Tuesday 24 September 2019

Mythbusters Jr. on Odysseus’ axes

Earlier this year, an episode of ‘Mythbusters Jr.’ tried to repeat Odysseus’ feat of shooting an arrow through twelve axeheads. With the constraints imposed by the Mythbusters Jr. team, their archer Byron Ferguson wasn’t able to achieve the feat. But a Mythbusters Jr. machine did, after careful calibration.
Mythbusters Jr. (2019) attempt to replicate the bow contest from Odyssey book 21.
The set-up they choose for the attempt (Mythbusters Jr. 2019) is twelve axes firmly fixed vertically on their shafts, each with a loop at the top of the shaft where the two blades meet. We’re told that the hole in the loop is 3 inches in diameter (76.2 mm). We aren’t told how far apart the axeheads are, but I’ve measured on a screenshot with minimal foreshortening, and that suggests that the spacing is very close to four times the diameter of the loops, or one foot (304.8 mm).

Mythbusters Jr.: San Francisco, USA, 2019

Here’s how the programme introduces the task:
Narrator. Even over a short distance, an on-target arrow may wobble. But does that really mean that it doesn’t fly straight? A definitive answer demands a definitive test. So it’s all hands to the workshop to reconstruct a legendary arrow obstacle course. This particular challenge is actually a myth in itself, and it involves a dozen replica double-bladed battleaxes.
     While Greek hero Odysseus was fighting the Trojan wars, Penelope was left to fend off a bunch of unwanted admirers. She promised to marry whichever man could fire an arrow through twelve axeheads, confident that the shot was impossible. But Odysseus returned, and in disguise, took the shot -- and nailed it.
     If the Mythbusters could repeat that success, it would prove beyond doubt that an arrow flies straight and true.

Rachel Pizzolato. Here we have our twelve axes with the target of three inches in diameter, inspired by Odysseus’ archery trick shot. So we’re going to have Byron take this shot, and see if he can get through all twelve with his longbow. They say it’s impossible -- so good luck, bro.

Narrator. It’s a daunting prospect. Even Byron has his doubts.

Byron Ferguson. Now I know shooting through a three-inch ring shouldn’t be a very hard shot, and it’s not. Shooting through three or four of them, not a hard shot. Shooting through twelve of them -- heh, it’s a very hard shot, doing it with a traditional bow.
As it turns out, Byron can’t manage the shot. He can consistently get an arrow through anywhere up to half of the loops, but the slightest brush against metal makes the arrow go off course and shatter.

The Mythbusters Jr. team go on to devise a mechanical set-up that can outdo the human expert. I congratulate them on their success! The way they set it up, the task truly is legendary.

There are a few potential misunderstandings involved, though, which the team weren’t aware of -- and at least one error, where they got something quite wrong.

At several points in the episode it’s claimed that the feat has never before been achieved in real life. This isn’t true. There is in fact documentary evidence of it being accomplished at least once before, and maybe twice.

Corridor Crew: Los Angeles, USA, June 2018

First, the more doubtful case. In a video released on YouTube on 7 June 2018, members of the popular ‘Corridor Crew’ channel -- they have 2.6 million subscribers at the time of writing -- compete to see who can shoot an arrow through twelve axeheads with holes in the blades. They don’t cite measurements, but the holes look no bigger than 3 inches in diameter, and may be smaller. The distance between the axes looks likely to be around a foot.
Nick Laurant’s successful shot, with the arrow circled (Corridor Crew 2018, 5:54)
In the video, each member of the crew takes one shot. Two of them, Niko Pueringer and Nick Laurant, succeed. At the end the two successful archers have a second try, and though Laurant misses, Pueringer repeats his shot. Comments interspersed throughout the video indicate that Pueringer is an experienced archer.

In all three successful shots, the arrows graze multiple axeheads and send them spinning on the spot, yet the arrow remains on target enough to get through all twelve holes.

This is an interesting reversal of the Mythbusters Jr. scenario. The axeheads are made of some light, soft substance, not metal; and they rotate freely rather than being fixed. More importantly, the archers are all amateur -- and yet two of them succeed on their first shot.

However, it’s much harder to give this test credence, in comparison with the Mythbusters Jr. test, for three reasons.
  • The video is entertainment, not documentation. It’s just not careful enough.
  • Corridor Crew don’t provide any technical details of their test -- such as materials used, the draw weight of the bow(s), measurements of the holes, the distance between the axes, and the distance between the archer and the first axe.
  • Corridor Crew are known primarily for their skills with movie techniques like stunts and special effects. Many of their videos are advertised specifically as videos where ‘VFX artists react to’ special effects in films, or VFX artists create ‘deepfakes’, where CGI is used to make an actor look like some real person. In their archery video they don’t even claim to be presenting events as they actually happened -- so we can’t even take it for granted that their evidence is presented in good faith.
The second and third reasons really go back to the first one. There’s nothing unreasonable about making an entertainment video, and for the record I am prepared to believe that Niko Pueringer could legitimately make the shot. It’s just that the tone of the video weighs against taking it very seriously.

It would be useful to know more about the differences between the two tests. With the details they give -- that is, none -- it’s just hard to evaluate.

Brain and Skinner: Durban, South Africa, 1978

Peter Brain (source:
Brain’s obituary, 2005: 92)
In fact we need to go back a lot earlier. Forty years earlier, Peter Brain and D. D. Skinner performed a successful test in South Africa. Brain was a prominent immunologist and part-time classicist. In his 50s he learned ancient Greek and did a classics degree, and later published a well-respected book on Galen. Skinner was an amateur archer and, I suspect, a former biologist -- he collaborated on a published biology paper in the early 70s, but I haven’t managed to trace a career in the field after that point.

They give detailed textual documentation about their efforts in an academic journal. Skinner pulled off the feat successfully, and because of their high-quality documentation, there is a good presumption that they are reporting their tests accurately.

Mythbusters Jr. (2019) believe the main obstacle to getting the arrow to fly straight is the ‘archer’s paradox’: the arrow flexes as it passes the handle of the bow, and the resulting flex and spin continues throughout its flight, increasing its cross-section. Brain and Skinner (1978) don’t experience that problem. One reason is that they use 4 inch openings (101.6 mm), instead of the 3 inches in Mythbusters Jr., and apparently this was enough to avoid the problem.

Another is that they station the archer at a distance such that the first opening is equidistant between the archer and the last opening: with this extra distance, the flexing of the arrow may have reduced in the first half of its flight. Their reason for doing this is that they think a more important problem is the vertical rise and drop of the arrow in the course of its flight. So first, they determine the vertical variance over the total distance, to ensure that it’s at least possible for a human to replicate the feat. They decide that the peak of the flight should be at the first axehead, so the arrow will be dropping the whole time while it’s passing through the axeheads:
Our first experiment, conducted in an office corridor,
-- presumably outside Brain’s office at the Natal Blood Transfusion Service. These guys are the original corridor crew! --
established the fall of the arrow over the second half of its flight (i.e. the part occupied by the axes) for various values of x. Having shot several arrows into a target from a distance x, our archer retired a further x, and, aiming at the same mark without altering his sights, shot a further series of arrows. The difference in height between the first and second groups is the fall over the second distance x.
Given a bow with a 47 pound draw (i.e. relatively light), they obtain the following figures:
If we use rings 4 inches in diameter, and take account of the over-all diameter of the arrow (it has fletches at the rear end to make it fly straight, and no part of the arrow may touch any of the rings), then a fall of 2 inches is about as much as we can allow. This is obtained when x is 12 feet. Placing the rings a yard apart, as suggested by Page, would mean a fall of more than a foot in the second half of the 66-foot flight, and this makes the shot quite impossible. We therefore decided to put our rings one foot apart.
The feat as depicted in the 1997 miniseries The Odyssey. Armand Assante (front) as Odysseus, Alan Stenson (rear) as Telemachus.
So they settle on the same spacing used in the Mythbusters Jr. test. Their design of the rings is different, however:
To simulate the rings we cut twelve pieces of expanded polystyrene, 9 inches square and 3/4 inch thick, and made a 4-inch-diameter hole in the middle of each. These were attached with rubber bands to cross-pieces nailed to a horizontal plank 11 feet long, so that they stood vertically with the holes one behind the other and a foot apart. These rings are extremely light and the slightest touch causes obvious movement, while any hole or nick is easily seen.
Unlike the Mythbusters Jr. team, they don’t have access to a high-speed camera. The test is successful:
After three sighting shots with only the first and last rings in place, in the course of which the first ring was damaged, we fitted all the rings and he made a perfect shot; no ring was touched ... His next shot nicked one of the middle rings, but the following three were all perfect.
(My emphasis.) Skinner feels that 3-inch rings would at least in principle be possible:
We then increased the distance between the archer and the first ring, and found that the shot was still possible when this was 15 feet (a total course of 26 feet) but not when it was 18 feet. The archer thinks that at the original distance of 11 feet he could probably do it with slightly smaller rings, say 3 inches in diameter, but we have not tried this
Niko Pueringer’s shots in the Corridor Crew video tend to support this. However, there are several factors that could affect the outcome:
  • Distance from the first axe. Skinner stands far enough away that the arrow is already on its descent as it passes the first axe; Pueringer and Ferguson are much closer. What effect does this have?
  • Material of the axeheads. The Brain-Skinner and Corridor Crew tests use a soft material, Mythbusters Jr. use metal. Is the task harder if the fletching brushes against metal, as opposed to a soft substance?
  • Mobility of the axeheads. The axeheads rotate freely in the Corridor Crew test, but are fixed in the other two. Does rigidity make the task harder?
None of the experiments control for these factors. It could be that a lot depends on them.

Anyway, if we imagine Odysseus’ feat as a historical event, we need to remember that the first part of the feat was about strength -- being strong enough to string the bow. So his bow would presumably have a much heavier draw. Maybe on a par with a longbow with a 120 pound draw, or even more. A much heavier draw weight could double the arrow’s speed, and that would reduce the drop by half.

Other interpretations

The set-up of the axes in Ulysses 31,
episode 31 (1982)
There’s a question over the exact set-up of the axes in Odyssey book 21. If you look again at the stills from the Mythbusters Jr. and Corridor Crew experiments, above, you’ll notice they have quite different ideas of what exactly the archer is supposed to be shooting through.

In Mythbusters Jr., the axes are double axes with a metal loop at the top of the shaft. In Corridor Crew, the axes have holes in the the blades themselves. That doesn’t even begin to exhaust the possibilities.

This is because the Odyssey itself doesn’t give any details on what, precisely, is going on. The text doesn’t tell us where the holes are, how far apart they are, how high off the ground the holes are, whether the axes are fixed as in Mythbusters Jr. or rotating freely as in Corridor Crew.

In point of fact we’re not even told there are holes.

Here’s what we are told. The winner of the contest will be:
διοϊστεύσῃ πελέκεων δυοκαίδεκα πάντων

... whoever shoots through all twelve axes
-- Odyssey 19.578
At 21.114 and 21.126-127 we have people trying to string the bow and dioisteus(ein) te sidērou, ‘shoot through the iron’. At 21.328 the phrasing is dia d’ hēke sidērou, also ‘he shot through the iron’. Here’s the description of Telemachus setting up the axes:
πρῶτον μὲν πελέκεας στῆσεν, διὰ τάφρον ὀρύξας
πᾶσι μίαν μακρήν, καὶ ἐπὶ στάθμην ἴθυνεν,
ἀμφὶ δὲ γαῖαν ἔναξε.

First he placed the axes, after digging a continuous trench,
a single long one for all of them, and made (them) straight in a line,
and he pressed the earth around them.
-- Odyssey 21.120-122
Here’s when Odysseus finally shoots through the axes:
τόν ῥ’ ἐπὶ πήχει ἑλὼν ἕλκεν νευρὴν γλυφίδας τε,
αὐτόθεν ἐκ δίφροιο καθήμενος, ἧκε δ’ ὀϊστὸν
ἄντα τιτυσκόμενος, πελέκεων δ' οὐκ ἤμβροτε πάντων
πρώτης στειλειῆς, διὰ δ' ἀμπερὲς ἦλθε θύραζε
ἰὸς χαλκοβαρής.

He took the string and the arrow-notches and drew the bridge (of the bow),
on the spot, sitting in his chair, and shot the arrow
aiming in front of him, and did not miss any of the axes
from the first steileiē, but it went through to the doors,
the bronze-heavy arrow.
-- Odyssey 21.419-423
Homer isn’t exactly giving us detailed documentation. Even if we limit ourselves to interpretations that are taken at all seriously, there are at least four ways scholars explain what’s going on here:
  1. The arrow goes through gaps of some kind in an intricately-shaped axehead, or a gap between a curved axehead and the shaft. This could be suitable for Bronze Age Minoan double axes, but we don’t have evidence of similar shapes in the Iron Age.
  2. The arrow goes through metal hanging-rings, or onkia, at the butt-end of the axe shaft. There’s no mention of onkia in the text. The rationale for this explanation is that the word steileiē, which I’ve left untranslated in Odyssey 21.422, might possibly mean ‘shaft’ or ‘haft’ -- but its exact meaning is uncertain. (See Sauge 2014: 66-67 for discussion of its meaning.)
  3. The axeheads are detached from the shafts and placed vertically with the blade resting in the earth; the arrow is supposed to go through the sockets. Shaft sockets are way too small for the task to be remotely feasible in real life.
  4. The idea is to shoot an arrow so powerful that it pierces metal axeheads. This is obviously implausible, but (a) this is myth, not history; (b) it takes the repeated phrase dia sidērou ‘through the iron’ literally.
The set-up of the axes as imagined by (1) Page 1973: 112, Fig. 6; (2) Page 1973: 101, Fig. 3; (3) Delebecque 1975: 59, Fig. 3; (4) Pocock 1961: 349, Fig. 1.
If the openings are too small, or too close to the ground, the task is superhuman. That isn’t necessarily an obstacle: this is legend, after all. The idea of the contest, the setting, and the genre all encourage the idea that Odysseus is performing a superhuman feat beyond the reach of any living mortal.

But if we’re going to go that direction anyway, why not take a good look at explanation 4? That’s the interpretation favoured by Walter Burkert (1973), and I have to say I find it very, very attractive. You can imagine an arrow fired so hard that it pierces or shatters a brittle Iron Age axehead. Someone like Odysseus, then, should be able to get through twelve of them!

The fact that it’s physically impossible is, once again, no obstacle. Remember that the first part of the task was to string the bow -- a feat of strength, not aim -- and not one of the suitors was able to do it. Only Odysseus was mighty enough to bend the bow enough to attach the string. (His son Telemachus could too, except that he basically let his father win.)

The idea of a weapon that only one person can wield is a fairly standard kind of folktale motif. Another example appears in the Iliad, the spear that only Achilles can wield (Iliad 16.139-144). Another, in Irish myth, is the gáe bolga of Cú Chulainn. The Iliad also features plenty of cases where heroes can lift things no living person could. (Heroes use inhuman strength to lift boulders at Il. 5.302-304, 13.378-383, 13.443-450, and 20.285-287.)
Left: Arjuna shoots at a fish's eye to win Draupadi (source: a 19th century edition of the Mahabharata). Right: Ulysses (Kirk Douglas) shoots through twelve axes to win Penelope (source: Ulysses, 1954).
And it is definitely a thing, in myth, to have stories where a hero courts a wife by performing an archery feat that’s impossible for anyone else. The strongest parallels are in Indic myth. In the Mahabharata Arjuna competes for the hand of Draupadi by stringing a bow that no one else can string and then shooting five arrows at a fish’s eye, somehow getting the arrows through a ‘wheel’ that’s in the way. In the Ramayana Rama competes for the hand of Sita by drawing on a bow that no one else can draw, and drawing it so hard that the bow shatters.

In Burkert’s eyes, the Odyssey story also has resonances in Egyptian iconography, where we see depictions of pharaohs who can shoot arrows through sheets of metal. In itself, that’s entirely realistic, as shown by the still below.

Personally, I think all of this is plenty to justify taking Homer at his word. ‘Loops’ and ‘holes’ aren’t mentioned anywhere in the text. Odysseus quite literally sends the arrow through the iron of the axes.
An arrow shot through a steel car door (source: TWANGnBANG, YouTube, 2013). The bow used was a PSE TAC-15 crossbow, with power equivalent to a 150 pound draw.

References and further reading

  • Bérard, Jean 1955. ‘Le concours de l’arc dans l’Odyssée.’ Revue des études grecques 68.319: 1-11.
  • Brain, Joy 2005. ‘Peter Brain.’ Natalia 35: 92-94.
  • Brain, Peter; Skinner, D. D. 1978. ‘Odysseus and the axes: Homeric ballistics reconstructed.’Greece & Rome 25.1: 55-58.
  • Burkert, Walter 1973. ‘Von Amenophis II. Zur Bogenprobe des Odysseus.’ Grazer Beiträge 1: 69-78.
  • Corridor Crew 2018. ‘Can you fire an arrow through twelve axes? (Odysseus archery challenge.)’ YouTube (retrieved Sep. 2019).
  • Delebecque, Édouard 1975. ‘Le jeu de l’arc de l’Odyssée.’ In: Bingen, J.; Cambier, G.; Nachtergael, G. (eds.) Le monde grec. Pensée, littérature, histoire, documents. Hommages à Claire Préaux. Brussels: Éditions de l’Université de Bruxelles. 56-67.
  • Fernandez-Galiano, Manuel 1992. ‘Books XXI-XXII.’ In: A Commentary on Homer’s Odyssey, volume III. Books XVII-XXIV. Oxford: Clarendon Press. 129-310. (137-147 on the axes and the bow contest)
  • Fries, Carl 1937. ‘Zur τόξου θέσις.’ Philologische Wochenschrift 43 (23 Oct. 1937): cols. 1198-1199.
  • Monro, D. B. 1901. Homer’s Odyssey. Books XIII-XXIV. Oxford: Clarendon Press. (176-177 on the axes and the bow contest)
  • Myres, John L. 1948. ‘The axes yet again.’ Classical Review 62.3-4: 113.
  • Mythbusters Jr. 2019. ‘Battery blast.’ Television episode, Season 1, Episode 3, first broadcast (USA) 16 Jan. 2019.
  • Page, Denys L. 1962. Folktales in Homer’s Odyssey. Cambridge, MA: Harvard University Press. (95-113 on the axes and the bow contest)
  • Pocock, L. G. 1961. ‘The arrow and the axe-heads in the Odyssey.’ American Journal of Philology 82.4: 346-357.
  • Sauge, André 2014. ‘L’arc et l’olivier.’ Gaia 17: 63-82.
  • Stubbs, H. W. 1948. ‘The axes again.’ Classical Review 62.1: 12-13.

Thursday 5 September 2019

Learning Latin: why conjugations?

Verb conjugations were invented to torment first-year Latin students. OK, that wasn’t really the aim. But it is the effect. Learning four sets of endings is a pain. It’s also a waste of time.

Things would be hugely simplified for beginner Latin students if textbooks would explain thematic vowels properly.
What do you mean I need to learn four conjugations?
Latin has four basic types of verbs, or conjugations. Here’s a typical table for the verbs clamare shout, habere have, dicere say, and audire hear. The table shows the forms corresponding to I shout, you shout, she shouts, and so on. Each conjugation behaves slightly differently: I’ve added highlighting where the forms are distinctive to one conjugation.
1st conj. 2nd 3rd 4th
1 sg. (I) clamo habeo dico audio
2 sg. (you) clamas habes dicis audis
3 sg. (she, he) clamat habet dicit audit
1 pl. (we) clamamus habemus dicimus audimus
2 pl. (y’all) clamatis habetis dicitis auditis
3 pl. (they) clamant habent dicunt audiunt
The endings, at least, are nice and systematic. Looking down each column, you see -o, -s, -t, -mus, -tis, -nt (I shout, you shout, she shouts, etc.). The problem is the bit in between the stem and the ending, which changes depending on which conjugation the verb belongs to.

The outcome is that students have to memorise four separate sets of forms. There are 22 distinctive forms highlighted in the table, and it’s a pain to learn every single one of them.

As it happens, it’s also wasted effort. In reality, there are only two genuinely anomalous forms. Except for those two forms, you can have a full understanding of Latin verb conjugations -- in the present tense, at least -- in terms of just two things:
  1. Stem-sounds, that is, the sound that comes at the end of the verb stem: this will be either a consonant, or one of three possible vowels.
  2. Thematic vowels, that is, an unstressed vowel that appears in between a consonant stem and a consonant ending -- like in English hated.
Textbooks hint at these things -- some textbooks, anyway -- but they never explain them properly, they never get to the point.
A fairly typical introduction to Latin verb conjugations. (The yellow highlighting is my doing.)
As things stand, students have to memorise four sets of endings, with 22 distinctive forms. BOOOO-RING. Things are much easier if you learn (1) what the four conjugations really are, and (2) how thematic vowels work.

A better verb table

Here’s a revised table. This time, the highlighting isn’t there to mark differences between conjugations. Instead,
  • yellow marks the stem-sound, that is, the sound at the end of the stem;
  • green marks a contraction;
  • pink marks a thematic vowel.
1st conj.
1 sg. (I) clamo habeo dico audio
2 sg. (you) clamas habes dicis audis
3 sg. (she, he) clamat habet dicit audit
1 pl. (we) clamamus habemus dicimus audimus
2 pl. (y’all) clamatis habetis dicitis auditis
3 pl. (they) clamant habent dicunt audiunt
The real difference between the conjugations isn’t that they take different endings, it’s that they have different stem-sounds. ‘1st conjugation’ simply means a-stem, 2nd is e-stem, 3rd is consonant-stem, and 4th is i-stem.

This way, you can see that the verb system is actually extremely consistent. The actual endings -- the -o, -s, -t, etc. -- are still identical for every verb-type. 1st, 2nd, and 4th conjugation verbs have vowel stems, highlighted in yellow. And in most forms, the stem vowel is there in plain view. So, for example, e-stem verbs have
  • e + -o  >  -eo
  • e + -s  >  -es
  • e + -t  >  -et
  • e + -mus  >  -emus
  • e + -tis  >  -etis
  • e + -nt  >  -ent
3rd conjugation verbs have consonant stems. There, too, the consonant is in plain view, highlighted in yellow.

But take a look at the endings -- -o, -s, -t, -mus, -tis, -nt -- and notice that most endings are consonantal. Because of that, consonantal endings need a thematic vowel, to make the word pronounceable: to separate the dic- from the -s, -t, -mus, etc. This vowel is normally /i/, but when there’s a nasal sound it moves to the back of the mouth, /u/.
  • c + -o  >  -co
  • c + -s  >  -cis
  • c + -t  >  -cit
  • c + -mus  >  -cimus
  • c + -tis  >  -citis
  • c + -nt  >  -cunt
(When there’s an /r/ the thematic vowel becomes more open, producing /e/, as in dicere and diceris.)

The net result is that, in this revised version of the table, there are only two anomalies, instead of twenty-two:
  1. the contraction in clamo;
  2. the surplus thematic vowel in audiunt.
Compare that to the 22 distinctive features in the first version of the table. Easier, huh?

(Noun declensions developed in a similar way, but their history is more complex and you can’t simplify them as much. The declensions are, respectively, a-stem nouns (1st declension), o-stem (2nd), consonant-stem and i-stem (3rd), u-stem (4th), and e-stem (5th). In early Latin their endings were more similar to each other than they were by Caesar’s time.)

The mixed conjugation

The mixed conjugation is the reason we can’t have nice things. It is Latin’s fifth verb-type. And it is not determined by the sound at the end of a verb stem -- or at least, not straightforwardly. The mixed conjugation is the miscellaneous conjugation; the whatever-I-don’t-care conjugation; the Lord-High-Everything-Else conjugation.

Mixed conjugation verbs are hybrid, with elements of both consonant-stem and i-stem verbs, the 3rd and 4th conjugations. That’s exactly how they’re normally taught, and I can’t really tidy it up any further, because the mixed conjugation didn’t come about as systematically as the other ones. Mixed-conjugation verbs aren’t consistent in their linguistic origins, and there’s no getting around that.

Some mixed conjugation verbs are relatively friendly. Take cupio desire. That’s a very tidy case, because for some of its history, cupio can actually be treated as a 4th conjugation verb in disguise. If you look at its principal parts, except the infinitive --
cupiō, ______, cupīvi/cupiī, cupītum
-- a trained Latinist will immediately recognise all the hallmarks of a standard 4th conjugation verb. If you look up an etymological dictionary, you’ll see it comes from an i-stem. At heart, cupio is a 4th conjugation verb, with an irregular second principal part.

(Of course it’s not as simple as that ... it never is. cupio went through a phase shift in the 1st century BCE. In Lucretius, its imperfect subjunctive appears as cupīret, just as you’d expect for a 4th conjugation verb. Just a few years later, in Cicero, it appears as cuperet, treated as mixed conjugation.)

Some other verbs shift between consonant stem or i-stem depending on a variety of factors, like facio do, capio catch, iacio throw. They’ll be i-stem in the present indicative, but consonant-stem in the past participle -- stuff like that. Some are much more consonant-ish: rabio rave is solidly consonant-stem in its origins, but somehow acquired elements of an i-stem verb. Conversely, pario give birth was originally i-stem, but somehow lost the i altogether in the important participle parens parent. Often a mixed-conjugation verb is one that was originally i-stem in the present tense but consonant-stem in the past tense, like fugio flee, past tense fug-i I fled.

The perfect tense

Next time I teach Latin, I’m going to abandon conjugations altogether for the present tense. I’ll teach thematic vowels instead. Only the mixed conjugation needs special treatment.

But maybe Latinists will raise objections over the perfect tense: aha! the four conjugations do behave differently in the perfect! So you do need conjugations! Well, kind of. Here’s how the traditional conjugations look in the perfect tense:
  • 1st (a-stem): para-  >  parav-i
  • 2nd (e-stem): habe-  >  habu-i
  • 3rd (consonant-stem): inconsistent
  • 4th (i-stem): audi-  >  audi-i / audiv-i
Well, you could do it that way. Or you could learn what a glide is.

A glide is the opposite of a thematic vowel. Remember how a thematic vowel is a sound that pops up between two consonants to make the word pronounceable? Well, a glide is a sound that pops up between two vowels.

English has glides too. Try saying this sentence out loud: The law is just. The sound that comes up between law and is will vary depending on your dialect. For most people, it’ll be either /r/, /w/, or a glottal stop.

In Latin, glides are normally /w/ or /y/. (/r/ only in the genitive plural of 1st/2nd/5th declension nouns.) For example, the word filius son is going to be pronounced /feeleeyus/. With that in mind, let’s look at some perfect tense verbs.

Take the a-stem verb para- prepare. The perfect tense should, by rights, be para-i. But that’s hard to say ... so you add a glide /w/. The result is /parawee/ (as pronounced in the republican period, at least), spelled paravi I have prepared.

The same thing happens with i-stem verbs, but there you have a choice as to which glide you use. So audi- hear can become either /audeewee/ or /audeeyee/, spelled audivi and audii I have heard.

Consonant-stem verbs don’t need a glide, so you often end up with the ending attached directly to the stem: ascend-i I have climbed, vert-i I have turned, em-i I have bought. (More often the stem will be mutated, but let’s not go into that just now: you have to deal with irregularities like that with the other conjugations too.)

It’s the e-stem verbs that are the odd ones out. There, the stem-vowel stays short and the glide moves it back in the mouth, so instead of /habewee/ you get /habuwee/, written habui I have had.

Now, I can see a case for keeping conjugations around for the sake of the future tense. When I suggest abandoning conjugations, it’s really absolute beginners that I have in mind. There’s no point memorising four paradigms. Much better to learn a single paradigm, with just a couple of anomalies.