Sunday, 1 October 2017

Grist for Leibniz's Mill (2017)

From The Philosopher, Volume CV No. 2 Autumn 2017


GRIST FOR LEIBNIZ’S MILL
By Danko Antolovic



“What do you see?” I ask a friend who is looking at a tree. ‘I see a tree, of course,’ comes the remarkable reply. I do not actually know what my friend is seeing – I experience only my own perceptions, and those of another could be wildly different – nor do I have any experience whatsoever of my friend's ‘I’, the self-awareness of another.

And yet, the conceptual framework behind this little conversation is so universal that a child would give me the same reply. There is a world out there, and there are individual minds, all of whom see that world more or less the same way, and they all have a direct experience of themselves and of the world. On the surface of it, the minds are immersed in the world and are of one piece with it. All is well.

But how does the mind, immersed in the sights and sounds of the world, actually perceive? We know that perception is mediated by the sense organs, and we can follow the optical and acoustic images of the world into our eyes and ears. We understand how light and sound trigger neural activity in the sensor cells, and how the resulting signals travel into the brain. Once there, following the stimuli becomes rather more complex, but we know, in broad strokes, that sense stimuli give rise to somewhat permanent neural imprints called memories; they trigger bursts of chemical changes associated with emotions; they are fed into decision-making systems and compared with existing memories; and they take part in initiating motor signals which make the body act upon the world.

This modern picture of the mind corresponds very well to what is sometimes known as Leibniz’ Mill metaphor. Gottfried Wilhelm Leibniz, philosopher and distinguished mathematician, proposed this in 1714 in an essay called The Monadology. Essentially, the idea is that should a machine have a mind (or might appear to have one), we should be able to scale it up in size, if needed, and walk into it, just as we would walk into a mill. Inside, we would see mechanical parts pushing and pulling at each other in mechanical ways; the machine could be arbitrarily complex and perform arbitrarily complex tasks, but in all the pushing and pulling we could never find a somebody, an entity aware of itself and of the world. And indeed, even today, all of our understanding of the workings of the nervous system has so far shed very little light on self-awareness: all we see inside are electrochemical signals running around in electrochemical ways!

And so, Leibniz argues, the mind cannot be mechanistic, since it does not arise from the causes and effects of the material world. It is not of one piece with the world at all: rather, it stands outside it. But if that is so, how can the mind perceive the world and act upon it? All interactions in the world are causes and effects, parts of the world pushing and pulling at each other, and an entity not taking part in this mechanism could not interact with the world at all. Leibniz observes, correctly,  that the material world is governed by the principles of conservation, and that the mind acting upon the world "from outside" would violate these principles.

Leibniz resolves this conundrum by postulating that God had arranged the world in such a way that every substance was created, in the beginning, with due regard for every other. In that picture, mind and matter are separate substances, following their separate laws, and in doing so they behave as if they were interacting, even though they are not. Leibniz called his primordial substances ‘monads’, and their parallel coexistence the ‘pre-established harmony’.

A ready objection to Leibniz’ Mill is that it is merely an argument from plausibility. It seems indeed very implausible that a clockwork mechanism from Leibniz' time, with its cogwheels, pegs and levers, could give rise to self-consciousness, but still: if we do not understand the nature of the goal, we cannot know whether it is attainable or not. Do we really know what to look for inside the mill?

Ostensibly scientific alternatives to the mill are occasionally proposed as phenomenal (material) explanations of self-consciousness that would resolve Leibniz’ mechanistic dilemma: quantum mechanics is a perennial favourite, as are things like emergent properties of complex systems. None of them are particularly convincing.


All of our understanding of the workings of the nervous system has so far shed very little light on self-awareness: all we see inside are electrochemical signals running around in electrochemical ways!


Quantum mechanics asserts certain non-intuitive things about the behaviour of matter, but it is fundamentally mechanistic: its causes and effects, albeit understood as probabilities rather than certainties, can be summed up in an equation of motion. It is unclear why quantum mechanics would be a more promising medium in which the conscious self could arise than the clockwork mechanisms of classical physics.

Complexity, on the other hand, is a vague concept, which can signify various things. There are properties that do ‘emerge’ from systems with many parts, things that are not obvious in the components but become visible in the system's behaviour as a whole. Some examples are ferromagnetism, coherent movements of schools of fish and flocks of birds, and self-organising of neural nets. But all of these phenomena are explicable mechanistically, in terms of the underlying physics, and if awareness ‘emerges’ in this fashion, it must also be so explicable; without a physical theory that could account for the conscious mind (and reconcile it with the known picture of the physical world) complexity alone explains nothing. In my view, interpreted strictly as an empirical observation Leibniz’ allegory of the mill has held out very well over time.

A remarkably factual insight into the question of the mechanistic mind was offered by Roger Penrose in an essay called ‘Setting the Scene: the Claim and the Issues’ (part of The Simulation of Human Intelligence, edited by Donald Broadbent, published by Blackwell in 1993). Penrose argues that human minds are capable of insights which must elude the machines because of the machines’ very nature. The argument goes as follows:

Suppose we wish to ascertain whether an algorithmic calculation, which we can envision as a computer program, stops and yields an answer, or goes on forever. Penrose offers two examples:
1) Find the smallest integer that is not a sum of squares of three integers (including zero). It would be easy to construct a program which, for each integer n, goes mechanically through all triplets of squares not larger than n, and tries to add them up to n. Will that search ever come to an end? If we try it, we find out that number 7 is not a sum of three squares, and, luckily, the program stops very soon.

2) Find the smallest odd integer which is a sum of two even integers. We could construct a simple searching program, along similar lines as in Example 1, but we know in advance that it would never stop: there is no such number, no matter how large an integer we check.
These examples show that the human mind can answer the halting question for some calculations; perhaps not for all of them, but if it can work out an answer, it can do so correctly and in finite time. Suppose now that this ability is itself implemented within the brain as an algorithm, A, which reads and processes any computation, any program, ‘C’, as its input. The algorithm A is required to stop if it finds out that C does not stop, i.e. it must give a correct verdict of C’s not halting. It should be able to read the program we wrote for Example 2, analyse it, and halt with the verdict that this calculation never halts.

It can be shown with a bit of clever and fairly technical reasoning (known as Gödel's theorem, after the logician Kurt Gödel), that, no matter what the actual details of A, it is always possible to find a C, with suitable inputs, such that A equals C, and must report on its own halting! Now, if A halts in this particular case, by assumption it has given the correct answer, and the answer is that it itself does not halt! This is a contradiction, and the only logical possibility is the opposite of our assumption: A does not halt, and therefore cannot give the answer for that case.

So, the proposed algorithmic calculation A inside the brain cannot answer at least that one question. But we know the answer: A does not halt. We have arrived at this answer by the reasoning of Gödel's theorem, and by deriving a contradiction by assuming that A does halt. It is very difficult to disagree with Roger Penrose’s conclusion that the mind cannot be completely reduced to an algorithmic computing machine: after all, we just did something an algorithm mathematically can't do!

Consider again Example 2: we solved its halting problem intuitively, by appealing to the concept of disparate sets (an integer is either even or odd, never both), and to the concept of distributing multiplication over addition. We intuit these concepts as applying to all integers, and we know immediately that we are looking for odd numbers where there can't be any. The very idea of checking every individual number, in a program-like fashion, strikes us as ridiculous.

We could envision adding such higher-level concepts to our program A, to form an enhanced program A*. This program would be able to solve a broader range of halting problems, but the crucial question is: how are the enhancements implemented? If they are implemented in the same algorithmic fashion as the original A, then A* is again fully algorithmic, and cannot answer its own halting question, for the same reasons as A. The human mind can again do so, for the same reasons as before, and we are back at the original quandary.

What can we do to escape this quandary? An informal assertion, known as the Church-Turing thesis (after mathematicians Alfonso Church and Alan Turing), says that all algorithms can be expressed and computed by means of so-called Turing machines. A Turing machine is a very simplified mock-up of a computer, capable of storing, retrieving and manipulating symbols according to pre-set rules. The important point is that it is physically realisable, and that every computing device ever made (or proposed to be made in a non-magical fashion) is functionally equivalent to a Turing machine. There is no a priori requirement that it be so, but no one has made a non-Turing computer yet, following the known laws of nature. Any device or program A, that we know how to make (or realistically imagine), will be algorithmic and land us in the same quandary again.

There is a striking similarity between Leibniz’ allegory of the mill and the Church-Turing thesis. Leibniz observes that all the machines we know how to make are mechanistic devices, capable only of mechanical functions. The Church-Turing thesis observes that all the computing machines we know how to make are Turing machines, capable only of algorithmic calculations. Where Leibniz asserts that a mill cannot have a mind, the more precise analysis by Penrose says that any known computing device, which is always a Turing machine, fails to match all the capabilities of the mind. Neither the mindlessness of the Leibniz’ Mill nor the Church-Turing thesis have ever been proven, but nor have they ever been contradicted. They seem to hint at a fundamental limitation on what can be expected of the phenomenal world as we know it.

Where does this leave us, regarding self-awareness and subjective experience? We have shown that there exists mathematical reasoning that no Turing machine can perform, but a mind can. This reasoning is itself wrapped in a larger experience of the self – it is I, a self-aware entity, who is doing the reasoning – and it is difficult to see how an algorithmic device could generate the conscious understanding of a process which it cannot even perform. Unlike the halting problem, awareness is not a concept we know how to define in precise terms, so we cannot prove or disprove its computability. Nevertheless, the above analysis of the limits of algorithmic computation strongly suggests that awareness is not such a computation.

But let us carry this a step further. Let us suppose that (some portion of) the brain is a non-Turing machine, based on some still unknown, non-algorithmic physical laws. Penrose speculates that that may be the case, and his supposition is a rather appealing way out of the halting-problem quandary. This hypothetical machine performs broadly conceptual reasoning, and it makes it possible for the human mind to solve the halting problem of program A. We don't know what its computational limitations might be, but the interesting question is: does it imply awareness?

Is self-awareness necessary in order to arrive at Gödel’s theorem and the solution of the halting problem? Or could a hypothetical non-algorithmic robot reach the same results, without any awareness of itself and of what it is doing? We are inclined to think so: after all, the self-aware human mind can run through algorithmic computations just fine, and understand what it is doing (for example, multiplication by hand), yet its self-awareness is immaterial for the computational process, and such tasks are routinely handed over to non-aware Turing machines (pocket calculators).

Furthermore, we could ask whether the emphasis on computation in the theory of mind is altogether misguided. Setting aside the mathematical arguments for a moment, we can ask ourselves what self-awareness feels like. At the risk of generalising on flimsiest grounds of introspection, it feels like the presence of a being – my own. Likewise perception, once all its neural mechanisms and signal processing are accounted for, feels like the presence of another being, presence of something that is.

In contrast with this immediate experience, what is computation, really? In the physical sense, it is a chain of events in which phenomenal objects undergo distinct changes, regularly and reliably. Such is a computation on a pocket calculator (or a supercomputer): electrical contacts being closed by the keypad buttons lead to switching of electrical circuits, resulting in light being emitted from the LED display. All of that is something more than a mere physical happening, such as wind or rain, only because the human mind interprets the inputs and the outputs as very good approximations of an abstraction. We think of pressed keys and displayed light patterns as numbers and arithmetic operations, and it is this interpretation that gives meaning and relevance to an otherwise indifferent physical process. It is the same interpretation that adds three pebbles to five pebbles to make eight of them, even though a pebble is not a number, but a piece of phenomenal world, immersed in the world and changing with it with every passing moment.

Physical computations of this kind need not be human-made, and can exist independently of any minds. For example, genetic code is a fairly crisp and unambiguous mechanism by means of which intricate molecular structure is maintained and propagated within unconscious matter. It precedes the appearance of the mind, and in the physical sense it does not differ from the wind and the rain: it became a ‘code’ in the human sense, i.e. an embodiment of an abstraction, only retroactively, by being understood by the mind.

As for non-algorithmic ‘computation’, such as proving a theorem, this usually begins with a specific, outstanding question; the question may be pressed by material reasons (for example, a technological advance with the prospect of marketable products) or emotional ones (professional prestige). The entire body of accepted mathematics stands available as the starting point, and the reasoning process links mathematical concepts, according to accepted rules of logic, into the chain of proof which, hopefully, ends with an answer to the stated question.  Deciding which concepts to consider is, of course, the core of the mathematician's talent, and that selection is often guided by an ‘intuition’, that is to say, by the ability to recognise similarities with past mathematical problems. Our intuitive solution of Example 2 illustrates this process; a conceptual solution of Example 1 is also known, but is far less obvious.

There is an overall similarity between algorithmic (Turing) computation and conceptual reasoning: both manipulate given inputs according to set rules, and yield a result. We accept the possibility of a non-algorithmic (non-Turing) component of the mind, even if it is far from obvious whether and how this component could be implemented in non-aware robots. However, nothing in the conceptual reasoning seems to indicate that self-awareness is a necessary component of it. In order to solve the halting problem in Example 2, a robot would have to manipulate the concepts of arithmetic, instead of following a Turing-like program that was built on these concepts. A large step for a robot, perhaps one relying on new and still unknown physics, but it is not self-evident that the robot would have to be aware of itself in order to take that step.

In fact, it is very difficult to see how these chains of symbol – and concept – processing operations could produce, or, in contemporary parlance, compute that ‘presence of a being’ which is the subjective experience. Insofar that they are of relevance to the conscious mind at all, they require purpose and interpretation that are extraneous to them, and which are given to them by the very same self-aware agency they are supposed to be the foundation of. They differ little in their nature from a mill, a machine made for the extraneous purpose of grinding wheat. And in the absence of a mind to call it a machine and envision a purpose for it, the mill, too, is just another indifferent manifestation of the phenomenal world.

With an eye on David Hume's wise admonition that all generalisations are only habits of the mind, we are reluctant to preclude in advance a phenomenal explanation of the self – perhaps there is one, hidden in the unknown depths of the phenomenal world. Still, at the present – and foreseeable – state of our understanding, all we can realistically hope to find in the neural labyrinths of the brain are Turing machines and more Turing machines. And these clockwork-like gadgets can't even match our capacity for mathematics, let alone loop back onto themselves somehow, and give rise to self-awareness.

It is possible that the Church-Turing thesis is saying something fundamental about the structure of the phenomenal world; or, perhaps it merely expresses an incompleteness of our knowledge of that world, a limitation that could be overcome in time. As things stand today, however, we cannot casually dismiss Leibniz’ insistence that the self, that one thing each of us knows truly is, must be something irreducible, a monad, and not an agglomeration of moving parts. Mindful of the questions which this leaves open, we conclude with Leibniz’ own words:
‘That which is not truly one being is not truly a being either.’



Read more:

Leibniz, Gottfried Wilhelm. The Monadology, 1714. Translated by Robert Latta, 1898, http://home.datacomm.ch/kerguelen/monadology/

About the author: Danko Antolovic is a scientist and technologist. He is the author of Whither Science? a collection of essays on the present and future of modern natural science. He has also written for The Philosopher in the past (Descartes’ Menagerie of Demons, Volume 103 No. 2, September 2015)

Address for correspondence: Danko Antolovic <dantolov@iu.edu>


Vital Education (2017)

From The Philosopher, Volume CV No. 2 Autumn 2017

At sunrise you start to look at the shape of the ocean. (Photo courtesy of the Polynesian Voyaging Society

VITAL EDUCATION
By Andrew Porter



It would be fun to be light and breezy about the topic of education, but it seems an increasingly stiff breeze confronts us, with battleship gray clouds to windward. While some in response merely button up their jacket to the chin, others are setting about putting in a reef, and taking another look at the chart. The education world presents to us the sky in two directions, one the dark squall line of bad sailing in one direction, and the bright blue sky off in the other direction. On our boat in the middle, we consider the ideal blue out there to leeward and are not at all sure the squall will slide by us. We share thoughts about it with our boat-mates.

We like the idea and fact of education because it offers lavish expansion. We sense only the elasticity of the current lineaments, but foresee that it may, this decade or this century, show itself to be a good water-field for sailing instead of a very poor one. It may reveal itself of such expansion that our ignorance finally comes to light. 

Education in theory offers power to our potency. Full potency, as the germination of seeds teaches us, is in the living—a joining of the actual and potential. We learn from the green, organic world that potentiality and actuality never live in separate camps, nor separate tents, and if in separate but close bodies, well, there’s a lot of potential there.

What is it we shall call this singularity, this complete and thorough integration? We currently call it life, which we imagine as a kind of replete vitality, burgeoning and strong, delicate and assured. Inside becomes outside, outside becomes inside—and structures and timely processes, in the growth toward maturity, hold. What is this astonishing dance with resilience and reason, this sobriety with such elastic abandon? Life would not be life without continual potential. And education is meant mainly for performing this ceremony between the actual and potential.



The reason Finnish schools have become a model of sanity, balance, and education done right is that they pay attention to body, mind, and spirit. They do not let any of the three wander off and be left to its own devices. The ideas behind these schools and others like them are about the whole person, the whole teacher, and the whole community.



This wholeness suggests that fullness might come from education. How we might creatively craft it seems like an old question, but it is fresh as can be. What other models do we have that might serve to guide us in good directions?

 A Polynesian navigator sailing with Captain Cook could tell, at any given time and thousands of miles away, what direction Tahiti was. Such a traditional navigator, practicing his skills in the modern day—2500 miles away from Tahiti—says to those who would learn from him on the canoe: keep the vision of the island in your mind—if you lose that, you are lost. As he utilizes the stars and waves and sun and color of the sky, he conceives of pointing the canoe in a certain direction and bringing the island to the canoe. The parallels—or pontoons—to our lives and our voyages, whatever longitudinal position we are in, are obvious.

Polynesian wayfinding has a corollary in the navigation of education, which, we might say, also ‘involves navigating on the open ocean without sextant, compass, clock, radio reports, or satellite reports’. (According to http://www.pbs.org/wayfinders.) Education, for teacher and student, is non-instrument navigation, and the preparation is not for the current materialistic world, but for some depth of life. Are we developing the skill to navigate life, with its vast reaches of water and its beautiful small islands, by natural means? What are the parameters of this wayfinding? This is the perennial question.

‘The wayfinder depends on observations of the stars, the sun, the ocean swells, and other signs of nature for clues to direction and location of a vessel at sea. Wayfinding was used for thousands of years before the invention of European navigational instruments.’

Has education gotten to the point of sincerely believing that the dome overhead will provide the most significant answers? Does our philosophy of education need to consult something, or will it always be adamant that it will rely on the non-natural? Is it only a question of memorising where the stars come up and where they go down?
‘The star path also reads the flight path of birds and the direction of waves.’
We read ourselves into the environment in the process.

 In life as in canoe voyaging, ‘you cannot look up at the stars and tell where you are. You only know where you are (in this kind of navigation) by memorizing where you sailed from. That means constant observation’. Mau, master non-instrument navigator as well as mentor and teacher, says you must compact ‘every time you change course, every time you slow down’ into a mental construct that allows and creates a continuity with integrity. You may be even now in the ‘box’, among a shield of islands, from which Tahiti is only 170–180 miles away.



Latitude matters. What will tell you? The stars. Education should awaken us to see them.
‘How do you tell direction? We use the best clues that we have. We use the sun when it is low down on the horizon. Mau Piailug has names for how wide the sun appears, and for the different colors of the sun path on the water”. And sunrise, as they say, is the most important part of the day. "At sunrise you start to look at the slope of the ocean—the character of the sea. You memorize where the wind is coming from.’ 
To his young students, Mau  says, ‘Everything you need to see is in the ocean, but it will take you twenty more years to see it.’ One student says that Mau ‘can be inside the hull of the canoe and just feel the different wave patterns as they come to the canoe, and he can tell the canoe's direction lying down inside the hull of the canoe. I can't do that.’



Education, as a reflection of the world, too often foists the non-natural on us, even as a goal, but we are all students — are we open to better outcomes? In the course of life, do we know the signs? Birds, at dawn, go ‘about 130 miles out… but when the sun goes down, [they] will rise up from the water so [they] can see, and will go straight back to land… The flight of the bird is the bearing of the island.’ 
 


Mau, correcting a student’s course north to the opposite direction, south, says to ‘wait one hour and you will find the island you are looking for’. After an hour, Mau ‘gets up on the rail of the canoe and says, “The island is right there”.’
‘And we all stood up and we climbed the mast and everything and we just couldn't see it. Vision is not so much about what you do—but how you do it. It is experience. Mau had seen in the beak of a bird a little fish. He knew that the birds were nesting, and they were taking food back before they fed themselves.’


Education, perhaps, is like being a loggerhead turtle hatchling, under the cover of sargassum, growing and learning. What is all this development for? we might ask. For holistic and intellectual development, we say, to prepare young people for all aspects of life—the working world, the culture, society, and individual interests. But to the extent education is meant to prepare them for society, I still ask: you mean the current mode of society or for an imagined society vastly improved, on the other side of a revolution? Isn't education the crux of the conceptions that would underpin going far beyond current society, which would surely be a Tahiti?



Present conditions in the world proclaim they are master, and we are serving slaves. Things as they are assert their claim to adamancy and dominance. But we must, to break our subservience, have the last word with them, as well as words with them before. Education, from whatever end it is engaged in, is worse than substandard if it is not such a chrysalis. Education should be a process of becoming more discerning, at current society's expense — more savvy to connect only with the world as fully vitalized by nature and by the fullest, most ethical forms of humanity. If we shirk responsibility on this issue our education fails appallingly.

Imagine preparing students for an improved world that doesn't, by most standards, exist — how wonderful! Butterflies flutter and live by innate powers; we must summon ours, yet with a similar naturalness. I want to be principally educated in the depths to which nature is illuminative about my best self, and how collective selves fit into that. It is a rich and far-reaching field of study. Present conditions — some tawdry, convoluted, lifeless, some wrong, ugly, and unawake — wither and desiccate in such learning.



You may agree that education is too vested and invested in society. Education’s particular duty is not only to be a retreat and respite from vicious, ignorant, or inertial societal ways, but an entire denunciation and demolition of them. It may be, however, that the prominent voice is: ‘Society is a mess and we know it. Nobody expects it to be redeemed, but we will deal with it the way it is. It's downright annoying, I know, but we've gone well past trying to change it for the better; our motto is: deal with it or get out of it.’

Education can properly do neither. Education that lives up to its name is a radical idea that does not ‘deal with’ society and its foibles any more than does a splendid, singular individual whose shadow society, later, partly becomes. Education also cannot retreat completely from society, but must articulate society's complete renovation, which is, on the scale from mild reform to radical revolution, four-fifths of the way to the latter. 

If education, then, is to guide us and free us, let it be for what we wish we did find, and will, because of the thoroughgoing sincerity of our wish. This aspiration may involve comedy or tragedy, but the process of education rightly involves renewal and regeneration of high aspiration grounded in nature’s potency. 



There is nothing more important in education than educating young people in what power properly is. It is to exercise freedom through the power of rightful wishing. Power is not, as some would have it, making everything conform to your life; rather, power is making your life conform to everything real, sound, and natural. Education has the chance to teach us that if the world knew what power is, it would be saved. The current forfeiture of power is sad and even terrifying. If education were geared to this one life-lesson, that a tool is best when power is equal between you and it, between human and nature, between freedom and order, everything efficacious would flow from it.

But as it is, the realm of education seems to feel itself largely powerless.

 Are the great majority of schools, we might ask, educating students away from their proper education? Education today is not a Shaolin temple, with master and pupil talking about the ripples on the water to learn intimately about flow and constancy and the exigencies of life. But isn’t education capable of riding youthful wonder better, of lighting a view of, say, environmentally responsible living, and thereby being a revolutionary force? 

Plato says in the Laws:
‘Education is the way to produce good men, and, once produced, such men will live nobly…’ 
– but I feel a slight chill in the spine, caused by fear and hope, when I read him say:

‘When [education] takes a false turn which permits of correction, we should, one and all, devote the energy of a lifetime to its amendment.’ 

How shall we assess the current schemes of amendment; do educators at all levels retain the ability to see what a true turn would be? Education can be started afresh, even, or most particularly, for ourselves. What else but the Good in some form is the end which children’s education seeks to fulfill in phases? What else could we possibly allow to be the means? 

What is all the education worth if you cannot recognise the good? Is education to make us savvy to the fact that there are competing goods? Are the long-extended roots and branches of the good outside the curriculum? Then education is outside itself.

 Education should not be afraid go to the roots of what it is hoping to inculcate. It should ask the big and basic questions: What is the end we seek? Do we distinguish between a straight-cut ditch and a meandering stream? What is the capacity of a human, and for what? Where and when students — which we all are — will receive beneficent influences is hard to reason out. We know the general scope of productive influences but we tend not to know where they will alight upon us. Look how students have different interests and bents at different ages. Has their wonder become lost?

The great force of intuition, as Emerson says, is too quickly channeled into tuition. How can a sound first instinct change properly in the process of learning and experience, and how can further experience suggest a new intuition?

 An ideal education, perhaps, says:
‘Follow your early intimations. Spend time on the suggestions of your wonder. Time and life, like fruit, are perishable. Appreciate the day with those early insights. Let your imagination play with its newly-sprung intimations, and run with their morning aspect. Let them lead you. Strengthen your legs in walking with them, and feel the flexible vitality of life.’
 

As education seeks to stimulate and extend natural development, it can have, as an objective for its students, wonder as a state of being. Wonder tends to see equally well within and without, and sacrifices neither the material nor spiritual. Wonder is nixed at too great a cost. And the most educated will tell you that learning tends to happen most powerfully in the various legitimate ways of being glad to be alive. This wonderment engenders the capacity for being further clued in to the richness of life, that amalgam of innocence and experience. One is not able to be fully glad to be alive without intellectual honing, familiarity with value, and realisation of connection. 


A colleague at school told me his opinion that kids are winding up not sufficiently educated. Alienation, lack of values, and unconcern for reality are, alarmingly, on the increase. What happens to the richness of life in this? Can the necessary and desirable aspects of living be deepened in a ‘dumb’ education system? For instance, if it is crucial that we alter education to guide people in living much more ecological lives, in tune with the health of the planet, don’t we need to start with vision and passion? What will bring about a series of curricula to vastly improve our relationship with the Earth? If we believe with Henry David Thoreau that ‘in Wildness is the preservation of the world’, how shall we understand or assimilate to that capitalised term?



Becoming in tune with reality, near and far, is perennially the boiling away of a number of illusions. The fullness and freedom of life depends on education, crucial in refining what is best to learn. A more sustainable, organic, and ecological life presents itself to the wise as highly desirable; how is education adept at crafting this both practically and theoretically? Education is an expeditious way to get to the most savored moments. Life seems to indicate that it wants to see itself in its most salubrious and complete form.



A former academic dean told me she said to a student that the purpose of education is neither to go to college nor to get a job, but to deal with life when a safe falls on your head or you have a withering disease. I added that education has great meaning not just in bad circumstances but in good ones too. If, without education, I said, you can only go to one-tenth the depth of happiness and understanding, you are as bad off as if you can't cope. 


Education at its best makes you glad that your capacities are taxed to be equal to what it illuminates. Greater savvy in distinguishing between what will be good and what will not be good is worth the price of admission. A safe falling on your head is only the half of it. What about when the safe of truth falls three feet from your head into the soft sand, and opens to reveal ingots of potential happiness, diamonds of ready understanding, and emeralds of latent life? That is when education, properly called, wells up and out into being, achieving equilibrium with goodness. 

So education is Janus-faced, looking to the dark gray sky to windward and to the cerulean blue to leeward. An ease of the sheets will send us more toward the lofty lighter end of things. Then there is one face, sunset-lit, letting the storm clouds, perchance, slide by. When the stars come out and the sky is clear, that face will front light still, reflecting the sparkle aloft in its own orbs, dreaming of tomorrow’s compelling breeze.




Andrew Porter is an experienced educator in the United States, and has taught English in both private and public schools.

Address for correspondence: Andrew Porter <aporter344@gmail.com>


Tuesday, 8 August 2017

BOOK REVIEW: Surfing with Sartre (2017)

From The Philosopher, Volume CV No. 1 Spring/ Summer  2017
 


SURFING WITH SARTRE 
Review article* 
By Martin Cohen



Now I’m all in favour with popularising philosophy - but surfing? It doesn’t auger well. Surfing and philosophy seems to go together like... chalk and cheese. Of course, there is a very broad kind of philosophy of life that well, surfers could be said to symbolise - but against this small justification is the uncomfortable fact that surfing is a physical sport which has very little to do with philosophy. Indeed, Sartre was writing in the years before surfing became a mainstream leisure pursuit. It really doesn’t help, as here, to suppose that ‘had’ he known surfing he would have liked it.

In fact, it turns out that there is very little in Sartre that does fit with Aaron James’s surfing philosophy, so it is clearly more a marriage of convenience than of substance. Nonetheless, James does manage to use surfing to provide a framework to explore big Sartrean (better, ‘existentialist’) issues such as freewill, determinism, and of course, the meaning of life. James even goes so far to say:
‘It would be an exaggeration to say that the whole meaning of human existence could be continued in one moment, in a single act of riding a wave, yet is it as though the whole meaning of human existence can be contained in one moment, in a single act of riding a wave. ‘
And, philosophically speaking, Surfing with Sartre is a clear and well-informed guide, whose choices of examples are often illuminating.
‘This is a book of philosophy. It asks whether the surfer might happen to know something about questions for the ages, about knowledge, freedom, control, flow, happiness society, nature and the meaning of life. It’s a book about surfing, but also not, or not just, because the surfer knows, or at least sense, without necessarily caring, turns out to be of world-historical moment, for nothing less than the future of work, the planet, and human civilization.’
Paddling his board out further, James even suggests that the surfer is ‘a model of civic virtue’. This is partly because, if we all worked a lot less, say a 24-hour week, ‘the climate crisis would be less terrible’. James notes that, of course, not working could include other activities than surfing such as gardening or ‘spending time with the kids ‘. (That might offend some moms – and he doesn’t include being a philosophy professor in the ‘not really working’ category)

‘The question is one of ethics’, he continues firmly. Surfers are revolutionaries. Leisure revolutionaries. Speaking of revolutions reminds him of Sartre, who was of course a Marxist. Marxists used to link work with identity, but James argues that this is old thinking and that instead, surfers are ‘on the side of history’ by creating their identity though their leisure pursuit.

He explains a bit more about this by saying that surfing is not about imposing your will, but transcending it. To surf a wave is described thus:
1. To be attuned to a changing natural phenomenon,
2. so as to be carried along by its propulsive forces by way of bodily adaptation,
3. where this is done purposefully and for its own sake.
In this is a ‘kind of freedom, self-transcendence, and happiness’.

‘I realize this might sound like some mash-up of surf camp musings and philosophical blathering’, says James apologetically, in a rare moment of doubt - and for me, he’s not far wrong!

Indeed, rather vainglorious accounts of how to surf dominate the book. Learn how to fade, snap, cutback, anticipate and tube ride. This last maneouvere, it turns out, is surfer nirvana. If you want to know more about it - buy the book. If you want to know more about Sartre, the same advice does not apply.

James briefly reports that both W. V. Quine and Peter Strawson - ‘the two towering figures who later did the most to undo logical empiricism’ - ‘dabbled’ in surfing. However, more space is given to John Rawls who James crowns ‘the 20th century’s most influential philosopher’. What, not Sartre? Or any others from a whole range of non-surfing thinkers including Edmund Husserl and Ludwig Wittgenstein? Nonetheless, both of these get regular nods here.

James examines the different kinds of freedom possible.
‘Freedom for the surfer isn’t radical self-determination but a kind of achievement, in adaptive attunement. It’s a way of being efficacious without control, precisely by giving up any need for it.’
Think of the kind of freedom described by John Locke with his example of the man in a locked room. The man is not truly free, even if he has no with to leave the room - even if he does not know the door is locked. But no, it is not this kind of freedom. Surfers exhibit freedom, but it is more than ‘freedom from’ - it is freedom to do something. Is it then more like that offered by Sartre’s compatriot and fellow existentialist, Albert Camus? He reinvented the tale of Sisyphus in order to have the hero pushing the rock up the hill - for eternity- in an act of defiance.

Indeed, James says radical freedom, Sartre’s kind of freedom, isn’t necessary. A person can ‘be carried along by necessity, going along with the flow of the universe and yet be free’. Noting that the ‘concept of control sweeps away the workings of fate and fortune’, the surfer’s answer is that we have less control that we usually imagine.

James segues to consider toilets, which he rightly sees as marvellous things and wrongly insists we only have thanks to the emergence of probability theory and statistical analysis. (I still haven’t worked that one out yet… )
‘In sum, then the surfer wisdom for success as a person is this. Take it easier. Accept. Persist. Focus, Leave time. Don’t compare. And mix things up.’
Mix things up? But yes. Freedom means that the ‘average Joe ‘can strike up a conversation with a pretty girl lying on the beach’, muses James. On the other hand, it does seem to mix things up to say that by ‘the light of surfer reason’, it is not permissible ‘to lie in bed when the waves are pumping.’ Not here the transcendence of surfers. Nor indeed is there much evidence of transcendence in an imagined surfer dispute: ‘You snaked me, bro! No way, you go fuck yourself, bro. Let’s take it to the beach, bro!’

But, okay, let’s do that, let’s take it to the beach. Because, in fact, I’ve done quite a lot of swimming with surfers, and while I’m sure they’re generally very nice chaps (they are nearly all men) frankly, I don’t share James’s glorification of the project. The surfers I see are sitting on the their boards for hours on end just chatting and waiting for a middling swell to come in, at which point they may or may not balance precariously on their boards.

Secondly, and more substantially, in my observation, surfing is all about the gaze of the other. This is indeed a great existentialist theme, first discussed, not only by Sartre, but by his partner of many years, Simone de Beauvoir, who being a woman barely rates in surfer philosophy.

Surfing is indeed distinctive in the importance attached to the image of the ride on the wave: it is not enough for the one surfer to have the pleasure and the thrill all alone. Often surfers are accompanied by their own cameraman/ woman who sites placidly on the beach waiting, maybe for hours, to immortalise their glorious moment. But even if there is not camera, is it not significant that surfers do prefer to operate in company, and if they cannot do that, to be within the gaze of humble beach dwellers?

In all these ways surfing may indeed tell us something about the relationship of the individual and their milieu. But I ‘m not sure it is anything very much. It is thus for Aaron James to convince us that Surfing with Sartre is more than a personal conceit, more than an ornate folly constructed by an academic philosopher who happens to be a keen surfer.

Surfing and philosophy do seem to me, despite his protestations, to be completely different kinds of activities. That’s not to discount the value of surfing though. James disagrees with Mill’s division of higher and lower pleasures without appreciating that his specific target was ‘pushpin’, a kind of gambling, and there’s no reason to think that Mill would not have appreciated the aesthetics of life on the ocean wave – just as he appreciated the noble landscapes of the English Lake District. I think Mill might have appreciated body surfing, but been suspicious  of hours spent waiting for a tube roll. And I suspect Mill would, unlike James, have thought that the poet Baudelaire was on to something when he wrote that: ‘to reduce everything to a single truth, work is less boring than pleasure’.

Sartre tells us that we are condemned to absurdity. That view would perhaps seem absurd to a surfer. Indeed, James favours the ‘surfer-friendly’ conclusion ‘that we face *too much* meaning. There are too many things worth doing!

On the contrary, generically, as Sartre wrote in a digression in his novel Nausea (1938), life doesn’t make sense. This ‘bad faith’ is its ‘secret power’. What else do we have in life other than the ‘spurious meanings’ that we invent?
‘Descartes shut himself in an egocentric cage, and like Sartre he struggled to escape. But the door was always open, if one puts the body first. To perceive is to know how to engage what lies beyond one’s head. Perception is not simply located in the brain.’ 
 True knowledge comes, for James, anyway, from the existential feel of those tube rides.
 


*Surfing with Sartre: An Aquatic Inquiry into a Life of Meaning
By Aaron James
Doubleday, 2017
ISBN-10: 0385540736


The Philosopher’s verdict: Intriguing, but still not really suitable for the beach.



Monday, 1 May 2017

The Law of the Conservation of Being (2017)

From The Philosopher, Volume CV, Spring 2017

In this medieval woodcut, the human need for order is challenged by these witches and devils dancing in a circle

THE LAW OF THE CONSERVATION OF BEING
 
By Sayed Abolfazl Arjmand




Things change their forms. When we talk of new things we are really only talking about new forms of old things. It is an ontological mistake, a mistake about conceptual categories, to say that new things have come into existence, because previously they already existed in their old forms. The creation of new things did not start with their new forms any more than we should say that the old things have gone out of existence, because they continue to exist, although they may now look different from how they used to in the past. 

In changing their forms, things may appear or disappear. They appear if we can sense them and they disappear when we cannot sense them anymore. For example, if we put a glass of water in a room, the water will disappear in a few days. Shapeshifting creatures like werewolves and vampires will know that the water has not gone out of existence, but has only changed its form: in this case from a visible liquid to an invisible gas. The being or existence of water continues - it is conserved in another form, although we cannot observe it anymore. Again, in reverse order, the invisible water vapour suspended in the air may take on visible form as water droplets on a cold surface.

In everyday language, we define lifetime as the period of time that something exists, but a more precise definition is the period of time that something has a particular form or state. The lifetime of the Earth is estimated to be about five billion years, but this period refers to the planet in its present spherical shape. Before this period the Earth existed in a shapeless gas state. After solidification, our planet has continued to undergo minor changes up to now, and these changes will continue forever. At each moment a new form is born, but we neglect these changes as trivial and only consider as the Earth’s birth time the transformation from gaseous state into a solid sphere those five billion years ago.

Because things change continuously, we can say that they are created and destroyed at every moment. Each death is followed by a birth and each birth is followed by a death. After something dies, it loses its previous form and takes on a new form. Seen from this perspective, death is not the end of existence, but only the end of a particular form of existence. Similarly, birth is not the beginning of existence, but only the beginning of a new form.

Different things are different forms of the same thing. For example, sodium, chlorine, and salt are different forms of something that we call matter. Despite their different forms, these substances are essentially the same and they can transform into each other. Sodium is a silvery metal and chlorine is a yellowish-green gas - both of them are poisonous to humans. Yet, when they combine, table salt is produced. In reverse order, by decomposing the salt, we can obtain sodium and chlorine again.

We give different names to different forms of the same thing. In other words, all different forms with different names can be categorised under a single name. Sodium, chlorine, and salt can be categorised under the single name chemicals or indeed as matter. This brings me to another important category in science - which is energy. Light and heat are forms of energy and they can transform into each other. Light from the Sun, when absorbed by objects on the Earth, is transformed into heat. Mutatis mutandis, (taken in the sense of ‘the same thing the other way around’) a hot object loses energy by radiation; that is, its thermal energy is transformed into light or electromagnetic energy.

During the 18th century, Antoine Lavoisier proposed a law for the conservation of matter. According to this, in a chemical reaction, the total amount of consumed materials is equal to the total amount of the products. Famously, the law implies that matter can neither be created nor destroyed, but only change form. This principle was later proved to be approximate, not exact because of the conversion of tiny amounts of matter into energy. The typical values for matter converted to energy in a chemical experiment are so tiny that it is only very recently that it has become possible to detect and measure them.

It is important to restate that we cannot eliminate all experimental imprecisions.Given that  it is only very recently that we can measure the tiny amount of matter converted into energy, it is probable that an even tinier amount of matter converts into something other than energy and we are not able to detect or measure it now. In future we may discover this unknown thing and take it into account. If there was something that we neglected in the past, there still may be something that we neglect now.

As an example to explain the law, consider again the case of water. Water is a compound of hydrogen and oxygen. When hydrogen burns, it combines with oxygen, and water is produced. The law of the conservation of matter claims that the total amount of the consumed gasses is equal to the total amount of the produced water. This can nowadays be shown experimentally, using precision devices to weigh the starting components and the final compound.

However, in burning hydrogen, some heat is also produced in addition to water. If the total amount of water produced were really exactly equal to the total amount of the consumed gasses; that is, if no matter is lost, from what source then is the heat produced? Did the heat come out of nothing?

Scientists explain that an infinitesimal amount of matter disappears in burning hydrogen and transforms into heat, albeit the amount is so small that it cannot be easily detected or measured. If, for example, we produce three million kilograms of water through the chemical reaction of burning hydrogen, only one gram of matter transforms into energy; that is, one part in three billion parts. It is extremely difficult to notice this extremely small loss of matter.

Early scientists were not aware of transformation of tiny amounts of matter into energy during chemical reactions, and the law of the conservation of matter that they deduced was based on a small error. Even eliminating this error does not guarantee that the law will be exact, because it is possible that another tiny amount of matter transforms into something other than energy; something unknown to us at the present time. we can not prove that the only things existing in the universe are matter and energy. Other forms of existence and other types of transformations can occur, and as a result, scientific conservation laws can be violated.

Many scientific laws are only approximately correct and while they are useful in daily life, they cannot describe the universe exactly. In fact, the equals sign (=) in formulas describing physical transformations and chemical reactions might be changed to ‘approximately equal’. Yes, we describe the universe by the scientific laws we ‘discover’, but on the scale beyond the scope of human abilities and imaginations, these laws fail to be correct and exact.

Consider the case of the previously unanticipated ‘Dark Matter’ and ‘Dark Energy’, that cosmologists now routinely use to make sense of the universe. Astronomical observations have led scientists to the idea that the visible matter in universe is much less than the invisible matter.

For example, our solar system has most of its mass concentrated in the Sun. Within such an orbital system with most of the mass at the center, the orbital speed of the planets decline with distance from the center. For example, the Earth rotates around the Sun each year, while Neptune rotation takes 165 years! This is not the case observed in galaxies, where the rotational speed of visible stars is the same from center towards the edge. If the whole galaxy rotates with the same velocity, its mass is not concentrated at the center, contrary to what we observe from visible stars which are concentrated at the center of the galaxy. So there must be invisible matter in the dark space between visible stars. This unknown theoretical substance is called dark matter.

Nowadays, dark matter is hypothesised to permeate all of the universe, but its density is extremely low. Imagine a spherical volume as big as the Earth. The quantity of dark matter distributed uniformly in such a big volume is less than one gram! Such a thin substance is extremely difficult to be detected or measured. Now suppose that in a physical change or chemical reaction, some dark matter or other unknown substance is lost or produced. It is practically impossible to detect its existence or measure its amount. Things that we can detect or measure are not the only things that exist.

Many scientists also believe in the existence of an unknown form of energy which they call dark energy. Again, they hypothesise it because with ordinary matter and energy they cannot explain some astronomical observations. Ordinary matter and ordinary energy are two forms of being. Dark matter and dark energy are two other forms which do seem to exist. There may be still other forms of existence, completely unknown to us. All these forms can transform into each other. So it is possible that some amount of a known thing completely disappears and transforms into some other unknown and undetectable thing.

To conclude, then. In modern science, a series of conservation laws has been proposed by scientists and these laws are claimed by them to govern physical quantities such as matter, energy, electrical charge, and so on. The first law was Lavoisier’s idea of conservation of matter. Although this approximate law has proved invaluable in our daily life, it was later discovered that matter can transform into energy and that, therefore, the total amount of matter in the universe is not conserved.

Trying to formulate a more accurate law, scientists used the fact that matter and energy are of the same essence and asserted the law of conservation of the two quantities under a single name mass. According to this law, if a certain amount of matter is lost, an equivalent amount of energy is gained, and vice versa, so that the total amount of mass in the universe is constant. But we can argue that this law is still erroneous, because we cannot prove that the only existing things in the universe are matter and energy. There may be other unknown forms of being that matter and energy can be transformed into.

If all things were made, for example, of matter, then in changing from one state to another, we could claim that the total amount of matter would conserve. But given that there is something other than matter; for example, energy, then matter can transform into energy, and conservation of matter will be violated. Even if we combine matter and energy into a single concept as mass, the conservation of mass can be violated for the same reason.

Scientific conservation laws are philosophically problematic, because each of these laws apply to a certain form of being like matter, energy, mass, and so on, which can be transformed to other known or unknown forms. True conservation can only be applied to being itself. By being, I mean the common essence of all things that does not change in transformations. Being cannot be created or destroyed, but it can appear in different forms. It can disappear, but even in its hidden form, it has always been and will always be.

The cycle of existence means that new things existed previously in old forms. Old forms disappear and new forms appear, but their existence or being never starts or ends. Being cannot change into something other than being, because there is nothing other than being. Although being cannot be clearly defined, we can say that everything is a presentation or sign of being. Being is present wherever there is something.

Let us return to where we started. From a viewpoint of conservation of being, we can have a better imagination of the birth of the universe. While being has no beginning or end, the universe as a form of being can have a beginning or end. The universe came into view from a hidden state. Before the Creation or the Big Bang, we can imagine that there was no matter and no energy at all, but that being was there - in a hidden form.

Such ideas can also be applied to states of human being. If we exist now, then we have always existed and will always exist, although in different forms or states. When we are asleep, we exist, even if we are usually unaware of our existence. Similarly, a newborn child exists, even if at first it is not aware of its existence. During our life we experience many periods of time during which we continue to exist but are not consciously aware of it. We may be in the same state before our birth and after our death.

The law of the conservation of being can build bridges between science, philosophy, and religion. It rationalizes believing in an eternal thing that all different forms come out of it and return back to it. This eternal thing can be neither matter nor energy which are derivable and transformable quantities. Scientific laws of conservation of such quantities as matter and energy are approximations of the philosophical law of the conservation of being.

The law can be viewed as a modern restatement of the ancient philosophical thesis nihil fit ex nihilo. That is: nothing comes from nothing. It implies that if there is something now, it has always been and will always be, although in different forms.




Address for correspondence:


Sayed Abolfazl Arjmand is an Iranian electrical engineer whose scientific interests extend through philosophy and theology. Email: abarjm@yahoo.com 



BOOK REVIEW: Uncertainty

From The Philosopher, Volume CV No. 1 Spring  2017
 


UNCERTAINTY  
Review article 
By Thomas Scarborough



It would be helpful to begin at the beginning. Probability, while it was known by the ancients, found its first serious application in the 16th Century, through game probability. In the case of game probability, it may be a fairly simple matter to predict an outcome. A coin toss, for instance, will yield either heads or tails with a probability of 0.5, which is an equal chance of either – if the situation is theoretically perfect. Another example is throwing a dice. The chance that it will turn up any given number is one in six.

Now consider, rather, two dice. Things become more complex now – such that one could do with the help of a simple mathematical formula. For instance, to calculate the probability that the sum of two dice will be 5, one divides the number of favourable outcomes by the total number of possible outcomes. This might lead us to believe that probability is much like game probabilty – but this is deceptive. The real world is seldom as simple as a game – even the most complex of games. Chess and bridge, for instance, may be simplicity itself in comparison with grasping the spread of an epidemic, or predicting the outcome of a vote – as we so well know. To deal with more complex uncertainties, one begins to depend heavily on analysis.

But how then does one establish just what it is that is uncertain in a given analysis? and how does one factor this into one’s thinking? This, writes the author, is not answered by grasping for equations, let alone models. It requires ‘slow, maturing thought’. It is more a matter of philosophy than of mathematics. Yet people shun the effort. Instead, they grasp at pre-packaged probability theory, which is far too easily applied without further thought. In fact, the author sketches a situation of crisis proportions. There is altogether too much that we get wrong.


How, then, does one establish what it is that is uncertain in a given analysis? and how does one factor this into one’s thinking? It requires ‘slow, maturing thought’.


In principle, the science of uncertainty would seem to be simple. In science one has, on the face of it, certainty. This is encapsulated by scientific laws, for example a = F/m. Apply a certain force F to mass m, and the acceleration of m is a. To recast this in terms of probability, the results of such laws have a probability of 1. On the other hand, there may be complete uncertainty, which too represents a kind of certainty. This has a probability of 0, because it is certain that it will never happen. The chances are nil. In both cases, one knows perfectly – or imagines that one does – what one is dealing with, and what one should anticipate.

However, any figure between 0 and 1 introduces an interesting situation – not merely in practice, but often enough in principle. Assume that the probability of something happening is 0.7. In such a situation, one neither has complete certainty nor complete uncertainty, and the reason for this is that we have uncertain influences on our analysis of a situation, beyond our knowledge or control – alternartively, too complex to contemplate. More importantly, one cannot pin these factors down precisely, or one would be dealing with certainty, not uncertainty. This pinning down of uncertain factors, contends the author, is where far more mistakes are made than is generally understood.

The publisher describes this work as a textbook. It begins with what one might call a componential analysis of probability. It carefully examines such concepts as truth, induction, chance – and many besides. Then it applies these observations to the field of modelling. While the mathematics are complicated, this is compensated for by the authors’s gift of explanation.

The book really brightens up when one reaches worked examples of what can and does go wrong, and how probability calculations for the self same situations may easily turn out to be quite different. The examples are generalised, too, so as to be meaningful beyond specific contexts. Some particularly illuminating sections of the book include a series of graphs and equations in which the quantification of GPAs, the probabilities of developing cancer, or how one might validate homophobia, are discussed.

I have one demurral ato make. In places, the style seems unnecessarily to get in the way of the content. In particular, outbursts such as ‘Die, p-value, die, die, die!’ or ‘p-values, God rot them!’, while they are certainly memorable, do not seem to serve the book well as the serious academic work that it is.

All in all, if the author is right, then our world has strayed down a path which is dangerously simplistic – and this tendency towards simplistic thinking has much to do with how we think about uncertainty. One might go so far as to say: that we have misapplied, and continue to misapply, theory which has to do with things of critical importance, including the very future of humanity.

The Philosopher’s verdict: Useful warnings about the complexities of simplistic thinking.



Uncertainty: The Soul of Modeling, Probability & Statistics
By William Briggs Springer International Publishing
ISBN: 978-3-319-39755-9 
(Hardcover £42.00 ) 978-3-319-39756-6
 (eBook £27.94), 258pp 2016.