He developed what was perhaps the first model of Big History based on the modern understanding of non-equilibrium thermodynamics in *The Self-Organizing Universe* (Jantsch 1980). This book – his widely-acknowledged masterwork (and for good reason) – is still a stunning example of integrative multidisciplinary scholarship even after four decades, and anyone who is interested in a deeper understanding of the physical processes underlying Big History would do well to get hold of a copy.* He also made fundamental contributions to – among other things – futures studies, general systems theory, urban planning, integral approaches to consciousness, and the list goes on. He would definitely be one of the people I would invite to an “ultimate dinner party”, along with Einstein, Darwin, etc. No question.

Here’s a taster of some of his thoughts on the integrative power engendered by the paradigm of evolutionary self-organisation. First (quoted in Zeleny 1981, p.120, and most probably referring to Jantsch 1981a):

The new paradigm of self-organization, and with it the focal concept of autopoiesis, ends the alienation of science from life. It forms the backbone of an emergent science of life that includes a science of our own lives, the biological as well as the mental and the spiritual aspects, the physical as well as the social and the cultural.

And, from his final book *The Evolutionary Vision* (Jantsch 1981b):

the greatest importance of today’s evolutionary vision may lie not in its present propositions and concepts, but in the new questions it poses in many areas of scientific endeavour and especially in the unifying transdisciplinary ‘pull’ it exerts in these areas. (p.210)

Of [great] importance will be a precise formulation of the relations between biological/ecological/sociobiological evolution on the one hand and psychological/sociocultural evolution on the other. … The evolutionary vision opens up the possibility of understanding all creative dynamics in a unified way. (p.212)

And, finally, what appear to be his last words in print:

The evolutionary vision is itself a manifestation of evolution. The reward for its elaboration will not only be a new (or partly revived) natural philosophy or an improved academic understanding of how we are interconnected with evolutionary dynamics at all levels, but also an immensely practical philosophy to guide us in a time of creative instability and major restructuration of the human world … . With such an orientation, science will also become more realistic and meaningful for the concerns of human life. It will be not merely an end product of human creativity, but a key to its further unfolding in all domains. (p.213)

For more information about him, the Wikipedia page is a useful source, and there is an excellent biography of Jantsch by Leah MacVie, which also contains links to some of his many works listed there.

Two final comments from his contemporaries and colleagues are in order. One from Milan Zeleny (1981, p.120):

his ideas will be missed with an increasing intensity. He will be re-discovered, recognized, and acknowledged as one of the most original systems thinkers of recent decades.

And one from Harold Linstone (in Linstone et al. 1981, p.3):

We are grateful to Erich Jantsch — his mind rocketed through intellectual space with dizzying speed, leaving a bright trail for us.

Indeed. I wonder what other treasures and illuminations we might have received from him if he had indeed lived to today…

Meanwhile, watch for a related paper in an upcoming special issue of the *Journal of Big History*.

* Even second-hand copies tend to be a bit expensive, some ridiculously so (I found it through Addall.com). But, luckily, it appears to be possible (at least at the time of this writing) to download a free PDF copy from __https://monoskop.org/File:166495032-The-Self-Organizing-Universe-by-Erich-Jantsch.pdf__

Voros, J 2012, ‘Macro-prospection: Thinking about the future using macro- and Big History’. Paper presented at *Global Future 2045 International Congress*, Radisson-Slavyanskaya Hotel, Moscow, Feb 17-20. http://hdl.handle.net/1959.3/216156. https://youtu.be/77OlQ_3yakI

——— 2012, ‘Complexity + Consciousness: A model of Big History based on self-organising complexity, incorporating consciousness’. Paper presented at *Teaching and Researching Big History: Exploring a new scholarly field; the International Big History Association inaugural conference*, Grand Valley State University, Grand Rapids, Michigan, Aug 2-5. http://hdl.handle.net/1959.3/229485.

Capra, F 1981, ‘Erich Jantsch 1929-1980’, *Futures*, vol. 13, no. 2, Apr, pp. 150-151. doi:10.1016/0016-3287(81)90022-7

Jantsch, E 1980, *The self-organizing universe: Scientific and human implications of the emerging paradigm of evolution*, Pergamon Press, New York. (PDF)

Jantsch, E 1981a, ‘Autopoiesis: A central aspect of dissipative self-organization’, in M Zeleny (ed.) *Autopoiesis: A theory of living organization*, Elsevier-North Holland, New York, pp. 65-88.

Jantsch, E (ed.) 1981b, *The evolutionary vision: Toward a unifying paradigm of physical, biological and sociocultural evolution*, Westview Press, Boulder, CO, USA.

Linstone, HA, Maruyama, M and Kaje, R 1981, ‘Erich Jantsch 1929–1980’, *Technological Forecasting and Social Change*, vol. 19, no. 1, Feb, pp. 1-5. doi:10.1016/0040-1625(81)90045-7

Zeleny, M 1981, ‘Erich Jantsch (1929–1980)’, *Human Systems Management*, vol. 2, no. 2, Jul, pp. 118-120. doi:10.3233/hsm-1981-2208

There is a KudoBoard where people have posted their memories of the MSF.

Q: What now?

A: Trust emergence…

]]>In *gauge field theories* the “connection” carries the gauge field, while the “curvature” corresponds to the field strength, a view that was argued in a book by Göckeler and Schücker (1989), which I had also been reading at that time. Since electromagnetism is often introduced as the archetypal gauge field in mathematical treatments of differential geometry (such as that by Göckeler & Schücker), it seemed to make intuitive sense to me that introducing electromagnetism into an extension of GR intended to model electromagnetism by way of a geometrical object might require it to enter by way of the *connection*, rather than as an additional field just lying around in spacetime, as it is in Einstein-Maxwell Theory (EMT). Hence, in this view, the SSMC is an obvious candidate.

In what follows, I will establish some basic definitions for some mathematical operations that will be required in the next post (Part III) where we will examine the geometry of the SSMC as a precursor to seeking field equations that may be implicitly contained in the geometry.

As noted previously in Part I, I do *not* intend to follow the standard pathway for finding field equations from a formal mathematical “variational procedure” (a standard approach to classical field theories), which is a very common way that GR is sometimes introduced and developed in contemporary accounts and in many texts. (There are problems with this approach anyway, as it turns out, which I’ll talk about in Part IV, on searching for field equations.)

Rather, I wish to follow and perhaps generalise the original pathway Einstein himself followed when working out GR, which was to look for candidate geometrical objects guided by considerations of *physics*. It was only after the field equations were written down that a variational approach showed that the field equations so postulated were “compatible”. In 1917 Einstein wrote in a letter to Felix Klein (cited in Pais 1982, p.325):

It does seem to me that you highly overrate the value of formal points of view. These may be valuable when an *already found* [his italics] truth needs to be formulated in a final form, but fail almost always as heuristic aids.

As Pais then goes on to note, this is indeed striking when compared to how Einstein later searched for a unified field theory based on generalising the formal mathematical variational procedure which can be used to derive the field equations of GR – in effect, ignoring his own advice to Klein. As I delved through the derivations of various versions of non-symmetric forms of Einstein’s unified field theory (EUFT) from 1925 to 1955 during my doctoral work, the contrast between his being guided by considerations of physics in GR and by a desire for formal simplicity in EUFT was indeed quite marked. Pais observes (p.325) that, back then in 1917, Einstein still “knew with unerring instinct how to select complexes from nature to guide his scientific steps.” One could do worse, then (I think), than to seek to emulate the “unerring instinct” of the Einstein of 1917 and to forego – to the degree possible – any over-reliance on “formal points of view” and, instead, to have considerations of physics front-of-mind and center-stage.

As Pais also notes on that page, Einstein’s last act while dying in hospital was to work on the most recent pages of calculations on his unified field theory, after which he collected up his notes, laid down his pen, and went to sleep. He never woke up. This is all the more remarkable since he had said to his collaborator Infeld (1942, p.234) some two decades earlier:

Life is an exciting show. I enjoy it. It is wonderful. But if I knew that I should have to die in three hours it would impress me very little. I should think how best to use the last three hours, then quietly order my papers and lie peacefully down.

This is one of the reasons I found it so enormously compelling working on Einstein’s attempts at a unified field theory – it was *literally* the last thing he worked on during his amazingly productive life of doing fundamental and revolutionary physics. The overall tone of this little planet in the vast cosmos was immeasurably raised for his having lived here at all, and may be the one genuine claim to fame we have in the universe (as the cartoon at the top of this post suggests, published the day after his death in 1955). He pursued that quest for a unified theory right to the very end…

So, let us now return to that quest, albeit via a much simpler and much less formal pathway than he followed, to see if we might be able to make some headway towards a geometrically-unified account of gravity and electromagnetism that is based on what I think is the simplest step at all possible beyond the elegantly beautiful simplicity of GR.

In the following, I will largely follow the index-placement conventions of Schouten (1954), since this affords the easiest manner of comparison with his analysis. His discussion is contained in Chap. III (commencing p.121), but which I shall greatly abridge, leaving aside all the detailed definitions of different spaces, as well as changing his notations in a couple of places later where I think it is more useful or intuitive.

In a general (curved) space, it is necessary to introduce something called a *connection *(Schouten renders it as* connexion*) which, in the component notation, is usually denoted . It is important, among other things, for defining differences in the values of functions at “nearby” points, since you need some sense of what “nearby” actually means in order to be able to do this. It is not a tensor, but it does help to define (see below) so-called *covariant derivatives* of tensors, which are themselves also tensors, as well as being the basis for the important *curvature *tensor. As mentioned in the previous post, the use of tensors is greatly to be preferred, owing to their desirable properties, so the definition of a tensorial *covariant* derivative allows this to be done for the very important operation of taking derivatives.

The *covariant derivative* is defined as follows, for an “upper” index (note the “+” sign):

and as follows for a “lower” index (note the “-” sign):

Here represents an ordinary *partial* derivative with respect to the coordinate , which does not (usually) yield a tensorial object (i.e., one that behaves like a tensor) unless it operates on a scalar function. (Technically, a scalar is a tensor of “rank 0”, and an ordinary partial derivative on a scalar ends up being a tensor of rank 1. The “rank” of a tensor essentially corresponds to how many indices it has. Thus, a vector is a tensor of rank 1. It’s in this way that a tensor is just like a vector only more so! ) The order of the lower indices on the is important, and the sum of the partial derivative term combined with the term produces the tensorial covariant derivative. There is a summation implied by the repeated index appearing both up and down in a single term in the equations (1).

In addition to a connection, there may also (but not necessarily) be defined a (second-rank, or “rank 2”) tensor **g**, with components , which is symmetric, , called the *metric* tensor (or simply *the metric*), which in essence endows the space with the concept of distance, and defines how distances can be measured in the space. It is not necessary for a general space possessing a connection to also have a metric, but GR does.

In a 4-dimensional space, such as that which is used to represent spacetime, this tensor can be represented by a matrix, where the Greek indices and conventionally each range over all *four* dimensions of spacetime: “0” – time; 1,2,3 – space. It has the general form

where the various components each represent functions of the coordinates and, as is shown, the component functions located across the main diagonal are the same (symmetry). As a matter of interest, Newton’s theory is essentially contained in the component given as .

From the (components of the) metric one can define (the components of) an inverse metric, (note that the indices are up) by way of

again recalling that repeated upper and lower indices imply a sum over that index, in this case on the indices and in the above, and where is the so-called *Kronecker delta* such that

for and for

which can be visualised as a matrix with 1s on the diagonal and 0s elsewhere:

The inverse metric also ends up being symmetric from this construction: .

In general, the position an index occupies on an object (whether “up” or “down”) is important, and needs to be kept track of, as does its relative placement with respect to other indices (i.e., whether “left” or “right” of an index). The metric is used to “raise” and “lower” indices, as follows (for some object A):

The effect of a summation with a Kronecker delta is to change the repeated (summed) index into the non-repeated one, thus:

If a connection is *metrical *(or just *metric*), then the covariant derivative of the metric tensor with respect to that connection vanishes:

This is an important property because it means that taking covariant derivatives is compatible with the raising and lowering of indices (technically, these operations are said to “commute”) and so indices can be freely raised and lowered in objects containing covariant derivatives without having to keep track of which was first, the covariant derivative or the raising or lowering.

The (non-tensorial) object

is known as the *Christoffel symbol* of the metric tensor . It is symmetric in the lower indices.

There is an important relationship between the metric, the connection and the Christoffel symbol, if the relationship (6) is assumed to hold (i.e., that the connection is metric), and if the connection in that relationship is assumed to be symmetric in the lower indices, . In this instance, Equation (6) implies that:

Thus, this is how the Christoffel *symbol* ends up being the *Christoffel connection, *and so ends up being *the* (unique)* symmetric metric(al) connection*.

Any general connection in a space containing a metric can be written as the sum of the Christoffel connection and a tensor which represents, as it were, the “deviation from ‘Christoffel-ness'”:

Note that this is *not* the torsion tensor, which is often denoted by **T** in some texts; the torsion will be the anti-symmetric part of **T** and be denoted by **S**, following Schouten’s notation.

By substituting (9) into the equations (1), the covariant derivative can be expressed in terms of the Christoffel connection {} and the tensor T, thus:

,

which can be re-grouped as follows:

The terms in the parentheses ( ) on the right-hand sides of Equation (11) are covariant derivatives using the Christoffel connection {}. Denoting a covariant derivative using the Christoffel connection by , the equations (11) can be re-expressed as:

and the important property that the Christoffel connection is *metric* can be written:

.

Symmetry or anti-symmetry in indices is denoted by round or square brackets, respectively, and there is a division by a factor of for the *n* indices involved in the (anti-)symmetrisation. For our purposes, the symmetric and anti-symmetric parts of a general rank-2 tensor can be denoted

and any tensor can always be separated into a symmetric and an anti-symmetric part:

It is also possible (Carroll 2004, p129) to split the symmetric part into two further components: the *trace *, and a trace-free part , where *n* is the dimension of the space. For a 4-dimensional space like spacetime, (15a) can be rewritten as

These three elements of the tensor **B** define “invariant subspaces” such that, as Carroll notes, under a change of coordinates “the different pieces are rotated into themselves not into each other” (*ibid*.). They are, therefore, in a certain sense, quasi-independent pieces of the whole tensor.

This index (anti-)symmetrising process generalises to other tensors having more than two indices. For our purposes later we need only consider (anti-)symmetrisation of no more three indices. Thus, symmetrising over 3 indices, hence the factor , by taking permutations of the indices, yields

while the analogous anti-symmetrisation looks like

This operation is most easily done by first doing a cyclic permutation to generate the first three terms, and then swapping the 2nd and 3rd indices of each of these three terms, to give the second three terms (note how the first index is the same for the 1st and 4th, 2nd and 5th and 3rd and 6th terms). For symmetrisation, all signs are made positive, whereas for anti-symmetrisation, the odd permutations (i.e., the “swapped” indices in the 2nd group of three terms) are all negative, whence, (16b) is easily obtained from (16a) by making each *odd* (“swapped”) permutation negative.

If any index is excluded from the index mixing, it is separated off by way of vertical bars | |, thus:

and similarly for anti-symmetry,

noting that the factor of division is because only 2 indices are being mixed.

OK, so that sets the scene for the next part, where we will examine the geometry of the space of the semi-symmetric metric connection to see what geometrical objects exist there and how these compare to or differ from the objects we are familiar with from the Riemannian space of GR.

*Next time: Part III: The Geometry*

Carroll, SM 2004, *Spacetime and geometry: An introduction to general relativity*, Addison-Wesley.

Göckeler, M and Schücker, T 1989, *Differential geometry, gauge theories, and gravity*, Cambridge monographs on mathematical physics, Cambridge University Press.

Infeld, L 1942, *Quest: The evolution of a scientist*, Readers Union / Victor Gollancz, London.

Pais, A 1982, *Subtle is the Lord: The science and life of Albert Einstein*, Oxford University Press.

Schouten, JA 1954, *Ricci-calculus: An introduction to tensor analysis and its geometrical applications*, 2nd edn, Springer-Verlag, Berlin.

*Main image: Cartoon in *The Washington Post* 19 April 1955 by Herb Block.*

Now, if you know General Relativity (hereafter “GR”) – which is Einstein’s theory of gravitation – then you’ll know that Einstein worked with geometrical objects called “tensors” (or more precisely, *tensor fields*) to formulate the field equations of GR using “tensor analysis” or “tensor calculus”. *(“What’s a tensor,” you ask? Well, a tensor is a bit like a vector, only **more** so. In actual fact, a vector is a particular **type** of tensor, but this is not the place for more detailed definitions.)*

This formulation was done principally in what is known as the “component” (notation) form of tensor analysis, which uses symbolic representations of the component functions that describe an object, rather than a more geometrically-oriented abstract representation of the object itself. (This latter is much more common these days, and mathematicians tend to prefer to stick to the elegant component-free representation for the most part. Physicists, on the other hand, tend to work more directly with the component notation, mostly for pragmatic reasons, given that they are usually wanting to carry out calculations, which generally requires accessing individual components.)

*\begin{brief explanatory aside}*

For example, an ordinary 3-vector (i.e., a vector in 3-dimensional space) is often written simply as a boldface letter **v**, which emphasises its “geometric object” aspect. But, when we are instead looking at the vector’s components along the **x**, **y** and **z** directions, it is often written something like this:

where the “hat” forms and represent the unit “basis vectors” that point in the , and directions, respectively, and and represent the component functions of the vector **v** in the , and directions.

The three basis vectors and can also be written as and , or simply by where **x** can represent a “generic” coordinate (not just the *x* direction), and it is understood that the index *i* ranges over all (in this case, three) dimensions. Thus, , and . The superscript notation should not be confused with powers, so is not “**x** squared”, but rather “coordinate 2”, and so on). In this way, the above 3-vector **v** can then be represented by

where the are the respective *components* of the vector, in whatever *general* coordinate system is being used, which does not necessarily need to be the more familiar simple *x, y, z* of conventional Cartesian coordinates. The in this case could in fact represent unit basis vectors for *any* convenient 3-dimensional coordinate system that we may wish to use (such as polar coordinates, , and , for example). This is one of the (many) beauties of tensor notation – the general *form* of an equation in component notation is the same irrespective of the specific coordinate system used, but one needs to be aware that the *values* of the component functions will generally change with a change of coordinate system, because the basis vectors themselves are different in different coordinate systems. The geometrical object itself doesn’t change, of course, but any *representations* of it will obviously change if the coordinates which are being *used* to represent it change. In this way, the vector-object **v** can be *represented* by its components , for some general coordinate system . Purists tend to baulk at statements like “the vector ” because, strictly speaking, those are the *components* of the vector **v** (in a given coordinate system ), not the vector itself. However, this misuse of language is very common and widely understood, and it persists because it does help to simplify discussions of tensors (of which a vector is a particular type, as noted). In the above equation, the summation sign is often omitted, since repeated upper and lower indices – the index *i* in this case – usually imply a summation, so the above equation would more conventionally be written

which saves a bit of writing (although the index placements – i.e., up or down – can change in more general spaces than the 3-D space with which we are familiar).

*\end{brief explanatory aside}*

So, to the matter at hand.

As we will see later, the geometrical space that is used as the basis for GR (“Riemannian” or sometimes just “Riemann” geometry) has a special set of assumptions about the nature of some important objects defined in the geometrical space, mostly to do with certain types of “symmetry” they possess. Now, as I was working on mathematical *extensions* to GR – and in particular Einstein’s own *non-symmetric* unified field theory (although I also looked at a few others along the way) – you might get an intuitive sense right away that because of its “non-symmetric” nature it was going to be even more complicated than anything found in (symmetric) GR (which, we’ll see, is complicated enough!). And indeed it was, both in terms of the underlying geometry, as well as in terms of the field equations for the two fields Einstein was attempting to unify, these being gravitation (which is what GR is a theory of, as mentioned) as well as electromagnetism.

We will see later that the geometrical space of GR, Riemannian geometry, can be derived from two key assumptions concerning two fundamental objects found in certain geometrical spaces – the *metric tensor*, usually denoted by , which essentially defines distances – and the *connection*, usually denoted by , which essentially defines how to form derivatives of functions in a space that may be “curved” (there are of course other properties of these objects, but I’ll delay any further discussion until much later). In particular, because of the possibly-curved nature of generalised geometric spaces, the familiar simple *partial* derivatives of functions need to be augmented by additional terms involving the connection in order to produce what are called “covariant” derivatives, which are important when working with differential equations in general non-flat (i.e., “curved”) spaces.

In general, the metric of a geometrical space is a “symmetric” tensor, which can be represented – for a four-dimensional space – by a symmetric matrix of functions (i.e., the components reflected across the main diagonal from each other are the same), so that there are only 10 independent functions among the 16 components in total that are found in a matrix.

The connection, by contrast, is not a tensor, and does not necessarily possess any sort of “symmetry”, so it can in general be “non-symmetric”. However, any general non-symmetric connection can always be uniquely decomposed into the sum of a symmetric part which is *not* a tensor, and an anti-symmetric part which *is* a tensor, which latter is generally known as the “torsion” tensor (the anti-symmetry introduces a kind of “twisting” into the connection, hence its name).

The important assumptions underlying the Riemannian geometry of GR are that if, in a general space, the connection is assumed to be (i) *symmetric* (and thereby having no torsion), and (ii) *metrical* or *metric *(sometimes *metric compatible*), which means that the covariant derivative of the metric tensor with respect to that connection vanishes (i.e., = 0), then one recovers *uniquely* the underlying Riemannian geometry of GR, as well as the extremely important relationship which defines the connection wholly in terms of functions of the metric – the so-called “Christoffel symbol” or *Christoffel connection*, which we might therefore characterise as *the* (unique) *symmetric metric connection*.

This relationship between metric and connection ends up making every important tensor in the space – including the tensor known as the *curvature* (or *Riemann*) tensor – ultimately a function of the metric. It is in this way that Einstein’s theory of gravitation is a pure geometrical theory of gravity, because a curvature tensor wholly expressible in terms of the metric produces a geometrical space whose “shape” is, as it were, “doubly” defined by way of the metric, while the field equations of GR are ultimately equations for the metric via the curvature as it relates to and is influenced by the distribution of matter-energy in spacetime. In other words, in GR, the mathematical geometrical “space” (Riemannian geometry) is assumed to represent actual spacetime itself – quite successfully, as it turns out, since it has been fully verified in every experimental test it has ever been subjected to for the last century (although see later in this series of posts for some further comments about this).

Pre-empting things a little bit (I’ll go into more detail in later posts), Einstein’s original field equations of 1915 can be written in the form:

where is a complicated geometrical object (now called the *Einstein tensor*, built out of objects derived from the Riemann/curvature tensor, and thus ultimately out of functions of the metric) which defines the gravitational field; and is a tensor describing the distribution of matter-energy in spacetime (the *energy-momentum tensor*), which is related to by a constant involving important physical quantities, which, for simplicity, we will just render here as *k*. (In Nov 1915 Einstein actually wrote it in a slightly different form, but the separation of geometry and matter-energy on each side of the equation was still there). The physicist John A. Wheeler famously said of the field equations of GR that: “Matter tells spacetime how to curve. Spacetime tells matter how to move.” Here, in the above equation (1), matter is T, and spacetime is G.

Now, my PhD work was on a *non-symmetric* *generalisation* of GR undertaken by Einstein himself, begun about a decade after GR was published. Einstein’s unified field theory (hereafter “EUFT”) *dropped* the assumptions of symmetry of the underlying space in an attempt to see if electromagnetism could also be incorporated into such an expanded non-symmetric geometrical theory. The search for such a unified field theory was prompted in Einstein’s mind by the (to him quite unsatisfactory) separation of geometric field and mass-energy in Equation (1). He said of it (writing in Schilpp 1949, p.75):

The right hand side is a formal condensation of all things whose comprehension in the sense of a field-theory is still problematic. Not for a moment, of course, did I doubt that [the] formulation [] was merely a makeshift in order to give the general principle of relativity a preliminary closed expression. For it was essentially not anything *more* than a theory of the gravitational field, which was somewhat artificially isolated from a total field of as yet unknown structure.

And (Einstein 1954, p.311):

It is sufficient – as far as we know – for the representation of the observed facts of celestial mechanics. But it is similar to a building, one wing of which is made of marble (left part of equation), but the other wing is made of low grade wood (right part of equation). The phenomenological representation of matter is, in fact, only a crude substitute for a representation which would do justice to all known properties of matter.

As I noted in my PhD thesis (1996, chap. 2, sect. 2):

It was this “crude”-ness which prompted Einstein’s further work toward a unified field theory – a theory where there would be pure field equations with no explicit sources. In other words, EUFT was motivated by the desire to get rid of the as a separate object. Rather, the particles would be regions where the (geometric) field is very inhomogeneous. It was his hope that a more general theory would eliminate the singularities which are present in GR.

It is widely held that he did not succeed in this quest (indeed, this is now folklore in physics – and many people have written about and sometimes lamented that he spent his final years on such a “fruitless” search…). However, my doctoral work demonstrated that the two main published analyses of the electrodynamics of EUFT – which allegedly showed that EUFT does not produce the correct equations of motion for charged particles and so must therefore be physically unviable – are actually *inconclusive* as a test of the viability of EUFT; so, therefore, it argues, one cannot conclude, on the basis of those analyses, that the theory is indeed unviable. Of course, this statement is *quite different* from saying the theory *does* work. It’s just that *one cannot say anything,* *one way or the other* about the viability of EUFT on the basis of those earlier analyses, and so – since it was rejected on the basis of those analyses – it was actually rejected for the wrong reason. This result was written up for a journal article, eventually published in 1995 (Voros 1995).

During the time that I was trying to work out the electrodynamical terms implied by a suitably-refined analysis of the electrodynamics of EUFT, I was delayed for several months while awaiting a copy of a PhD thesis from the University of Toronto. That thesis (Wallace 1940) contained the details of how to derive the equations of motion for charged particles when Maxwell’s electromagnetic theory is added to GR by making the represent the electromagnetic field (the so-called “Einstein-Maxwell Theory”, EMT). If it was to be considered viable, then EUFT would need to be able to produce a similar, if not the same, result for equations of motion for charged particles as EMT does, so an understanding of how that was done in EMT was essential.

Very early in my candidature, I had found the aforementioned book by Schouten in the University’s library, which I was reading to try to understand more fully the various properties of non-Riemannian geometrical spaces – including the space of EUFT – and the various important tensors which can be defined within them in the general case beyond the special assumptions of the Riemannian geometry of GR. Internal disputes at UT led to a delay in getting hold of Wallace’s work, and it was due to this delay that, for something useful to do while I waited, I went back to Schouten’s book and continued exploring a most beguiling idea I had come across there earlier, during my preparatory research into general geometrical spaces – an idea which I’ll describe below.

As noted above, the Christoffel connection is the *unique* connection which emerges from assuming a (symmetric) metric tensor and a torsion-free (i.e., symmetric) connection, while simultaneously assuming that the connection is also metrical/metric (i.e., the covariant derivative of the metric with respect to that connection vanishes) – to wit: *the* symmetric metric connection. Schouten noted his results as part of a wide-ranging and magisterial discussion of the properties of general geometrical spaces, and then very elegantly derived specific cases resulting from particular assumptions to show how these special cases arise as a result of those assumptions.

One of the consequences for EUFT, arising from the relaxation of the simplifying assumptions of symmetry found in GR, was its incredible complexity, both in terms of the underlying geometry as well as the field equations – I used to (only half-jokingly) say that . As a result, since I was interested in extensions to GR in general, even while looking at EUFT in particular, I was also always on the lookout for ideas that might indicate a somewhat smaller step from GR than is the full-blown *leap* into EUFT – that is, for somewhat more “minimalist” (as it were) extensions to the (Riemannian) geometry of GR which might include an object that could describe the electromagnetic field.

In electromagnetic theory, the electromagnetic field is often represented by an anti-symmetric tensor, conventionally written , which can also be represented by a anti-symmetric matrix. In contrast to the 10 independent components of a symmetric tensor/matrix (like the metric, say), an anti-symmetric tensor/matrix has only 6 independent components. Now, it turns out that any general non-symmetric tensor/matrix (which will have 16 components in total) can be written as the unique sum of a symmetric and an anti-symmetric (or “skew”) tensor/matrix (thus, 10 + 6 components in total). This observation was almost certainly one of the reasons Einstein sought to use a more generalised non-symmetric “fundamental tensor” (i.e., a non-symmetric ), which would hopefully contain both the metric (gravity) and electromagnetism in a single geometrical formalism.

But, the electromagnetic field can also be represented by a 4-vector *potential* from which the skew tensor is constructed. Indeed, from an empirical perspective, the so-named Aharonov-Bohm Effect shows that the potential is not merely a mathematical artifice, which it was assumed to be for quite a long time, but indeed actually has a physically measurable effect, so it can considered “real” in an important sense. So, perhaps, the focus on when thinking about modelling electromagnetism could reasonably be relaxed in favour of another representation of the electromagnetic field, based on, say, a 4-vector … or so I thought.

Now enter a discussion from Shouten, chapter III, section 2, which introduces a type of connection called *semi-symmetric* for which the skew part (i.e., the torsion) has the most interesting form (which is clearly anti-symmetric in the indices and )

,

where is a 4-vector field, and is the so-called Kronecker delta (he called it the “unity tensor” and denoted it by ), such that

for and for ,

which can be visualised as a matrix with 1’s on the diagonal and 0’s elsewhere:

In other words, a *semi-symmetric connection* seems to introduce a *single* 4-vector field into the connection! This is *very* interesting! And, furthermore, in Section 4 of the same chapter (on p.142), it is observed that there is a **unique**, “*metric *semi-symmetric connection”, which adds to the usual Christoffel connection of Riemannian geometry an extra term of the form

.

Wow! If *ever* there was a candidate for a minimalist extension of GR which introduces only a single 4-vector field, then this has *got* to be it! I called it the MSSC (“metrical semi-symmetric connection”) for a long time (indeed my main notebook and the sundry loose notes all use this shorthand term), but I have since recently found that mathematicians working on this topic tend to refer to it as the *semi-symmetric metric connection*, so I have now changed the way I refer to it in order to reflect this.

Hence, the upcoming series of posts, of which this one is marked as the first. The intention is **to (re-)examine the*** semi-symmetric metric connection*** (SSMC) as a possible extension to the (Riemannian) geometry of GR, in order to see whether it might be able to model the addition of the electromagnetic field to GR in a geometrically-unified way, **given that the SSMC adds only a single new object to Riemann geometry – to wit, an object of precisely a most very-highly suggestive form, namely, a 4-vector.

I spent a lot of time trying to nut this idea out over the years, starting about 1989/1990 or so when I first saw the SSMC in my preliminary reading of Schouten and more seriously subsequently to that, but each time have had to put it aside – not the least of which reason in those days was to actually *finish* the PhD on the topic I had started with – and definitely once the Wallace thesis showed up and I could get on with the electromagnetic calculations for EUFT. Following completion, of course, there was paid work to find, then marriage, etc, and life beyond the comparative haven (I now realise) of postgraduate study ramped up considerably – and had practically nothing to do with physics anymore – so the SSMC exploration project has waxed and waned over the years (mostly waned).

But, every few years I go back to my notes – the earliest ones were from around 1990/91 (now lost), and I copied some of the later loose notes into a workbook in early 1998 to ensure they didn’t get lost, too) – or sometimes directly to Schouten’s book itself, and try once again to derive plausible field equations implied by this form of connection, using arguments based in physics, much as Einstein had done for the field equations of GR arising from results in Riemannian geometry. But, I have never quite got there… It always feels like I get close, but my ability to shuffle tensors and tensor indices around is very oxidised these days, compared to 30 years ago, so it always seems as though there is some clever trick or an important insight that is dangling *just* beyond the reach of my increasingly-addled, and now quite middle-aged, brain …

Nonetheless, I hope that by making these explorations public and open – and having to clarify and explain to others what I am trying to do – it might lead to some new ideas or insights that might nudge my thinking over the edge and yield a coherent mathematical theory which, one hopes, could be tested – both for internal consistency and for empirical validity. A poster that was attached to the wall above my desk when I was a PhD student was a quote from 1969 Nobel Laureate Murray Gell-Mann. In an interview for *Omni* magazine in 1985 he noted (Schultz 1985, p.94):

In theoretical physics we use very simple tools: pencil and paper, eraser, chair and table. More important than any of these is the wastebasket. Almost every idea that occurs to a theoretical physicist is wrong. And it can be wrong on various grounds. The simplest grounds for being wrong have to do with logical inconsistencies. Once the idea or theory is logically consistent, there is also the question of whether it agrees with a system of well-established observations. The theory has to agree with itself, and it has to agree with nature. Those are the requirements, and most theoretical ideas don’t meet them. So we crumple up most of our pages of scribbles and throw them away.

When, after many a long session of scribbling tensor equations in the various theories I was looking at, it turned out that some calculation or other yielded either no result or landed in a dead-end from which no return was possible, I would – as Gell-Mann said – have to crumple up those pages of scribbles. Then, while hurling them towards the nearest wastebasket or recycling bin – and to the frequent consternation of my fellow students in our shared office – I would very often say out loud and with no small amount of exasperation: “and here’s *another* one for *you*, Murray!” Then, it would be time for more coffee, and a sanity break, before starting it up all over again… Over the years people have asked me what it was like to do theoretical physics. The only sensible explanation I’ve ever been able to come up with is this: Listen to the second movement of Beethoven’s Ninth Symphony. For me, it’s like that.

So, that’s the background – how and why the SSMC came to be lodged in my mind 30-odd years ago. It has hung around on the backburner ever since, occasionally popping up for a brief visit, sometimes even being treated to a more extended stay for a bit of tensor-fun-and-games every few years. But, overall, I feel that I had pretty much stalled on the exploration of this quite lovely and elegantly simple idea. So, I am undertaking this series of blog posts with the intention of them hopefully triggering new insights to see if, just maybe, the SSMC could be the basis of a “minimalist” classical geometrically-unified theory of gravity and electromagnetism – the two “macroscopic” fields – based on extending GR. Even a “limited” unified theory of just these two macroscopic fields (as opposed to the full-blown complete unified field theory of *everything *which is the current Holy Grail of physics) would still be an interesting thing to have.

Of course, there have been attempts to add torsion to GR before (e.g., “Einstein-Cartan theory”) but these have tended to involve non-symmetric energy-momentum tensors and attempting to model “spin” (a property of quantum particles). I am not going down that line. At least, not until I see how far SSMC geometry can be pushed *vis á vis* classical electromagnetism. I also want to avoid the use of a variational procedure to derive the field equations, preferring rather to use arguments and ideas from physics to do so, just as Einstein did for GR. More on that later.

Sometimes, the process of explaining something to someone else causes unexpected connections and produces insights that a silent internal conversation with oneself will never yield.

Therefore, let’s see how it goes, *this time around* …

*Next time: Part II: Mathematical preliminaries
*

Einstein, A 1954, *Ideas and opinions*, Bonanza Books, New York. Based on *Mein Weltbild* edited by Carl Seeling, and other sources. New translations and revisions by Sonja Bargmann.

Schilpp, PA (ed.) 1949, *Albert Einstein: Philosopher-scientist*, vol. 1, Harper and Row, New York.

Schouten, JA 1954, *Ricci-calculus: An introduction to tensor analysis and its geometrical applications*, 2nd edn, Springer-Verlag, Berlin.

Schultz, R 1985, ‘Interview: Murray Gell-Mann’, *Omni*, vol. 7, no. 8, May, pp. 54-58, 92-94.

Voros, J 1995, ‘Physical consequences of the interpretation of the skew part of in Einstein’s nonsymmetric unified field theory’, *Australian Journal of Physics*, vol. 48, no. 1, pp. 45-53. http://adsabs.harvard.edu/abs/1995AuJPh..48…45V arXiv:gr-qc/9504047.

Voros, J 1996, *On the electrodynamics of Einstein’s non-symmetric unified field theory*, PhD thesis, Dept of Physics, Monash University, Melbourne, Australia. (Australian) National Bibliographic Database (ANBD) Record number 12976078. https://nla.gov.au/anbd.bib-an12976078. A version typeset as a normal-sized, two-sided book is available as a PDF from both Academia.edu and ResearchGate.

Wallace, PR 1940, *On the relativistic equations of motion in electromagnetic theory*, PhD thesis, Dept of Mathematics, University of Toronto, Toronto, Canada.

*Main Image – the title section of the 1915 paper describing General Relativity: “The Field Equations of Gravitation”. Image Credit: John D Norton, University of Pittsburgh. **https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_pathway/index.html*

I had seen it before, of course, as it is one of the most striking of the many superlatively beautiful and photogenic images that the Hubble Space Telescope has made available to humanity as part of its astounding legacy. But when I saw it *again* on NASA’s Astronomy Picture of the Day on that day in late August 2010, I saw it in a quite different context – one prompted by having thought deeply for some months about what *galaxy-scale macro-engineering* might look like. And so, picture it: *that* idea, coupled with *that* image, and you can see, I hope, how the question asked in this post’s title would come immediately and insistently to mind (at least, for me!). As I thought about it even more for a few weeks, I even ended up tweeting about it – so strongly had the idea installed itself into my head! – https://twitter.com/JosephVoros/status/26173613969 (see Figure 2).

In fact, there were five tweets in all (first, second, third, fourth:shown here, fifth) which, fortunately, were so far in the distant past of the tweet-stream that when I decided to delete thousands of tweets as a precursor to getting off social media entirely a couple of years ago (well, it worked, for a while…), they were no longer easily accessible, and so survived the bulk-cull. Thus, luckily, they still exist as an historical record of what was at the time an hysterical time of intense SETI-focussed cogitation!

Of course, there is a fair bit of background thinking that underpins the suggestion that Hoag’s Object might (with any luck!) be an example of galaxy-scale macro-engineering. It started with a paper written over a decade ago for the *Journal of Futures Studies *(‘Macro-perspectives beyond the World System‘ [1]), which itself was an extension of an idea from an earlier paper for the same journal [2]. The jumping-off point for that paper was an observation by Johan Galtung [3], who had proposed a three-level schema for conducting social analyses of various types – at the individual, the social-system, and the world-system levels – which all come under the umbrella of what is part of a broad “macrohistorial” approach to looking for possible “patterns” in history (all taking place on Earth, of course). He noted [3, p.3]:

The macrohistorical approach also makes sense beyond this [three-level schema]. Imagine if we discovered other worlds with historical processes. We could then move up one level and write an interworld history as raw material for a macrohistory of interplanetary or even intergalactic systems, incorporating biological and physical systems, and their rhythms.

This of course prompted the thought that, in order to extend the schema (as he suggested was possible), another framework would be required which *began* with world systems, rather than ended with them – such as, for example, the above-mentioned Kardashev schema. The Kardashev scale, as originally proposed in 1964, had three levels also – planetary, stellar, and galactic – and the civilisations Kardashev designated as Types I, II or III map to these levels of structure, respectively [4]. The Macro-perspectives paper [1] then went on to discuss various perspectives that move beyond an Earth-based scope or context (as the title suggests), including, of course, the observation that other technological civilisations might exist, as implied by the Karadashev scale, which thereby brings our attention to the search for extraterrestrial intelligence (SETI). It was in this context – while examining various parameters which researchers have used to think about SETI and the consequences of detecting extraterrestrial life or intelligence – that the idea was mooted of conducting a full-blown parametric analysis of possible detection scenarios. The 2007 paper noted [1, p. 16] that:

From a futurist’s perspective, the range and scope of possible detection scenarios are of some interest, as an understanding of the extent and contours of this scenario space could help us prepare for the implications of such an event. … [O]ne can imagine several parameters which might characterise the scenario space of contact: *proximity*, ranging from proximal to distal (e.g., terrestrial, solar system, nearby stellar system, within our galaxy, in another galaxy); *complexity* of life, from simple (e.g., bacteria), to complex (e.g., reptiles), to intelligent; and, the nature of contact, whether direct (face-to-‘face’), or indirect (e.g., fossil traces, or mediated through technology, such as an intelligent probe). Additional parameters might also include, in the case of intelligent life, the *motivation* of the extraterrestrials towards us (hostile, benign, indifferent, helpful, etc.), as well as the age or stage of development of their civilisation (such as its Kardashev type, among other things).

Fast-forward a decade and the follow-up paper to this suggestion – ‘On a morphology of contact scenario space‘ [5] – has now appeared in the journal *Technological Forecasting and Social Change*, as mentioned in an earlier post. The approach used to conduct the parametric analysis is a variant of the technique of “morphological analysis” developed by Fritz Zwicky, the legendary Caltech astrophysicist of the early-to-mid 20th Century CE who, among other things, inferred the existence of “dark matter” as early as the 1930s, but which suggestion was not followed-up until Vera Rubin (re-)discovered it in the 1970s.

I had written a paper in 2009 on the use of morphological methods in foresight [6] which had discussed a number of approaches to morphological analysis (and which, I am very happy to say, won the “Outstanding Paper” award for the journal volume for that year in the Emerald Literati Awards for Excellence, 2010). A move to another city at around that time had necessitated daily long train commutes to get to/from my university for work, and it was on these commutes that the 2009 morphology paper was mostly written (as well as during a two-week stint while quite ill in bed). Once it was published it was not long before I began trying out various parameters for a possible scenario space for “contact”, building upon the idea from, and parameters mentioned in, the 2007 paper. The long train commutes provided an opportunity to while away the traveling time by experimenting with various scenarios that might emerge from the (very!) many possible configurations which would be contained in the parametric “configuration space” of any proposed morphological array that attempted to be seriously realistic (see below).

In this particular investigation I used the variant of morphological analysis known as “field anomaly relaxation” or “FAR” (developed by Russell Rhyne, see [6]), where the parameters are called Sectors, the parameter values are called Factors, and which uses a mnemonic “word” of up to six or seven letters to represent the morphological space, derived from letters contained in the Sector names. There is some degree of latitude in the choice of the Sector-designation letters used to produce the mnemonic “word” and, obviously, the more memorable the mnemonic, the better! The mnemonic which eventually came to be used was LSEARCH (“ell-search”) and the resulting “Sector/Factor array” that was eventually published is shown in Figure 3. A few other parameters for possible subsequent analysis and exploration were also mentioned as potential extensions to this “minimalist” morphology for contact scenario space, but were not used in that particular instance of analysis, although they could be one day in follow-up work…

A single specific “configuration” in the total morphological “configuration space” is selected by choosing one Factor from each Sector for all of the (in this case, seven) Sectors. In the array shown in Figure 3, one can see that there are therefore possible configurations in the total morphological configuration space, each of which represents one potential contact scenario. (Not all of these are necessarily “coherent” or “consistent”, and usually some “pruning” of the configuration space is generally possible which can reduce the total configuration space of all theSomething that can be quite fun when exploring a newly-constructed morphological space is to – as it were – “spin” the Sectors at random like the reels in a poker/slot machine to see what “hand” is so dealt, and then to reverse-engineer what the configuration(s) in the morphological space might represent in the “real world” that the morphology is being used to model.

One of the morphological “hands” that emerged in this way (during the above-mentioned train commutes) can be rendered as: – the and indices are “free” in the sense that no *specific* index values are assigned to them (here think of free indices such as are found in some forms of tensor analysis). represents “some entity of unspecified nature”, while represents “a sign of indeterminate character” (i.e., possibly intentional, possibly not). The other terms indicate: – an intelligent entity; – a physical sign (i.e., not an electromagnetic signal); – extra-galactic (i.e., outside our own galaxy); – “indirect” contact (i.e., there is no actual direct contact between us and the entity); and – a Kardashev type that is II or III or some transition between these (i.e., at least stellar possibly heading towards or at galactic scale). In other words: this designation characterises what might be called *galaxy-scale macro-engineering *outside the Milky Way Galaxy*. *Couple this designation with the image shown in Figure 1, and I hope you can see why I found this idea so intriguing on that day in 2010.

As is remarked in Ref. [5, sect. 7], this idea was so intriguing that it has stayed very firmly in mind ever since. It was mentioned in the 2010 running of what had come to be called the “scary aliens” lecture of the MSF unit *Dimensions of Global Change*, the final unit of the first year of the MSF back in those days*. *This had been the customary final lecture of that unit since 2003, so students would finish their first year of the MSF with what was intended to be a series of fun, big-picture, and mind-blowing macro-perspectives, including SETI and possible contact (hence, “scary aliens”). (This lecture was also the basis of Refs [1] and [2], both of which have now been updated, edited and abridged into the book chapter for the *Big History Anthology* [7], mentioned in an earlier post). This was then followed by: a conference presentation at the International Big History Association inaugural conference in Grand Rapids, Michigan, in August 2012 [8], later written up as part of a selection of papers from that conference [9]; a public event (held, appropriately, in a planetarium) at the Asia-Pacific Foresight Conference in Perth, Western Australia in November 2012 [10]; as well as forming the final part of a presentation at the Big History Anthropocene conference held at Macquarie University in Sydney in early December 2015 [11] (also mentioned in an earlier post, and embedded below).

For me, this is an idea that just cries out to be tested experimentally (and I hope for you, too!). Of course, there are many papers dealing with the striking core-gap-ring structure which attempt to explain the galaxy’s unusual morphology by modelling naturally-occurring dynamics (many of these are cited in [1] and also in [9]), and most of the hypotheses remain viable, so there is no criticism of the viability of those hypotheses intended. It’s just that, given the thinking leading up to the LSEARCH designation shown, it does invite the further suggestion that perhaps, *just perhaps,* the processes involved in giving rise to the highly unusual structure of Hoag’s Object *might* not be *entirely* natural… And *that*, I think, suggests that taking a much closer look – “just in case” – is worth a bit of time and effort, given the astonishing pay-off that it might possibly yield…

Luckily, it is not too difficult to think of several empirical observations that could be made to begin to investigate this beguiling possibility, including [1, p.135; 9, pp.12-13]:

- examination of the radiation coming from behind the galaxy through the ‘gap’ between the core and ring for any anomalies (e.g., diffraction, scattering, polarisation) compared to analogous background radiation from immediately adjacent to it;
- spectroscopic examination of the composition of the ring for any anomalies in the extent or character of star-forming regions or in the chemical composition (e.g., metallicity profile) compared to what would be expected from the ‘usual’ processes of stellar evolution going on in analogous spiral galaxies of similar diameter and age; and
- examination of the peri-core region for any possible time-keeping or other beacons that may be being used to coordinate in time any putative galaxy-scale engineering activities that might require synchronisation.

The idea of an, as it were, “Galactic Mean Time” to aid synchronisation of engineering activities is prompted, in part, by the presence of an intriguing “osculating braid” structure in the stars of the ring [12, p.463], and also, in part, from a whimsical short-story by Seth Shostak [13]. The star-forming regions appear to be synchronised in space, which could, of course, simply be a pressure-shock effect from cascading supernovae. But, what if this effect is being *deliberately* produced or nudged-along, or perhaps is being made to move in the direction *opposite* to what is expected for comparable galaxies where similar dynamics occur? An effectively-immortal species with a macro-engineering bent might decide – perhaps as a way to while away the endless aeons – to create an aesthetic effect by setting off supernovae in synchronisation so as to generate a braid of star-forming regions in the ring, which would require a standardised galactic clock. In other words (putting on a “preposterous futures” thinking hat), could the braid actually be an example of galaxy-scale installation art?

Or, perhaps the braid may be being used to signal to other galaxies, since only *really* long-lived species (like themselves) would notice any anomalous motion of such a braid structure. There would thus likely only be a response possible from similarly long-lived species, as opposed to shorter-lived ones who might not be that interesting to them (after all, we don’t bother to make “contact” with mayflies, do we?). In this regard, it is interesting to note that there is visible in the gap (at roughly the “12:30” position) what appears to be another, presumably much more distant, galaxy which appears to have a similar morphology to Hoag’s Object. Could that more distant galaxy have been a trigger for the intelligent entities in Hoag’s Object (the “Hoagsians”?) to re-engineer their own galaxy (e.g., by seeding in them the idea of undertaking their own galactic macro-engineering and possible ring-braiding project as a form of “reply”)?

On my *ultra*-preposterous futures thinking days I like to imagine that, at some stage, if we humans manage to get our act together and become really serious about our long-term future, we too (or, rather, what is perhaps more likely is that our *post-biological descendants*) could do something like this to our own galaxy. Then, there would be *three* such beautiful Hoag-type galaxies in a row, at least in this neck of the Cosmos… And, who knows, maybe there is an even larger daisy-chain of such macro-engineered galaxies emerging in both space and time throughout the Universe as it evolves. Picture in your mind for a moment the utterly *stupendous* scale of such a thing: A Universal Daisy-Chain of macro-engineered Hoag-type galaxies embedded in the overall background Cosmic web… *Utterly preposterous! *Of course it is! And that’s why it’s totally beguiling and irresistibly captivating, too!

The Square-Kilometer Array (SKA) is now being set up. I would think that Hoag’s Object might make a very nice calibration target which could be used for configuring and fine-tuning the instrument during its commissioning and subsequent testing. At the very least, it might yield some new data and deeper insights into the history or dynamics of the intriguing structure of Hoag’s Object. But, as I am suggesting here and have suggested elsewhere, it also holds out the quite enchanting possibility of being potential confirmation of . Given its quite large distance from us ( million light-years) [12], this could be a contact scenario that would be much less likely to engender the degree of fear or concern that might otherwise occur if the proximity of contact is somewhat closer. You only have to look at how contact scenarios with have been depicted in popular culture to see that most are not assumed to go that well (with some notable exceptions, of course [5, sect. 6])… If Hoag’s Object’s striking structure is one day demonstrated to be have been the result of deliberate engineering, then we could get all the benefits of detecting without the potential terror that any proximity might bring with it. I’d call that a win!

The contact scenario paper [1] ends with the following comments (p.136):

[it is] fondly to be hoped that an empirical observing program of Hoag’s Object be undertaken to search for any subtle signs of possibly-artificial activities, given the astonishing pay-off that such a modest investment might just yield….

One of these years, when I get the time, I’ll explore these ideas in much more depth and scientific rigour, and write it up more fully for a suitable journal, in the hope of elaborating more specific technical details of how to undertake any proposed empirical observations. In the meantime, though, I already have the title I’ll use for that follow-up article (hopefully sooner than in another decade…!): it is the (very captivating!) research question:

*Is Hoag’s Object a Dysonian artefact?*

Now I just need the time and headspace to do it.

[1] Voros J. Macro-perspectives beyond the world system. Journal of Futures Studies 2007;11(3):1-28. http://jfsdigital.org/articles-and-essays/2007-2/vol-11-no-3-february/articles/macro-perspectives-beyond-the-world-system/

[2] Voros J. Nesting social-analytical perspectives: An approach to macro-social analysis. Journal of Futures Studies 2006;11(1):1-21. http://jfsdigital.org/articles-and-essays/2006-2/vol-11-no-1-august/articles/nesting-social-analytical-perspectives-an-approach-to-macro-social-analysis/

[3] Galtung J. Macrohistory and macrohistorians: A theoretical framework. In: Galtung J, Inayatullah S, editors. Macrohistory and macrohistorians: Perspectives on individual, social, and civilizational change. Westport, CT, USA: Praeger Publishers; 1997. pp. 1-9. Available from: http://www.metafuture.org/product/macrohistory-and-macrohistorians/

[4] Kardashev NS. Transmission of information by extraterrestrial civilizations. Soviet Astronomy 1964;8(2):217-21. Available at: http://adsabs.harvard.edu/abs/1964SvA…..8..217K. See https://www.centauri-dreams.org/2014/03/21/what-kardashev-really-said/ for a detailed discussion of Kardashev’s proposal.

[5] Voros J. On a morphology of contact scenario space. Technological Forecasting and Social Change 2018;126:126-37. doi:10.1016/j.techfore.2017.05.007. arXiv:1706.08966.

[6] Voros J. Morphological prospection: Profiling the shapes of things to come. Foresight 2009;11(6):4-20. doi:10.1108/14636680911004939. Also available at: http://hdl.handle.net/1959.3/69196

[7] Voros J. Big Futures: Macrohistorical perspectives on the future of humankind. In: Rodrigue B, Grinin L, Korotayev A, editors. The way that Big History works: Cosmos, life, society and our future. From Big Bang to galactic civilizations: A Big History anthology, vol. III. Delhi: Primus Books; 2017. pp. 403-36. ISBN: 978-93-86552-24-2.

[8] Voros J. Galactic-scale macro-engineering: Looking for signs of other intelligent species, as an exercise in hope for our own. Paper presented at: Teaching and Researching Big History: Exploring a new scholarly field; the International Big History Association inaugural conference, 2012 Aug 2-5; Grand Valley State University, Grand Rapids, Michigan, USA.

[9] Voros J. Galactic-scale macro-engineering: Looking for signs of long-lived intelligent species, as an exercise in hope for our own. In: Grinin L, Baker D, Quaedackers E, Korotayev A, editors. Teaching and Researching Big History: Exploring a new scholarly field. (Selected papers from the inaugural International Big History Association Conference held at held at Grand Valley State University, Grand Rapids, Michigan, USA, 2-5 August 2012.) Volgograd, Russia: Uchitel Publishing House; 2014. pp. 283-304. ISBN: 978-5-7057-4027-7. Available from: http://hdl.handle.net/1959.3/366566 and http://arxiv.org/abs/1412.4011/.

[10] Voros J. Galactic-scale macro-engineering: Looking for signs of long-lived intelligent species, as an exercise in hope for our own. Presentation at: Planetary Future Event, 3rd Asia-Pacific Foresight Conference, 2012 Nov 16-18; Horizon: The Planetariuim (Scitech), Perth, Western Australia.

[11] Voros J. The Anthropocene, “Threshold 9” and the long-term future of humankind. Presentation at: The Big History Anthropocene Conference: A Transdisciplinary Exploration, Big History Institute, Macquarie University, Sydney, 9-11 Dec 2015. https://youtu.be/Z7gU3ZsSWr0. The SETI/macroengineering sequence starts at around 20m 40s.

[12] Schweizer F, Ford WK, Jr, Jedrzejewski R, Giovanelli R. The structure and evolution of Hoag’s object. The Astrophysical Journal 1987 Sep 15;320:454-63. doi:10.1086/165562

[13] Shostak GS. In touch at last [Visions]. Science 1999 Dec 3;286(5446):1872-4. doi:10.1126/science.286.5446.1872

]]>The (current) citation information is:

Voros, J 2018, ‘Big History as a scaffold for Futures education’, *World Futures Review, *vol.10, No.4, Dec, in press. Special Issue: ‘Foresight Education’, P Bishop (ed.). doi:10.1177/1946756718783510. Swinburne RB: http://hdl.handle.net/1959.3/443505

The **Abstract** is as follows:

This paper does several things. Firstly, it reports on some of the history of the Master of Strategic Foresight (MSF) at Swinburne (2001-2018) to provide some background information that, it is hoped, may be useful for others seeking to create or develop under- and post-graduate foresight courses in the future. Secondly, it also describes some observations made during the early years of the MSF regarding some of the characteristics of the students undertaking it – as compared to other non-foresight students also undertaking comparable-level postgraduate studies – which had a bearing on how we designed and revised the MSF over several iterations, and which, it is similarly hoped, may also be useful for foresight course designers of the future. Thirdly, it notes that the introduction of “Big History” in 2015 at both undergraduate and postgraduate levels seems to have engendered a somewhat easier “uptake” of futures/foresight thinking by those students who were introduced to it, in contrast to cohorts of comparable students in previous years who were not. It is speculated that the Big History perspective was an important factor in this, and some related writings by other academics supporting this conjecture are sketched. It is then argued that, in particular, Big History seems to be especially well-suited to the framing of global-scale/civilizational futures. Finally, a number of remarks are made about how and why I believe Big History provides an ideal basis for engendering futures/foresight thinking, especially with regard to global/civilizational futures, as noted, as well as for framing The Anthropocene.

This paper forms another (very likely the last) in a sequence about the life history of the MSF, which is due to shut down at the end of this year. Earlier papers can be found linked from Richard Slaughter’s professional web site at: https://foresightinternational.com.au/archive/afi-history-and-program/

The most recent paper before the one cited above is linked at the bottom of the above web page – it is a review of the (up to then) 16 years of the MSF at Swinburne, by Peter (*“*Captain Foresight”) Hayward and myself, done at Richard’s request. At the end of that paper, I remarked on the way that Big History seems to have been an amazingly effective way to instill futures thinking into students, who seemed to “take” to futures thinking much more easily as a result of having had an introduction to Big History. The new paper extends this discussion with some further reflections, while also seeking to set down for posterity some more observations about the 18-year run of the MSF and the students who undertook it.

The paper winds up with the following observation:

in recent years, in both public outreach and professional talks, I have come to regard and portray Big History and Futures Studies as a “cosmic perfect match” – a “multidisciplinary marriage of timely moment” between multi-disciplines perfectly suited to the sense making and action which we humans need to undertake at this critical time in the history of our civilization, our species and our planet* … *Therefore, may the children of the (hopefully fecund!) marriage of Big History and Futures Studies be engendered with all of the virtue, wisdom and foresight that our species now desperately needs so much, so urgently, and in such measure….

Near the close of the Introduction, it says:

the comments and remarks made herein are intended as precursor observations that, I sincerely hope, may be useful in framing or encouraging further research into how futures thinking might be more practically encouraged to emerge in students of all ages, through utilizing Big History as a “scaffold” for futures education.

And this is the primary motivation for the paper – that this cosmic perfect match of timely moment be encouraged and supported through any and all means – including, as one possibility, some none-too-subtle “matchmaking” on the part of educators, both in Big History and in Futures Studies.

I hope it is both useful and enjoyable to read.

*Main image: the “lines” of Big History (a metaphor from the Big History Project www.bighistoryproject.com) married with the Futures Cone (a metaphor from Futures Studies, discussed elsewhere on this blog)*

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The full reference is:

Voros, J 2017, ‘Big History and anticipation: Using Big History as a framework for global foresight’, in R Poli (ed.) *Handbook of Anticipation: Theoretical and Applied Aspects of the Use of Future in Decision Making*, Springer International, Cham, Switzerland, chap. 95, pp. 1-40. **doi:**10.1007/978-3-319-31737-3_95-1

I also have had published online recently a journal article in *Technological Forecasting & Social Change*, which combined three of my favourite topic areas:

- scenario-based futures thinking;
- morphological methods;
- astrobiology & the Search for Extra-Terrestrial Intelligence (SETI).

The reference to that is:

Voros, J 2017, ‘On a morphology of contact scenario space’, *Technological Forecasting and Social Change,* vol. 126 (Jan), pp. 126-137. Special Section: ‘General Morphological Analysis: Modelling, Forecasting and Innovation’, T Ritchey & T Arciszewski (eds). ** doi:**10.1016/j.techfore.2017.05.007 **arXiv:**1706.08966.

This is also available, as you can see, as a pre-print at arXiv. I am especially happy with this article as it represents the sequel to an idea from a paper published 10 years ago about examining parameters that might usefully describe scenarios of ‘contact’. I hope it is not another 10 years before the next paper in this sequence…

I am also awaiting the final formal publication of another book chapter, in the final volume of the *Big History Anthology*, which has been in production for six years now and has gone through a couple of different publishers before one kept their word to actually publish it.

The reference is (there is chapter/page info because the book is being printed now and and is due to be formally published in mid September):

Voros, J 2017, ‘Big Futures: Macrohistorical perspectives on the future of humankind’, in B Rodrigue, L Grinin & A Korotayev (eds), *The way that Big History works: Cosmos, life, society and our future*, From Big Bang to galactic civilizations: A Big History anthology, vol. III, Primus Books, Delhi, chap. 22, pp. 403-436. ISBN: 978-93-86552-24-2

I am particularly chuffed with this chapter as it is the last chapter in the last volume of the 3-volume *Anthology* series. As such, I get to, as it were, have the last word on Big History I am also exploring the possibility of self-archiving so that it might become available through an online repository at some point soon.

So, in all, a busy few months since the previous post, all while teaching out the last running of Foresight Knowledge and Methods 1, along with the second-last running of Powering 21st Century Innovation (the 2015 running of which gave rise to the name of this blog), as well as convening two other units on Purposeful Leadership (taught by my wonderful colleagues Nita Cherry, and Peter Hayward aka “Captain Foresight”). This semester, it is the second-last running of 21st Century Challenges, and another iteration of my undergrad Big History unit, which has finally hit some healthy numbers. It seems that, despite the fact that the MSF is being shut down, there might still be a future for me at Swinburne, teaching Big History, not Futures Studies. The irony…

A complete listing of my publications is now being curated at ORCID – the Open Researcher and Contributor ID initiative. The URL is https://orcid.org/0000-0001-8697-0080.

See you next time there is a breath that can be drawn ..

]]>The final session — Session 6 — was themed *Humanity’s Long-Term Prospects*, and included talks from astrobiologist David Grinspoon, philosopher Clément Vidal, Big History Institute PhD candidate Elise Bohan, and, naturally, a futurist: me. The actual order was: David; myself; Elise; and Clément, and the organisers had a very clear and well thought-out rationale for this sequence.

David’s talk — Cognitive Planetary Transitions: An Astrobiological Perspective on the Sapiezoic Eon — laid out some of his thinking, developed and refined over the last several years, on the nature of different types of planetary changes — a taxonomy that includes four kinds:

*random*(think asteroid or cometary impacts, such as the end-Cretaceous event ~65 Ma);*biological*(think the Great Oxygenation Event ~2.3 Ga due to “those irresponsible cyanobacteria” polluting the atmosphere with oxygen and leading to a mass exinction of species);*inadvertent*(think anthropogenic climate change as but one clear example of the many changes we have made to the Earth system); and*deliberate*(an existence proof of which is the Montreal Protocol formulated to reduce the hole in the atmospheric ozone layer due to chloroflurocarbons).

This last notion — that we *could actually* get our act together well enough to make positive changes to Earth with some wisdom, rather than the negative changes we’ve made so far by being mostly clueless — led David to suggest that the Anthropocene, which is being proposed (hence the conference) as a possible new *epoch* in Earth history, might in fact be the first stage of a new (much larger time-scale) *eon*, the Sapiezoic Eon, wherein wise long-term sentience becomes a key factor in the history of the Earth. This is a quite wonderful idea, and one that I find great resonance with, probably because we both grew up reading science-fiction that imagined a “grown-up” humanity expanding into the Galaxy. In fact, we can then immediately wonder whether there has been the equivalent of a Sapiezoic on other planets elsewhere… More recently, David has wondered — in his terrific book *Earth in Human Hands* — what other sentient beings (“*Exo sapiens*“) might get up to, once they crack the nut of the existential risk posed by what Carl Sagan called “technological adolescence”.

My talk sought to take a futurist perspective on the Anthropocene, viewing it as the place where Big History and the Big Future meet — where our increasing agency as a species has bumped up against the physical limits of the biosphere. In this view, also, sentience plays an important role — we are where information about the (very long cosmic) past meets anticipations of the (expanding and hopefully sentient) future. This observation is an homage to Erich Jantsch who noted, in his 1980 masterpiece *The Self-Oganizing Universe*, that with the emergence of consciousness as a part of cosmic evolution comes an ability for the universe to not only be aware of *past* information through the usual processes of causality, but also to imagine future information via imagination, hence: *anticipation*. I view Big History as our specific (idiographic) instance of the broader (nomothetic) process of Cosmic Evolution, as the latter has played out here on Earth. Therefore, astrobiology and its subset, SETI (the Search for Extra-Terrestrial Intelligence) are supersets of Big History, and all are sub-sets of Cosmic Evolution. Consequently, the talk looked at two main futures – the “nearer” future of “Threshold 9” (i.e., extending David Christian’s eight-threshold view of Big History to the “next” threshold, also based around energy and energy flows), and the “much further” future of astrobiology/SETI, imagining what we might do as part of our, or what “someone” else may have done as part of their, post-Anthropocene analogue future – in this case a *post-biological* species re-engineering its own galaxy.

The idea of post-biological intelligence linked nicely to Elise’s talk about trans-humanism and the transcension of biology by humanity, which has been occurring in stages throughout human history with each new piece of technology that augments our physical being and/or cognitive capacity. In this case, the long trend is clear – we are gradually becoming more and more augmented by technology, for which the logical asymptotic endpoint is that we will eventually *become* technologically-based intelligence. This is the idea underpinning the well-known concept of The Singularity, and it was the starting point for my own imaginings of post-biological beings undertaking galactic renovations…

Finally, Clément spoke about “The Big Future: The next 14 billion years” outlining numerous further Thresholds, which led to re-engineering, and even “eating”, stars – his “starivore” hypothesis – and ultimately all the way up to “re-booting” the entire Universe with a new Big Bang 2.0 – a kind of Cosmic Ctrl-Alt-Delete! A very fitting bookmark ending to the historical view we have of the *first* 14-odd billion years of cosmic history…

In all, it was a really great conference, and our session in particular was obviously a total blast, if you like wide-open thinking at the very edge of possibility, and even of preposterousness …

]]>The MSF Wake was held on the evening of Friday 25th November 2016 at the wonderful Kelvin Club in the Melbourne CBD (off Russell Street). We had around 150 people attend, a mixture of current and past students, as well as their partners, who were of course also invited to join us — since most partners of people doing the MSF tend to also “do” the course “by proxy”, as it were, it was wonderful to have them along, too.

We wanted to celebrate the MSF *in style*, so we made the event “Black Tie Optional” (i.e., “doll up to your heart’s content if you want to, but you don’t have to”). I even managed to convince The Captain to put on a dinner suit — photographic evidence of this admittedly outlandishly *preposterous* claim is attached below

Richard A. ~~Sorcerer~~ Slaughter, the Foundation Professor of Foresight at Swinburne and founder of the MSF program was also in attendance, and wrote his own reflections on the evening at his blog over at richardslaughter.com.au. As he notes there, it was a really very happy occasion, and continued long (and I mean *long*) after we had to vacate the ballroom at 11 pm. I think we were finally kicked out of the downstairs Bar around 1:15 am, although by that stage it was after far too many Martinis, so I am a bit hazy on the exact details – you rarely get a chance to celebrate 16 years of your life devoted to work, so it was a bittersweet night.

As the last futurist from the original MSF four-some, it falls largely to me to teach out the program, along with some guest lectures from various of our friends and guest lecturers from years past (as well as a guest spot or two from The Captain…). The new teaching year commenced last week with what is (*almost certainly*: I’m a Bayesian, after all ) the final intake of the foundational unit *Foresight Knowledge & Methods 1. *With this came the sheer fun of playing with introductory ideas about the future again after several years since I taught it last. I’ll have more to say in future posts about some of the key concepts we are covering in FKM1 (including Bayesian Inference, of course…).

A fun, fun night and a truly inexpressible joy to have been able to share it with so many of the MSF community, students, partners and other friends of the MSF. For more shots from the MSFwake, as well as remembrances from students of the MSF, head over to the MSF Kudoboard.

*Image credit: SassNvibe (Facebook: @sassNvibe);
*

Voros, J 2017, ‘Big History and anticipation: Using Big History as a framework for global foresight’, in R Poli (ed.) *Handbook of anticipation: Theoretical and applied aspects of the use of future in decision making*, Springer International, Cham. doi:10.1007/978-3-319-31737-3_95-1,

*while the text in this post is from the section of that chapter entitled ‘Types of Alternative Futures’, pp. 10-13, and the “cone” diagram itself is: Fig. 4, p. 11.
*

Futurists have often spoken and continue to speak of *three* main classes of futures: possible, probable, and preferable (e.g., Amara 1974, 1981; Bell 1997, and many others). These have at times lent themselves to define various forms of more specialised futures activity, with some futurists focusing on, as it were, *exploring the possible*; some on* analysing the probable*; and some on *shaping the preferable*, with many related variations on this nomenclature and phraseology (e.g., again, Amara 1991, and many others). It is possible to expand upon this three-part taxonomy to include at least 7 (or even 8) major types of alternative futures.

It is convenient to depict this expanded taxonomy of alternative futures as a ‘cone’ diagram. The ‘futures cone’ model was used to portray alternative futures by Hancock and Bezold (1994), and was itself based on a taxonomy of futures by Henchey (1978), wherein four main classes of future were discussed (possible, plausible, probable, preferable). Some years later I found out that this idea of a cone graphic was used even earlier than Hancock and Bezold (1994) by Charles Taylor (1990), in which he wrote of a “cone of plausibility” that defined a range of *plausible* futures extended over an explicit timeframe, including a kind of ‘back-cone’ into the past. He also included “wildcards” in his approach, but other futures categories mentioned here were not explicitly depicted in the diagram given by Taylor as they were by Hancock and Bezold.

Over the years that I have been using the Futures Cone in foresight teaching and practice, I have found it useful to adapt it and add more classes to the initial few. The most recent version of the Futures Cone as I now use it is as depicted in the figure shown.

The 7 types of alternative futures defined below (or 8 if one also includes a specific singular ‘predicted’ future, which I generally don’t do any more) are all considered to be *subjective* *judgements* about ideas about the future that are *based in the present moment*, so the categories for the same idea can obviously change over time as time goes on (the canonical example of which is the Apollo XI Moon landing, which has gone through most of the categories from ‘preposterous’ to ‘projected’ and thence into history as ‘the past’). In brief, these categories are:

**Potential**– everything beyond the present moment is a potential future. This comes from the assumption that the future is undetermined and ‘open’ not inevitable or ‘fixed’, which is perhaps*the*foundational axiom of Futures Studies.**Preposterous**– these are the futures we judge to be ‘ridiculous’, ‘impossible’, or that will ‘never’ happen. I introduced this category because the next category (which used to be the edge of the original form of the cone) did not seem big enough, or able to capture the sometimes-vehement refusal to even entertain them that some people would exhibit to some ideas about the future. This category arises from homage to James Dator and his Second Law of the Future—“any useful idea about the future should appear ridiculous” (Dator 2005)—as well as to Arthur C. Clarke and his Second Law—“the only way of finding the limits of the possible is by going beyond them into the impossible” (Clarke 2000, p. 2). Accordingly, the boundary between the Preposterous and the Possible could be reasonably called the ‘Clarke-Dator Boundary’ or perhaps the ‘Clarke-Dator Discontinuity’, since crossing it in the outward direction represents a very important but, for some people, very difficult, movement in prospection thinking. (This is what is represented by the red arrows in the diagram.)**Possible**– these are those futures that we think ‘might’ happen, based on some future knowledge we do not yet possess, but which we might possess someday (e.g., warp drive).**Plausible**– those we think ‘could’ happen based on our current understanding of how the world works (physical laws, social processes, etc).**Probable**– those we think are ‘likely to’ happen, usually based on (in many cases, quantitative) current trends.**Preferable**– those we think ‘should’ or ‘ought to’ happen: normative value judgements as opposed to the mostly cognitive, above. There is also of course the associated converse class—the*un**-preferred*futures—a ‘shadow’ form of*anti*-normative futures that we think should*not*happen nor ever be allowed to happen (e.g., global climate change scenarios comes to mind).**Projected**– the (singular) default,*business as usual*, ‘baseline’, extrapolated ‘continuation of the past through the present’ future. This single future could also be considered as being ‘the most probable’ of the Probable futures. And,- (
**Predicted**) –*the*future that someone claims ‘*will*’ happen. I briefly toyed with using this category for a few years quite some time ago now, but I ended up not using it anymore because it tends to cloud the openness to possibilities (or, more usefully, the ‘preposter-abilities’!) that using the full Futures Cone is intended to engender.

The above descriptions are best considered not as rigidly-separate categories, but rather as nested sets or *nested* *classes* of futures, with the progression down through the list moving from the broadest towards more narrow classes, ultimately to a class of one—the ‘projected’. Thus, *every* future is a *potential* future, including *those we cannot even imagine*—these latter are outside the cone, in the ‘dark’ area, as it were. The cone metaphor can be likened to a spotlight or car headlight: bright in the centre and diffusing to darkness at the edge—a nice visual metaphor of the extent of our futures ‘vision’, so to speak. There is a key lesson to the listener when using this metaphor—just because we cannot imagine a future does not mean it cannot happen…

Then there are all of the *imaginable* ones (i.e., *inside* the cone), beginning with the sub-class of those that we judge to be unreasonable, (i.e., ridiculous), or impossible—‘preposterous’ in my alliteration— and the further sub-class of those that we judge to be ‘reasonable but which would require *knowledge we do not yet possess but which we might possess in the future*’ and so ‘might’ happen—‘possible’.

Then there is the sub-class of those that we think are *reasonable based on what we currently know*, and so ‘could’ happen; thus, ‘plausible’. And so on through the rest: the sub-class of futures based on *the playing out of current trends*—‘probable’; and finally the *default* *extrapolation of* *current dynamics*—the (single) ‘projected’ future, the only class in the whole schema containing only a single future, although different people will ‘project’ different futures, so it is really a single-member class containing many ‘single’ futures, as it were. The similarly single-member class of ‘predicted’ future, which had a similar underlying rationale—namely, what ‘will’ happen depends a lot on whom you ask—is very rarely used, except to make a specific point.

The class of *preferred* futures—what ‘should’ or ‘ought to’ happen—can take in any or all of the classes from preposterous to projected, because these futures must be at least imaginable (so inside the cone), and because people’s idea of what they prefer—and how they judge others’ preferences—can range from the default projected future thought to be coming all the way outward to (what is considered) outlandish preposterous-ness.

To this set, one may also add **Wildcards—**by definition low probability *events* (sometimes referred to as ‘mini-scenarios’) that would have very large impact if they occurred (Petersen 1997, 1999). Since they are considered ‘low probability’ (i.e., outside the Probable zone), any member of any class of future outside the range of *probable* futures could be considered by definition a wildcard (although this usage is not common, as the focus tends to be on ‘high impact’ events). Thus, in this view, some wildcards are considered plausible, some possible, some preposterous, and—the scariest of all—some we have not even imagined or dreamed of yet (i.e., potential)… These last are not even classifiable as ‘black swans’ (Taleb 2007), but rather as, perhaps, ‘scarlet splofflings’ (Q: ‘what the hell are they?!’ A: ‘exactly!’).

This taxonomy finds its greatest utility when undertaking the Prospection phase of the Generic Foresight Process (Voros 2003) especially when the taxonomy is presented in reverse order from Projected to Preposterous. Here, one frames the extent to which the thinking is ‘opened out’ (implied by a reverse-order presentation of the taxonomy) by choosing a question form that is appropriate to the degree of openness required for the futures exploration. Thus, “what preposterously ‘impossible’ things *might* happen?” sets a different tone for prospection than the somewhat tamer question “what is projected to occur in the next 12 months?”

Amara, R 1974, ‘The futures field: Functions, forms, and critical issues’, *Futures*, vol. 6, no. 4, pp. 289-301. doi:10.1016/0016-3287(74)90072-X

——— 1981, ‘The futures field: Searching for definitions and boundaries’, *The Futurist*, vol. 15, no. 1, pp. 25-29.

——— 1991, ‘Views on futures research methodology’, *Futures*, vol. 23, no. 6, pp. 645-49. doi:10.1016/0016-3287(91)90085-G

Bell, W 1997, *Foundations of futures studies*, 2 vols, Transaction Publishers, New Brunswick, NJ, USA.

Clarke, AC 2000, *Profiles of the future: An inquiry into the limits of the possible*, Millennium edn, Orion Books, London.

Dator, JA 2005, ‘Foreword’, in RA Slaughter, S Inayatullah & JM Ramos (eds), *The knowledge base of futures studies*, Professional CD-ROM edn, Foresight International, Brisbane, Australia.

Hancock, T & Bezold, C 1994, ‘Possible futures, preferable futures’, *Healthcare Forum Journal*, vol. 37, no. 2, pp. 23-29.

Henchey, N 1978, ‘Making sense of futures studies’, *Alternatives*, vol. 7, no. 2, pp. 24-28.

Petersen, JL 1997, ‘The wild cards in our future: Preparing for the improbable’, *The Futurist*, vol. 31, no. 4, pp. 43-47.

——— 1999, *Out of the blue: How to anticipate big future surprises*, 2nd edn, Madison Books, Lanham, MA, USA.

Taleb, NN 2007, *The black swan: The impact of the highly improbable*, Random House, New York.

Taylor, CW 1990, *Creating strategic visions, *Strategic Studies Institute, US Army War College, Carlisle Barracks, Carlisle, Pennsylvania, USA.

Voros J 2003, ‘A generic foresight process framework’, *Foresight*, vol. 5, no. 3, pp. 10-21. doi:10.1108/14636680310698379