Are degree’s valid in the divisional charts?

Yes.

How do you calculate them?

Using ratios.

For example, 10 daśāṁśa fit in a zodiac sign. So each daśāṁśa segment is 3 degrees of actual space, and represents one sub-sign. So, the ratio is “3° of real space = 30° of sub-space”. Thus, if a planet is 1° into it’s daśāṁśa it is 10° into that sub-sign.

Does this mean we also have nakshatras in the subdivisions

No.

Subdivisions are divisions of rāśi (zodiac signs). Nakshatras are not part of the Rashi.

Not only that, but we do not allow recursive divisions at all – even for rāśī. We do not divide a daśāṁśa into another 10 parts, and then each of those 10 into another 10 parts, etc. If we did, we would create an Alice-in-Wonderland Rabbit-Hole of infinite regression where every point in the chart is always simultaneously present at every point in the zodiac (which might sound cosmically good if you are trippin’ on LSD, but is really, really bad if you are trying to make any intelligible sense out of a chart).

If we can specify degrees in the divisions, do degree-based aspects work in those divisions? For example, can we say “Venus is in opposition to the Sun in the Navāṁśa”?

I have not made up my mind about this yet. When I look at it one way, the answer I would give is “yes.” When I look at it another way, “no.” So I am reserving judgement until I have more confidence.

I don’t consider it a high priority to figure out, because we can already get more information than we can juggle, without having to dabble in this.

Then, what would you use degrees for in the subdivisions?

The rhetorical side of that question is one of the reasons I might answer “yes” to the previous question.

However, there is a very, very, very important use to them, which was certainly utilized in classical astrology but is almost unknown now. The technique is to do what most people would call a “biwheel” chart, where the inner chart is the d1 and the outer chart is the divisional (d9, etc.). With degrees you can see where divisional placements line up exactly with main chart placements – and when this happens, it adds a lot of power and importance to the interpretations.

I plan to offer a report on this as soon as I am clear in my mind about exactly what the report should contain.

Is dignity cumulative through the divisions, or is it only determined by the main chart?

It is cumulative.

This is defined very clearly in almost every classical text. It is usually called varga-vimshopaka. I have used this in all my readings are reports since before I even started offering them to the public. Here is a video from several years ago, explaining it:

A few caveats: The d1 is always weighted very heavily in this system. And also, the dignity of a planet within a particular division is always the most relevant dignity for that division.

How should dignity be calculated in the unconventional divisions, which are not represented as zodiac signs (2, 3, 16, 30, and 60).

Please remember that not every classic defines the divisions in the same exact way. Phāladepīka, which you are familiar with from my live-streams, defines d60 and d16 in a way I did not see elsewhere. In most cases, only 2, 3 and 30 are treated unusually.

I have seen three approaches to dealing with dignity in these unusual divisions: (1) translate them conventional zodiac signs. (2) use them as is (3) make special rules.

Translating: The divisions in 3 & 30 (“trekka” & “trimṣa“)are divisions owned by planets. We can translate them to signs easily, using this formula: “planet = domicile/trikona.” So the Sun’s division would be in Leo, Jupiter’s would be in Sagittarius, Etc. Once you have translated, you can apply normal dignity rules.

As Is: Keep the divisions as they are – and calculate dignity ranging only from bitter-enemy, to best-friend, because these are the dignities arising from the relation between house-guest (occupant) and house-host (ruler).

Special Rules: Division 2 (“hora”) has only two “signs” – one for the Sun (could be translated to “Leo”), and one for the Moon (could be translated to “Cancer”). Classics (Parāśara, for example, if my memory is correct here) specifies special rules for its dignity. I believe I explain them in the video I linked above.

Phāladīpikā’s d60 is also a division into only 2 segments: “good” or “bad” – so the unspoken dignity rule here is that “good” = exalted dignity and “bad” = debilitated dignity.

Phāladīpikā’s d16 is incomprehensible to me. Most texts define it like a standard zodiac subdivision.