree will be discussed in this article. The bestiary of Monster Hunter lore contains hundreds of species presented as huntable creatures, but also items coming from fishing, insect harvesting and farming. However, cladistic is inappropriate for such a sizeable of data set (Darlu & Tassy, 1993). Thus, I only studied taxa from the first generation of Monster Hunter games, which are Monster Hunter (2004), Monster Hunter G (2005), and Monster Hunter Freedom (2005).

METHODOLOGY

To determine links between taxa and imagine a plausible evolutionary story, we decided to use the cladistic approach. By observing morphological characteristics shared by studied species, this classification method allows the creation of relative taxa groups with their hypothetical common ancestor, called clades, based on shared characters (synapomorphies). Created in the beginning of the 20th century, this methodology became popular with the work of Willi Hennig after the Second World War.

Thirty-nine taxa were morphologically analyzed. Twenty-four of them are huntable monsters. We also analyzed seven fishes obtained in-game by fishing: Burst arowana, Bomb arowana, Golden fish, Sushifish, Shringnight carp, Speartuna and Knife Mackerel. As they are very inspired by real-life counterparts (arowana, carp, tuna and mackerel), I used this close inspiration to describe internal anatomic characteristics invisible in game to the naked eye. A similar reasoning was applied to humans and pigs, present in the game and in the real world. Three insect-like creatures, Godbug, Flashbug and Thunderbug, were studied and came from collecting actions. To conclude, we incorporate wyverians, a humanoid lifeform, into the data set.

In total, eighty-five characters were studied, concerning morphology, physiology and reproduction. Character states were polarized using their repartition on the Earth (i.e. real-world) evolutionary tree; states were unordered. The character matrix was built on Nexus Data Editor (v.0.5.0; Page, 1998) and the heuristic search of the most parsimonious trees was made on PAUP (v.4.0; Swofford, 2003). To root the strict consensus tree, I decide to create two hypothetical outgroups. To test the robustness of the consensus tree, the Bremer support was calculated. The matrix used in the analysis is available as a Supplementary File to this article [1].

RESULTS

The heuristic search calculated 214,958 trees. Among them, 12 trees are the most parsimonious with a length of 165. A strict parsimonious tree was calculated, with a length of 167 steps (Fig. 1). The Consistency index (CI) is 0.623, the Rescaled consistency index (RC) is 0.556, and the Retention index (RI) is 0.899. These indexes, greater than 0.5 but close to is (except for the Retention index) indicate some cases of convergence in the consensus tree. The Bremer support was calculated to check the robustness of nodes: 16 nodes have a value of 1 and are considered weak, unsupported by a lot of character states. These weak nodes are mostly situated in the ichtyan and the insectoid clades. Among the other nodes, 15 have a value of 2 and 9 have a value of 3 or more, considered strong and supported by several character states.

DISCUSSION

The topology of the consensus tree (Fig. 1) shows some similarities with the real-world tree of life, as expected given the real-life inspiration of the monsters. A first division is made between “invertebrates”, represented by insectoid lifeforms, and “vertebrates”. The latter represent the major part of the dataset. Inside this clade, we observe a dichotomy with an ichtyan clade formed by fishes and “fish wyverns” called piscine wyvern in the Monster Hunter franchise. All fish taxa are the sister group of a tetrapod taxon (i.e. creatures with four limbs). Two other characters resulting from terrestrialization, the lacrimal canal and the atlas vertebra, are visible on real-world frog, human and pig. In the continuation of the article, I will present the details of each clade.

Insecta clade

A first basal group appears in the consensus tree. This clade groups Vespoid, Hornetaur, Flashbug, Thunderbug and Godbug (Fig. 2). All possess a chitinous exoskeleton, a pair of antennas, ribbed wings and six legs. These characters are similar to Earth’s insects and more precisely to the subclass Pterygota (Misof et al., 2014).

Vespoid has a social behavior evoking hymenopterans. Hornetaur, by having strong jumping legs and wings overlapping the abdomen at rest, looks like orthopterans such as locusts, grasshoppers, and crickets. Flashbug, Thunderbug and Godbug formed by the occurrence of moniliform antennas and the presence of elytra, modified hardened forewings distinctive of the order Coleoptera. To conclude, Flashbug and Thunderbug also share a bioluminescent abdomen, similar to real-life fireflies from the lampyrid family.

“Ichtyan” clade

Within the large vertebrate group, we observe a first clade formed by Speartuna, Knife Mackerel, Shringnight carp, the family of the Arowana (Burst arrowana, Bomb arowana and Golden fish), Cephadrome, and the two species of Plesioth (Fig. 3). These taxa share a lateral line, scale-covered skin, and fins formed by lepidotrichs. They also have opercula to protect their gills.

This clade is divided into two subunits. The first one groups Speartuna, Knife Mackerel, Shringnight carp and the family the Arowana species. All of them are closely based on real animals. They all possess ray fins, a characteristic of the real-world actinopterygian clade. The occurrence of premaxillary mobility allows us to refine the comparison with the Teleostei (Betancur-R et al., 2013).

In opposition, Cephalodrome, Plesioth and Green Plesioth form a group that I call Ambulichtyii (“walking fishes”). They present lobe fins, pelvic fins transformed and erected in back legs similar structures, a prograd biped posture and terrestrial locomotion, hence their name. This capacity to live out of the water during long periods can evoke mudskipper fish from the genus Periophthalmus (Steppand et al., 2022). It also represents, in the case of Cephalodrome who live constantly on land, a second episode of terrestrialization in in-game vertebrates. Plesioth species and Cephalodrome also have a pressurized pocket inside their body, allowing them to produce sand projectiles (Cephalodrome) and a water beam (Plesioth species). The head is fixed to the body by a neck and doesn’t show visible nostrils, suggesting a partial or complete loss of olfaction. Finally, these three taxa possess neurotoxin glands in their fins, allowing them to defend against predators.

An important point to develop in light of this consensus tree is the position of fishes and tetrapod-like creatures. Contrary to Earth, where tetrapods are contained inside lobe-finned fishes (which together are the sister group of ray-finned fishes), the Monster Hunter consensus tree presents a different topology (Fig. 1). This evolutionary tree suggests tetrapods outside the lobe-finned fishes. This result can be explained by the lack of sarcopterygian fishes (e.g., lungfishes and coelacanths) in the game, as well as the lake of basal tetrapodomorphs (e.g., Panderichtys, Tiktaalik and stegocephalians). Plesioth and Cephadrome (the “ambulichtyies”) share more characters with fishes than with tetrapods. More recent games of the franchise have creatures that could change the topology of the tree into a more Earth-like tree of vertebrate evolution, like Climbing Joyperch, which is very similar to Tiktaalik, and Petricanths in Monster Hunter World. Future complementary studies should highlight and resolve this “Monster Hunter Romer’s Gap”.

Tetrapod clade

As the sister group to the “ichtyan” clade, the consensus tree (Fig. 1) shows a group with four-limbed creatures, similar to the Earth’s Tetrapoda clade (Fig. 4). This one is supported by the occurrence of chiridian limbs (i.e. with joints and digits), atlas vertebra and lacrimal canals, observable in humans, pigs, and frogs. Like on Earth, amphibians (represented here by the frog) are the most basal tetrapods, due to the lack of an amniotic shelled egg (Benton, 2014). Frogs also have a sprawling quadruped locomotion in opposition to the other tetrapods, which present an erect posture.

The other taxa in the tetrapod-like group form a clade based on the production of amniotic eggs, observed in humans, pigs and highly suspected in Apceros, Aptonoth, and Rathalos. Digits, four at forelimbs and hindlimbs, end in claws. These characteristics tend to compare this clade with the real-world amniote clade. However, in opposition to real amniotes, these of Monster Hunter show an ancestral and common endothermy. On Earth, heat production strategies appeared independently in therapsids and archosaurs (Legendre & Davesne, 2020).

The amniote clade is divided into three subunits: the theropod-like clade, the mammal-like clade and the wyverns. We also observe that Fatalis is alone at the same branching level. Its scrawling locomotion, the ancestral type in tetrapods, prevents it from being included in one of the other clades with erect locomotion (via convergence). Its supplementary pair of chiridian limbs, forming wings on its back, are a unique autapomorphy and does not permit exact classification. On Earth, no vertebrate species has six limbs. A plausible hypothesis to explain these extra arms can be an abnormal expression of homeotic genes during the embryo development, duplicating the forelimbs. However, supernumerary limbs also need to be functional with their own nervous system and brain modifications, such as the sensory cortex to touch, the motor cortex to move, and the cerebellum for coordination.

Theropod clade

Within the tetrapod group, Genprey, Velociprey, Giaprey, Ioprey, and Lao-Shan Lung form a clade based exclusively on the occurrence of a dewclaw on the hindlimbs (Fig. 5). Quadruped locomotion is the ancestral type visible on Lao-Shan Lung, the most basal taxa of the clade. All the others possess prograd bipedality and a reduction of the forelimbs, similar to theropods from Earth. Genprey, Velociprey and Giaprey exhibit five digits on their hands in comparison to most basal taxa, which have four. Five fingers are visible on frogs (one is vestigial), the most basal taxa of the tetrapod clade. This fifth digit can be a recurrence of the lost digit, for example by homeotic genes reactivation. It can also be a newly-acquired “sixth” digit, fulfilling the same function of the ancestral lost digit. Finally, these three creatures have a raptorian claw on their feet, similar to the paravian dinosaurs like dromaeosaurs, troodontids and Balaur (Hendrickx et al., 2015).

Even though it was not used as a character in the analysis, Ioprey, Genprey, Velociprey and Giaprey all display social behavior, living in packs led by an alpha. Gregariousness seems to be a synapomorphy of this clade.

Mammalian clade

A mammalian clade appears in the big amniote group (Fig. 6). This one is defined by a viviparous reproduction, a heterodont and bunodont dentition, and lips. All taxa of this clade present an outer ear visible by an auricle and the occurrence of hairs and fur. Some characters are only visible on humans and pigs, such as nipples and placenta occurrence, though they are suspected on others by parsimony. Lastly, all of them present loss of scales. This well-resolved clade is very similar to Earth’s placental mammals phylogenetic tree (Kitazoe et al., 2007; Song et al., 2012).

We find firstly human and wyverian forming a humanoid clade based on orthogrady, bipedality, and disappearance of the tail. This clade is the sister of a second one, containing feline taxa and ungulates. This Feruungulata-like clade is defined by the occurrence of a rhinarium, ears situated highly on the head and a digitigrady of anterior members.

In felids, formed by Melynx and Felyne, we observe secodont teeth in association with their carnivorous diet, retractable claws and whiskers. In opposition, the euungulates are herbivorous with bunodonty. They also present a distinctive unguligrady locomotion and a reduction of the tail. As on Earth, we observe a clear distinction between perissodactyls (with Kirin and mesaxonian unguligrady) and artiodactyls (with paraxonian unguligrady). The latter have also a reduction of the inner and outer digits, forming two dewclaws.

To conclude, Bulfango, Mosswine and pigs present a snout, a character distinctive of suids. Pigs, the only domesticated taxa of this study, seems to have Mosswine as wild ancestor, sharing with it a hairless pink skin.

Wyvernian clade

Dragon-like creatures form a huge clade within the tetrapod one (Fig. 7). The included taxa (Rathalos, Diablos, Monoblos, Yian Kut-Ku, Yian Garuga, Gravios, Gypceros, Khezu and their subspecies) share in common a prograd bipedality. They also have the capacity of flying, with forelimbs transformed into wings with dactylopatagium and plagiopatagium. However, this clade has a quadrupedal origin, represented in the tree by the two herbivorous Aptonoth and Apceros. These two taxa also share with wyverns the occurrence of upper and lower rhamphotheca forming a beak. The tail ends with osteodermic caudal structures like a stegosaur’s thagomizer or an ankylosaur’s tail club. Furthermore, they share the production of amniotic eggs with shell.

Diablos, Monoblos and white Monoblos form a first inner group that I called Ceratowyvernia. These three taxa have in common a skull extension in a frill, ornated by epiparietal bones. It is possible that this bony structure has a display function during male-to-male fights or reproduction, as suggested in ceratopsian dinosaurs (Fig. 8) (Farke, 2004; Fark et al., 2009), hence their name Ceratowyvernia (“Horned wyverns”). In the elongation of the frill, a scapular shield protects the neck’s base and the back’s front.

Ceratowyvernia also present, on the feet, a migration of the inner digit to the back of the feet with an almost complete anisodactyl position. Anisodactyly is generally presented in arboreal animals for perching, like real-world songbirds. However, anisodactyly is also present in some cursorial birds and it seems to be a foot morphology enabling an ecological flexibility that allows some birds to cope with environments with strong aridification periods (Raikow & Bledsoe, 2000; Martin & Sherratt, 2023). Monoblos, White Monoblos and Diablos live in deserts and semi-deserts. However, these environments seem to be relatively stable and not quick to change. Another explanation of this morphology in Monoblos and Diablos could be behavioral. Martin and Sherratt (2023) showed that, in Australia, some birds present a light anisodactyly to propel them in water by paddling, such as the grey teal Anas gracilis, or swimming, such as the little penguin Eudyptula minor. Monoblos and Diablos are not semi-aquatic wyverns, but present fossorial behavior, using their head and strong forelimbs to dig and move underground. Anisodactyl feet could have been selected to aid propulsion in the soil.

Ceratowyvernia is the sister group of a clade defined by the occurrence of a pressurized pocket in the body. In Gypceros, Khezu and their subspecies, this organ is used to stock venom (in the former) or electrified mucus (in the latter). These taxa also present a scaleless skin and flexible tail, without a thagomizer, allowing whipping in Gypceros and sucking substrate in Khezu. I decided to call them Xenowyvernia because of their atypic appearance, locomotion and way of life.

Gravios, Yian Kut-Ku, Yian Garuga, Rathalos and their subspecies form a clade that I called Pyrowyvernia, referring to the pressurized organ containing a flammable substance used for hunting or defense. With the exception of Gravios, all of the others are carnivorous taxa. During their hypothetical evolution, they developed different morphological traits in that sense. Yian Garuga, Yian Kut-Ku and Rathalos subspecies have an anisodactyl foot selected to catch prey. They also possess a bony sting at the tip of the tail. This bone is hollow with a canal connected to a venom gland. This organ was, however, lost during the evolution of the group and is absent in Yian Kut-Ku and Blue Yian Kut-Ku, where only an atrophied bony sting remains. Yian Garuga, Yian Kut-Ku and Rathalos subspecies also develop efficient hearing, with the occurrence of a scale transformed in an auricle-like structure, convergent to the outer ear of mammals. This adaptation was further selected upon, with the apparition in Yian Garuga and Yian Kut-Ku of large, parabolic, somital and mobile ears to locate prey by sound. We choose to name this clade Audiowyvernia (“hearing wyverns”).

As previously mentioned, all wyverns in this study have wings, similar to those of bats, with patagium tensed between fingers and the flank. However, the occurrence of wings does not necessarily mean capacity of powered flight. Some wyverns, such as Rathalos, Yian Kut-Ku, Yian Garuga and Gypceros, are active flyers. They can fly away to change places, for example, and can even hunt prey (such as you, the hunter) from the sky, like the dive-bombing flight of Rathalos, inspired by birds of prey hunting techniques. On the other hand, some wyverns cannot fly high or for a long time. One example is the Khezu, which prefers to walk, even when moving away. Gravios is so massive that it can take flight only for a few seconds and a few meters above the ground. Diablos and Monoblos are not as massive as Gravios, and possibly could fly; however, they prefer walking or digging as locomotion.

The most parsimonious scenario tells of a progressive flying acquisition, from a wingless ancestor to a wyvern with wings but incapable of (or limited) powered flight, similar to Diablos and Monoblos (Fig. 9). Next, evolution would have selected flight that became a strong behavior in Gypceros, Yian Kut-Ku, Yian Garuga and Rathalos. This hypothesis suggests that patagium could appear before flight, making it an exaptation.

Although wings of wyverns are anatomically close to bat wings, it is difficult to use their evolutionary story as comparison. The oldest known bats, like Icaronycteris from the Eocene, already look like current ones, which does not allow us to fully understand the origin of flight in this mammal clade (Brown et al., 2019). Pterosaurs, the other vertebrate with patagium, are a similar story. Their strongly modified anatomy does not allow us to clearly and fully understand the origin of this group and, at the same time, their flight ability (Witton, 2013).

The only other group of flying vertebrates are birds. Since the discovery of Archaeopteryx (1861), different hypotheses have been made to explain the emergence of flight in this clade. Garner et al. (1999) proposed the “Pouncing model”, from an ambush predator ancestor. Williston (1879) and Ostrom (1979) proposed the “Cursorial model”, where wings were positively selected by accentuating stability on the run. Marsh (1880) proposed the “Arboreal model”, from an arboreal ancestor that soared from tree to tree. Today, scientists tend to think that these hypotheses do not exclude each other (Segre & Banet, 2018).

In the case of wyverns, the taxa from the first Monster Hunter games are heavy creatures, from hundred kilograms to several tons. The “Arboreal model” cannot be used to explain the emergence of flight; Monoblos and Diablos weigh several tons, so no tree could sustain that. The “Pouncing model”, from an ambush predator ancestor jumping from higher ground, is unlikely. The external group to wyverns, Apceros and Aptonoth, are herbivorous, as are the most basal wyverns, Diablos and Monoblos. Thus, the “Cursorial model” seems to be the most plausible; with the exception of Khezu, all wyverns are good runners, so it is possible that the origin of flight lies in this behavior. Studying other wyverns from more recent games, including the smaller ones, should allow us to confront this hypothesis and better understand the emergence of flight in the wyvern clade.

CONCLUSION

The bestiary of Monster Hunter is rich in diversity thanks to a series of successful games, born in 2004 with the eponymous game. Today, there are more than 300 in-game taxa, including predators and prey, and different species and subspecies. In this article, I tried to apply cladistic methodology to the bestiary from the first games, the so-called “First generation”, in order to obtain results with a historical, solid, and reproducible scientific method. The consensus tree presents great similarities with our planet’s tree of life. This can be easily explained by the large inspiration of creature designers in past and present nature. The cladistic method, by using the same polarization of states characters than on Earth, can also explain the similarity between this fictional fauna and the real-world one.

However, the weak representation of some taxa, like sarcopterygian and tetrapodomorph, resulted in meaningful differences to the evolution of vertebrates on Earth. Future studies, more focused on some clades and using taxa from all canon games, should be able to better develop some branches of the tree. Many novelties would be expected for the invertebrates, which were only represented in the first generation by insects. More recent games introduced new clades, such as crustacean-like creatures (Herminataur and Caenataur species), chelicerate-like ones (Nercyllia and Rakna-Kadaki species), and cephalopods (the cuttlefish-like Nakarkos and the octopus-like Nu Udra). Finally, in the tetrapod clade, more mammalian and reptilian taxa could result in a better resolution of the current polytomy; for example, the erect position that appears via convergence in mammals, theropods and wyverns, could be interpreted differently on a more detailed tree with more tetrapod-like taxa.

The fauna of the Monster Hunter franchise, with its rich lore and its strong Earth nature inspiration, can be a topic or reflection of evolutionary biology, as we saw in this article. In a more down-to-earth manner, it is also a good exercise for biology students and enthusiasts, allowing them to learn this method, its application, and also its limits. In the same thought exercise, the flora of the different biomes could also be studied. Further away, landscapes, minerals, and climates also give this franchise an interesting geoscientific content to explore.

REFERENCES

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Betancur-R, R.; Broughton, R.E.; Wiley, E.O.; et al. (2013) The tree of life and a new classification of bony fishes. PLoS Currents 5.

Brown, E.E.; Cashmore, D.D.; Simmons, N.B.; Butler, R.J. (2019) Quantifying the completeness of the bat fossil record. Palaeontology 62: 757–776.

Darlu, P. & Tassy, P. (1993) La Reconstruction Phylogénétique: concepts et méthodes. Editions Matériologiques, Paris.

Farke, A.A. (2004) Horn use in Triceratops (Dinosauria: Ceratopsidae): testing behavioral hypotheses using scale models. Palaeontologia Electronica 7(1): 1–10.

Farke, A.A.; Wolff, E.D.; Tanke, D.H. (2009) Evidence of combat in Triceratops. PLoS ONE 4: e4252.

Garner, J.P.; Taylor, G.K.; Thomas, A.L.R. (1999) On the origins of birds: the sequence of character acquisition in the evolution of avian flight. Proceedings of the Royal Society of London B 266: 1259–1266.

Hendrickx, C.; Hartman, S.A.; Mateus, O. (2015) An overview of non-avian theropod discoveries and classification. PalArch’s Journal of Vertebrate Palaeontology 12: 1–73.

Kitazoe, Y.; Kishino, H.; Waddell, P.J.; et al. (2007) Robust time estimation reconciles views of the antiquity of placental mammals. PLoS ONE 2: e384.

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About the author

Christopher Sevin, MSc., is a French independent scientific educator. Graduated with a Masters’ degree in Vertebrate Paleontology, he works in scientific communication, cladistics applied to pop culture and the evolution of the Limagne Basin (France) during the Oligocene–Miocene transition.

[1] Download supplemental file HERE

America’s earliest science fairs gave students the chance to do independent research. Today, they’re a competitive gloss to glorified internships. It’s time for a new format.

It’s confusing when someone changes their profile picture. I made a joke about how, to reduce confusion, there should be a feature that gradually morphs your old profile picture into your new one.

And then I figured, why not make it real?

I also added horse mode, where instead of directly morphing from your starting picture to your ending one, you turn into a horse in between.

For the last few weeks, as I’ve been building this out, my DMs have looked like this:

The majority of my friends didn’t even question why I was sending pictures of them as a horse or morphed with others, they just accepted this was a thing I was really into at the time for some reason.

And so they sentenced other people to be horseified.

Why did you do this?

AnimorPFP is a cultural critique of the fragility of one’s online identity, the inherent impermanence in a digital ecosystem in which the inhabitants are intangible.

We increasingly live our lives online, where our presence is represented by a static image, carefully curated to control how we are perceived. Making it jarring for that identity, that single image that represents the totality of an individual, to switch unexpectedly. It’s striking, the lack of object permanence in the digital sphere, as if we are once again infants, confounded by peek-a-boo.

So we must ask: In this era of tech, in a life lived online, what does identity entail? What does it mane to exist online? If one’s digital persona is masked with horse, if one’s visage is more strongly and more often associated with horse than one’s own face, then what separates mankind from equine?

My thoughts on this matter are too profound to be illustrated by prose alone, so I have prepared a poem:

There once was a fella named Harold
He planned to change his PFP but was imperiled
For it defined his identity
Without it, he felt a non-entity
A neighsayer might even claim he was Gerald!

Although to be serious for a paragraph, there is a genuine point to be had about this era of social media, where instead of following friends, the majority of people we follow are strangers. Even more so, our front pages are filled with people we don’t even follow, the algorithm decides who we stay updated on. The “problem” that AnimporPFP solves didn’t meaningfully exist ten years ago, before the rise of the influencer and algorithmic feeds. Back when social media facilitated mutual engagement with friends more than parasocial relations.

(Albeit there were always anonymous or follower-based forums like Tumblr, Reddit, and Twitter, but the quintessential social media was friends-based Facebook and old Instagram. Nowadays, essentially every major platform is grounded in serving you content from people you don’t know, and often don’t even follow.)

How does it work?

Why, with the beauty of mathematics, of course!

First, we need to understand what the faces in the start and end images look like, so we map facial features across 468 points (using MediaPipe Face Landmarker). Then, these points are used as references for dividing the face into a series of triangles (Delaunay triangulation). We compare the positions of the triangles in the start image to those in the end image, and as the slider moves along, the triangles warp to the end positions, while fading in the colors of the end image (via WebGL).

Thanks to existing software, creating this was actually very easy. Except for horse mode, which was very difficult and 99% of the work. I know what you’re thinking, that is an incredibly useless feature in an already pointless project. And to that I say fuck you, I’m turning you into a horse.

I also asked Chat for some technical advice, and this is where you can really tell it was heavily trained on Reddit content, as it first explained to me why my own joke was funny. And lowkey roasted me in doing so. I’m not sure what it means by “overengineered,” I think this is a reasonable solution to a serious problem.

I’m just serving AnimorPFP on one of my personal sites, instead of buying a new domain, because to be frank guys, I have spent hundreds of dollars on domains and it’s getting quite ridiculous at this point.

You can try this super helpful tool out for yourself at animorpfp.rawandferal.com.

See you next time, whenever that may be.

Love,

danielle (𝓇𝒶𝓌 & 𝒻𝑒𝓇𝒶𝓁)

Here’s a new preprint from Anthropic: “How AI Impacts Skill Formation”. AI coding bots make you bad at learning, and don’t even speed you up. [arXiv]

The researchers ran 50 test subjects through five basic coding tasks using the Trio library in Python. Some subjects were given an AI assistant, some were not.

The subjects coded in an online interview platform, and the AI users also had the AI assistant.

The researchers used screen and keystroke recording to see what the test subjects did — including those no-AI test subjects who tried using an AI bot anyway.

Afterwards, the researchers tested the subjects on coding skills — debugging, code reading, code writing, and the concepts of Trio.

The coders in the AI group were slightly faster, but it was not statistically significant. The main thing was that the AI group were 17% worse in their understanding:

The erosion of conceptual understanding, code reading, and debugging skills that we measured among participants using AI assistance suggests that workers acquiring new skills should be mindful of their reliance on AI during the learning process.

It’s just a single study and quite limited. You should expect to see AI bros dismiss the study saying it’s one library, it’s not enough coders, it’s an old model — and not to do better studies addressing their own objections.

If you don’t do the work, you don’t learn, and you don’t remember. Watching a bot do your job teaches you nothing. You end up incompetent. And you won’t work faster anyway.

• Video — Podcast

I. From “Show Me” to “Let Me Try”

Early math is very example-heavy. Both in classes, textbook explanations, and in worksheets. In the worst cases, you run into what is commonly called “Drill and Kill”, which means providing students with an enormous number of repetitions on a particular skill until their intellectual curiosity is crushed. That is, drill the topic until their spirit is killed.

That said, it does get a bad rap because when kids are starting to learn math, they do not have enough maturity to instantly get what is being shown to them, so they need to be shown *what* to do so that they can do it themselves.

Ideally, it’s a drill with decreasing support until the student masters the skill with no support given.

As kids get older and math gets complicated, the support and examples become less and less, until you get into higher-level undergraduate and graduate textbooks, where the student is supposed to come up with all of their own examples. Ultimately, the books at that level present the material in the form of axioms, definitions, theorems, and proofs. Two undergraduate math books famous for this are Landau’s Foundations of Analysis and Rudin’s Principles of Mathematical Analysis (a.k.a. Baby Rudin).

However, parents and kids are rarely told that this transition is coming or how to even deal with it.

One way to start very early in preparing for this transition is to have your kid start making their own example problems for the math material they are learning.

As they get older, their examples will improve, and by the time they reach the definition-theorem-proof format, they’ll be rock-solid at creating examples.

Not only that, but if your kid is very mathematically advanced, it gives them something to do when they are bored in math class, since they’ve already seen the material being presented ages ago.

II. The Cognitive Shift From Examples Provided to Examples Created

You can start with this cognitive shift regardless of where your kid is mathematically and what age they are currently celebrating. The earlier you start, the longer your kid will have to train their example-creation muscle, but you can start at any time.

The cognitive shift is from being a consumer of examples to a creator of examples.

Instead of thinking, “doing these exercises will teach me the technique”, it’s more of a “doing these exercises will show me how the technique works, so I can teach and test my understanding of how the technique works.”

It’s a bit of a small, subtle shift, but it does two things: a) creates a sense of ownership about learning the material, and b) enhances doing and reading the exercises. Once learned, your kid will constantly be on the lookout for how they could potentially create a similar problem.

Even at the earliest level, if a kid is doing a bunch of exercises to study multiplicative identity, for example:

• 1 x 1 =

• 2 x 1 =

• 3 x 1 =

• 4 x 1 =

They can start thinking about things like: What if we multiply by 1 to the 1s we’ve already multiplied?

• 1 x 1 x 1 =

• 2 x 1 x 1 =

• 3 x 1 x 1 =

• 4 x 1 x 1 =

Or maybe they think about whether they can substitute a fraction for the first number

• 1/2 x 1 =

• 2/2 x 1 =

• 3/2 x 1 =

• 4/2 x 1 =

Notice that this isn’t about making their math skills “faster” or solving more “difficult” problems; it’s about making sure they are exploring the technique even more deeply.

III. Why This Helps Kids Who Are “Bored”

Boredom often creeps into your math kid’s life in school math classes. They enjoy working on math, so it comes easier to them the more they do it. Suddenly, they are “ahead of the class” and bored with the material being presented.

One approach is to start petitioning the school for advanced work, grade-skipping, pull-in instruction, pull-out instruction, grade-telescoping, etc. However, it’s not clear whether this will alleviate boredom in the long term, let alone whether the teacher, school, or district will even consider it.

What we can do as adults who work with kids who love math is explain that the surface is easy, but the idea may not be. Boredom often means the *presentation* is easy—not the concept. That is, the work they are doing in their classroom is easy, but that doesn’t mean that the idea is simple.

For example, consider multiplication as repeated addition. A mathy kid will soon have most of the multiplication tables memorized, so they can sail through any work in this area easily and quickly. If they talk about being “bored” with this, ask them to come up with example questions where repeated addition may or may not work, or how it might work differently.

For instance, does multiplication as repeated addition work with negative numbers? Have them come up with some simple examples where either the first number or the second number is negative. Does it work? What does it even mean to do a repeated addition of a negative number?

Creating more complex versions of easy problems restores challenge and because the kids themselves are coming up with the questions, not you, the problems will be right at the edge of their mathematical maturity. Ask them to change numbers or constraints, or even context.

This can be done at home and, probably more helpfully, at school. At school, they can do it silently in their head or on the side of a piece of paper. They still do the school work, but they also build their problem-creation muscle at the same time.

What we really like about this method is that it doesn’t require the teacher’s permission or the creation of new material. Additionally, if they finish an assignment/test/work early, they can turn the waiting time into time for mathematical thinking.

IV. A Practical, Research-Aligned Ladder for Problem-Posing

Once you’re bought in and your kid, maybe with your help, starts creating their own problems, a question that comes up is - well, is it a well-posed problem? That is, is it really using and testing the technique correctly?

There is a huge mountain of research and practical experience that goes into problem creation for helping cement learning. I’m not going to go into that here.

I think it would be more helpful to give you the synthesized version.

There are 5 general levels that the problem-posing can go through:

Level 0 — Solve (baseline)

• Solve a standard example that’s an exact copy from the book/lecture

• This is to make sure the student understands the method

• Example: The lecture/book showed an example of 3 * 4 = 3 added four times = 12, so the student poses the problem 3 * 4.

Level 1 — Near-Transfer Problem Posing

• Change one element (numbers, context)

• Same structure, same method

• Strongly supported by research for young learners

• Example: The lecture/book showed an example of 3 * 4 = 3 added four times = 12, the student poses the problem 2 * 4.

Level 2 — Method-Preserving Problem Posing

• Change many elements, same underlying technique

• Structure preserved, surface changed

• Student explains *why* the same method applies

• Example: The lecture/book showed an example of 3 * 4 = 3 added four times = 12, the student poses the problem 7 * 5.

Level 3 — Constraint-Driven Problem Posing

• Given constraints, not a template

• Requires planning, verification, and reasoning

• Example: The lecture/book showed an example of 3 * 4 = 3 added four times = 12, the student poses the problem 3 * some number = a number that must be less than 10. As a bonus, they could say what the minimum and maximum numbers are that would work to be less than 10.

Level 4 — Error-Sensitive Problem Posing

• Design a problem that exposes a misconception that they or they think another student may trip up on

• Shows near-teaching-level understanding

• Example: The lecture/book showed an example of 3 * 4 = 3 added four times = 12, the student poses the problem 3 * 0 because what does it even mean to add 3 zero times? Do you end up with 3 or 0? That may trip some students up. Being able to spot potential sources of confusion indicates the edges where the mathematical technique might not work or require a different approach.

As with most aspects of parenting, it’s helpful to work with your kid through examples of different types of problems they might encounter. You and they don’t always need to reach Level 4 for each topic/technique, as higher levels are unlocked only when a deeper understanding of the mathematical technique develops. So when they first encounter a technique, ideally, you start at level 0 and try to replicate examples they saw in class or in the book. Then, as they work on homework, they may move up one or two levels as they see other worked examples and solve problems on their own. Eventually, maybe a few sections or even chapters, they (and you) might arrive at level 4 problem posing.

V. Problem Posing Builds Mathematical Maturity

As in the last paragraph, as the student becomes more comfortable with the material, their ability to delve deeper into questions that test the actual technique will improve. They’ll be able to identify the structure and formulate questions that probe it. They’ll come up with questions that test the boundaries of a technique, when it works, and when it doesn’t. They may reach the point where they can ask questions about when this technique breaks and what to expect when it does.

Mathematical Maturity means being able to do the above with skill and efficiency, unprompted. This is how mathematicians actually work, which is why, as students progress further along their mathematical journey, the books and courses they study have fewer and fewer worked examples. And as they explore the four levels of questions for each new mathematical object/technique/idea, it reinforces what they’ve learned about previous mathematical ideas. Which further entrenches and enhances their understanding of the subject.

Lastly, as they keep posing these problems, they will start to build intuition about how things might work, where they may break down, and how they can apply them in multiple places such that when they hit the abstraction of high school algebra or college mathematics or Ph.D. level mathematics, it’ll feel natural rather than a step up that may be too big to cross.

Down the line, kids will start seeing math as mathematicians see math: objects to explore, not rules to obey. Mathematicians treat concepts like numbers, shapes, sets, and many other things as real abstract objects that can be investigated, much like a biologist would investigate a new creature. Instead of applying memorized formulas, mathematicians “poke and prod” mathematical objects to see what happens, looking for patterns and relationships.

VI. The Parent–Child Dynamic Shift

One fun aspect of this question-posing technique is that it inverts the power dynamic between the adult and the child. Since the child is the one asking the questions, it’s now the adult who has to do the work and come up with the answer. Which the child then checks. In effect, the kid is now the teacher, and you are now the students.

As an adult, it can be helpful to make silly mistakes or make a big show of how hard the problems they made are. Obviously, don’t overdo it. Kids are very smart, and you don’t want them to think you’re making fun of them. But gentle teasing can be fun to work with and will give you some insight into what they understand.

Plus, after a day of being in school where they have the lower hand in the power dynamics with the teacher, it can be wonderful for the kid to feel like they have the upper hand. Especially when the rest of their day involves being corrected, evaluated, or rushed.

You can even ask them to assign you homework for the next day or week. It’s a fun way to make math time feel less “let’s do more worksheets” and more “let’s figure out how to trick my parent.”

VII. What Happens When Kids Create Examples They Can’t Solve

They got you. They asked a problem you couldn’t solve. And when you ask them to solve it, they can’t solve it either! Oops! And maybe a hooray as well!

This will happen all the time because there’s a lot of math that’s either not well taught at the elementary school or not well specified. This is a feature, not a bug. Many well-known problems in professional mathematics are easily stated but remain unsolved.

Going back to our multiplication as a repeated addition example. What if the kid asks you to multiply 2 and 1/2, that is, 2 * 1/2? If you subscribe to the first number being the thing you’re going to add repeatedly, what does it mean to do “1/2” of an addition? It leads to either trying to work around it by introducing new techniques (multiplication is commutative: a * b = b * a; 2 * 1/2 = 1/2 * 2, so it’s two repeated additions of 1/2), or trying to explain multiplication another way (multiplication is later taught as “scaling” up and down, rather than repeated addition”).

When it happens, it leads to great questions like:

• Why does this one work?

• Why doesn’t this one?

• What changed?

These questions help you discuss each of your understandings, and you may even revisit definitions to better understand the mathematical idea. These questions lead to recognizing patterns that stick because they were studied and prodded, not memorized.

VIII. The Bigger Picture: Play as Serious Work

For kids who love math, this form of building understanding almost feels like “play”. The goal isn’t to complete 100 problems before bed; it’s to poke and prod this “thing” to figure out how it actually works.

Playing around through exploration then opens up many fun questions and possibilities.

One exploration that I loved as a kid and helped me memorize the 9’s multiplication table row was *that the “tens” place goes from 0 to 9, and the “ones” place goes from 9 to 0.*

09
18
27
36
45
54
63
72
81
90

What is it about multiplying by 9s, that is, doing repeated additions of 9, that makes this pattern form?

Why is it that multiplying by 8s, that is, doing repeated additions of 8, doesn’t make this pattern form?

08
16
24
32
40
48
56
64
72
80

In the 8’s example, the “tens” places go: 0, 1, 2, 3, 4, 4, 5, 6, 7, 8, while the “ones” place goes “8, 6, 4, 2, 0, 8, 6, 4, 2, 0”.

I won’t ruin it for you by answering it here, but ask your kid to work with you to figure out why this happens. As a hint, think about how the “tens” place and the “ones” place are both used when counting up to 10.

IX. Closing: A Quiet Superpower

When your kid can invent their own examples, they will have a very useful tool for when they are stuck or bored. They will know how to test ideas, come up with examples that might help them solve the problem, and explore why something isn’t working on their own.

Later, they’ll be able to trust themselves when math (or other STEM subjects) textbooks stop holding their hands.

It’s a long process, and it’ll take years to get there, but if you start now, gently, playfully, and without pressure, they’ll get there. And over time, math stops feeling like something that happens *to* them and starts feeling like something they can explore. And as a bonus, your math will also get better!

X. Closing

That’s all for today :) For more Kids Who Love Math treats, check out our archives.

Stay Mathy!

Talk soon,
Sebastian

The PS1 was an unrivaled time for soundtracks that go incredibly hard. Games like Ridge Racer Type 4,  No One Can Stop Mr. Domino, Ape Escape (and basically anything that Soichi Terada ever did), Ace Combat 3 Electrosphere and Ghost in the Shell: Megatech Body all punch well above their weight. Hell, even the Animorphs game kinda goes. In that vein, if you have never listened to the soundtrack to Sheep, Dog 'n' Wolf AKA Looney Tunes Sheep Raider, you should correct that right now because it contains at least one incredible heater.

Sheep, Dog ‘n' Wolf was a bizarre celshaded stealth action puzzler that came out in 2001 starring Ralph Wolf (NOT Wile E. Coyote) and described at the time by Infogrames’ Director of Marketing as “E-Rated Metal Gear.” The soundtrack was done by a musician named Eric Caspar, and though a lot of it feels like boilerplate production music, it does have bangers. 

One track in particular stands out, an ambient DnB track that could easily fit into any racing game from the era. It is unclear what this track is called or if it has a name, although I have seen a few sites like KHInsider and Discogs cite it as “Fronzy Last/Fronzylast_v3.” The track itself appears in the Planet X stage later in the game, which you can see by watching this speedrun attempt.

Anyway, enjoy this oddly specific track that keeps appearing in my YouTube suggested feed. Also check out this extremely of-the-era full page print ad complete with Typewriter font.