Polytropy

Index to this series

We are still in the latter part of Book VI of Plato’s Republic, where Socrates undertakes to explain the education of the philosopher-kings (502c–d). They are not literally so called, as we noted last time. They are going to need to “be able to bear the greatest studies” (503e), and “the idea of the good is the greatest study” (505a). People are confused about what the good is:

• many say it is pleasure;
• a few, knowledge (505b).

It rather the case that

• so the Good makes it possible to have
  • knowledge (508d), and perhaps even
  • pleasure (509a),
• as the sun makes it possible to see (508b–d).

We looked at that much last time.

Sections of this post:

• Docility and Stability
• Life on Mars
• The Divided Line
• Convention

Docility and Stability

There will be few philosopher-kings or “most precise guardians” (503b), because each will combine qualities rarely found together. He will be both docile and stable.

The word “docile” meant teachable in the fifteenth century; in the eighteenth century, it came to mean tractable. To be this is to be ductile, the word having the Indo-European root *deuk- “to lead,” while the root of “docile” is *dek-¹ “to take, accept.” Of these two roots,

• The former, *deuk-, gives us “deduce,” “seduce,” and “traduce,” but also “educate”;
• the latter, *dek-¹, gives us “doctrine,” “dogma,” “orthodoxy,” and “discipline.”

The amateur such as myself might suspect that the root of “teach” was one of these two; the scholars say it is *deik- “to show,” which gives us also “token,” “dictum,” “judge,” “paradigm,” and “theodicy.”

Etymology then reveals not that “teachable,” “docile,” and “ductile” are cognate, but that their meanings are interconnected. I think we can see this anyway. Learning needs self-discipline, and if you have that, you can probably follow somebody else’s discipline too.

The poor student may be unable to sit still and study, or may instead be immovable, which is also what a guardian should be.

Appealing to etymology for a claim about meaning is like attributing an aphorism to a famous person: it tells you where the thing comes from, but does not make it correct.

Socrates happens to play an etymological game in this reading, though later, at 509d:

νόησον τοίνυν, ὥσπερ λέγομεν, δύο αὐτὼ εἶναι, καὶ βασιλεύειν τὸ μὲν νοητοῦ γένους τε καὶ τόπου, τὸ δ᾽ αὖ ὁρατοῦ, ἵνα μὴ οὐρανοῦ εἰπὼν δόξω σοι σοφίζεσθαι περὶ τὸ ὄνομα.

Jowett

You have to imagine, then, that there are two ruling powers, and that one of them is set over the intellectual world, the other over the visible. I do not say heaven, lest you should fancy that I am playing upon the name (οὐρανός, ὁρατός).

Shorey

Conceive then, as we were saying, that there are these two entities, and that one of them is sovereign over the intelligible order and region and the other over the world of the eye-ball, not to say the sky-ball, but let that pass.

Bloom

Well, then, conceive that, as we say, these two things are, and that the one is king of the intelligible class and region, while the other is king of the visible. I don’t say ‘of the heaven’ so as not to seem to you to be playing the sophist with the name.

Bloom has a note explaining what Jowett puts in the text, that there is a similarity – not much of one, it seems to me – between the words for heaven – οὐρανος – and the visible – ὁρατός. The intellectual or intelligible is νοητός, and according to Bloom,

the question is raised, on the basis of the words, as to the relation of the heavens to the intelligible world.

That is a fine question, while perhaps being irrelevant to the question of what Plato has to teach us, since we now have a different understanding of the physical world. Today we have been to the moon, and we may go further; the problem of justice will remain.

Life on Mars

Wonder if he’ll ever know
He’s in the best-selling show
Is there life on Mars?
It’s on America’s tortured brow
That Mickey Mouse has grown up a cow

– David Bowie

In considering last time Socrates’s dismissal of those who thought knowledge, prudence, or thinking was the good, I suggested that “Too much thinking today involves how to get … a few people to go to Mars.” I have gone back to expand on this a bit.

Here is more. A new article is called “Elon Musk Would Rather Spend His Money on Mars than Help People on Earth” (Vanity Fair, October 28, 2021). This cites “Musk Wants to Use Money Democrats Would Tax for Mars Plans” (Bloomberg, October 28, 2021). Apparently Musk could pay $50 billion in taxes over five years, but would rather do something else:

My plan is to use the money to get humanity to Mars and preserve the light of consciousness.

This confirms Musk’s support of what one writer calls “longtermism,”

which emphasizes how our actions affect the very long-term future of the universe – thousands, millions, billions, and even trillions of years from now.

That’s from “Why longtermism is the world’s most dangerous secular credo” (Aeon, 19 October 2021), by Phil Torres, who in Socratic fashion explains the credo with an analogy. The death of Frank Ramsey at age 26 was bad for him, but worse for humanity, who lost out on all that he might have gone on to do. The extinction of humanity would likewise be bad for each of us, but worse for those who never got a chance to be born. Thus (with my bolding),

the longtermist ideology inclines its adherents to take an insouciant attitude towards climate change … Because … it probably isn’t going to compromise our longterm potential over the coming trillions of years … Since realising our potential is the ultimate moral goal for humanity, and since our descendants cannot become posthuman, colonise space and create ~10⁵⁸ people in computer simulations without technologies far more advanced than those around today, failing to develop more technology would itself constitute an existential catastrophe – a failure mode (comparable to Ramsey neglecting his talents by spending his days playing pool and drinking) that Bostrom calls ‘plateauing’.

Bostrom here is Nick Bostrom, the founding director of the Future of Humanity Institute at Oxford. Torres argues that the expection of ever better living through technology is why we have an ecological emergency in the first place.

Behind the extraction and burning of fossil fuels, decimation of ecosystems and extermination of species has been the notion that nature is something to be controlled, subjugated, exploited, vanquished, plundered, transformed, reconfigured and manipulated … This is precisely what we find in Bostrom’s account of existential risks and its associated normative futurology.

Thinking about how to plunder nature can be done well or ill, by its own standards; whether the thinking is good is another question.

It so happens there’s a 2016 film called News from Planet Mars, about the problem of dealing with other people’s shit. I wrote about it in “35th Istanbul Film Festival, 2016, part 3.” I enjoyed the film, but thought it would not be a classic; it was like the work of writers whom Maugham described in Mrs Craddock (1902):

It is a relief sometimes to look away from the bright sun of perfect achievement; and the writers who appealed to their age and not to posterity have by contrast a subtle charm. Undazzled by their splendour, one may discern more easily their individualities and the spirit of their time; they have pleasant qualities not always found among their betters, and there is even a certain pathos in their incomplete success.

The blinding brightness of the sun will figure in the Allegory of the Cave in the next reading, so let us leave that aside for now.

Meanwhile, Lewis Lapham’s response to calamity seems more realistic. This is from “Omens,” Notebook, Harper’s, January, 1998:

Against the siege of dismal prophecy the reading of history provides a reliable defense, and when told that Arab terrorists have been seen on the Brooklyn piers, or that the earth can no longer bear the weight of its population, I take refuge in Edward Gibbon’s pages on ancient Rome or seek the company of Gordon Woods’s observations of the American Revolution.

The attitude bothered me at the time; but Lapham may be describing the likes of Musk and Bostrom when he goes on to say,

even a dim sense of the past suggests that without history we become orphans, deprived of our kinship with a wider self – i.e., with those who have gone before and those who will come after – marooned in a perpetual and therefore terrifying present, easy marks for the quack evangelists and political demagogues who speak only to the mysteries of the eternal now and thus would cheat us of our inheritance.

I defy anybody to claim kinship with future consciousnesses who displays no sense of kinship with those already here. Musk apparently wants somebody to survive, probably himself included; or perhaps he is different from Peter Thiel, who, “As a hedge against the looming apocalypse,”

has taken out New Zealand citizenship and bought a 500-acre estate, despite spending scarcely any time in the country. He helped to bankroll the Seasteading Institute, which aims to create independent, ocean-based communities free from all government control. Like several other tech titans, Thiel is interested in trying to defy the ageing process, and ideally to defeat it altogether. He is particularly associated with the novel field of biology known as parabiosis, which involves experiments in blood transfusion from the young to the old.

That’s David Runciman, “Competition Is for Losers,” London Review of Books, Vol. 43, No. 18 (23 September 2021). Lapham has perspective:

Like the fear that the sun might not come back in the morning, the foretelling of the end of the world is as old as the wind in the trees … usually it turns out that the soothsayers have been misinformed.

Are Musk, Bostrom, and colleagues such soothsayers? Unlike them, it seems, but with Lapham, I do not worry about the extinction of the human species.

The Divided Line

Two classes of visible things, and two classes of knowable or intelligible things, can be conceived as corresponding to four parts of a line. I summarized this metaphor last time under the heading “Potted Plato,” but then said little more. Now I am going to.

After describing the seemingly contrary qualities that will be needed by the philosophical ruler, Socrates recalls (504a)

that by separating out three forms in the soul we figured out what justice, moderation, courage, and wisdom each is.

In short, four things were identified by means of three things. This happens again, when three points of division will give us the four parts of the Divided Line.

Is it coincidence? I received the impression that the leader of our second discussion of this reading thought not, though he wanted somebody else to make the connection explicitly.

Me, I am more concerned with how the notion of an hypothesis determines the division of the intelligible part of the Line. There will be more about hypotheses in the reading after next (the latter part of Book VII). Meanwhile, hypotheses seem like the absolute presuppositions of Collingwood, elaborated on by me most recently in “Nature.” Let us just look at the whole account of the Divided Line (509d–1e) systematically – I’m trusting Bloom to have translated faithfully. The interlocutor is Glaucon, to whom Socrates first describes the division of the Line itself:

Then, take a line cut in two unequal segments, one for the class that is seen, the other for the class that is intellected – and go on and cut each segment in the same ratio.

We thus get four segments, say a, b, c, and d in order, with

Then also

and we could not have such a proportion unless b = c.

Our discussion leader was keen on observing that

• the line is given as already cut in a some ratio;
• this ratio is not of equality.

I can only note that

• the nontriviality of the ratio lends significance to the equality of the two middle segments, b and c;
• in mathematics, when we consider an arbitrary object such as a triangle, we are indifferent to whether the arbiter is ourselves or somebody else.

Socrates continues with the visible section of the Line.

“Now, in terms of relative clarity and obscurity, you’ll have one segment in the visible part for images. I mean by images first shadows, then appearances produced in water and in all close-grained, smooth, bright things, and everything of the sort, if you understand.”

“I do understand.”

“Then in the other segment put that of which this first is the likeness – the animals around us, and everything that grows, and the whole class of artifacts.”

“I put them there,” he said.

“And would you also be willing,” I said, “to say that with respect to truth or lack of it, as the opinable is distinguished from the knowable, so the likeness is distinguished from that of which it is the likeness?”

“I would indeed,” he said.

In the latter part of Book V, the person who confused the likeness for the reality was described as a dreamer who had opinion rather than knowledge (476c–d). Strictly, perhaps, the notion of a likeness, as perhaps seen in a shiny surface, was then and now only a metaphor for how (for example) beautiful things, as being beautiful, are strictly only images; they “participate” (μετέχω) in the beautiful itself (τι αὐτὸ καλὸν).

This is what we turn to next. See how many times the word “hypothesis” or its plural can be highlighted in the remainder of the passage. See also that part c of the Line, explained in terms of mathematics, and labelled by Bloom and by Cornford before him as comprising “mathematical objects,” is concerned not exclusively with these things, but with arts (τέχναι) in general, at least according to the speech near the end that is unusually long for Glaucon (unless we go back to Book II) and is called “most adequate” by Socrates.

“Now, in its turn, consider also how the intelligible section should be cut.”

“How?”

“Like this: in one part of it a soul, using as images the things that were previously imitated, is compelled to investigate on the basis of hypotheses and makes its way not to a beginning (ἀρχή) but to an end (τελευτή); while in the other part it makes its way to a beginning that is free from hypotheses; starting out from hypothesis and without the images used in the other part, by means of forms themselves it makes its inquiry through them.”

“I don’t,” he said, “sufficiently understand what you mean here.”

Can we not yet sufficiently understand? Try this. A “beginning that is free from hypotheses” is more literally an “anhypothetical beginning” (ἀρχὴ ἀνυπόθετος). Plato seems to have coined the adjective, whose usage Liddell and Scott illustrate only with the instance here, the one below, and one in a later philosopher called Philodemus.

Ordinarily we have a beginning somewhere, such as a flat tire or a bag of rice. Be our end to fix the leak or cook the grains, we normally proceed on the hypothesis that the way to reach that end is the way we have always gone. Socrates prefers the example of mathematics, as follows.

“Let’s try again,” I said. “You’ll understand more easily after this introduction. I suppose you know that the men who work in geometry, calculation, and the like treat as known the odd and the even, the figures, three forms of angles, and other things akin to these in each kind of inquiry. These things they make hypotheses and don’t think it worthwhile to give any further account of them to themselves or others, as though they were clear to all. Beginning from them, they go ahead with their exposition of what remains and end consistently at the object toward which their investigation was directed.”

“Most certainly, I know that,” he said.

If the odd and the even are to be understood as hypotheses, so too perhaps the acute, right, and obtuse angle, these all having straight sides; however, in Euclid there are suggestions of angles formed with circles by chords or tangents. In any case, one might have expected grander hypotheses, such as the postulates of Euclid; apparently these were still being developed. If we have those postulates, it is not legitimate to ask why they allow us to use a ruler and compass to draw straight lines and circles; they just do.

“Don’t you also know that they use visible forms besides and make their arguments about them, not thinking about them but about those others that they are like? They make the arguments for the sake of the square itself and the diagonal itself, not for the sake of the diagonal they draw, and likewise with the rest. These things themselves that they mold and draw, of which there are shadows and images in water, they now use as images, seeking to see those things themselves, that one can see in no other way than with thought.”

“What you say is true,” he said.

This seems clear enough. Greek geometry makes essential use of diagrams. The diagram is a particular visible object. It could lie in a surface, where it could be the image or shadow of a solid construction; it could be that construction itself.

By some mysterious process, we can use a particular diagram to draw conclusions about all diagrams of the same form – or rather about some ethereal diagram that cannot actually be drawn or constructed.

“Well, then, this is the form I said was intelligible. However, a soul in investigating it is compelled to use hypotheses, and does not go to a beginning because it is unable to step out above the hypotheses. And it uses as images those very things of which images are made by the things below, and in comparison with which they are opined to be clear and are given honor.”

“I understand,” he said, “that you mean what falls under geometry and its kindred arts.”

That much seems to repeat what was already said. Now we go further, into dialectic.

“Well, then, go on to understand that by the other segment of the intelligible I mean that which argument itself (αὐτὸς ὁ λόγος) grasps with the power of dialectic (ἡ τοῦ διαλέγεσθαι δυνάμις), making the hypotheses not beginnings but really hypotheses – that is, steppingstones and springboards (ἐπιβάσεις τε καὶ ὁρμάς) – in order to reach what is free from hypothesis (ἀνυποθέτος) at the beginning of the whole. When it has grasped this, argument now depends on that which depends on this beginning and in such fashion goes back down again to an end; making no use of anything sensed in any way, but using forms themselves, going through forms to forms, it ends in forms too.”

“Dialectic” here is really a verbal noun: “talking [things] through.” We can always in principle step back, question, and talk about what we are doing, be it studying mathematics or preparing a meal. We may refer to this stepping back as philosophy, and there are additional relevant words from Wilfrid Hodges in “An Editor Recalls Some Hopeless Papers,” which I made use of for the latter part of Book I:

In English-speaking philosophy (and much European philosophy too) you are taught not to take anything on trust, particularly if it seems obvious and undeniable. You are also taught to criticise anything said by earlier philosophers. Mathematics is not like that; one has to accept some facts as given and not up for argument.

Might Hodges have said more simply that mathematics is not at the far end of the Divided Line?

Socrates’s concluding discussion of “forms” may be obscure:

εἴδεσιν αὐτοῖς δι᾽ αὐτῶν εἰς αὐτά, καὶ τελευτᾷ εἰς εἴδη.
by-forms themselves through them into them and ends in forms.

Shorey’s down-to-earth note on this alludes to an academic conflict:

The description undoubtedly applies to a metaphysical philosophy that deduces all things from a transcendent first principle. I have never denied that. The point of my interpretation is that it also describes the method which distinguishes the dialectician as such from the man of science, and that this distinction is for practical and educational purposes the chief result of the discussion, as Plato virtually says in the next few lines.

Here are those next few lines, in which Glaucon makes his speech.

“I understand,” he said, “although not adequately – for in my opinion it’s an enormous task you speak of – that you wish to distinguish that part of what is and is intelligible contemplated by the knowledge of dialectic as being clearer than that part contemplated by what are called the arts. The beginnings in the arts are hypotheses; and although those who behold their objects are compelled to do so with the thought and not the senses, these men – because they don’t consider them by going up to a beginning, but rather on the basis of hypotheses – these men, in my opinion, don’t possess intelligence with respect to the objects, even though they are, given a beginning, intelligible; and you seem to me to call the habit of geometers and their likes thought (διάνοια) and not intelligence (νοῦς), indicating that thought is something between opinion and intelligence.”

It is not obvious to me that Socrates has been working out a technical vocabulary. Glaucon may be recognizing that, as a word, διάνοια comes from νοῦς.

“You have made a most adequate exposition,” I said. “And, along with me, take these four affections arising in the soul in relation to the four segments: intellection (νόησις) in relation to the highest one, and thought (διάνοια) in relation to the second; to the third assign trust (πίστις), and to the last imagination (εἰκασία). Arrange them in a proportion, and believe that as the segments to which they correspond participate in truth, so they participate in clarity.”

“I understand,” he said. “And I agree and arrange them as you say.”

It is appealing to have a diagram of everything, labelled with the four Greek words just distinguished. It can make you think you understand something. As Bloom says,

The divided line is a sketch of a cosmos which can give ground to the aspirations of the philosophic soul. The splendor of this vision is meant to dazzle the mind’s eye as the sun dazzles the body’s eye.

I have been avoiding Bloom’s commentary, but I looked at it here to see if he made a connection between hypotheses and what Cephalus thinks about justice, or what primitive humans do in founding a city. He doesn’t seem to make it.

Convention

I suggested last time that Thrasymachus had tried to free himself from all conventional hypotheses about what the good life was. Or perhaps there are not several such hypotheses, but only one, namely that the good life is the just life; but Cephalus and his son Polemarchus have trouble articulating what justice is, at least when they are talking to Socrates. Thrasymachus does too, but makes the novel proposal that the good life is the unjust life.

Glaucon continues the argument in Book II, saying at 358e–9b, in Shorey’s translation,

By nature, they say, to commit injustice is a good
and to suffer it is an evil,
but that the excess of evil in being wronged is greater
than the excess of good in doing wrong.
So that when men do wrong and are wronged by one another and taste of both,
those who lack the power to avoid the one and take the other
determine that it is for their profit to make a compact with one another
neither to commit nor to suffer injustice;
and that this is the beginning of legislation and covenants between men,
and that they name the commandment of the law the lawful and the just,
and that this is the genesis and essential nature of justice –
a compromise between the best,
which is to do wrong with impunity,
and the worst,
which is to be wronged and be impotent to get one’s revenge.

πεφυκέναι γὰρ δή φασιν τὸ μὲν ἀδικεῖν ἀγαθόν,
τὸ δὲ ἀδικεῖσθαι κακόν,
πλέονι δὲ κακῷ ὑπερβάλλειν τὸ ἀδικεῖσθαι
ἢ ἀγαθῷ τὸ ἀδικεῖν,
ὥστ᾽ ἐπειδὰν ἀλλήλους ἀδικῶσί τε καὶ ἀδικῶνται καὶ ἀμφοτέρων γεύωνται,
τοῖς μὴ δυναμένοις τὸ μὲν ἐκφεύγειν τὸ δὲ αἱρεῖν
δοκεῖ λυσιτελεῖν συνθέσθαι ἀλλήλοις
μήτ᾽ ἀδικεῖν μήτ᾽ ἀδικεῖσθαι:
καὶ ἐντεῦθεν δὴ ἄρξασθαι νόμους τίθεσθαι καὶ συνθήκας αὑτῶν,
καὶ ὀνομάσαι τὸ ὑπὸ τοῦ νόμου ἐπίταγμα νόμιμόν τε καὶ δίκαιον:
καὶ εἶναι δὴ ταύτην γένεσίν τε καὶ οὐσίαν δικαιοσύνης,
μεταξὺ οὖσαν τοῦ μὲν ἀρίστου ὄντος,
ἐὰν ἀδικῶν μὴ διδῷ δίκην,
τοῦ δὲ κακίστου,
ἐὰν ἀδικούμενος τιμωρεῖσθαι ἀδύνατος ᾖ:

The question now is whether a convention or contract or compact against injustice is anything like the hypotheses that Socrates talks about towards the end of our present reading, as at 511b–c. We saw it in Bloom’s translation; here’s Shorey’s:

Understand then, that by the other section of the intelligible I mean that which the reason itself lays hold of by the power of dialectics, treating its assumptions not as absolute beginnings but literally as hypotheses, underpinnings, footings, and springboards so to speak, to enable it to rise to that which requires no assumption and is the starting-point of all, and after attaining to that again taking hold of the first dependencies from it, so to proceed downward to the conclusion, making no use whatever of any object of sense but only of pure ideas moving on through ideas to ideas and ending with ideas.

Shorey gives the passage seven footnotes, one of which is to the phrase “literally as hypotheses” (τῷ ὄντι ὑποθέσεις), which

emphasizes the etymological meaning of the word … the thing to note is that the word according to the context may emphasize the arbitrariness of an assumption or the fact that it is the starting-point – ἀρχή – of the inquiry.

I have corrected two typos in the Perseus Project rendition of the note. Shorey’s Index of Subjects refers, under Hypotheses, only to that note.

Bloom’s Subject Index has no entry either for convention or for hypothesis. When I search the epub file of his book, I find “hypothesis” or “hypotheses” in the text of the Republic only at 510b–1d (in our current reading) and 533b–c. Bloom’s note on the first use is,

An hypothesis is, literally, “a placing under,” and should perhaps be rendered as “supposition” (cf. Meno, 86 ff., and Phaedo, 99d ff.).

In his commentary on 543a–69c, Bloom will refer to “the hypothesis of the dialogue, according to which the city is the soul writ large.” That’s it for Bloom on hypothesis.

Bloom’s Subject Index has an entry for Compact, which leads only to 359a–b, quoted above, where the Greek is middle-passive aorist infinitive συνθέσθαι of the verb συντίθημι.

In that same index, the headword “Contract” is followed by a parenthetical symbolē, although in Shorey’s Loeb text, συμβολή does not occur, but in almost every cited passage, the word is ξυμβόλαιον – or if it is a verb, συμβάλλειν, as noted below. I going to go through all of the instances that we have seen so far, without trying to draw any conclusions for now.

Book I (first part), 333a

Polemarchus says that, in peacetime, justice is good for contracts; Socrates proposes (and Polemarchus agrees) to call these partnerships (τὸ κοινώνημα).

Book I (second part), 343d

Thrasymachus says that in any contracts that the just and unjust man undertake together, the latter has the advantage when the partnership (ἡ κοινωνία) is dissolved.

Book II, 362b

Glaucon describes how the unjust man who seems just “contracts and has partnerships with whomever he wants” (συμβάλλειν, κοινωνεῖν οἷς ἂν ἐθέλῃ).

Book IV

• The completion of the city with Adeimantus.

  424b–d

  Socrates says, “there must be no innovation in gymnastic and music,” and Adeimantus agrees, lest

  establishing itself bit by bit, [lawlessness] flows gently beneath the surface into the dispositions and practices, and from there it emerges bigger in men’s contracts with one another; and it’s from the contracts, Socrates, that it attacks laws and regimes with much insolence until it finally subverts everything private and public.

  425c–425d

  Socrates asks Adeimantus,

  what about that market business – the contracts individuals make with one another in the market, and, if you wish, contracts with manual artisans …

  Adeimantus replies, “It isn’t worth-while to dictate to gentlemen. Most of these things that need legislation they will, no doubt, easily find for themselves.”

  426d–e

  If however the city does not get the right laws, it will be like the sick man who refuses good advice; of the statesmen of such a city, Socrates says,

  such men are surely the most charming of all, setting down laws like the ones we described a moment ago and correcting them, always thinking they’ll find some limit to wrongdoing in contracts and the other things I was just talking about, ignorant that they are really cutting off the heads of a Hydra.

• In the search for justice with Glaucon, 443c–e, Socrates says of the just man that he “harmonizes the three parts” in his soul, and

  if there are some other parts in between, he binds them together and becomes entirely one from many, moderate and harmonized. Then, and only then, he acts, if he does act in some way – either concerning the acquisition of money, or the care of the body, or something political, or concerning private contracts. In all these actions he believes and names a just and fine action one that preserves and helps to produce this condition, and wisdom the knowledge that supervises this action …

The remaining two references, 554c and 556b, are still to come.