Addendum on the Retrodiction Wall

Saturday

---

In my last post, The Retrodiction Wall, I introduced several ideas that I think were novel, among them:

● A retrodiction wall, complementary to the prediction wall, but in the past rather than the present

● A period of effective history lying between the retrodiction wall in the past and the prediction wall in the future; beyond the retrodiction and prediction walls lies inaccessible history that is not a part of effective history

● A distinction between diachronic and synchronic prediction walls, that is to say, a distinction between the prediction of succession and the prediction of interaction

● A distinction between diachronic and synchronic retrodiction walls, that is to say, a distinction between the retrodiction of succession and the retrodiction of interaction

I also implicitly formulated a principle, though I didn’t give it any name, parallel to Einstein’s principle (also without a name) that mathematical certainty and applicability stand in inverse proportion to each other: historical predictability and historical relevance stand in inverse proportion to each other. When I can think of a good name for this I’ll return to this idea. For the moment, I want to focus on the prediction wall and the retrodiction wall as the boundaries of effective history.

The retrodiction wall in the past and the prediction wall in the future mask inaccessible portions of history from us.

In The Retrodiction Wall I made the assertion that, “Effective history is not fixed for all time, but expands and contracts as a function of our knowledge.” An increase in knowledge allows us to push the boundaries the prediction and retrodiction walls outward, as a diminution of knowledge means the contraction of prediction and retrodiction boundaries of effective history.

We can go farther than this is we interpolate a more subtle and sophisticated conception of knowledge and prediction, and we can find this more subtle and sophisticated understand in the work of Frank Knight, which I previously cited in Existential Risk and Existential Uncertainty. Knight made a tripartite distinction between prediction (or certainty), risk, and uncertainty. Here is the passage from Knight that I quoted in Addendum on Existential Risk and Existential Uncertainty:

1. A priori probability. Absolutely homogeneous classification of instances completely identical except for really indeterminate factors. This judgment of probability is on the same logical plane as the propositions of mathematics (which also may be viewed, and are viewed by the writer, as “ultimately” inductions from experience).

2. Statistical probability. Empirical evaluation of the frequency of association between predicates, not analyzable into varying combinations of equally probable alternatives. It must be emphasized that any high degree of confidence that the proportions found in the past will hold in the future is still based on an a priori judgment of indeterminateness. Two complications are to be kept separate: first, the impossibility of eliminating all factors not really indeterminate; and, second, the impossibility of enumerating the equally probable alternatives involved and determining their mode of combination so as to evaluate the probability by a priori calculation. The main distinguishing characteristic of this type is that it rests on an empirical classification of instances.

3. Estimates. The distinction here is that there is no valid basis of any kind for classifying instances. This form of probability is involved in the greatest logical difficulties of all, and no very satisfactory discussion of it can be given, but its distinction from the other types must be emphasized and some of its complicated relations indicated.

Frank Knight, Risk, Uncertainty, and Profit, Chap. VII

This passage from Knight’s book (as the entire book) is concerned with applications to economics, but the kernel of Knight’s idea can be generalized beyond economics to generally represent different stages in the acquisition of knowledge: Knight’s a priori probability corresponds to certainty, or that which is so exhaustively known that it can be predicted with precision; Knight’s statistical probably corresponds with risk, or partial and incomplete knowledge, or that region of human knowledge where the known and unknown overlap; Knight’s estimates correspond to unknowns or uncertainty.

Frank Knight’s tripartite distinction among certainty, risk, and uncertainty can be employed in a decomposition of the epistemic continuum into the knowable, the partially knowable, and the unknowable.

Knight formulates his tripartite distinction between certainty, risk, and uncertainty exclusively in the context of prediction, and just as Knight’s results can be generalized beyond economics, so too Knight’s distinction can be generalized beyond prediction to also embrace retrodiction. In The Retrodiction Wall I generalized John Smart‘s exposition of a prediction wall in the future to include a retrodiction wall in the past, both of which together define the boundaries of effective history. These two generalizations can be brought together.

Effective history lies between the brick walls of prediction and retrodiction.

A prediction wall in the future or a retrodiction wall in the past are, as I noted, functions of knowledge. That means we can understand this “boundary” not merely as a threshold that is crossed, but also as an epistemic continuum that stretches from the completely unknown (the inaccessible past or future that lies utterly beyond the retrodiction or prediction wall) through an epistemic region of prediction risk or retrodiction risk (where predictions or retrodictions can be made, but are subject to at least as many uncertainties as certainties), to the completely known, in so far as anything can be completely known to human beings, and therefore well understood by us and readily predictable.

If we open up the prediction wall or the retrodiction wall and allow them to be thick, we can interpolate Knight’s tripartite epistemic continuum into both the boundary of future knowledge and the boundary of past knowledge.

Introducing and integrating distinctions between prediction and retrodiction walls, and among prediction, risk and uncertainty gives a much more sophisticated and therefore epistemically satisfying structure to our knowledge and how it is contextualized in the human condition. The fact that we find ourselves, in medias res, living in a world that we must struggle to understand, and that this understanding is an acquisition of knowledge that takes place in time, which is asymmetrical as regards the past and future, are important features of how we engage with the world.

This process of making our model of knowledge more realistic by incorporating distinctions and refinements is not yet finished (nor is it ever likely to be). For example, the unnamed principle alluded to above — that of the inverse relation between historical predictability and relevance, suggests that the prediction and retrodiction walls can be penetrated unevenly, and that our knowledge of the past and future is not consistent across space and time, but varies considerably. An inquiry that could demonstrate this in any systematic and schematic way would be more complicated than the above, so I will leave this for another day.

. . . . .

. . . . .

. . . . .

The Retrodiction Wall

Wednesday

---

Prediction in Science

One of the distinguishing features of science as a system of thought is that it makes testable predictions. The fact that scientific predictions are testable suggests a methodology of testing, and we call the scientific methodology of testing experiment. Hypothesis formation, prediction, experimentation, and resultant modification of the hypothesis (confirmation, disconfirmation, or revision) are all essential elements of the scientific method, which constitutes an escalating spiral of knowledge as the scientific method systematically exposes predictions to experiment and modifies its hypotheses in the light of experimental results, which leads in turn to new predictions.

The escalating spiral of knowledge that science cultivates naturally pushes that knowledge into the future. Sometimes scientific prediction is even formulated in reference to “new facts” or “temporal asymmetries” in order to emphasize that predictions refer to future events that have not yet occurred. In constructing an experiment, we create a few set of facts in the world, and then interpret these facts in the light of our hypothesis. It is this testing of hypotheses by experiment that establishes the concrete relationship of science to the world, and this is also a source of limitation, for experiments are typically designed in order to focus on a single variable and to that end an attempt is made to control for the other variables. (A system of thought that is not limited by the world is not science.)

Alfred North Whitehead captured this artificial feature of scientific experimentation in a clever line that points to the difference between scientific predictions and predictions of a more general character:

“…experiment is nothing else than a mode of cooking the facts for the sake of exemplifying the law. Unfortunately the facts of history, even those of private individual history, are on too large a scale. They surge forward beyond control.”

Alfred North Whitehead, Adventures of Ideas, New York: The Free Press, 1967, Chapter VI, “Foresight,” p. 88

There are limits to prediction, and not only those pointed out by Whitehead. The limits to prediction have been called the prediction wall. Beyond the prediction wall we cannot penetrate.

The Prediction Wall

John Smart has formulated the idea of a prediction wall in his essay, “Considering the Singularity,” as follows:

With increasing anxiety, many of our best thinkers have seen a looming “Prediction Wall” emerge in recent decades. There is a growing inability of human minds to credibly imagine our onrushing future, a future that must apparently include greater-than-human technological sophistication and intelligence. At the same time, we now admit to living in a present populated by growing numbers of interconnected technological systems that no one human being understands. We have awakened to find ourselves in a world of complex and yet amazingly stable technological systems, erected like vast beehives, systems tended to by large swarms of only partially aware human beings, each of which has only a very limited conceptualization of the new technological environment that we have constructed.

Business leaders face the prediction wall acutely in technologically dependent fields (and what enterprise isn’t technologically dependent these days?), where the ten-year business plans of the 1950’s have been replaced with ten-week (quarterly) plans of the 2000’s, and where planning beyond two years in some fields may often be unwise speculation. But perhaps most astonishingly, we are coming to realize that even our traditional seers, the authors of speculative fiction, have failed us in recent decades. In “Science Fiction Without the Future,” 2001, Judith Berman notes that the vast majority of current efforts in this genre have abandoned both foresighted technological critique and any realistic attempt to portray the hyper-accelerated technological world of fifty years hence. It’s as if many of our best minds are giving up and turning to nostalgia as they see the wall of their own conceptualizing limitations rising before them.

Considering the Singularity: A Coming World of Autonomous Intelligence (A.I.) © 2003 by John Smart (This article may be reproduced for noncommercial purposes if it is copied in its entirety, including this notice.)

I would to suggest that there are at least two prediction walls: synchronic and diachronic. The prediction wall formulated above by John Smart is a diachronic prediction wall: it is the onward-rushing pace of events, one following the other, that eventually defeats our ability to see any recognizable order or structure of the future. The kind of prediction wall to which Whitehead alludes is a synchronic prediction wall, in which it is the outward eddies of events in the complexity of the world’s interactions that make it impossible for us to give a complete account of the consequences of any one action. (Cf. Axes of Historiography)

Retrodiction and the Historical Sciences

Science does not live by prediction alone. While some philosophers of science have questioned the scientificity of the historical sciences because they could not make testable (and therefore falsifiable) predictions about the future, it is now widely recognized that the historical sciences don’t make predictions, but they do make retrodictions. A retrodiction is a prediction about the past.

The Oxford Dictionary of Philosophy by Simon Blackburn (p. 330) defines retrodiction thusly:

retrodiction The hypothesis that some event happened in the past, as opposed to the prediction that an event will happen in the future. A successful retrodiction could confirm a theory as much as a successful prediction.

I previously wrote about retrodiction in historical sciences, Of What Use is Philosophy of History in Our Time?, The Puppet Always Wins, and Futurism without predictions.

As with predictions, there is also a limit to retrodiction, and this is the retrodiction wall. Beyond the retrodiction wall we cannot penetrate.

I haven’t been thinking about this idea for long enough to fully understand the ramifications of a retrodiction wall, so I’m not yet clear about whether we can distinction diachronic retrodiction and synchronic retrodiction. Or, rather, it would be better to say that the distinction can certainly be made, but that I cannot think of good contrasting examples of the two at the present time.

Effective History

We can define a span of accessible history that extends from the retrodiction wall in the past to the prediction wall in the future as what I will call effective history (by analogy with effective computability). Effective history can be defined in a way that is closely parallel to effectively computable functions, because all of effective history can be “reached” from the present by means of finite, recursive historical methods of inquiry.

Effective history is not fixed for all time, but expands and contracts as a function of our knowledge. At present, the retrodiction wall is the Big Bang singularity. If anything preceded the Big Bang singularity we are unable to observe it, because the Big Bang itself effectively obliterates any observable signs of any events prior to itself. (Testable theories have been proposed that suggest the possibility of some observable remnant of events prior to the Big Bang, as in conformal cyclic cosmology, but this must at present be regarded as only an early attempt at such a theory.)

Prior to the advent of scientific historiography as we know it today, the retrodiction wall was fixed at the beginning of the historical period narrowly construed as written history, and at times the retrodiction wall has been quite close to the present. When history experiences one of its periodic dark ages that cuts it off from his historical past, little or nothing may be known of a past that once familiar to everyone in a given society.

The emergence of agrarian-ecclesiastical civilization effectively obliterated human history before itself, in a manner parallel to the Big Bang. We know that there were caves that prehistorical peoples visited generation after generation for time out of mind, over tens of thousands of years — much longer than the entire history of agrarian-ecclesiastical civilization, and yet all of this was forgotten as though it had never happened. This long period of prehistory was entirely lost to human memory, and was not recovered again until scientific historiography discovered it through scientific method and empirical evidence, and not through the preservation of human memory, from which prehistory had been eradicated. And this did not occur until after agrarian-ecclesiastical civilization had lapsed and entirely given way to industrial-technological civilization.

We cannot define the limits of the prediction wall as readily as we can define the limits of the retrodiction wall. Predicting the future in terms of overall history has been more problematic than retrodicting the past, and equally subject to ideological and eschatological distortion. The advent of modern science compartmentalized scientific predictions and made them accurate and dependable — but at the cost of largely severing them from overall history, i.e., human history and the events that shape our lives in meaningful ways. We can make predictions about the carbon cycle and plate tectonics, and we are working hard to be able to make accurate predictions about weather and climate, but, for the most part, our accurate predictions about the future dispositions of the continents do not shape our lives in the near- to mid-term future.

I have previously quoted a famous line from Einstein: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” We might paraphrase this Einstein line in regard to the relation of mathematics to the world, and say that as far as scientific laws of nature predict events, these events are irrelevant to human history, and in so far as predicted events are relevant to human beings, scientific laws of nature cannot predict them.

Singularities Past and Future

As the term “singularity” is presently employed — as in the technological singularity — the recognition of a retrodiction wall in the past complementary to the prediction wall in the future provides a literal connection between the historiographical use of “singularity” and the use of the term “singularity” in cosmology and astrophysics.

Theorists of the singularity hypothesis place a “singularity” in the future which constitutes an absolute prediction wall beyond which history is so transformed that nothing beyond it is recognizable to us. This future singularity is not the singularity of astrophysics.

If we recognize the actual Big Bang singularity in the past as the retrodiction wall for cosmology — and hence, by extension, for Big History — then an actual singularity of astrophysics is also at the same time an historical singularity.

. . . . .

I have continued my thoughts on the retrodiction wall in Addendum on the Retrodiction Wall.

. . . . .

. . . . .

. . . . .

Futurism without predictions

Monday

---

“From the relation of the planets among themselves and to the signs of the zodiac. future events and the course of whole lives were inferred, and the most weighty decisions were taken in consequence. In many cases the line of action thus adopted at the suggestion of the stars may not have been more immoral than that which would otherwise have been followed. But too often the decision must have been made at the cost of honour and conscience. It is profoundly instructive to observe how powerless culture and enlightenment were against this delusion; since the latter had its support in the ardent imagination of the people, in the passionate wish to penetrate and determine the future. Antiquity, too, was on the side of astrology.”

Jacob Burckhardt, The Civilization of the Renaissance in Italy, translated by S.G.C. Middlemore, 1878, Part Six, MORALITY AND RELIGION, “Influence of Ancient Superstition”

---

A few days ago Neil Houghton read my post The Third Law of Geopolitical Thought and made the following comment on Twitter:

● Neil Houghton — I add prospective agency. RT @geopolicraticus The Third Law of Geopolitical Thought: human agency in time and history

I responded with a question, and a miniature dialogue developed (within the tightly constrained limits of Twitter):

● Nick Nielsen — How would you define prospective agency? Is this agency understood in terms of possibility and potentiality?

● Neil Houghton — Great question… in one word, foresight… in more a transdisciplinary practice between, across and beyond orders of time

● Nick Nielsen — The whole problem is separating the wheat from the chaff: the wheat is the big picture; the chaff, trivial predictions.

● Neil Houghton — Yes. seeing gradience is an aspect of the problem; the difference between the big picture and trivial prediction is one such gradience.

● Nick Nielsen — Seeing the big picture in both space and time yields a different kind of foresight than the attempt to predict future events.

● Neil Houghton — Foresight as gradience between freedom and destiny (for example) … please say more of your different kind of foresight.

This brief exchange points to something that I consider to be important, so I will attempt to give an account of the distinction I proposed between seeing the big picture and attempting to make predictions.

The most familiar form of futurism consists in making a series of predictions. Like any prognosticator of the future, regardless of methodology, the futurist is caught in a bind. The more specific his predictions, the more likely he is to be caught out. Even if the general drift of a prediction is correct, supplying a lot of details means more ways of potentially being wrong. And the more vague a prediction, the less interesting they are likely to be.

Some futurists take pride in their detailed lists of predictions, and although detail is an opportunity to be wrong, it also provides a lot of fodder for utterly pointless debate. In The Law of Stalled Technologies I wrote the following about Ray Kurzweil’s specific predictions:

Kurweil’s futurism makes for some fun reading. Unfortunately, It will not age well, and will become merely humorous over time (this is not to be confused with his very real technological achievements, which may well develop into robust and durable technologies). I have a copy of Kurzweil’s book that preceded The Singularity is Near, namely The Age of Spiritual Machines (published ten years ago in 1999), which is already becoming humorous. Part III, Chapter Nine of The Age of Spiritual Machines, contains his prophecies for 2009, and now it seems that the future is upon us, because it is the year AD 2009 as I write this. Kurzweil predicted that “People typically have at least a dozen computers on and around their bodies.” It is true that many people do carry multiple gadgets with microprocessors, and some of these are linked together via Bluetooth, so this prophecy does not come off too badly. He also notes that “Cables are disappearing” and this is undeniably true.

Kurzweil goes a little off the rails, however, when it comes to matters that touch directly on human consciousness and its expressions such as language. He predicted that, “The majority of text is created using continuous speech recognition”, and I think it is safe to say that this is not the case. I don’t want to parse all his predictions, but I need to be specific about a few particularly damning failures. Among the damning failures is the prediction that, “Translating Telephone technology … is commonly used for many language pairs.” Here we step over the line of the competence of technology and the limitations of even the most imaginative engineers. While machine translation is common today for text, everyone knows that it is a joke — quite literally so, as the results can be very funny though not terribly helpful.

Kurzweil gives a decade-by-decade running commentary of predictions. I once had somebody scold me about ridiculing Kurzweil’s predictions, because, I was told, the dates given were intended to indicate the initial dates of a ten year period, which gives him a ten year window to be right, thus kicking all his predictions another ten years down the road. This is the kind of ridiculous debate over pointless predictions that is an utter waste of breath. Predictions can be parsed like this until the end of time; this is precisely why people are always trying to show that Nostradamus predicted something. Add vagueness to ambiguity and you create the deconstructionists’ dream: anything can mean anything.

Just to unearth one more prediction, for 2019 Kurzweil predicted:

“Paper books or documents are rarely used and most learning is conducted through intelligent, simulated software-based teachers.”

Even if we give Kurzweil another ten years, I can guarantee you that, if I am still alive in 2029, that I will still have my personal library, it will probably be bigger than it is now, and I will consult it every day, as I do now. This does not, for me, constitute rarity of use. However, I will readily acknowledge that there is, already today, no need whatever to print textbooks, since knowledge is changing so rapidly and students usually don’t retain their textbooks after they have been used for a class. In situations such as this, it makes much more sense to make the material available on the internet. But even if we don’t bother with textbooks anymore, there will be a continuing role for books. At least, for me there will be a continuing role for books.

Whether you want to take pride in a list of specific predictions, having convinced yourself through a charitable hermeneutic that they have all come true, or whether you would rather it were all forgotten as a great embarrassment along with jetpacks, flying cars, and unisex jumpsuits, this model of futurism will always have a certain novelty value, so I will predict that “laundry list futurism” (like the poor) will always be with us.

There is, however, another kind of futurism, which we may not even want to call futurism, but which does incorporate a vision of the future. This other model of futurism is not about offering a laundry list of predictions, but rather about understanding the big picture, as I have said, both in space and time, i.e., geographically and historically. Here, “seeing the big picture” means having a theory of history that embraces the future as well as the past. This approach is about seeing patterns and understanding how the world works in general terms, and from an understanding of patterns and how the world works, having a general idea of what the future will be like, just as one may have a general idea of what they past was like, even if one cannot jump into a time machine and march with Alexander the Great or listen to Peter Abelard debate.

The big picture in space and time — and the biggest picture is what I have called metaphysical ecology and metaphysical history — is a theory, which if it is to be coherent, consistent, and universally applicable, must be applicable both to the past and the future. Ultimately, such a theory would be a science of time, although we aren’t quite there yet. I hope that, before I die, I can make a substantial contribution in this direction, but I recognize that this is a distant goal.

In the meantime, familiar sciences are engaged in precisely this enterprise, though on a less comprehensive scale. Let me try to explain how this is the case.

When we work in the historical sciences, the scale of time is so great that we must settle for retrodiction, because this is what can be done within one human lifespan, or within the lifespan of a community of researchers engaged in a common research program, but if we could afford to wait for thousands or millions or billions of years we could make predictions about the future. When, on the contrary, we work in the natural sciences as in physics, we must make predictions about the future, because we must create an elaborate apparatus to test our theories, and these did not exist in the past, so retrodiction is as closed to us as prediction is closed to the historical sciences. If we could go back in time with a superconducting supercollider, we could make retrodictions in physics, but at the present stage of technology this time travel would be more difficult than the experiment itself.

We accept the limitations of science that we are forced to accept, perhaps not gladly, but of necessity. What alternatives do we have? If we would have knowledge, we must have knowledge upon the conditions that the world will allow us knowledge, or refuse knowledge altogether. We are confident that our theories of physics apply equally well to the past, even if they cannot be tested in the past, and we are confident that our theories of paleontology would apply to the future if only we could wait long enough for the bones of the present to be fossilized.

In the fullness of time, if industrial-technological civilization continues in existence, the limits of science will be pushed back from the positions they presently occupy, but they will never be eliminated altogether. However, our strictly scientific knowledge can be extrapolated within a more comprehensive philosophical context, in which the resources of logical and linguistic analysis can be brought to bear upon the “problem” of history.

When I first began writing about what I began to call integral history, and which I now call metaphysical history, my aim at that time was to give an exposition of an extended conception of history that made use of the resources both of traditional humanistic narrative history and the emerging scientific historical disciplines, such as genomic resources which have taught us so much about the natural history of our species. I have subsequently continued to expand my expanded conception of history, and this is what I call metaphysical history, elaborated in the context of ecological temporality.

A further extension of the already extended conception of metaphysical history would be a conception of history that sees the big picture by seeing time whole, past, present, and future together as one structure that exhibits laws, regularities, patterns, and, of course, exceptions to all of the same.

This, then, was what I meant when I said that, “Seeing the big picture in both space and time yields a different kind of foresight than the attempt to predict future events.” The kind of foresight I have in mind is an understanding of historical events, both past and future, in a larger theoretical context. It is “foresight” only because it is, as the same time, hindsight. Both the past and the future are comprehended in an adequate theory of history.

I have no desire to produce a laundry list of predictions; I have no desire to say what I think the world will look like in 2019 or 2029 or 2039. I think that most of these predictions are irresponsible, though it may land a prophet on the front page of the National Enquirer. Not all such attempts at prediction, however, are irresponsible from my point of view. I have several times discussed George Friedman’s book The Next 100 Years, which strikes me as a responsible exercise in laundry list futurism. I have also discussed Michio Kaku’s book Physics of the Future: How Science Will Shape Human Destiny and Our Daily Lives by the Year 2100.

Kaku’s book is particularly interesting to me in the present context, because Kaku has a very specific method for his futurism. He has interviewed scientists about the technologies that they are developing now, in the present, and which will become part of our lives in the foreseeable future. I realize now that Kaku’s methodology may be characterized as a constructive futurism: he is immersed in the details of technology, and extrapolating particular, incremental advances and applications. This is a bottom-up approach. What I am suggesting, on the contrary, is a profoundly non-constructive approach to the philosophy of history, a top-down understanding that looks for the largest structures of space and time and regards all details and particulars as fungible and incidental. That is my vision of a theory of history, and I think that such a theory would give a certain degree and kind of foresight into event in the future, but certainly not the same degree and kind of foresight that one might gain from the constructive methods of Kaku and Friedman.

. . . . .

. . . . .

. . . . .

Historical Sciences

Saturday

---

Stephen Jay Gould has emphasized throughout his corpus that the historical sciences are distinct, that is to say, that they represent a distinct approach to science and that they should be recognized as involving a distinct approach. In the Prologue to The Flamingo’s Smile he wrote:

History perverts the stereotype of science as a precise, heartless enterprise that strips the uniqueness from any complexity and reduces everything to timeless, repeatable, controlled experiments in a laboratory. Historical sciences are different, not lesser. Their methods are comparative, not always experimental; they explain, but do not usually try to predict; they acknowledge the irreducible quirkiness that history entails, and acknowledge the limited power of present circumstances to impose or elicit optimal solutions…

Later, in an essay on SETI in the above-mentioned collection, he elaborates:

The historical sciences try to explain unique situations — immensely complex historical accidents.

From a philosophical standpoint, Gould’s point is both interesting and inadequate. He essentially constructs a straw man to represent what he takes to be the non-historical sciences, but we can leave this aside. I agree with Gould that we should recognize the historical sciences as a particular approach to science.

Given that there are historical sciences, these sciences could be classified according to the objects of study, but they could also be classified according to the historical period or scope of history such sciences embrace. According to the latter scale, cosmology would be the most comprehensive of the historical sciences, taking in the entire history of the universe. Next would follow astronomy and astrophysics, which study the very long lives of galaxies and stars. After this perhaps would come geology, which studies the time periods appropriate to the surfaces of the planets that orbit the stars studied by astrophysics. These latter disciplines — astronomy, astrophysics, and geology — are less temporally comprehensive than cosmology, but still embrace far more of time than most of what are commonly considered historical sciences.

After these scientific preliminaries we would come to the ordinarily recognized historical sciences of paleontology, paleobiology, and paleobotany, then anthropology, and archaeology. There must be the objects of geology before there can be the objects of paleontology; there must be the objects of paleontology before there can be the objects of anthropology, and there must be the objects of anthropology before there can be the objects of archaeology. Last of all among the historical sciences comes history itself, that is to say, the human history of the historical period.

The familiar image of the historical sciences.

We need not stop here, however, as our temporal classification of the sciences is suggestive. Particle physics — that paradigm of the “hard” sciences that today thrives on enormous experiments employing Brobdingnagian machines — could lay claim to studying the smallest time scales, thus assimilating the paradigm of the natural sciences, and even the mathematicized natural sciences, to the paradigm of the historical sciences. As the sophistication of particle physics increases, physicists study particles and other exotic objects that last for small fractions of a second, pushing the boundary of time investigated near to zero. And here the minute time scales of particle physics coincides with the incredible time scales of cosmology, as much Big Bang theory concerns itself with the constitution of the universe during the early fractions of a second immediately after the Big Bang.

There is a strange, sublime beauty in big, sexy science.

As limiting cases of the historical sciences, particle physics and cosmology would seem to have to gone as far as we can go, but there is another step yet that we can take. If we consider on the one hand the totality of time, which, if construed as eternity, might be the object of eschatology (thus assimilating theology to the historical sciences), or if construed as infinity could be the object of mathematics. On the other hand, at the opposite extreme of temporal infinity are temporal instants: single, unextended points in the continuum of history, which construed as points or real numbers would assimilate the objects of mathematics to the historical sciences.

Low-tech research methods in mathematics.

What is the lesson here? Ought we to bring the methods of the historical sciences to bear on point set topology? Ought we to bring to bear the methods of the exact, mathematical sciences — those caricatured by Gould as “a precise, heartless enterprise that strips the uniqueness from any complexity and reduces everything to timeless, repeatable, controlled experiments in a laboratory” — on history? The answer should be obvious: we should cast the net of rational thought as widely as possible. If it is fruitful to bring historical methods to the mathematicized sciences, we should do so. And if it is fruitful to being the methods of the mathematicized sciences to the historical sciences, we should do that too. The cross-fertilization of the sciences is a powerful spur to development and often a source of new and exciting ideas.

. . . . .

. . . . .

. . . . .