Thanks for your kind comments. It seems to be a pattern that the people with the strongest (negative) emotional responses to my paper have not read it properly. I'm not sure whether they read poorly because they are already upset over what is clearly a very emotive issue for many (for whatever reason) or are upset because they misunderstood what they read. Perhaps it's a combination.

I can only answer for myself, but I explicitly and repeatedly point out in my paper that Valens uses moirikos 'by degree' in several ways, and that he could, hypothetically, be talking about equal houses in some places. But I do find it less of a stretch of the imagination (more parsimonious, in the academic phrase) to assume until otherwise proved that he was consistent in preferring one house system.

The idea of a 'sign-based MC placement' (which I understand to mean a whole-sign house other than the 10th, in which the MC is 'floating') does not occur, as far as I have seen, in Valens, nor have I seen it in any other classical source. Until I do, I will assume that it is a modern invention.

"Until I do, I will assume that it is a modern invention."

I hope everyone pauses over that remark.
No entrenched position here. No declaration of refusing to be persuaded otherwise or denying the possibility, or hating the very idea of it. Just an intelligent stance of wanting to see some actual evidence first.

Martin

Let me publicly congratulate you on having your paper published. It was very illuminating for me in many respects. I also find it particularly helpful that it was published under open access: as every potential reader may access it, an open discussion about your evidence, arguments, and conclusions is not hindered by availability barriers.

If I may, I would like to start such an open discussion, sharing my most pressing concerns with you and anyone who has read your paper thoroughly and is interested in discussing it. For this discussion, I would like to invite all attentive readers, especially but not exclusively those with a favorable opinion of your paper. Mark, please accept my special invitation.

I will have several direct questions, and so that we can keep track of them, I mark the ones to you as AQ (author questions) and the ones to the readers willing to participate as RQ (reader questions).

1/16 Your two hermeneutic principles

You state (p. 4) that your reading of your source texts “rests on two partly related hermeneutic principles???: giving preference to “an internally coherent model providing an explanation for all statements on a given topic in a single-author work??? and considering the possibly infrequent but “more detailed and explicit statements by an author??? not as “aberrations??? but something more significant than the less detailed statements.

I agree that these principles are, at least provisionally, reasonable. However, I perceive there are quite a few potential issues with Hellenistic astrological texts in general and with the primary source of your observations, Valens’s Anthologies, in particular. First, what we have of the Anthologies is contained in three incomplete manuscripts, MVv: the earliest of them, V, was copied in the 13th century, some 900 years after Valens’s lifetime; also, a considerable portion of the text is found only in S, a 16th-century, arguably deficient apograph of the now damaged V. As a consequence of the highly imperfect transmission, the text is in poor condition: the beginning and the end of the Anthologies are missing, and so are tables and portions of the text; a few passages are duplicated in the wrong place; and there are some demonstrable insertions like marginal notes and chapter headings. Book IX, extant in S but actually not designated as “Book IX??? there, is a disorganized collection of chapters, which often belong to different parts of the eight books. Many emendations and corrections are needed to make the text sound grammatically correct and meaningful. It is impossible to spot all the corruptions, so suspicion is justified even if a passage sounds fine. Second, the text available to us was arguably updated no earlier than 249, about 60 or 70 years after Valens wrote the latest datable portions of the Anthologies, and it was supplemented after 455 or even 504; the extent of the introduced modifications is hard, if not impossible, to assess.

On the other hand, it is apparent that Valens had different ideas of consistency than we do. For example, in III 11,4, he proposes an idiosyncratic solution to calculate the Lot of Fortune for nocturnal nativities, which he then never uses. Or, there is a nativity that he uses four times, which is calculated with degree-and-minute precision for the planets and degree precision for the ascendant and midheaven in III 5,6–10 (I will return to this in sections 8 and 10 below), but in VIII 8,14–26, he gives different positions for the ascendant and the Sun; and whereas in III 11,14–16, he calculates its Lot of Fortune by sign to be in Cancer and uses it accordingly, in IV 8,1–24, he calculates it probably by degree so that it will be in Leo—and uses it accordingly. There are more examples like this. Also, in addition to the issues with consistency, Valens’s professional honesty is no less a matter, as the evidence collected in Cristian Tolsa’s paper (pp. 412–414 and p. 400 with reference to Otto Neugebauer’s A History of Ancient Mathematical Astronomy) indicates.

In light of these circumstances—the poor state of Valens’s text and the issues with his consistency and honesty—I think it is hardly reasonable to uphold your hermeneutic principles in their original, rigorous form. AQ1: Do you find these circumstances relevant when analyzing the various passages from Valens? RQ1: Do you find these circumstances—the poor state of Valens’s text and the issues with his consistency and honesty—relevant when you assess the information given by Valens?

2/16 Your interpretation of πλατικός platikos

Throughout your paper, you consistently translate the adjective πλατικός platikos as “rough.??? I understand platikos, deriving from πλάτος platos, “breath??? or “width,??? means something like “broad,??? “general,??? “overall,??? or “summary??? in the sense of “not narrow, particular, focused, or detailed??? but not “rough??? in the sense of “inexact, imprecise, inaccurate, or approximate??? and thus “inferior to the exact, precise, or accurate.??? In fact, “rough??? is not found among the recorded lexical meanings—neither in the Liddell-Scott-Jones lexicon nor, as far as I know, anywhere else, including ancient lexicographers—and is not warranted by etymological analysis either. Despite all this, it would be possible to argue that Valens, who uses this adjective and its adverbial form 9 times, or Firmicus, in whom its adverbial form appears 12 times as a Greek quasi-technical term instead of a fitting Latin expression, meant platikos in the sense of “rough??? indeed, provided that the illuminating occurrences in these two authors are surveyed. Yet, this does not happen in your paper, although in relation to the word δωδεκατημό??ιον d??dekatēmorion, you emphasize—very rightly, I believe—that “the meaning of the word must be determined, as far as possible, from the context in each case??? (p. 20 n. 38 ). Instead, you provide analyses of Valens’s and Firmicus’s statements exclusively in accordance with your unverified presumption that platikos means “rough??? in the sense of “approximate??? and so “inaccurate.???

As this interpretation fundamentally determines your approach to the subject you investigate, I hardly think it is a trivial issue. AQ2: Do you think that a proper lexical analysis of platikos in Valens and Firmicus is needed to justify its interpretation as “rough???? RQ2: Do you find knowing the precise meaning of platikos in Valens and Firmicus relevant to the understanding of the intentions of these authors? If you do, do you think that Dr. Gansten presented you with the relevant evidence to justify his choice of translating and interpreting platikos as “rough????

3/16 Your relativization of the meaning of ζῴδιον z??dion – Ptolemy

On pp. 15–16, you hypothesize that the word “sign??? (ζῴδιον z??dion) originally had an alternative meaning: one of the 30-degree segments beginning with the ascendant, which is practically what we would call an equal place. As confirming evidence, you rely on two testimonies, one from Valens and another—an entire chapter—from Firmicus. On pp. 19–20, you also import Ptolemy, Apotelesmatics III 11,3 into the argumentation, but as in this text, “twelfth-part??? (δωδεκατημό??ιον d??dekatēmorion), a demonstrably polysemous and flexible term—in Apotelesmatics I 22,1, also meaning a two-and-half-degree segment of a sign—and not z??dion is used, I do not think it can prove or disprove your hypothesis in any ways. Ptolemy, Apotelesmatics I 13,2–3, which you cite on p. 20 with the concession that it and similar—but unreferenced—occurrences are “more open to interpretation,??? appears even less relevant as evidence.

Since I do not see how these passages from Ptolemy are relevant to determining whether z??dion had an alternative meaning, I do not understand their presence here. AQ3: Do you find Ptolemy’s passages using d??dekatēmorion relevant to determining whether z??dion had an alternative meaning? RQ3: Is it apparent to you that on pp. 19–20, in the middle of the argumentation about the possible alternative meaning of z??dion, passages using d??dekatēmorion and not z??dion are cited and discussed? If it is, do you find these passages relevant to determining whether z??dion had an alternative meaning?

4/16 Your relativization of the meaning of ζῴδιον z??dion – Valens

Your first real evidence is Valens IX 3,21–25, cited on p. 17. Your translation says, “count from that same degree [i.e., the degree of the ascendant—LL] up to the completion of a thirty-degree [arc], the subsequent sign,??? and you conclude (pp. 17–18 ), “we have here an explicit reference to a sign […] as a unit of thirty degrees […] measured […] from the rising degree.??? In p. 17 n. 29, the tone is less confident: following the suggestion of a reviewer, you allow that the translation “[…] up to the completion of [the] thirty-degree [arc] of the subsequent sign??? is also viable; still, you relegate this concession into a footnote. RQ4: When you read Dr. Gansten’s paper, did you notice that this alternative translation is no less plausible than his preferred interpretation? However, you reject this alternative interpretation for two reasons: one, because it would require the insertion of a definite article, and two, by appealing to the supporting evidence of Firmicus (your other evidence, which I will revise in section 5 below) and, to a lesser degree, of Ptolemy (the relevancy of which, as I showed it in section 3 above, is questionable).

Valens IX 3,21–25, extant only in S, is a paragraph of merely 12 Teubner lines, the end of which—as you also acknowledge in p. 17 n. 31—is corrupt. Only in this short paragraph, the first modern editor, Wilhelm Kroll, had to employ four corrections to make the text grammatically correct and meaningful, one of which corrections is precisely an insertion of a definite article. (This is unmarked in the translation; actually, it corresponds to what is rendered as “their??? in “according to their extensions in degrees.??? The other insertion, of a preposition, into the next sentence is duly marked.) Consequently, the lack of a definite article may well be explained by textual corruption here as well. However, I do not think such a definite article is even necessary: a verbatim translation of the text as “[…] up to the completion of a thirty-degree [arc] of the subsequent sign??? in the sense of “[…] up to the completion of a thirty-degree arc, whose completion belongs to the subsequent sign??? is also meaningful.

Also, your interpretation raises a number of questions. If, in accordance with your understanding, z??dion means practically “equal place??? in this paragraph, then Valens’s instructions may be paraphrased as “count from the degree of the ascendant up to the completion of thirty-degree arc, which is the subsequent equal place.??? Honestly, I do not understand what the first equal place can be subsequent to. AQ4: In light of your interpretation, what does “subsequent??? (ἑξῆς hexēs) mean here? Also, a paraphrasis of the continuation would sound like this: “As two places fall together in one equal place, they reveal the specific meanings of both places […] You must also consider in what equal place the ruler of the equal place falls and what place it rules […] And if platicly (roughly? or rather, in the summary manner?) one place is considered for each equal place […]??? For me, the text loses its sense, and the sentences remain meaningful only if we retain the meaning of z??dion unambiguously as “sign.???

All in all, I do not think that your proposed modification of meaning offers a viable alternative to the interpretation of z??dion just as “sign??? (like Aries, Taurus, etc.). AQ5: Do you think, with your proposed alternative interpretation, this paragraph still makes sense? If you do, could you explain their meaning? RQ5: Do you think, with Dr. Gansten’s proposed alternative interpretation, this paragraph still makes sense?

5/16 Your relativization of the meaning of ζῴδιον z??dion – Firmicus

As your other evidence, you refer to Firmicus’s Mathesis—specifically, to its II 19—where he “offers a description of the twelve places in which signum [“sign,??? the Latin equivalent of Greek ζῴδιον z??dion—LL] alternates repeatedly [emphasis added—LL] with locus [“place,??? the Latin equivalent of Greek τόπος topos—LL]??? (p. 18 ). It is a description of the equal places, “in which the words ‘place’ (locus) and ‘sign’ (signum) are used interchangeably of such thirty-degree segments, and of which it is enough to quote one [emphasis added—LL]??? (p. 19)—the translation of the entry for the 6th equal place (II 19,7) follows, in which the word signo, “sign,??? stands indeed where one would expect loco, “place.??? RQ6 (please answer this question before reading on): In light of the phrases highlighted in the quotations from Dr. Gansten—“alternates repeatedly??? and “enough to quote one???—how many occurrences do you expect?

Actually, the passage cited on p. 19 is the only unquestionable one. There may be one more occurrence, the same type of anomaly for the 2nd equal place (II 19,3), only if the correct reading preserved in manuscript N (but not in PR) is rejected as a later correction. (This reading is approved in the Kroll–Skutsch–Ziegler edition and dismissed in the Monat edition, so there is no scholarly agreement on this issue, which is barely decidable indeed.) AQ6: Do you think that by writing “alternates repeatedly??? and “enough to quote one,??? you represent the attested frequency of this anomaly to your readers properly? RQ7: Do you think that by writing “alternates repeatedly??? and “enough to quote one,??? Dr. Gansten represents the attested frequency of this anomaly properly?

There is another issue, which you do not take into consideration. In all the three surviving manuscripts NPR, the entry for the 2nd equal place begins as (II 19,3; emphases added) “The second place from the ascendant is established in the second place??? (secundus ab horoscopo locus in secondo loco constituitur). Since this sentence is obviously corrupt, the first modern editor of the Mathesis, Karl Sittl, emended loco to signo, “[…] in the second sign,??? which is approved in both later editions. (The same error occurs in manuscript M for the 9th equal place, but of course, here the editors unanimously followed the correct majority reading of NPR.) Therefore, as the suspicious presence of “sign??? for “place??? is also attested in the inverse direction as “place??? for “sign,??? a pervasive textual corruption affecting the whole chapter—perhaps due to the ambiguous abbreviations of loco and signo in the archetype—seems to be a plausible explanation.

AQ7: Do you find the apparent corruption of signo to loco in II 19,3 relevant to determining whether the reading signo in II 19,7 is merely an error or it is evidence supporting your hypothesis? RQ8: Do you find the apparent corruption of signo to loco in II 19,3 relevant to determining whether the reading signo in II 19,7 is merely an error or it is evidence supporting Dr. Gansten’s hypothesis?

6/16 Your portrayal of the evidence where ζῴδιον z??dion stands for τόπος topos

In light of sections 3–5, the proof of your hypothesis about the alternative meaning of z??dion/signum as “equal place??? is based (1) on a very specific interpretation of the syntactic value of a word in Valens IX 3,21, which is not more plausible than the other, not supporting, interpretation; (2) on one word in Firmicus, Mathesis II 19,7 (and possibly in II 19,3), which may be the result of textual corruption; and (3) the use of d??dekatēmorion in Ptolemy, Apotelesmatics III 11,3–4, which is hardly relevant. However, this hypothesis serves as your means to make it possible that the sources where (pp. 12–13) “the places are sometimes [emphasis added—LL] explicitly referred to as ‘signs’ (ζῴδιον z??dion; Latin signum)??? can be dismissed as irrelevant in determining whether whole signs constituted (p. 12) “the standard system of places […] in the full normative sense.??? In p. 13 n. 25, you refer to Stephan Heilen’s Hadriani genitura, 691ff. as “an extensive if not exhaustive [emphasis added—LL] list??? of these references, and on p. 13, you allow that “[f]rom time to time [emphasis added—LL], Valens, too, conforms to this pattern???—a translation of Valens IV 11,49 follows, for which you explain the use of “effective signs??? (χ??ηματιστικὰ ζῴδια chrēmatistika z??dia) and cognate expressions with the specific context (p. 13 n. 23). RQ9 (please answer these questions before reading on): In the quotations from Dr. Gansten, how many references does the word “sometimes??? suggest to you? Does the phrase “if not exhaustive??? suggest to you that Heilen’s list is exhaustive or that it is not? And how many occurrences in Valens does the expression “from time to time??? suggest to you?

Actually, in Heilen’s list, 14 author names—many of whom are known only from their fragments—are included in a single sentence that finishes with “and so forth??? (“und so weiter???); references to three more authors and four Demotic ostraca are added subsequently. In Heilen’s footnotes for Dorotheus, Valens, and Ptolemy, the abbreviation “e.g.??? (“z.B.???) strongly suggests that the quoted occurrences constitute only a selection. All in all, Heilen’s list—which includes many authors in which no awareness of equal or quadrant houses is attested and no ambiguity in the meaning of the word “sign??? has been recorded—cannot be exhaustive. In fact, if we confine our search only to Valens’s use of the phrase “effective signs??? (χ??ηματιστικὰ/χ??ηματίζοντα ζῴδια chrēmatistika/chrēmatizonta z??dia), we will find 31 occurrences (including Valens IV 11,49, cited on p. 13) appearing in various contexts in every book except for Books VI and VIII. AQ8: Do you think that your portrayal of this issue on pp. 12–13, including the presented range of evidence and the expressions by which you describe them, allows your readers to evaluate the extent of the use of the word “sign??? in the sense of “place??? objectively? RQ10: Do you think that Dr. Gansten’s portrayal of this issue on pp. 12–13, including the presented range of evidence and the expressions by which he describes them, allows you to evaluate the extent of the use of the word “sign??? in the sense of “place??? objectively?

7/16 Your portrayal of the definitions of the whole-sign places

On p. 12, you state, “whole-sign places are never formally defined in the surviving ancient manuals of astrology.??? I find this statement vague, restrictive, and not even true. I do not know what you mean by “formal definition,??? but for me, a definition in an astrological text has already done its job once it makes clear what the definiendum is. (I guess you probably recycle the phrase “formal definitions??? from p. 1 of my essay, but I no longer maintain the view I expressed there.) AQ9: What do you mean by “formal definition????

Also, I have the feeling that by carefully choosing your phrase “ancient manuals of astrology,??? you gave yourself the possibility to relegate the evidence provided by Sextus Empiricus (not an author of a manual of astrology) and Of the Celestial Disposition (a manual of astrology, but perhaps not an ancient one) into a footnote (p. 12 n. 21) and then disregard it without evaluation. To be honest, I do not even know what exactly you mean by “ancient??? here and elsewhere. I presume it refers to the historical period ending around 500 CE, but I cannot see how it is a proper descriptor for the history of astrology, which acquired a distinctive form in the Hellenistic period and developed without external influence until about 800 CE. AQ10: What do you mean by “ancient????

Even more ignored is the 14th-century Isaac Argyrus, the likely figure behind “Olympiodorus??? in your quotation from Dorian Greenbaum in p. 21 n. 41 (which mention you leave uncommented): although his testimony (p. 75 ll. 25–27 Boer) is rather unambiguous—“some define the very sign whose degree is found to be in the ascendant or the midheaven as a whole place??? (οἱ μὲν γὰ?? τὸ ζῴδιον α???τό, οὗ ἡ μοῖ??α εὑ??ίσκεται ὡ??οσκοποῦσα ἢ μεσου??ανοῦσα, τόπον ὅλον ἀποφαίνονται)—you do not find it worthy of mentioning.

I believe evidence is evidence, no matter whether it is provided by an outsider or an inconveniently late source. I agree that it must be dismissed if it proves to be wrong, but I find no attempt of yours to discredit this group of evidence with arguments. AQ11: What are your reasons for dismissing the testimonies of Sextus Empiricus, Of the Celestial Disposition, and Isaac Argyrus? RQ11: Do you find the testimonies of Sextus Empiricus, Of the Celestial Disposition, and Isaac Argyrus important?

Apart from these, we can demonstrably find statements in “ancient manuals of astrology??? that show their authors’ awareness of whole-sign places or may even be considered to be definitions. A passing remark from Valens—IX 3,25, cited on p. 17: “if roughly [or rather, in the summary manner?—LL] one place is calculated for each sign […]???—belongs to the first group. Concerning this, I would add that Valens’s—and Manilius’s—alternative place system based on the Lot of Fortune also follows whole-sign considerations; you mention this nowhere.

To the second group belongs Firmicus, whose II 14–18 is a detailed description of the twelve places according to their platic (rough? or rather, general?) definition as signs. In this description (II 17), he even says that the “idle and dejected??? (pigra et deiecta) places are so designated because they are unconfigured with the ascendant. Suppose the platic method was simply a primitive, rough approximation; in that case, he could have just said that and detailed the angles and the good and bad places in the context of the equal division, where the logic of differentiating the good and bad places by their being configured or unconfigured with the ascendant remained equally valid. Instead, he devotes a few pages to describing the whole-sign places, and he even seems to use them, not the equal places, in his example nativity in II 29. (More about this in section 9 below.)

We also have the testimony of Paulus of Alexandria. In his Chapter 24, a detailed description of the places, he refers to them as signs about 6 times, and there is one more instance in the next chapter. In light of this, the elliptic beginnings of his entries for places 2 to 12—for example, p. 54 l. 15 Boer, “the second [noun missing] from the ascendant […]??? (τὸ δὲ δε??τε??ον ἀπὸ ὡ??οσκόπου […])—where a neuter noun is expected, must also refer to signs. Paulus’s whole-sign perspective is made even more explicit in Olympiodorus’s lectures on him.

Even though, as I believe, these are important and very relevant sources, you not only disregard them but not even mention them. AQ12: Do you think that the testimonies of Firmicus and Paulus count as evidence? RQ12: Do you think Dr. Gansten presents you with full evidence for definitions of whole-sign places—including whole-sign places based on the Lot of Fortune—so that you can form an independent opinion of their role in Hellenistic astrology?

8/16 The missing analysis of the horoscopic evidence – the calculation of basic horoscopes in Valens

Although you have some passing remarks on the horoscopic evidence in Valens and elsewhere, and you also cite a few horoscopes, you provide analyses only for ones by which you intend to confirm your theses (pp. 27, 31–32, 36, 37). When it comes to the questions of how the basic horoscopes were calculated—whether only by sign or by degree—and what place division method was employed in them, you only allude to your doubts—p. 5: “they do not preclude other methods [than whole-sign places—LL]???; p. 7: “not precluding measurement by degree???—and later, you keep repeating your assumptions—p. 23, emphasis added: “calculations by degree at least occasionally – and possibly often – underlie even examples where those degrees are not explicitly listed???; p. 32: “assuming that horoscopes listing only sign positions are necessarily evidence of a whole-sign-place system would clearly be precipitate, not to say misleading???; p. 37, emphasis added: “[w]hat looks like a ‘basic horoscope’ – a list or diagram of mere sign positions – may thus be based on tacit calculation by degree???; pp. 39–40: “the ancient practice of equating the zodiacal signs with the twelve places, at least provisionally [emphasis added—LL], is strongly corroborated by many examples from the Anthologies???—which you do not attempt to prove. AQ13: Do you think these assumptions would require proof, or if proof is not possible, the indication of this impossibility? RQ13: Do you think these assumptions would require proof, or if proof is not possible, the indication of this impossibility?

Let us first see whether Valens’s basic horoscopes were calculated originally just by sign, or they were calculated originally by degree but were then presented in a simplified basic format. This dilemma can be decided to a certain degree of confidence by examining the positions of the lots. As Valens says in the text cited on p. 36, sometimes a lot by sign falls in one sign but by degree, in another. For a single lot, this must happen in about 30% of the possible cases, but for two lots, the chance is about 60%. (The exact frequency depends on subjectively chosen initial conditions.)

Valens has 30 horoscopes employing only the Lot of Fortune (occasionally together with its derivations) and 21 more horoscopes with both the Lot of Fortune and Daimon. If you had investigated these horoscopes, you would have found that of the 21 horoscopes having the two lots, a single one shows any discrepancy. I already mentioned this in section 1 above: it uses counting by sign in Book III and, apparently, a calculation by degree in Book IV. On the other hand, of the 30 ones with the Lot of Fortune alone, 3 horoscopes show any deviation. The one in VII 4,11–15 is possibly due to textual corruption: the position of the Lot of Fortune does not matter in the interpretation, and the sign of the Moon, Pisces, may have been dropped from the list. There remain two horoscopes, in II 37,48–51 (which you cite on p. 37) and II 41,47–50. In both these horoscopes—and also in the third one, which calculates two Lots of Fortune in two different contexts—the Lot of Fortune has a prominent role in the interpretation.

So, we have a case in which the Lot of Fortune is counted both by sign and degree, and both versions are used in the interpretation, and we also have two instances where only a calculation by degree seems to provide the wished results. This feature, together with the lower-than-expected discrepancy in Valens’s horoscopic examples, suggests to me that Valens’s usual routine was casting horoscopes only by the platic method, but whenever he thought it was necessary, he employed calculations by degree, which may act as an alternative but not necessarily a replacement of results obtained via counting by sign. Actually, I would find an investigation to answer this very question, under what circumstances did Valens consider calculations—of planets, lots, and possibly places—by degree necessary? much more interesting than speculations about his possibly imaginary favored methods.

AQ14: Do you think these investigations would have been relevant to deciding how Valens’s basic horoscopes were calculated? RQ14: Do you think Dr. Gansten provides you with sufficient horoscopic data from Valens to enable you to independently determine, no matter how conclusively, how Valens’s basic horoscopes were calculated?

A minor point: on p. 36, you say, “with regard to lots, Valens repeatedly stresses the importance of considering degrees.??? RQ15 (please answer this question before reading on): How many occurrences does the expression “repeatedly??? suggest to you? Actually, the text you cite on p. 36 is the only instance of such an explicit statement. In the attested three (or four) verifiable occurrences of degree-precise calculations of lots in his example horoscopes, he deviates from his likely routine without notice.

9/16 The missing analysis of the horoscopic evidence – the attested place division methods in Valens’s basic horoscopes

Although the places are referred to in dozens of horoscopic examples—Valens providing more than half of them—dated earlier than the 5th century, the vast majority consists of basic horoscopes. At first sight, it seems impossible to reach any conclusion from them regarding the place division method used. However, there is one investigation that offers some insights, even if not fully conclusively: since with the equal and quadrant methods, the place cusps nearly always divide the signs, we would expect that two planets being in the same sign should often fall in two different places. We would especially anticipate seeing this feature if more than two planets are found in the same sign, or if two or more signs have two or more planets in them.

Valens has about 44 basic and semi-basic horoscopes where he explicitly refers to the places occupied by planets or lots. (By “semi-basic,??? I mean horoscopes with partial references to degrees. In the full horoscopes, these references appear—twice, of which one is relevant here—only in the form “planet P is at the beginning of sign S,??? suggesting the use of entry tables for calculation. Degree-precise data are available only if a horoscope reappears—always in an incomplete form—for various calculation exercises in Books I and VIII, and there is a reference to Venus being precisely in the ascendant in a horoscope, probably Critodemus’s, in II 22,36–37.) Apart from two horoscopic examples that I will return to in sections 11–12 below, the place-positions in them always conform with what we would expect by using the whole-sign method. However, within this pool of 44 horoscopes, we also find about 12 ones where two planets are said to be in the same place and about 6 more ones in which three planets are said to be in the same place, or two places are said to have two planets in each of them. As in these ca. 18 cases, we still see no discrepancy from the whole-sign perspective—although we should expect at least a few deviations if an equal or quadrant method had been employed—the conclusion should be that it is not very likely that either equal or quadrant methods were used for the places in Valens’s basic horoscopes. This, together with the conclusions in section 7 above, suggests to me that a basic horoscope usually is just what it looks like: a horoscope calculated without degrees, with whole-sign lots and whole-sign places. Then, if it feels fitting for whatever reason, the degrees of some elements—the ascendant, the midheaven, one or more planets, the Lot of Fortune, etc.—may be calculated more accurately afterward.

AQ15: Do you think these investigations would have been relevant to determining how the places were considered in Valens’s basic horoscopes? RQ16: Do you think Dr. Gansten provides you with sufficient horoscopic data from Valens to enable you to determine, no matter how conclusively, how the places in Valens’s basic horoscopes were considered?

I would add that Firmicus’s semi-basic example nativity in II 29,10–20 seems to fall into this class precisely: the references to the places of the planets, including the case when two planets are found in the same sign, always conform with the whole-sign scheme, and although Firmicus has already described equal places, he does not seem to use them here.

10/16 The missing analysis of the horoscopic evidence – the attested place division methods in Valens’s elaborate horoscopes

In the case of the elaborate horoscopes, we are not very fortunate: although there are various partial examples calculated by degree in Valens’s Books I, III, and VIII, no references to the places are found in them. In fact, only the two full horoscopes of III 5 allow an analysis. In relation to this part of the Anthologies (namely, III 3–5), you say (p. 23) “we find several [emphasis added—LL] example nativities giving both angles and planetary positions to the degree, and sometimes to the minute of arc.??? As long as we add the two partial examples in III 3—one of which is an undatable example referring only to the ascendant and the upper and lower midheavens—the use of “several??? is right: these are 4 examples in total. However, these two partial examples do not say anything about the places here; what is more, the datable horoscope of III 3,30–41 is reused in II 37,31–34 and VII 3,23–26 and 6,141–144, with a different ascending sign. In this alternative form, with Capricorn rising, it is one of the ca. 12 horoscopes I referred to in the previous section.

Of the merely two elaborate horoscopes that may provide any insight into the matter, you cite the second one (III 5,11–15) on p. 23, and add, “[t]here is no reason to believe a different system of places to be presupposed here than elsewhere in the text.??? Although you do not state this explicitly, you apparently refer to the quadrant method introduced, as you presume, in III 2. (More about this in sections 11–12 below.) This horoscope does not prove your claim, but at least it does not disprove it either: the luminaries are said to be cadent, which is just as true with the quadrant method as with the equal or whole-sign methods.

Still, I truly wonder why you chose to cite this second example of III 5 and not the first one (III 5,6–10). Is it perhaps because the first example—the one I referred to in sections 1 and 8 above—as it stands here, works only with the whole-sign method? The ascendant and the midheaven are at 17 Pisces and 25 Sagittarius, respectively, and it is said that Mercury at 11;25 Leo “was found cadent??? (ἀποκεκλικὼς εὑ??έθη): Mercury is indeed in the 6th sign from the ascendant but in the 5th equal or quadrant place. Also, when this horoscope reappears in III 11,14–16, we learn that the Moon is in an angle; taking its position at 12 Pisces as given in III 5,6, it will be in the ascending sign indeed but in the 12th equal or quadrant place.

AQ16: Do you think citing and analyzing the first horoscopic example in Valens III 5 would have been at least as relevant to determining how the places were considered in Valens’s elaborate horoscopes as the second nativity? RQ17: Do you think Dr. Gansten provides you with sufficient horoscopic data from Valens to enable you to independently determine what place divisions Valens used in his elaborate horoscopes?