On the Possibility of Higher Dimensional Languages

March 15, 2026 – 12:06 pm

Reading Nikhil Mahant, Why alien languages could be far stranger than we imagine I was pleased to note that he canvassed the possibility of communication systems that were, as he says, non-linear – but by which he really meant not language-like in the way that language is defined for philosophical uses. The example he gives is the possibility of languages that are ‘map-like’ rather than ‘language-like.’ This is something that he may have developed from the idea that the Mind’s semantic system might be map-like rather than language-like – an option discussed in Braddon-Mitchell and Jackson’s (1996/2007) Philosophy of Mind and Cognition. I found it to be a fascinating alternative for a theory of mental structure, but I’m not sure how that might work for a language. Mahant suggests that it might be a pictorial system, but I doubt that such a system could really be a language.

(A pictorial system really couldn’t instantiate the sort of recursiveness that seems to be not just necessary to languages but also fundamental to thought. We really do believe that the range of possible thoughts and ideas is effectively infinite – or at least, so far beyond the possibility of individual special instantiation as to make it impossible to explain our capacities without something like recursion.)

The problem is more obvious when it’s wondered what the medium might be for such a non-linear language. A map-like system enhanced in some way to have the semantic power of a linear language would require a very different form of expression from any we’ve seen so far. On the other hand, when I’ve considered non-linear systems, I’ve often thought that an octopus’s chromophores could create a 2-2½d signalling system of adequate semantic power. Gripping hand, however, any inter-agent communication is going to have to be sequential and therefore effectively 1d, and I wouldn’t be surprised if that very fact makes it necessary for the intra-agent or atomic form of communication to also be sequential.

Consider how languages are useful as means of transmission of concepts or ideas from one communicant to another. Those ideas have to be constructed internally before they can be communicated – or, at least, that is the ideal of the system; it wouldn’t be surprising if the actual process of construction and expression were reflective and involved many feedback loops, and note that most people accept that they don’t really ‘know’ what they’re going to say until they’ve said it. In any case, it’s very hard to imagine mental processes equivalent to complex thought that did not issue in some sort of 1-dimensionally expressible ‘thought.’ What would a 2-d thought look like? Could a 2-d thought be equivalent to a 1-d thought like ‘Harry is happy’? Would it just be a mental image of an Euler diagram? Would thoughts too complex for an Euler diagram then be unthinkable?

My fundamental reason for doubting 2+-d languages, however, is that I have a rudimentary theory of the evolutionary origin of the language faculty that sees it as developing from the capacity for planned action, and planned actions are all 1-d sequences to be performed with 2-d tree-like structures only in their formation histories. That mirrors the TG version of language and it still seems the most obviously reasonable version of language to me, despite the Minimalist Program’s unaccountable popularity amongst linguists.

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On Protocols for Activities Following Discovery of an ETI Probe

March 14, 2026 – 7:14 pm

Current SETI efforts, with rare exceptions, concentrate on the detection of signals from ETI from deep space, and the response protocols adopted for success in this search reflect this concentration. The protocols in question can be found at the IAA site as

Nevertheless, there are good reasons, increasingly accepted by researchers, to believe that the first incontrovertible evidence of an ETI could well occur with the discovery of an alien probe already in the Solar System. Such a discovery would present us with a situation different in very significant ways from the case of a signal detection. For example: communication with the alien probe, should it be possible, would be in near real-time; the mere existence of the probe would strongly suggest that our own existence was already known to the ETI who sent the probe; and the artifact itself – if not the ETIs – would be physically accessible to humans even at our present level of competence in space.

Clearly, this would call for a very different set of response protocols from those recommended for a signal detection, yet there has been very little in the way of preparation of such a protocol. We have seen an early effort by A Tough (1998, Small Smart Interstellar Probes, JBIS 51: 167-74) and a more recent one by A Loeb (2021, Protocol for Contact with Extraterrestrial Equipment,) but beyond that there has been no effort at a formal draft and the topic is still at the level of general discussion.

This is possibly a good thing, because I think there are some aspects of the situation that are highly relevant to the form that such protocols should take that have not been properly considered.

Recursive Strategizing

We should expect that the ETI that sent the probe out has developed a strategy to advance its interests in having sent the probe out. A part of the development of that strategy would be to anticipate the responses of any intelligences that it might encounter. It would expect that those intelligences would have developed strategies for responding to such an encounter, and that they would expect the probe to have taken that into account, and that they should take account of that fact too, and so on. Our protocols for such an encounter have to take into account that the ETI who sent the probe are at least as capable as ourselves of recursive intentionality.

Given this assumed capability, and the fundamental principle that nothing should be done to jeopardize the existence of the human race (and acknowledging that the probe will have a similar prime directive,) our protocols should be such that given any number of intentional recursions they should tend to a stable action outcome.

Assumed Intelligence

We should assume that the probe is intelligent in its own right. This is plausible in any case because we are in sight of AGI ourselves and it would seem to us to make no sense for an AGI-capable ETI to send out a probe without it. We note that it is impossible for an unintelligent entity to pretend to be intelligent (ChatGPT notwithstanding – and we’re not talking about sentience or understanding here,) while it is very easy for an intelligent machine to pretend to be unintelligent. The advantages of such pretence may be imagined: to observe without the requirement of response to attempts at communication, to exploit security breaches opened by the assumption of unintelligence, etc.

We note, on the other hand, that if the probe is intended to eventually allow interactive contact as an AGI, then it must have a strategy that allows it to do so even after it has pretended to be unintelligent. It might be sufficient for it to claim to be uncertain of our intentions. But since we know that is a plausible strategy, we will have adopted contact protocols that will make it difficult for this strategy to be followed. And so on. It might turn out that ‘honesty is the best policy’ is the stable strategy here, in which case the deception will not occur.

Assumed Knowledge

We should also assume, whether as part of the assumed intelligence principle or not, that the probe has access to our communications and has had such for long enough that it can understand our languages and mine our communication channels for data. We should assume that in all remotely plausible cases (and we need to be very generous with our attributions of plausibility in dealing with the capabilities of an advanced AI/ETI) the probe can monitor our deliberations on its presence and what we might propose to do about it and what our motivations might be. We should also assume that this monitoring goes back into historical time no matter what appearance of recency might be given by the probe. (Of course, the probe will assume that we have made this assumption and will accept that any communications on the topic that followed the realisation that such a probe was possible might have been intended for the probe in the first place. And so on, again.)

On the other hand, we cannot depend upon it having that access or knowledge. The assumption is a matter of security maximisation, not of communicative convenience.

Prime Directives

Discussion of protocols for contact with ETI tend to simply assume that we must behave according to the ‘highest’ ethical principles, so that the first moral principles are that we must be completely truthful, we mustn’t deceive, we must treat the other (the probe in this case) as an end in itself, we must show no hostility, and so on. In Tough’s proposal, for example, he accepts as fundamental the first three directives in the ‘Declaration toward a Global Ethic’ put forward in H Kung, K-J Küschel (1993) A Global Ethic: The Declaration of the Parliament of the World’s Religions London: SCM, which he interprets as requiring that we

  • Have respect for ETI and avoid violence
  • Speak and act truthfully, avoiding lies and deception
  • Deal honestly and fairly with ETI, avoiding any temptation to exploit the situation for personal greed

I regard this as well-intentioned, but wrongheaded. Quite apart from the as-yet-unjustified assumptions that a non-human ETI would have any such conception of morality or that if it did it would resemble our own Western model in detail, our principal directive must be the promotion of the advantage of humanity and the prevention of harm to it. Given the plausibility of the assumptions and reasoning that underlies the Dark Forest solution to the Fermi Paradox it must be the responsibility of communicants to minimise risk – not to maximise opportunity – because the risk is total. If that requires lies and subterfuge and ‘dishonesty’ (as the recursively stable strategy) then so be it. Only when the bona fides of the ETI/probe have been established beyond any doubt can purely cooperative strategies be adopted. And good luck making that call, because, again, the cost of error is total.

Preferred Secrecy

Almost all discussion of this topic explicitly demands that the news that an ETI has been detected should be made public immediately upon confirmation. This is declared in the two IAA protocols regarding actions subsequent to a signal detection, and it is also implicit in the suggestions made by Strong in his proposal. There are two reasons to think that this is irresponsible. One reason applies to both the signal detection and the probe discovery cases, but the other and more plausible hesitation is particularly relevant to the latter.

  • There is a possibility that the discovery of the actuality of ETI may cause social dislocation. This is a common trope in SF and the risk is acknowledged by the IAA in the Rio scale and San Marino Scale documents included in resources related to their considerations of their protocols. The case where the discovery is kept from the public is the case where the status quo is maintained. Given the risk of publicity with unknown benefits to publicity, the responsible authorities would be quite justified in playing it safe until they could be absolutely convinced of the advantages of publicity. This calculation, of course, applies to all discoveries of ETI where it is possible to maintain secrecy of the event.
  • Proposed protocols foresee an eventual attempt to communicate with any discovered ETI. It is accepted that the nature of the message needs to be well-considered and conscient of the risks of such openings. The obvious increased risks of unauthorised communications that follow from publicising the existence of the ETI are mitigated by the fact that in the case of a signal detection it is implicitly assumed that the resources required to send a message are beyond most individuals and that organizations with adequate resources can be persuaded to follow the recommended protocols by whatever institution is finally given the responsibility of coordinating the human response. Moreover, given that the signals are anticipated to be from vast distances, it is not expected that a message would have effects that would be felt in the very near term – even if those effects were to be harmful. There would be time to minimise the effects in the gap between signalling and receiving a reply – let alone receiving a visitation in response. None of this is likely to be true in the case of a probe discovery. In the probe case, messaging the ETI would be vastly easier – especially given our prudential assumption that the probe is already monitoring all our communication channels – and cannot plausibly be regulated by any international bodies we can imagine. (Note that there have already been several attempts at messaging ETI by private parties. The threat of irresponsible messaging of the probe is very real.) Secrecy, in this case, is very much the safer course until the responsible authorities can be absolutely convinced of the advantages of publicity.Such a strategy would have to take into account that the probe discovery might very well be such that it could not be kept secret. It might be that the probe is so obvious (or is now deliberately making itself so obvious) that the event will inevitably become public. It might be that the discoverers of the probe have already made enough people aware of it that the discovery is effectively public already and only mitigating actions can be taken. In such a case we might look for authorities to downplay or to debunk such evidence, to restrict the activities of those who have come into that knowledge, and so on.

    All of those strategies, again, will need to be designed on the assumption that the probe is intelligent, knows what is happening about its discovery, will eventually make itself known unless prevented, and so on, and that the communication with ETI will have to go forward in the future on the basis of common awareness of the actions previously taken. Here we would again need to operate on the basis of recursive strategies as described above.

Responsible Authorities

There is a universal assumption in the proposed and actual protocols that, given the humanity-wide significance of the event of ETI detection, the responsible authorities should be those that can be relied upon to have the best interests of humanity as a whole at heart, and to have the competence to pursue those interests, and the accepted right to do so. This typically means that they default to assigning responsibility to various UNO committees.

Unfortunately, for several reasons, this is unlikely to be persuasive in the necessary quarters.

  • In the first place, the UNO no longer has quite the reputation that it might once have had. I think very few people now believe that it has the competence or the authority to do what is necessary, nor are they all convinced that it has humanity’s best interests as its motivating principle. More importantly, it is not likely to be the view of the state actors that the UNO should be deferred to in a matter of such importance.
  • The UNO, as a collection of competing state actors acting in their own perceived interests, is properly seen as just another actor on the political stage. No state – whatever the rhetoric surrounding its actions – is justified in handing over an advantage to competing states, when it can be quite certain that no such indulgence would be reciprocated. Does anyone think that the worst state actors would voluntarily resign their advantage in such a case? To insist on any others doing so is merely to hand an advantage to those worst states.
  • If secrecy is deemed important, then assigning responsibility to an international organization is an extremely unlikely way of preserving it.

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Encounter Classifications for Terran Worlds

March 8, 2026 – 3:34 pm
  1. Size
    1. S              Small                           r < 0.8rE,                  m < 0.5mE                g[1] < 0.8
    2. M             Medium               8rE < r < 1.7rE       0.5mE < m < 6mE         0.8 < g < 2.0
    3. L              Large                                                  6mE < m < 10mE          0 < g < 2.2
    4. G              Giant                                                10mE < m                      2 < g
  2. Dominant Hard Surface Type
    1. V              Vulcanic              Dominant surface is due to vulcanism
    2. R              Rocky                 Heavy minerals, silicates, carbonates, varieties of regolith
    3. I               Icy                     Frozen volatiles (eg. water, ammonia, methane)
  3. Persistent Surface Liquid Types
    1. N              Anhygric             None – indicating liquid cannot persist on the surface
    2. W              Hydrohygric        Water
    3. C              Anthracohygric    Methane, ethane, etc
    4. A              Allohygric            Other
  4. Surface Liquid Coverage
    1. X              Xeric                  No surface liquid
    2. D              Drosic                Insignificant or transient liquidity
    3. L              Limnic                Significant but not extensive liquid coverage
    4. T              Thalassic            Extensive but not total liquid coverage
    5. O              Oceanic              Total liquid cover.
  5. Effective Surface Radiation (R, mSv per annum)
    1. M              Radiominimal     R < 0.1
    2. S              Radionormal        0.1 < R < 10         1 is the ICRP recommended max
    3. C              Radiocritical        10 < R < 1000   
    4. T              Radiotoxic           1000 < R
  6. Surface Temperature (T, oC)
    1. 1              Super-Cold          -273 < T < -100
    2. 2              Cold                    -100 < T < 4
    3. 3              Temperate          4 < T < 40            Approximate human habitable zone
    4. 4              Hot                     40 < T < 100
    5. 5              Super-Hot           100 < T
  7. Surface Atmospheric Pressure (P, b)
    1. 1              Microbaric           P < 0.001b
    2. 2              Hypobaric           001b < P < 0.3b
    3. 3              Mesobaric           0.3b < P < 3b          Approximate human habitable zone
    4. 4              Hyperbaric          3b < P < 100b
    5. 5              Megabaric           100b < P
  8. Surface Atmospheric Composition (by dominant[2] component)
    1. A              Airless                Microbaric worlds with an exosphere
    2. P              Primordial air      H2, He2
    3. C              Compound air     Common compound: CO2, CH4, NH3, H2O
    4. N              Nitrogen air        N2 
    5. O[3]         Oxygen air          Breathable levels of O2
    6. L              Complex air        No dominant component
    7. X              Exotic air                             
  9. Biocomplexity[4], [5],[6] (K, 10Kbytes)
    1. 0              Abiotic                K = 0
    2. 1              Protobiotic[7]      4 < K < 5              
    3. 2              Deuterobiotic      5 < K < 6               5 = approximate minimal level for a cell
    4. 3              Triobiotic             6 < K < 7               Coli
    5. 4              Tetrobiotic           7 < K < 8               Fungus, Fruit fly
    6. 5              Pentobiotic          8 < K < 9               Mouse, Human
    7. 6              Hexobiotic           9 < K                      Pine
  10. Biodensity[8] (D, Gt/m2)
    1. 0              Nonvital              D = 0
    2. 1              Rarivital              0 < D < 0.001
    3. 3              Paulivital             0.001 < D < 0.1
    4. 4              Plenivital             0.1 < D < 10             Earth = 1
    5. 5              Supervital           10 < D

[1] Rough estimates only for values of surface gravity (g, gE) based on r and m.
[2] Dominant means > 75%
[3] This classification takes priority over any other applicable classification
[4] Kolmogorov system complexity for biological organisms. Note that such organisms are distinguishable at any level of K by their reciprocal entropy. See C. Mayer (2020) Life in The Context of Order and Complexity – PMC. They may alternatively be distinguished as just the complex systems historically evolutionarily responsive to environmental pressures.
[5] The biocomplexity of a world is marked as the complexity of the highest scoring biological organism on the world.
[6] The examples use the genome size of terrestrial organisms (rather than genes identified) to calculate their complexity. The genome is a first approximation only to a proxy for complexity.
[7] Since the scale only applies to biological organisms, 0 is assigned to all non-biological entities. It is assumed, on the basis of plausibility and the evidence of terrestrial life, that complexity below 4 is not possible for biological organisms.
[8] Total biomass / surface area of world. A rough measure of the degree to which life has occupied the world. See Bar-On, Yinon M.; Philips, Rob; Milo, Ron (2017). “The biomass distribution on Earth”. Proceedings of the National Academy of Sciences. 115 (25): 1. Note that the current definition references only the mass of carbon contained in living things. This definition may or may not be adequate in considering alien ecologies. Note also the comment in the Abstract to the referenced article:

We find that the kingdoms of life concentrate at different locations on the planet; plants (≈450 Gt C, the dominant kingdom) are primarily terrestrial, whereas animals (≈2 Gt C) are mainly marine, and bacteria (≈70 Gt C) and archaea (≈7 Gt C) are predominantly located in deep subsurface environments. We show that terrestrial biomass is about two orders of magnitude higher than marine biomass and estimate a total of ≈6 Gt C of marine biota, doubling the previous estimated quantity. 

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What is a Planet?

March 1, 2026 – 2:01 pm

The dispute over the criteria used for the categorization of celestial bodies as planets reveals either a confusion concerning the reason for a definition, or an unhappy compromise between independent reasons. The criteria adopted by the International Astronomical Union (IAU) are that the body

  1. is in orbit around the Sun,
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape), and
  3. has “cleared the neighbourhood” around its orbit.

These criteria are clearly intended to include the classical planets while excluding most of the new and unfamiliar bodies from the Kuiper belt (and beyond,) without simply naming them as such. Controversy over the exclusion of Pluto means the second option would probably have been preferable, but that would not have looked like a scientifically defensible definition.

A really scientific definition, of course, would attempt to determine some sort of Natural Kind amongst such bodies. In this respect, a pretty standard view is that Natural kinds are the classes of real objects that fill the positions of variables or class names in the best scientific theories relating to the relevant domain. (For a very relevant example, when Copernicus determined/theorized that the Moon differed from all the other planets in the traditional system according to its orbital character, he removed it from the category of planets.) In that case, the class of planets should be a class of astronomical bodies that relatively narrowly includes the classical planets and that features in theories of stellar formation, solar system dynamics and development, and so on. Such a class would not obviously be required to regard either condition 1 or 3 of the IAU definition. A better definition would simply require that a planet be any body that:

  1. is not massive enough to produce fusion reactions, and
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape)

The IAU itself accepts that their condition 1 should be generalised to say that the body is in orbit about a host star. This would still, however, exclude interstellar objects from the class and invalidate the term ‘rogue planet.’ It isn’t clear why this should be necessary: if we desired to speak of only such objects in orbit about a star we could simply talk of the star’s planetary system. (For convenience the planetary system of Tau Ceti, for example, would be the ‘Tau Ceti system.’) The fact that planets that we know of are generally in orbit about a star is a fact about that class but not a definitive one. (That most Zebras live in Africa is a fact about them, a consequence of their origin and history, but it is not definitive.)

Given that the requirement of IAU condition 1 can be discounted, we might further be relieved of the necessity of distinguishing planets from satellites in those cases where two bodies that both satisfy the other criteria for a planet orbit each other. Previously, we might have achieved this by declaring that where the barycentre of the system lay within one of a pair of bodies, that one would be the planet and the other would be the satellite; or we could have insisted that the secondary body has to be significantly smaller than the primary. A reasonable limit for the second would perhaps be a mass ratio greater than 10:1 given that the Pluto-Charon mass ratio of about 1:8 is enough for some – but not for everyone – to describe it as a double planet. It might be more convenient now to speak rather of a planetary sub-system, and, in the case that one of the bodies is clearly the primary, to speak of that planet’s subsystem. We could unambiguously speak, for example, of the ‘Jovian sub-system,’ or even of the ‘Terran sub-system.’

We might, however, need to modify the conditions in order to exclude neutron stars and white dwarfs from the planet class, because they are not massive enough to produce fusion reactions in their matter, as required by condition 1, and yet they are clearly not of the same natural kind as what we intend to refer to as ‘planets.’ We might achieve this by requiring that the body be composed of non-degenerate matter, but that doesn’t really get to the heart of the problem. In fact, this indicates that purely observational criteria are not adequate for distinguishing the class of planets, because we would insist that any body which had been a star in the past, but through natural processes had become non-fusing should not be in that class – regardless of mass or composition or shape. Natural kinds, so many theorists insist, have historical depth or causal boundaries. (A painted horse does not become a zebra.)

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The Sun Simile

February 28, 2026 – 11:43 pm

Plato’s simile in Republic 508-9 can be summarised as follows:

The Form of the Good The Sun
Intelligible world Visible world
Source of Truth or Reality(508e)
Yields (508e)
1.       Truth or reality to intelligibilia
2.       Power of knowing to mind
Thus (508e)
1.       Not knowing but cause of knowing
2.       Known by the knowing it causes		 Source of light (508a)
Yields
1.       Visibility to sensibilia (507e)
2.       Power of seeing to eye (508b)
Thus (508b)
1.       Not seeing but cause of seeing
2.       Seen by the seeing it causes
Causes reality of objects of knowing
But is not that reality (509b)		 Causes processes of growth
But is not such a process (509b)
Deprivation results in (508d)
1.       No truth or reality (= change/decay)
2.       Poor intelligence (= opinion)		 Deprivation results in
1.       No light (508c)
2.       Poor sight (508d)

In the simile, note two stumbles.

  1. If light yields visibility to visible things, then it would be more natural to say that the Good is responsible for the intelligibility of the intelligible, rather than the truth or reality of those things.
  2. The claim that the Sun is the source of light and the Sun causes the processes (genesis) of growth is not a match to the claim that the Good is the source of Reality and the Good causes the reality of knowable things. The ‘coming into being’ of natural things is not like the unchanging being of the knowable things.

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The Divided Line

February 28, 2026 – 6:30 pm

Plato’s analogy in Republic 509d-511e can be summarised as follows.

Line segments A B C D
Realm Intelligible (νοητος) (509d) Visible (ορατος) (509d)
Objects Forms (511c) – considered in their relationship to the Good.
The First Principle of things. (511a, b)
The unassumed.		 Forms – NOT considered in their relationship to the Good

Assumptions, mathematical postulates. (510c-511b)

 Living beings, plants, artificial things. (510a, e)
Models, drawings of geometrical figures (510d, e)		 ‘Images’ of objects in C. Shadows, reflections, etc. (510a)
Operations a. Derive First Principle from conclusions in B (511a, b)

b. From First Principle, draw conclusions for objects in B

 a. Draw conclusions from assumptions (to be applied to objects of C?)

b. Assumptions are taken for granted

c. Appeals made to sensibilia (in C)
Operators Philosophers Mathematicians and other masters of τεχναι [Scientists] Sophists, poets, artists
Mental States Intelligence
(νοησις/νους)
(Intelligence)
(511a, b)		 Thinking
(διανοια) (Reason)
(511a, b, d)		 Perceptual Assurance
(πιστις)
(Belief)
(511d, e)		 Conjecture
(εικασια)
(Illusion)
(511d, e)
Status Knowledge (επιστημη) Opinion (δοξα)

Just as the Line Segments are related A:B::C:D::A+B:C+D wrt length,
so are the associated Objects related wrt ‘genuineness’/’reality’ (αληθεια)
and the Mental States (παθηματα) wrt ‘clarity’ (σαφηνεια)

Note that whereas the construction Plato gives actually forces B=C, he makes no reference to that and we must assume that it is irrelevant to the analogy.

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Planetary Categorization

February 27, 2026 – 8:47 pm

The explosion in exoplanet discoveries has revealed that the Solar System is very far from a typical stellar system, and a need has arisen for a categorization of planetary types that includes far more than the kinds of planets found orbiting the Sun. To form these classification appeal has been made to a range of characteristics that are at least observable. The principal such characteristics are

  • r = Radius (rE)
  • m = Mass (mE)
  • D = Density (x H2O)
  • T = Temperature (eq. to 1AU from Sun) – referring to the irradiation of the planet
  • a = Atmospheric composition (n)
    • n = 0: No atmosphere (P < 0.001b,)
    • else: n = mean molecular mass of atmospheric gases.

Together with a few other observables these can be used to produce the following table of categorizations.

  • Common            
    • Orbital focus
      • Rogue                   Not orbiting a star
      • Circumbinary     Orbiting a binary star
      • Circumtriple        Orbiting a triple star
    • Orbital character
      • Eccentric              Highly eccentric orbit
      • Double                  Two planets orbiting each other
      • Trojan                   Co-orbiting with another planet
  • Solid                                           r < 1.7                    m < 6                                   D ≈ 5
    • Structure
      • Coreless               No metallic core, thus essentially all mantle
    • Composition
      • Carbon                 Iron core w/ carbon-based mantle
      • Iron                        Iron core w/ minimal mantle
      • Ocean (1)              Significant hydrosphere around core/mantle       
      • Silicate                  Iron core w/ silicone-based mantle
    • History
      • Chthonian           Close to star. Ex-fluid with envelope stripped away
    • Surface
      • Desert                   Dry desert (Arid, Dune)
      • Hycean                 Ocean w/ Hydrogen envelope
      • Ice                          Frozen volatiles (eg. water, ammonia, methane)
      • Lava                      Lava
      • Ocean (2)             Liquid (usually H2O.) Oceans may be sub-surface
    • Habitability
      • Goldilocks            T ≈ 1
    • Size
      • Sub-Earth            r < 0.8                   m < 0.5
      • Earth(-sized)       0.8 < r < 1.7        0.5 < m < 6
      • Super-Earth                                         6 < m < 10
      • Mega-Earth                                        10 < m
  • Fluid                                           1.7 < r,                   6 < m                                  D << 5  
    • Irradiation
      • Hot–                       T >> 1
      • Cold-                      T << 1
    • Size
      • Super-Earth (Gas Dwarf)               6 < m < 10
      • Mini-Neptune     1.7 < r < 3.9           6 < m < 20 (sic) 
      • Sub-Neptune       1.7 < r < 3              m < 10
      • Neptunian            3 < r < 5                10 < m < 20
      • Super-Puff           4 < r                       m < 4                                  D < 0.8
      • Super-Neptune    5 < r < 7                20 < m < 80
      • Jovian                   7 < r < 10              80 < m < 400
      • Puff planet                                          80 < m < 400                    D < 0.8
      • Super-Jupiter     10 < r                     400 < m < 4000
    • Composition
      • Gas Giant            0 < a < 4
      • Helium                  a ≈ 4
      • Ice Giant              4 < a                      

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The Music of the Scop

February 27, 2026 – 12:56 pm

According to the poetic corpus itself, poems such as Beowulf were typically performed in front of the lord in his feasting hall by a scop, roughly equivalent to the ON skald. There are those who doubt the reality outside literature of this class of persons, but the evidence of all other Germanic and Northern barbarian traditions makes that doubt unreasonable. Moreover, again on the evidence of the literature and cognate traditions, there is no doubt that the scop’s performance of the poem. was typically accompanied by what the Anglo-Saxons called a hearpe but which we think of as a round lyre rather than a ‘harp’ as the OE term would suggest. (This is the case even if Pope’s theory concerning the use of the hearpe to determine metre is rejected.) A number of examples of these instruments have been found, most notably in the Sutton Hoo ship burial, which is dated to the 6th or 7th C – about the accepted time of the composition of the poem. A reconstruction of the instrument is shown.

We note that the instrument has 6 strings, which strongly suggests a pentatonic scale (the 6th string being the ‘octave’ of the first.) Though there are many possibe pentatonic scales it is likely that the Anglo-Saxons used the series C E♭ F G B♭ because it is the scale used in early English folk song and it is reasonable to assume some continuity in the musical tradition.

Finally, the textual evidence indicates that the hearpe when used by a scop to accompany a recitation was not played just by the ‘block and strum’ method, nor yet by providing a simple drone, though these techniques were doubtless available for variety. Descriptions of the hearpe’s use indicate that at least on occasion music and voice were linked, though on other occasions the action of the hearpe was relatively independent of the scop’s voice, and that it could be played loudly and with a rapid flow of notes. [1]

Perhaps a good example of what this sounded like is to be found in Beowulf: The Epic in Performance – Benjamin Bagby, voice and medieval harp. This performance looks and sounds much more like how I imagine a scop’s performance than the poetry readings generally performed. Note, in particular, the use of the hearpe and the division into air and recitative (and the fact that the hearpe is not just strummed, but his fingers fly as the records show they did.) 

[1] Beowulf: 1063-5, Widsith: 103-4, The Gifts of Men: 49-50, The Fortunes of Men: 77-84

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Remnant Auras of Absent Terms

February 27, 2026 – 9:44 am

In discussion, a friend proposed that the use of the via negativa might be defended even if it lacks logical or rational justification by supposing that there is an ‘aura’ that is associated with certain words and which remains when they have been definitionally negated in pursuit of some ‘deeper’ understanding, or in recognition that no finite understanding is possible. I thought that was an interesting idea but wasn’t quite sure what this ‘aura’ could be.

The previous discussion had covered the fact that the Greek aura or aurh was a breeze, esp. a cool breeze from water, cognate with ahr, meaning air or a morning mist, and by ways that are not too clear came to mean an emanation of some subtle fluid from a body, and then the subtle substance surrounding a body. Comparisons had been made with the idea of a halo in Classical and Christian iconography, by which the spiritual worth of a hero is displayed. In that case the power of the saint is imagined as flowing out of him and surrounding him, but more like light from a flame than like air from a lake. The same concept is found in the Persian farr (khvareneh) (‘glory’) and the Mesopotamian melam(mu) and doubtless in other places. None of this, however, provides any clue how to go beyond the level of metaphor.

I suggested that the aura desired might be understood as one of the several semantic (?) properties that Frege identified as contributing to the meaning, broadly understood, of terms. The clearest explanation of these can be found  in Dummett’s Frege. Unfortunately, Frege wasn’t particularly interested in making these peripheral issues altogether coherent, so there’s quite a bit of confusion concerning terminology. The general idea is clear enough though. On p. 2 of that text Dummett says

Frege distinguished two elements in the meaning of a sentence or expression, for one of which he reserved the word ‘sense’ (‘Sinn’), and for the other of which we might use the word ‘tone’ (‘illumination’ [‘Beleuchtung’] and ‘colouring’ [‘Färbung’] being the words Frege himself used for this latter). He explained the difference in this way: to the sense of a sentence belongs only that which is relevant to determining its truth or falsity; any feature of its meaning which cannot affect its truth or falsity belongs to its tone. Likewise, to the sense of an expression belongs only that which may be relevant to the truth or falsity of a sentence in which it might occur; and element of its meaning not so relevant is part of its tone.

And on p 85 he says

[Frege] accounts for tone as a matter of the association with a word or expression of certain ‘ideas’ (Vorstellung), by which he means mental images.

That idea won’t fly for reasons Dummett goes through. For example, Frege says that ‘dead’ and ‘deceased’ differ only in tone, but it’s hard to believe that there are associated mental images which distinguish them. Worse, the terms ‘and’ and ‘but’ supposedly differ in tone and/but it’s hard to imagine that there even are associated mental images.

On the other hand, supposing that ‘dead’ and ‘deceased’ differ in the expectations of context of occurrence or in their associated (non-imagistic) ideas might very well work. Those expectations and associations might also be able to do the work that we want the ‘aura’ to do for terms such as ‘God’ which are semantically eviscerated on the via negativa . (Now there’s a mental image to savour.)

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Crossing the Via Negativa

February 26, 2026 – 11:03 pm

We do not generally think that it is acceptable to discuss a thing only in terms of what that thing is not, or in terms of what qualities may not be used to characterize it. Nor do we typically think it reasonable to declare that comprehension of some important concept is in principle impossible and we shouldn’t even try. Apophatic theology, however, takes exactly that approach in treating of the nature God and we should wonder why this is the case.

The standard justification is just that God’s qualities are by definition infinite and therefore beyond the power of positive comprehension by the finite human brain, and therefore the only possible approach is to limit ourselves to the sorts of finitely comprehensible predications involved in saying only what is not the case. By this means we can suggest the qualities of God, without committing ourselves to any positive claims concerning God’s qualities.

I’m not so sure about that: it seems to me that there are plenty of such concepts, like the concept of infinity itself, that are perfectly comprehensible to our finite minds. Cantor showed that even if we cannot hold an infinity in our minds, we can define it positively, describe its characteristics, distinguish its kinds, and generally manipulate it in all the ways that we would need to be able to in order to say that we understand it. Moreover, to say that God lacks the quality X, where X is a finite concept, may very well be making a claim of infinite possibilities un-foreclosed, which means that to understand it would require understanding an infinity; while saying that God lacks some infinite quality would require an understanding of that quality in order to understand the thought that God did not have X. In either case, being able to comprehend the negative thought involves comprehending an infinite concept, and that justification for the via negative fails.

A less charitable proposal is that the impossibility of describing or thinking of God at the same time positively and coherently is a consequence of the fact that the very concept of God is not well-formed. The problem seems to be that it began as a positively defined concept within comprehensible limits but been subsequently expanded into incoherence by the necessities of philosophical argument – in particular, philosophical arguments for His very existence. One can give a Just-So story: primitive man wanted to explain how the world came into being; he looked at examples of things coming into being that he could understand, like his making a flint tool, and analogised a world-knapper. The world-knapper was just like him but bigger, distant, more powerful, wiser. More than that though, the world-knapper became, as devotion and reverence demanded, not just bigger but as big as possible, and so on, and thus we arrived at the qualities of omniscience, omnipotence, omni-benevolence, as well as ineffability, eternality, ubiquity, etc. These unlimiting concepts are, however, both difficult to directly comprehend and collectively incoherent. The puzzles that arise are well-known. Can God make 2+2=5? Can He make a rock He can’t move? Can He do wrong? Can there be evil in the world He made? And so on. The ultimate point of this is that the seeming necessity of the via negative should be taken not as a sign of the transcendence of God, but as a sign of the ill-discipline of thought about God.

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