A very nice question!

Off the top of my head, I'd say that we could perhaps approach the question by examining the different *representations* of time founded on physical, biological, psychological, social etc. quantities…

The approach "by level" strikes me as very judicious, and I'd wholeheartedly endorse it. From what I can grasp of 'chronotopoids', it seems that we're talking about what we might call "the narrative structure of spacetime"… if I understand aright, a Minkowski space would be a chronotopoid generated by special relativity, while (for example) the perfect aspect would be a chronotopoid generated by the English verb system – and would probably bear a privileged relation to both our psychological and our social construction of time (which would also be 'chronotopoids'). Similarly, measures – or spaces - based on biological or natural cycles would be chronotopoids.

So, if I've understood, it would seem that a chronotopoid is a kind of "narrative space" generated by some kind of account (physical, social…) in which events unfold. The nature of its structure is determined by the kind of 'narrative' (geometric in the physical sciences, causal or probabilistic in other fields…). An interesting feature is that it would seem to allow us to consider "under one head" both probabilistic and geometric spaces (for example, phase spaces and Minkowski spaces).

Is this more or less the idea, or have I got my head where the sun don't shine ?

Before starting, Roberto, could we ask for your definition of a “chronotopoid” and, more particularly, how it differs from a “spacetime”?

“I would propose to distinguish two major frameworks. Let's call them the ontological and the formal ones. As to the latter, we can develop as many different chronotopoids as we like, provided they respect some basic mathematical properties (consistency, mainly). Some of them may prove helpful in understanding reality (or fragments thereof), some may be purely formal exercises. I would propose to leave formal models and their machinery apart, because they are not the real issue under discussion.”

OK – point taken and agreed.

“What I would like to understand is whether there are real (=in the sense of being part of the furniture of the world) chronotopoids and how are they related one another.”

This is where the questions begin. Do *any* of the various ways in which we “carve spacetime” (taking the neo-Quinean view) correspond to the “ultimate furniture of the world”? By what criteria do we decide whether an account “carves spacetime at the joints”?

“The basic intuition is simple enough: really different types of entities may need different spatiotemporal structures.”

As you remark, this is highly ambiguous, and particularly if we are to open our definition to “entities” that are not evidently physical (and by the way, we can, I think, subsume both “psychological” and “social” entities under the description “mental”). Evidently, a “social entity” – which could be either object, event, or state of affairs – occupies space and time differently from a “purely” physical object, event, or state of affairs. There is apparently some ontological or metaphysical distinction between, for example, the First World War and the Statue of Liberty – but is it of the same kind as the distinction between, for example, a pebble and a hurricane? [Note that “social entities” are rarely ‘object-like’; they tend rather to be either events or states of affairs. Nonetheless, we could – and perhaps should - argue that the majority of “material objects” – be they trees, rocks, tables, or persons – are highly “conventional”, and thereby in part at least ‘social’].

What kinds of thing constitute our ontologies? I’ve suggested objects, events, and states of affairs; we could perhaps add (concrete) processes. But what about spacetime itself? Substantivalists would argue for its inclusion… And then there are universals… and propositions… and “mathematical entities”… And should we allow for merely “possible” entities - possibilia, possible worlds? (and we haven’t even started on the bizarre ontologies required by supernaturalist views).

Should we attempt to define what count as ‘entities’ a priori, or should we refuse “first philosophy” and base our ontologies on an a posteriori analysis of various conceptual schemes? Should we allow for a preferred or privileged account when making such an a posteriori investigation (as Quine ‘preferred’ the accounts given by the physical sciences)?

While I agree entirely with the need to categorise entities according to the conceptual scheme from which they are drawn, we should also perhaps consider the *nature* of the entity (object, event, etc).

Perhaps you’ve dealt with these questions in your papers…

Roberto

Some very interesting ideas, but - being somewhat slow on the uptake - I still need some clarification…

A first question: if we’re going to allow “multiple” chronological and topological spaces, *where* are they? We evidently can’t locate them in the ‘unique’ spacetime against which you’re arguing…

***

ONTOLOGIES: are we talking about the ontologies that different conceptual schemes commit us to, or are we talking about “the way the world is” (if we can make a distinction between the two)?

If I might recapitulate, you give as (?ontological) categories ‘particulars’, ‘structures’, ‘interactions’, and chronotopoids. I’ve no specific remarks to make on the first category, save to wonder about the criteria of individuation you’d give for these particulars. Would you include elementary particles in this category? (I can see some evident problems…)

By ‘structures’ (and taking part-wholes as the ‘model’) we *could* understand this as either concerning the structural *relation* (that is, the relation of part to whole, or the relation of one element of structure to another – such as chemical bonding) or the *structured object* itself (that is, a mereological object – or perhaps a molecule?). I’d imagine it’d be ‘more like’ the former...

Interactions. Hmm. Personally, I’d be tempted to class them with ‘structures’ under a wider heading of ‘relations’, but that has no bearing on the present discussion. Let’s admit that ‘causation’ is indeed an objective *phenomenon*, and that B occurs ‘because of’ A. This would also include the feedback relations necessary for interaction, and could cover anything from atomic interactions to social intercourse (would we find our elementary particles here, or under ‘structures’?).

A question – if a given relation from (interaction between) A to B follows an ‘earlier than – later than’ sequence, could B determine A?

This leaves “chronotopoids” as an ontological category. Until I can see “where” you’re projecting them, I can’t really see how they’d fit with the other categories – unless you’re suggesting that our discourse somehow “creates” or “generates” chronotopoids…

An aside: I wonder to what degree this has a bearing on the “serious tensing/detensing” debate (or vice-versa); we can indeed suggest local past-present-future relations and a local “passage of time” as the basis for what Zimmerman has called “irreducibly perspectival propositions” – and such propositions suggest an ontology at odds with the eternalist, B-theoretic ontology which our “best-candidate” theories of spacetime apparently favour.

Would the inclusion of chronotopoids correspond to the intuition that spacetimes are “substances”? Once again, I’m not sure how a chronotopoid relates to what I’d understand as a spacetime (I really must visit your site!), but would a Leibnizian relativist view about space and time subsume chronotopoids under “relations”?

As you remark, your suggestion is indeed at odds with much of contemporary work in ontology, though I find myself in agreement with your rejection of Campbell, Martin, Armstrong and Lowe.

In what way do you consider that such an ontology is preferable as a basis of discussion with “physical scientists”?

***

DOMAINS. As to your suggestion concerning “domain categories”, the triadic relation between “material” “psychological” and “social” (is this exhaustive?) seems reasonable, save that I’d raise a few quibbles over how you’d found a distinction between the “psychological” and the “social” - surely, the only access we have to the “psychological” (save through introspection) is through language and the observation of behaviour? If this is indeed the case, the “psychological” is thoroughly polluted with the social…

As to types – are you therefore suggesting that “material”, “psychological”, and “social” are “types” of entity – “strata of reality”, as you put it? I note that you consider that the social and the psychological “emerge from” the material (would “physical” not be a better term?). How does this emergence work? Are the emergent levels ontologically dependent on the subvenient levels?

The interrelation of the various strata appears self-evident (indeed, and as I’ve remarked, I’d be tempted to unite the “social” and the “psychological” under the category “mental”). Even if we accept that the physical world is real and mind-independent, the *way* in which we carve it up is mind-dependent, thus providing the required link between the ‘material’ stratum and the others.

As to your subdivisions: Evidently, the division of, say, matter and energy distribution into ‘physical’, ‘chemical’, ‘biological’, etc. phenomena is conventional, and is largely determined by measurement. The distinction between mass/count forms of matter could also be seen as comporting a certain conventional element (a gold ring is also a certain quantity of molecular gold).

It’s perhaps all well and good to speak of “causation” in philosophical contexts, but I’m not sure it’s really appropriate to a discussion with, say, the physical sciences – as John Earman has remarked, the notion of “causation” is “truly obscure”, and Steven Savitt reminds us that “the notions of cause and sufficient cause…have no correlate in any modern physical theory”. So, while we can speak of ‘motivations’ in psychology, I’d say that we’re talking about causal explanations rather than ‘actual causal relations’ – and I’d also argue that these causal explanations are social in origin.

Roberto

A long answer, I'm afraid - I'll break it into two parts for ease of reading...

“As far as I can see, chronotopoids (CT) "emerge" together with the relevant entities: material entities gives birth to material CTs while psychological entities gives birth to psychological CT, etc.”

This would seem to come back to the notion of a “narrative space”. What elements of discourse would be susceptible of generating CTs? I imagine tense would be a classic example (I’m convinced that tense and aspect have not received sufficient attention in philosophy).

As CTs emerge “with” the relevant entities, the view would seem at base relativist rather than substantivalist (I know, I’m still trying to relate your position to more conventional views on spacetime, but the ‘pluralistic Leibnizian framework’ would also suggest this). The “emerge with” also gives me the impression that you’re working from a neo-Newtonian understanding of ‘physical time’ (‘clock time’, as long as we bear in mind Einstein’s comments on clocks!), though this might be a matter of interpretation…

“In other words, the emergence of psychological entities is flanked by the emergence of psychological CTs (a kind of pluralistic Leibnizian framework). This has a number of consequences, notably the fact that some CTs may existentially precede other CTs. I defend the claim, however, that existential dependence does not necessarily imply categorical dependence”

Yes, this seems a reasonable enough position. I’d need more examples of ‘existential dependence’ and ‘categorical non-dependence’ to draw any further conclusions.

“Please note that we can easily recognize that there are emergent entities even if we do not know the details of the emergence. We know that life emerged from inanimate matter, even if we have almost no idea about how it happened.”

I agree, as long as we don’t fall back on emergence as a get-out-of-jail-free-card. All the same, most supervenience relations – and particular global relations – only tell us that there is *some relation* between the subvenient base and the supervening property; they rarely identify which particular (for example, mental) properties are emergent on which particular physical properties.

***

“Back to the main point: the issue is that spacetime (as the universal CT) presents itself a layered structure, where the layers are provided by the various CTs. If so we can understand the deep appeal exerted by "formal" or clock time and formal or geographical space. they are "neutral" framework to which all the various CTs can be projected (and then compared).”

Surely, the ‘formal’ representation of space and time would nowadays resemble a Minkowski space? Could we not argue that, if the other CTs can be projected on a four-dimensional spacetime, such a spacetime is at least ontologically fundamental - for certain purposes, at least? (There is, I agree, a fundamental difference between the space and time (or spacetime) apparent at the orders of magnitude of our phenomenal experience and the ‘Hilbert space’ of particle states and interactions – and, more generally, the ‘space’ in which QM applies has more in common with a phase space than with a spacetime. Indeed, the CT theory could be of value in understanding the “space” and “time” required by quantum theories - the 'degrees of freedom' required strike me as a promising avenue of reflection).

You say that spacetime, as the "universal CT", is a "layered" structure, and that the layers are also CTs. Is the universal CT composed of these layers, or are these layers 'carved' from the universal CT?

One remark. By your initial definition, CTs would seem to be spatiotemporal regions, particularly when we consider the parallelism between "layering" and "foliation". Yet the way in which those regions are constructed by one CT would differentiate them from other ways of constructing CTs. To give a rather 'sensationalist' example, the CT generated by cosmology would be coextensive with spacetime, yet would still be a proper part of spacetime, as cosmology doesn't allow for the construction of local CTs (cf. my remark about local distinctions between past, present, and future and a local 'passage of time'; these latter being partially 'psychological' or 'social' constructions). Cosmology doesn't really allow for the construction of psychological space; after all, physics isn't biology and certainly isn't psychology. Yet, psychological and social CTs must surely be part of spacetime – if not, we're obliged to adopt some form of dualism.

A concrete example would be Cresswell's use of the sub-interval property (or its lack) as a means of distinguishing between events and objects. In two lines: an object, such as a book, has the property of being a book at any sub-interval of its period of existence. An event such a journey from London to Paris, doesn't have the "sub-interval property" – no sub-interval of the complete journey is itself a journey from London to Paris. Objects and events would seem to 'occupy spacetime differently' – indeed, Peter Hacker has argued that objects are 'spatial' while events are 'temporal'. Yet surely this is just the way our talk of such things carves spacetime – 'events' occupy, or are defined on, a CT that is subtly different from that occupied by 'objects'.

"As to the proper understanding of time, I am unhappy with both the A and B series. Thinking about pure time (pure in the sense of a time considered independently from the objects that bear it), I tend to see time as a boundary. As any other boundary, it is a dependent entity. The actual moment now, if understood as a boundary, is both what exists (actually, the only thing that exist) and at the same moment it existentially depends from something that doesn't exist any more"

Ah-ha – a presentist! I must admit, dear Roberto, you're the first with whom I've had the pleasure of direct debate. There are several thousand objections I could raise, but the most obvious would be: how would you square the construction of CTs with the non-existence of other times? Here, I'm taking it that your definition of the present would be neo-Newtonian – a hyperplane of simultaneity having no extension in the temporal dimension (while the specious present is attractive it's both logically and metaphysically unacceptable as the foundation of the "universal Now" required by presentism). Yet, if we take psychological CT, these would actually seem to be constructed in a 'specious present' - we have no 'instantaneous experiences'. This would surely imply that any entity constructed in a psychological CT would have parts at other times – which, on strict presentism, implies that it would have parts that do not exist.

I'm not saying that the objection's fatal – it just means that everything in your ontology endures, which seems to complicate matters for your psychological and social CTs (it might even render psychological CTs epiphenomenal, as the 'space' in which they operate would seem to require a present at least 'large' enough to contain actual bodily sensations; this 'space' appears to have extension in the temporal dimension – unless I'm misunderstanding your use of 'psychological'). I believe that other objections *are* fatal for presentism, but I'll develop those elsewhere.

Roberto – once again, forgive the delay in replying!

"you will see that formal and substantival issues are intertwined"

Guilty as charged. As a substantivalist, I have a certain way of understanding or envisioning the relation obtaining between spacetime and the set of points we (to my way of thinking) project onto it when giving a 'formal approximation of its structure'. The closest analogy would be that of the terrain and the map; I suppose I have an intuitive tendency to picture the relation as 'iconic' (to use Peirce's term). Indeed, a semiotic analysis of the relation could be fruitful, as - to continue the Peircian analogy - I do nonetheless agree that we should be careful to bracket out our intuitive preference for iconicity when considering the relation between scientific accounts and "the world", as the relation is frequently *indexical* rather than *iconic*.

"The main issues here are: what is a point? and Which is the structure of the continuum?"

They are indeed, and I'm very relieved to find that others find such questions bothersome. In the mainstream philosophy of time it's rare to see anyone actually questioning what we actually mean when we talk about zero-dimensional points and temporally unextended 'instants'… ("point-events") have undoubted theoretical value in, for example, special relativity; but we should be wary of any too-hasty assimilation of the theoretical model and the 'actual structure of spacetime'. We should also question what "the continuum is but a set of points" means in *metaphysics*: whether we're using a neo-Newtonian or an Einsteinian model, "a set of points" is a mathematical, not a metaphysical, notion.

I can see the interest of smooth analysis in projecting – if I understand correctly – finitely short segments rather than points. If we take that the present is a finitely short segment, it can be long enough to have 'direction', yet not long enough to have 'curvature' – which, I suppose, would bear some analogous relation to the 'passage' of time (or perhaps I'm being over-imaginative). Anyway, in terms both of the traditional – 'Augustinian' – understanding of the passage of time and of the Parmenidian objections , I agree that the smooth analysis account is extremely elegant, though I think in terms of physics it still requires a neo-Newtonian understanding of spacetime if it's to serve as a foundation for any universal distinction between past, present, and future.

(forgive me if I make any gross misinterpretations in the following)

Whether of not spacetime is gunky or grainy is, I think, metaphysically distinct from its 'ontological structure' in terms of the distinction between past, present, and future. Whether this intuition can be reformulated in relativist terms depends on the relativist, though I can see no reason why it shouldn't be. The question of whether spacetime is smooth or some kind of 'quantum foam' is relatively unproblematic - there's a current of thought that holds that there's a definite limit around the Planck size; and even if there isn't, the differences between classic relativistic and quantum accounts imply a rupture between the kinds of geometric model we can apply.

I don't know how the smooth analysis account would project onto SR, nor its impact on the presentist view… The punctualist view isn't very promising for presentism - given the classic (SR) understanding of a four-dimensional spacetime, a point can only be both simultaneous with, and accessible to, itself, so if the 'present' is defined as being

(1) simultaneous with a certain time T (= "T has the same temporal co-ordinate as now"); and

(2) accessible to a hypothetical observer O at T

it follows logically that, on a punctualist understanding of the structure of spacetime, each point occupies solipsistically a 'local present' inaccessible to any other 'local present'. While a version of presentism – "extreme here-and-now-ism" – has been postulated (more, I think, as a straw man) in which a certain point is indeed given "privileged status as the one, real present time", and is thus "the only existing thing", I'm sure you'll agree that the position is metaphysically improbable and pragmatically indefensible.

However, could the smooth analysis account avoid the pitfalls of *extreme* here-and-now-ism by postulating a finitely small, non-zero, value for the "here-and-now'? Much would depend on the order of magnitude in the temporal dimension of the 'segment' of spacetime under consideration (would this be a hypersurface? Or am I mixing formalism and substantivalism again?), as on the classic SR-based metaphysical account, the 'here-and-now' would occupy a three-dimensional sphere with a radius of whatever distance light could travel in the non-zero interval under consideration.

I must say that it strikes me as unlikely that 'occurrences' over such finitely-short 'intervals' could found an objective passage of time in any sense that would correspond to our intuitive notions (Craig Callender has made similar remarks in a recent paper, "Finding ‘Real’ Time in Quantum Mechanics"). Furthermore, the problem of the absolute present, which involves finite intervals at orders of magnitude far higher, remains entire.

My conclusion - pending refinement of your points and correction of any misunderstandings I might be guilty of – is that you could reinforce the representation of local distinctions between the past, present, and future, and perhaps give a local direction of time (though Callender remarks that on the quantum scale this can have counterintuitive results), but that this seems more an answer to the A-theory/B-theory debate than an argument for a presentist account of the status of 'other times'.

(as for the second part of your message, thanks for the clarifications !)

“The principle of Microstraightness … suggests … that time be regarded as a plurality of smoothly overlapping timelets each of which may be held to represent a ‘now’ (or ‘specious present’) and over which time is … still passing” (both quotation from page 10).

I've just found a paper by Bell on "Infinitesimals and the Continuum" which seems to give a good summary of his views – I've only glanced at it – I'll read it tonight - but I notice that he speculates on a possible role in describing the Planck scale. All the same, I'd need to look into the idea from the QM side (I've found no immediate references in a quick check of the literature in the philosophy of physics) which, given my limitations in QM, could take a bit of time… I'll get back to you on Bell, then!

***

As I've remarked elsewhere, the "problems" we encounter when attempting to define time are generally unchanged since Augustine; defining it as a 'fundamental quantity' is, as you imply, just a matter of formalistic legerdemain. Nonetheless, the representation of time as a vector is more ancient than Augustine, and can be found in the commonplace spatial analogies we use when talking about time. To a large extent, the physical sciences have retained this representation of "time as vector" (and indeed, the Minkowski interpretation of special relativity could be seen as the most "elegant" or "refined" development of this way of representing time). The representation of time as vector is also used in other areas of 'knowledge' – the timelines used in history and grammatical analysis provide good examples.

So, while we can argue that the geometrical construction of time as an ordered series of 'points' or 'instants' is a matter of spacetime formalism, there would still seem to be a more general intuition that the relation between events in time can be given by a vector. Nonetheless, we should bear in mind that the representation of time as a *vector* already presupposes a 'dynamic': there is a directional component. The timelines used in grammatical or historical analysis show a clear 'direction' from the past to the future. The vectors in such semi-formal representations, like the vectors in any situation open to entropy, are not time-reversible. At first sight, McTaggart's famous A- and B-series would seem to be evident examples of time represented as a vector; events would seem to be organised in a linear sequence, and neither A-properties nor B-relations are time reversible – past can never become future, and earlier-than can never become later-than.

When you speak of a 'dynamic', I feel that you're talking not just of an order or structure such that an event E temporally precedes some other event F, but of a 'real passage of time' such that E was future, is present, and will be past (though this might be stated in terms too close to the traditional A-theory/B-theory opposition to do justice to your thought). Unless we're going to accept some fundamentally cyclical model of time (yes, I'm getting to the juicy bit!) even the rhythmic or cyclical phenomena on which we base our measurement of time would seem to 'unwind' along some vector (the first cycle is *earlier* than the seventeenth; the pendulum swings from left to right by being at the left *and then* arriving at the right…). Setting aside both the very small and the very massive, there would seem to be a definite 'order' to physical events between 'earlier and later' or 'past and present'; this 'order' can be approximated by a vector in spacetime.

All the same, this is still "time as order". We could perhaps modernise this to "time as a co-ordinate" and argue that the time in which things happen is not to be distinguished from the space in which they happen save as a formal exercise in spatiotemporal topology; what we have is still – for better or for worse – Quine's spacetime: a heterogeneous four-dimensional block which we can carve more or less to our guise (allowing for certain provisos concerning the preference for accounts which 'carve it at the joints').

***

The relation between rhythmic or cyclical processes and time is fundamental. This might seem in direct contradiction with my preceding defence of vector-based representation; nonetheless, I'd point out the very real difference between "representing spacetime" and "representing time". 'Spacetime' is, as I remarked above, a refinement of our intuition that there is something 'spacelike' about time, but this certainly doesn't exhaust "temporality" as a fundamental quality of our phenomenal experience. At best, we can understand spacetime in the Quinean or neo-Quinean sense; at worst, it is no more than a certain formal interpretation of special relativity that doesn't even apply to the extremely small or the extremely massive.

As with Mind – with which, I'm convinced it's closely linked – the 'problem of time' is in fact two problems. In the philosophy of mind, we have the problem of mind as an apparently causal element in human interaction (problems of intention etc.) and also the problem of mind as self-consciousness, first-person experience etc. In Time, we have the problem of time 'as a direction', which covers ontological questions such as "where is the past?" or "are earlier than-later than relations fundamental?" and also semantic questions such as "what is the status of tense?". Alongside this, we also have the problem of our phenomenal experience of time. Whether or not eternalism or presentism is true, we *experience* a real distinction between the past and 'other times'. Whether or not things are entirely present at each instant (or timelet) or are extended through time as they are through space, we only perceive brief stages of them.

The question of *why* we should perceive or experience time as something which flows is only of real meaning to a B-theoretical eternalist; this being the case, I'll shelve it for the instant. The 'quality' of both its passage and its extent in our phenomenal experience is another matter, and one which concerns eternalist and presentist alike. Neurological and psychological research has shown that a large part of our psychological experience of time is linked to internal rhythms, and our social representation of time is entirely based on natural rhythms. The "horological revolution" at the end of the 17th century provided us with means of 'measuring' time accurately at intervals short enough to approximate our sense of the 'immediate present' (how far they shaped this immediate present is hard to say). But, though they allowed 'measurement' at a lower order of magnitude, they still reproduced the cyclical basis of our 'social' time. Here, the face of the clock is as important as its mechanism – while the latter is a direct expression of periodicity, the former represents the periodicity of the Sun's apparent progression. This reproduction in miniature of the Sun's apparent progression is in part a social convention, allowing the new clocks to integrate the wider socially-defined divisions of the day.

This only scratches the surface of your message; unfortunately, tomorrow is another working day and I need to get some sleep. Also, I'd like to read through the Bell and check the Van Gelder & Port before going further…

Roberto - I've read the Bell article I mentioned, and find it very exciting; I'd like to make a few comments but - to keep the coherence of the thread - I'll post them in a new thread and continue my remarks on your other, equally interesting, points here.

(when I have a little more time!!!)

“I agree with your last note. I only would like to stress again the difference between the representation of time and time itself. I agree entirely that for any scientific / modeling / whatever purpose time must be represented and the only robust way to represent time we have found is to "spatialize" it, be it in the form of a line or vector or whatever. I have no problem at all with all this. My problem is not the representation of time, but time (the ontology of time, if you like).”

Having read the Bell, and having a better grasp of “where you’re coming from”, I might well modify certain of my comments (I’ll get down to that this evening). All the same, I’m not entirely convinced that the spatiotemporal view is ‘no more’ than its representation – I tend to see the Minkowski representation of spacetime as a four-dimensional manifold as being ‘projected onto’ spacetime, rather than as being ‘constitutive of’ spacetime. But then I’m a substantivalist… Shall we say that I’m convinced that spacetime is not ‘built up’ out of points (and, in part at least, for reasons similar to those given in the Bell paper).

”As far as I know, there is only an unique framework in which the order of temporal phenomena is naturally and systematically altered: the famous specious present we have already mentioned more than once.”

This is not a sentence I can give sufficient attention to between two professional e-mails – I’ll have to give it some serious thought. The specious present is one of the themes I’d like to touch on in my comments on the Bell paper.

As I not only have a good computer, but also a good synthesiser, I can indeed reproduce the experiment you suggest, taking a sine wave A (Lah) at 440 Hz, broad spectrum (unfiltered) white noise, and a sine wave G (sol) at around 392 Hz. I can also knock up the other sequences for comparison, and send them all to you as MP3s…

So, as soon as I’m free this evening, I’ll get to work…