Dance of the Shiva, q’i (chee) and Tibetan Sunyata. Manifestation of Mysticism.

अनेजदेकं मनसो जवीयो नैनद्देवाप्नुवन्पूर्वमर्षत् ।
तद्धावतोऽन्यान्नत्येति तिष्ठत् तस्मिन्नापो मातरिश्वा दधाति ॥

anejadekaṃ manaso javīyo nainaddevāpnuvanpūrvamarṣat |
taddhāvato’nyānnatyeti tiṣṭhat tasminnāpo mātariśvā dadhāti ||

The self is one. It is unmoving: yet faster than the mind. Thus moving faster, It is beyond the reach of the senses. Ever steady, It outstrips all that run. By its mere presence, the cosmic energy is enabled to sustain the activities of living beings.

तस्मिन् मनसि ब्रह्मलोकादीन्द्रुतं गच्छति सति प्रथमप्राप्त इवात्मचैतन्याभासो गृह्यते अतः मनसो जवीयः इत्याह ।

tasmin manasi brahmalokādīndrutaṃ gacchati sati prathamaprāpta ivātmacaitanyābhāso gṛhyate ataḥ manaso javīyaḥ ityāha |

When the mind moves fast towards the farthest worlds such as the brahmaloka, it finds the Atman, of the nature of pure awareness, already there; hence the statement that It is faster than the mind.

नित्योऽनित्यानां चेतनश्चेतनानाम्
एको बहूनां यो विदधाति कामान् ।
तमात्मस्थं योऽनुपश्यन्ति धीराः
तेषां शान्तिः शाश्वतं नेतरेषाम् ॥

nityo’nityānāṃ cetanaścetanānām
eko bahūnāṃ yo vidadhāti kāmān |
tamātmasthaṃ yo’nupaśyanti dhīrāḥ
teṣāṃ śāntiḥ śāśvataṃ netareṣām ||

He is the eternal in the midst of non-eternals, the principle of intelligence in all that are intelligent. He is One, yet fulfils the desires of many. Those wise men who perceive Him as existing within their own self, to them eternal peace, and non else.

east-2

Eastern mysticism approaches the manifestation of life in the cosmos and all that compose it from a position diametrically opposed to the view that prevailed until recently among the majority of Western scientists, philosophers, and religionists. Orientals see the universe as a whole, as an organism. For them all things are interconnected, links in a chain of beings permeated by consciousness which threads them together. This consciousness is the one life-force, originator of all the phenomena we know under the heading of nature, and it dwells within its emanations, urging them as a powerful inner drive to grow and evolve into ever more refined expressions of divinity. The One manifests, not only in all its emanations, but also through those emanations as channels: it is within them and yet remains transcendent as well.

The emphasis is on the Real as subject whereas in the West it is seen as object. If consciousness is the noumenal or subjective aspect of life in contrast to the phenomenal or objective — everything seen as separate objects — then only this consciousness can be experienced, and no amount of analysis can reveal the soul of Reality. To illustrate: for the ancient Egyptians, their numerous “gods” were aspects of the primal energy of the Divine Mind (Thoth) which, before the creation of our universe, rested, a potential in a subjective state within the “waters of Space.” It was through these gods that the qualities of divinity manifested.

A question still being debated runs: “How does the One become the many?” meaning: if there is a “God,” how do the universe and the many entities composing it come into being? This question does not arise among those who perceive the One to dwell in the many, and the many to live in the One from whom life and sustenance derive. Despite our Western separation of Creator and creation, and the corresponding distancing of “God” from human beings, Western mystics have held similar views to those of the East, e.g.: Meister Eckhart, the Dominican theologian and preacher, who was accused of blasphemy for daring to say that he had once experienced nearness to the “Godhead.” His friends and followers were living testimony to the charisma (using the word in its original connotation of spiritual magnetism) of those who live the life of love for fellow beings men like Johannes Tauler, Heinrich Suso, the “admirable Ruysbroeck,” who expressed views similar to those of Eastern exponents of the spiritual way or path.

In old China, the universe was described as appearing first as q’i (chee), an emanation of Light, not the physical light that we know, but its divine essence sometimes called Tien, Heaven, in contrast to Earth. The q’i energy polarized as Yang and Yin, positive and negative electromagnetism. From the action and interaction of these two sprang the “10,000 things”: the universe, our world, the myriads of beings and things as we perceive them to be. In other words, the ancient Chinese viewed our universe as one of process, the One energy, q’i, proliferating into the many.

In their paintings Chinese artists depict man as a small but necessary element in gigantic natural scenes. And since we are parts of the cosmos, we are embodiments of all its potentials and our relationship depends upon how we focus ourselves: (1) harmoniously, i.e., in accord with nature; or (2) disharmoniously, interfering with the course of nature. We therefore affect the rest: our environment, all other lives, and bear full responsibility for the outcome of our thoughts and acts, our motivations, our impacts. Their art students were taught to identify with what they were painting, because there is life in every thing, and it is this life with which they must identify, with boulders and rocks no less than with birds flying overhead. Matter, energy, space, are all manifestations of q’i and we, as parts thereof, are intimately connected with all the universe.

In India, the oneness of life was seen through the prism of successive manifestations of Brahman, a neuter or impersonal term in Sanskrit for divinity, the equivalent of what Eckhart called the Godhead. Brahman is the source of the creative power, Brahma, Eckhart’s Creator; and also the origin of the sustaining and supporting energy or Vishnu, and of the destructive/regenerative force or Siva. As these three operate through the cosmos, the “world” as we know it, so do they also through ourselves on a smaller scale according to our capacity. Matter is perceived to be condensed energy, Chit or consciousness itself. To quote from the Mundaka Upanishad:

By the energism of Consciousness Brahman is massed; from that: Matter is born and from Matter Life and Mind and the worlds . . .

In another Hindu scripture, it is stated that when Brahma awakened from his period of rest between manifestations, he desired to contemplate himself as he is. By gazing into the awakening matter particles as into a mirror, he stirred them to exhibit their latent divine qualities. Since this process involves a continuous unfoldment from the center within, an ever-becoming, there can never be an end to the creativity — universal “days” comprising trillions of our human years, followed by a like number of resting “nights.”

We feel within ourselves the same driving urge to grow that runs through the entire, widespread universe, to express more and more of what is locked up in the formless or subjective realm of Be-ness, awaiting the magic moment to come awake in our phase of life.

Tibetan metaphysics embraces all of this in discussing Sunyata, which can be viewed as Emptiness if we use only our outer senses, or as Fullness if we inwardly perceive it to be full of energies of limitless ranges of wave-lengths/frequencies. This latter aspect of Space is the great mother of all, ever fecund, from whose “heart” emerge endless varieties of beings, endless forces, ever-changing variations — like the pulsing energies the new physicists perceive nuclear subparticles to be.

In the Preface to his Tao of physics Fritjof Capra tells how one summer afternoon he had a transforming experience by the seashore as he watched the waves rolling in and felt the rhythm of his own breathing. He saw dancing motes revealed in a beam of sunlight; particles of energy vibrating as molecules and atoms; cascades of energy pouring down upon us from outer space. All of this coming and going, appearing and disappearing, he equated with the Indian concept of the dance of Siva . . . he felt its rhythm, “heard” its sound, and knew himself to be a part of it. Through this highly personal, indeed mystical, experience Capra became aware of his “whole environment as being engaged in a gigantic cosmic dance.”

This is the gist of the old Chinese approach to physics: students were taught gravitation by observing the petals of a flower as they fall gracefully to the ground. As Gary Zukav expresses it in his Dancing Wu Li Masters: An Overview of the New Physics:

The world of particle physics is a world of sparkling energy forever dancing with itself in the form of its particles as they twinkle in and out of existence, collide, transmute, and disappear again.

That is: the dance of Siva is the dance of attraction and repulsion between charged particles of the electromagnetic force. This is a kind of “transcendental” physics, going beyond the “world of opposites” and approaching a mystical view of the larger Reality that is to our perceptions an invisible foundation of what we call “physical reality.” It is so far beyond the capacity or vocabulary of the mechanically rational part of our mind to define, that the profound Hindu scripture Isa Upanishad prefers to suggest the thought by a paradox:

तदेजति तन्नैजति तद्दूरे तद्वन्तिके ।
तदन्तरस्य सर्वस्य तदु सर्वस्यास्य बाह्यतः ॥

tadejati tannaijati taddūre tadvantike |
tadantarasya sarvasya tadu sarvasyāsya bāhyataḥ ||

It moves. It moves not.  It is far, and it is near. It is within all this, And It is verily outside of all this.

Indeed, there is a growing recognition mostly by younger physicists that consciousness is more than another word for awareness, more than a by-product of cellular activity (or of atomic or subatomic vibrations). For instance, Jack Sarfatti, a quantum physicist, says that signals pulsating through space provide instant communication between all parts of the cosmos. “These signals can be likened to pulses of nerve cells of a great cosmic brain that permeates all parts of space (Michael Talbot, Mysticism and the New Physics).” Michael Talbot quotes Sir James Jeans’ remark, “the universe is more like a giant thought than a giant machine,” commenting that the “substance of the great thought is consciousness” which pervades all space. Or as Schrödinger would have it:

Consciouness is never experienced in the plural, only in the singular….Consciouness is a singular of which the plural is unknown; that; there is only one thing and that, what seems to be a plurality is merely a series of different aspects of this one thing, produced by a deception (the Indian Maya).

Other phenomena reported as occurring in the cosmos at great distances from each other, yet simultaneously, appear to be connected in some way so far unexplained, but to which the term consciousness has been applied.

In short, the mystic deals with direct experience; the intuitive scientist is open-minded, and indeed the great discoveries such as Einstein’s were made by amateurs in their field untrammeled by prior definitions and the limitations inherited from past speculations. This freedom enabled them to strike out on new paths that they cleared and paved. The rationalist tries to grapple with the problems of a living universe using only analysis and whatever the computer functions of the mind can put together.

The theosophic perspective upon universal phenomena is based on the concept of the ensoulment of the cosmos. That is: from the smallest subparticle we know anything about to the largest star-system that has been observed, each and all possess at their core vitality, energy, an active something propelling towards growth, evolution of faculties from within.

The only “permanent” in the whole universe is motion: unceasing movement, and the ideal perception is a blend of the mystical with the scientific, the intuitive with the rational.

Vector Representations and Why Would They Deviate From Projective Geometry? Note Quote.

Stereographic_projection_in_3D

There is, of course, a definite reason why von Neumann used the mathematical structure of a complex Hilbert space for the formalization of quantum mechanics, but this reason is much less profound than it is for Riemann geometry and general relativity. The reason is that Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics turned out to be equivalent, the first being a formalization of the new mechanics making use of l2, the set of all square summable complex sequences, and the second making use of L2(R3), the set of all square integrable complex functions of three real variables. The two spaces l2 and L2(R3) are canonical examples of a complex Hilbert space. This means that Heisenberg and Schrödinger were working already in a complex Hilbert space, when they formulated matrix mechanics and wave mechanics, without being aware of it. This made it a straightforward choice for von Neumann to propose a formulation of quantum mechanics in an abstract complex Hilbert space, reducing matrix mechanics and wave mechanics to two possible specific representations.

One problem with the Hilbert space representation was known from the start. A (pure) state of a quantum entity is represented by a unit vector or ray of the complex Hilbert space, and not by a vector. Indeed vectors contained in the same ray represent the same state or one has to renormalize the vector that represents the state after it has been changed in one way or another. It is well known that if rays of a vector space are called points and two dimensional subspaces of this vector space are called lines, the set of points and lines corresponding in this way to a vector space, form a projective geometry. What we just remarked about the unit vector or ray representing the state of the quantum entity means that in some way the projective geometry corresponding to the complex Hilbert space represents more intrinsically the physics of the quantum world as does the Hilbert space itself. This state of affairs is revealed explicitly in the dynamics of quantum entities, that is built by using group representations, and one has to consider projective representations, which are representations in the corresponding projective geometry, and not vector representations.

Are Categories Similar to Sets? A Folly, if General Relativity and Quantum Mechanics Think So.

maxresdefault3

The fundamental importance of the path integral suggests that it might be enlightening to simplify things somewhat by stripping away the knot observable K and studying only the bare partition functions of the theory, considered over arbitrary spacetimes. That is, consider the path integral

Z(M) = ∫ DA e (i ∫M S(A) —– (1)

where M is an arbitrary closed 3d manifold, that is, compact and without boundary, and S[A] is the Chern-Simons action. Immediately one is struck by the fact that, since the action is topological, the number Z(M) associated to M should be a topological invariant of M. This is a remarkably efficient way to produce topological invariants.

Poincaré Conjecture: If M is a closed 3-manifold, whose fundamental group π1(M), and all of whose homology groups Hi(M) are equal to those of S3, then M is homeomorphic to S3.

One therefore appreciates the simplicity of the quantum field theory approach to topological invariants, which runs as follows.

  1. Endow the space with extra geometric structure in the form of a connection (alternatively a field, a section of a line bundle, an embedding map into spacetime)
  2. Compute a number from this manifold-with-connection (the action)
  3. Sum over all connections.

This may be viewed as an extension of the general principle in mathematics that one should classify structures by the various kinds of extra structure that can live on them. Indeed, the Chern-Simons Lagrangian was originally introduced in mathematics in precisely this way. Chern-Weil theory provides access to the cohomology groups (that is, topological invariants) of a manifold M by introducing an arbitrary connection A on M, and then associating to A a closed form f(A) (for instance, via the Chern-Simons Lagrangian), whose cohomology class is, remarkably, independent of the original arbitrary choice of connection A. Quantum field theory takes this approach to the extreme by being far more ambitious; it associates to a connection A the actual numerical value of the action (usually obtained by integration over M) – this number certainly depends on the connection, but field theory atones for this by summing over all connections.

Quantum field theory is however, in its path integral manifestation, far more than a mere machine for computing numbers associated with manifolds. There is dynamics involved, for the natural purpose of path integrals is not to calculate bare partition functions such as equation (1), but rather to express the probability amplitude for a given field configuration to evolve into another. Thus one considers a 3d manifold M (spacetime) with boundary components Σ1 and Σ2 (space), and considers M as the evolution of space from its initial configuration Σ1 to its final configuration Σ2:

IMG_20170321_040643_HDR

This is known mathematically as a cobordism from Σ1 to Σ2. To a 2d closed manifold Σ we associate the space of fields A(Σ) living on Σ. A physical state Ψ corresponds to a functional on this space of fields. This is the Schrödinger picture of quantum field theory: if A ∈ A(Σ), then Ψ(A) represents the probability that the state known as Ψ will be found in the field A. Such a state evolves with time due to the dynamics of the theory; Ψ(A) → Ψ(A, t). The space of states has a natural basis, which consists of the delta functionals  – these are the states satisfying ⟨Â|Â′⟩ = δ(A − A′). Any arbitrary state Ψ may be expressed as a superposition of these basis states. The path integral instructs us how to compute the time evolution of states, by first expanding them in the  basis, and then specifying that the amplitude for a system in the state Â1 on the space Σ1 to be found in the state Â2 on the space Σ2 is given by:

〈Â2|U|Â1〉= ∫A | ∑2 = A2 A | ∑1 = A1 DA e i S[A] —– (2)

This equation is the fundamental formula of quantum field theory: ‘Perform a weighted sum over all possible fields (connections) living on spacetime that restrict to A1 and A2 on Σ1 and Σ2 respectively’. This formula constructs the time evolution operator U associated to the cobordism M.

In this way we see that, at the very heart of quantum mechanics and quantum field theory, is a formula which associates to every space-like manifold Σ a Hilbert space of fields A(Σ), and to every cobordism M from Σ1 to Σ2 a time evolution operator U(M) : Σ1 – Σ2. To specify a quantum field theory is nothing more than to give rules for constructing the Hilbert spaces A(Σ) and the rules (correlation functions) for calculating the time evolution operators U(M). This is precisely the statement that a quantum field theory is a functor from the cobordism category nCob to the category of Hilbert spaces Hilb.

A category C consists of a collection of objects, a collection of arrows f:a → b from any object a to any object b, a rule for composing arrows f:a → b and g : b → c to obtain an arrow g f : a → c, and for each object A an identity arrow 1a : a → a. These must satisfy the associative law f(gh) = (fg)h and the left and right unit laws 1af = f and f1a = f whenever these composites are defined. In many cases, the objects of a category are best thought of as sets equipped with extra structure, while the morphisms are functions preserving the structure. However, this is neither true for the category of Hilbert spaces nor for the category of cobordisms.

The fundamental idea of category theory is to consider the ‘external’ structure of the arrows between objects instead of the ‘internal’ structure of the objects themselves – that is, the actual elements inside an object – if indeed, an object is a set at all : it need not be, since category theory waives its right to ask questions about what is inside an object, but reserves its right to ask how one object is related to another.

A functor F : C → D from a category C to another category D is a rule which associates to each object a of C an object b of D, and to each arrow f :a → b in C a corresponding arrow F(f): F(a) → F(b) in D. This association must preserve composition and the units, that is, F(fg) = F(f)F(g) and F(1a) = 1F(a).

1. Set is the category whose objects are sets, and whose arrows are the functions from one set to another.

2. nCob is the category whose objects are closed (n − 1)-dimensional manifolds Σ, and whose arrows M : Σ1 → Σ2 are cobordisms, that is, n-dimensional manifolds having an input boundary Σ1 and an output boundary Σ2.

3. Hilb is the category whose objects are Hilbert spaces and whose arrows are the bounded linear operators from one Hilbert space to another.

The ‘new philosophy’ amounts to the following observation: The last two categories, nCob and Hilb, resemble each other far more than they do the first category, Set! If we loosely regard general relativity or geometry to be represented by nCob, and quantum mechanics to be represented by Hilb, then perhaps many of the difficulties in a theory of quantum gravity, and indeed in quantum mechanics itself, arise due to our silly insistence of thinking of these categories as similar to Set, when in fact the one should be viewed in terms of the other. That is, the notion of points and sets, while mathematically acceptable, might be highly unnatural to the subject at hand!

von Neumann & Dis/belief in Hilbert Spaces

I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space any more.

— John von Neumann, letter to Garrett Birkhoff, 1935.

15_03

The mathematics: Let us consider the raison d’ˆetre for the Hilbert space formalism. So why would one need all this ‘Hilbert space stuff, i.e. the continuum structure, the field structure of complex numbers, a vector space over it, inner-product structure, etc. Why? According to von Neumann, he simply used it because it happened to be ‘available’. The use of linear algebra and complex numbers in so many different scientific areas, as well as results in model theory, clearly show that quite a bit of modeling can be done using Hilbert spaces. On the other hand, we can also model any movie by means of the data stream that runs through your cables when watching it. But does this mean that these data streams make up the stuff that makes a movie? Clearly not, we should rather turn our attention to the stuff that is being taught at drama schools and directing schools. Similarly, von Neumann turned his attention to the actual physical concepts behind quantum theory, more specifically, the notion of a physical property and the structure imposed on these by the peculiar nature of quantum observation. His quantum logic gave the resulting ‘algebra of physical properties’ a privileged role. All of this leads us to … the physics of it. Birkhoff and von Neumann crafted quantum logic in order to emphasize the notion of quantum superposition. In terms of states of a physical system and properties of that system, superposition means that the strongest property which is true for two distinct states is also true for states other than the two given ones. In order-theoretic terms this means, representing states by the atoms of a lattice of properties, that the join p ∨ q of two atoms p and q is also above other atoms. From this it easily follows that the distributive law breaks down: given atom r ≠ p, q with r < p ∨ q we have r ∧ (p ∨ q) = r while (r ∧ p) ∨ (r ∧ q) = 0 ∨ 0 = 0. Birkhoff and von Neumann as well as many others believed that understanding the deep structure of superposition is the key to obtaining a better understanding of quantum theory as a whole.

For Schrödinger, this is the behavior of compound quantum systems, described by the tensor product. While the quantum information endeavor is to a great extend the result of exploiting this important insight, the language of the field is still very much that of strings of complex numbers, which is akin to the strings of 0’s and 1’s in the early days of computer programming. If the manner in which we describe compound quantum systems captures so much of the essence of quantum theory, then it should be at the forefront of the presentation of the theory, and not preceded by continuum structure, field of complex numbers, vector space over the latter, etc, to only then pop up as some secondary construct. How much quantum phenomena can be derived from ‘compoundness + epsilon’. It turned out that epsilon can be taken to be ‘very little’, surely not involving anything like continuum, fields, vector spaces, but merely a ‘2D space’ of temporal composition and compoundness, together with some very natural purely operational assertion, including one which in a constructive manner asserts entanglement; among many other things, trace structure then follows.

Representation as a Meaningful Philosophical Quandary

1456831690974

The deliberation on representation indeed becomes a meaningful quandary, if most of the shortcomings are to be overcome, without actually accepting the way they permeate the scientific and philosophical discourse. The problem is more ideological than one could have imagined, since, it is only within the space of this quandary that one can assume success in overthrowing the quandary. Unless the classical theory of representation that guides the expert systems has been accepted as existing, there is no way to dislodge the relationship of symbols and meanings that build up such systems, lest the predicament of falling prey to the Scylla of metaphysically strong notion of meaningful representation as natural or the Charybdis of an external designer should gobble us up. If one somehow escapes these maliciously aporetic entities, representation as a metaphysical monster stands to block our progress. Is it really viable then to think of machines that can survive this representational foe, a foe that gets no aid from the clusters of internal mechanisms? The answer is very much in the affirmative, provided, a consideration of the sort of such a non-representational system as continuous and homogeneous is done away with. And in its place is had functional units that are no more representational ones, for the former derive their efficiency and legitimacy through autopoiesis. What is required is to consider this notional representational critique of distributed systems on the objectivity of science, since objectivity as a property of science has an intrinsic value of independence from the subject who studies the discipline. Kuhn  had some philosophical problems to this precise way of treating science as an objective discipline. For Kuhn, scientists operate under or within paradigms thus obligating hierarchical structures. Such hierarchical structures ensure the position of scientists to voice their authority on matters of dispute, and when there is a crisis within, or, for the paradigm, scientists, to begin with, do not outrightly reject the paradigm, but try their level best at resolution of the same. In cases where resolution becomes a difficult task, an outright rejection of the paradigm would follow suit, thus effecting what is commonly called the paradigm shift. If such were the case, obviously, the objective tag for science goes for a hit, and Kuhn argues in favor of a shift in social order that science undergoes, signifying the subjective element. Importantly, these paradigm shifts occur to benefit scientific progress and in almost all of the cases, occur non-linearly. Such a view no doubt slides Kuhn into a position of relativism, and has been the main point of attack on paradigms shifting. At the forefront of attacks has been Michael Polanyi and his bunch of supporters, whose work on epistemology of science have much of the same ingredients, but was eventually deprived of fame. Kuhn was charged with plagiarism. The commonality of their arguments could be measured by a dissenting voice for objectivity in science. Polanyi thought of it as a false ideal, since for him the epistemological claims that defined science were based more on personal judgments, and therefore susceptible to fallibilism. The objective nature of science that obligates the scientists to see things as they really are is kind of dislodged by the above principle of subjectivity. But, if science were to be seen as objective, then the human subjectivity would indeed create a rupture as far as the purified version of scientific objectivity is sought for. The subject or the observer undergoes what is termed the “observer effect” that refers to the change impacting an act of observation being observed. This effect is as good as ubiquitous in most of the domains of science and technology ranging from Heisenbug(1) in computing via particle physics, science of thermodynamics to quantum mechanics. The quantum mechanics observer effect is quite perplexing, and is a result of a phenomenon called “superposition” that signifies the existence in all possible states and all at once. The superposition gets its credit due to Schrödinger’s cat experiment. The experiment entails a cat that is neither dead nor alive until observed. This has led physicists to take into account the acts of “observation” and “measurement” to comprehend the paradox in question, and thereby come out resolving it. But there is still a minority of quantum physicists out there who vouch for the supremacy of an observer, despite the quantum entanglement effect that go on to explain “observation” and “measurement” impacts.(2) Such a standpoint is indeed reflected in Derrida (9-10) as well, when he says (I quote him in full),

The modern dominance of the principle of reason had to go hand in hand with the interpretation of the essence of beings as objects, and object present as representation (Vorstellung), an object placed and positioned before a subject. This latter, a man who says ‘I’, an ego certain of itself, thus ensures his own technical mastery over the totality of what is. The ‘re-‘ of repraesentation also expresses the movement that accounts for – ‘renders reason to’ – a thing whose presence is encountered by rendering it present, by bringing it to the subject of representation, to the knowing self.

If Derridean deconstruction needs to work on science and theory, the only way out is to relinquish the boundaries that define or divide the two disciplines. Moreover, if there is any looseness encountered in objectivity, the ramifications are felt straight at the levels of scientific activities. Even theory does not remain immune to these consequences. Importantly, as scientific objectivity starts to wane, a corresponding philosophical luxury of avoiding the contingent wanes. Such a loss of representation congruent with a certain theory of meaning we live by has serious ethical-political affectations.

(1) Heisenbug is a pun on the Heisenberg’s uncertainty principle and is a bug in computing that is characterized by a disappearance of the bug itself when an attempt is made to study it. One common example is a bug that occurs in a program that was compiled with an optimizing compiler, but not in the same program when compiled without optimization (e.g., for generating a debug-mode version). Another example is a bug caused by a race condition. A heisenbug may also appear in a system that does not conform to the command-query separation design guideline, since a routine called more than once could return different values each time, generating hard- to-reproduce bugs in a race condition scenario. One common reason for heisenbug-like behaviour is that executing a program in debug mode often cleans memory before the program starts, and forces variables onto stack locations, instead of keeping them in registers. These differences in execution can alter the effect of bugs involving out-of-bounds member access, incorrect assumptions about the initial contents of memory, or floating- point comparisons (for instance, when a floating-point variable in a 32-bit stack location is compared to one in an 80-bit register). Another reason is that debuggers commonly provide watches or other user interfaces that cause additional code (such as property accessors) to be executed, which can, in turn, change the state of the program. Yet another reason is a fandango on core, the effect of a pointer running out of bounds. In C++, many heisenbugs are caused by uninitialized variables. Another similar pun intended bug encountered in computing is the Schrödinbug. A schrödinbug is a bug that manifests only after someone reading source code or using the program in an unusual way notices that it never should have worked in the first place, at which point the program promptly stops working for everybody until fixed. The Jargon File adds: “Though… this sounds impossible, it happens; some programs have harbored latent schrödinbugs for years.”

(2) There is a related issue in quantum mechanics relating to whether systems have pre-existing – prior to measurement, that is – properties corresponding to all measurements that could possibly be made on them. The assumption that they do is often referred to as “realism” in the literature, although it has been argued that the word “realism” is being used in a more restricted sense than philosophical realism. A recent experiment in the realm of quantum physics has been quoted as meaning that we have to “say goodbye” to realism, although the author of the paper states only that “we would [..] have to give up certain intuitive features of realism”. These experiments demonstrate a puzzling relationship between the act of measurement and the system being measured, although it is clear from experiment that an “observer” consisting of a single electron is sufficient – the observer need not be a conscious observer. Also, note that Bell’s Theorem suggests strongly that the idea that the state of a system exists independently of its observer may be false. Note that the special role given to observation (the claim that it affects the system being observed, regardless of the specific method used for observation) is a defining feature of the Copenhagen Interpretation of quantum mechanics. Other interpretations resolve the apparent paradoxes from experimental results in other ways. For instance, the Many- Worlds Interpretation posits the existence of multiple universes in which an observed system displays all possible states to all possible observers. In this model, observation of a system does not change the behavior of the system – it simply answers the question of which universe(s) the observer(s) is(are) located in: In some universes the observer would observe one result from one state of the system, and in others the observer would observe a different result from a different state of the system.