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How the rebalancing bonus works Luckily, while the outcome may be unintuitive the source of the unexpected return is mathematically very simple. While the compounded expected return is zero, the average return is decidedly positive. They were eroded away by the volatility. The standard deviation of the returns in the charted series is a very high But it should be pretty close without going overboard with the calculations.
The most important thing to note is that while the arithmetic average return is clearly the starting point of the geometric compound return, it is reduced by the square of the standard deviation. That means that the volatility has a much greater effect than you might normally think, and it always reduces the return you experience in real life. It looks like we found our demon. Because of the square in the equation, halving the volatility has a greater positive effect on the compound return than the negative effect of halving the average.
The end result is a positive return from two assets that, on their own, have zero expected return. And the outcome is only possible through the act of periodic rebalancing. You know when people talk about the benefits of buying low and selling high? Or put another way, the rebalancing bonus comes from playing multiple assets off of each other to make money more consistently.
For example, no normal investment oscillates so perfectly or avoids the effects of inflation over time. This shows the inflation-adjusted returns of US stocks large cap blend and interest-bearing cash T-bills from the beginning of all the way through the end of So what happened to our free money? Indeed, cybernetics appears retrospectively as a misguided attempt to cast information as a medium for feedback and control, the carrier for a reduction of uncertainty, which obfuscates its active epistemic role.
In this sense, pattern-governed regularities represent redundancies which enable compression and a lowering of the informational bound. This framing shifts information from a means of ordering the world around us to a dynamic articulation of contingency. The motivation is to render the theory from a computational standpoint, in which the informational complexity of a given expression is equivalent to the shortest program able to output it, a perspective known as algorithmic information theory Chaitin 5.
From this view, I will attempt to unify both information and computation under a theory of encoding, in order to assess some of their epistemic claims in a new light. Let us first take stock of the paradoxical nature of the Bekenstein bound with regards to the ontology of information it presupposes. If Planck volumes represent the voxels of our universe, and no Turing machine exists for describing quantum phenomena such as momentum in any single voxel, how can the information required to describe our universe be in any way bounded?
Absent a unified theory of physics, our inability to resolve indeterminacy in fundamental models would appear to preclude such a condition. Foundational physics does not offer a solution to what we might call the hard problem of simulation, namely the informational encapsulation of the principle of infinite precision, summarized by Gisin as such: — Ontological: There exists an actual value of every physical quantity, with its infinite determined digits in any arbitrary numerical base.
Bekenstein raises the prospect of simulating a region of spacetime with an informational resource that scales sublinearly to its volume, rendering our universe a holographic projection of a lower-dimensional encoding. This encoding would, in the first instance, represent no more than a statistical model; the map is definitively not the territory, absent further demons. The question which remains is this: What information, if any, would be lost in such a model? In other words, how can we grasp the lossy nature of compression which the principle of infinite precision implies?
Seemingly the continuum appears to demand infinite information storage at every point, rendering its intelligibility even theoretically implausible without recourse to hypercomputation. At stake is an assessment of what Bostrom calls the simulation argument, a trilemma which posits that either advanced civilizations become extinct, or else they do not engage in universe scale simulation, or else we live in a simulation. Bostrom uses this argument to mount a statistical case in defence of the third of these possibilities as the most likely hypothesis.
On this point, I will follow Gisin in claiming that we should reach for mathematical theories of continuity to orient our position, ultimately dropping a commitment to deterministic physics. The aim is to ground ontic structural realism in a theory of information, in which a process of encoding comes to define pattern. In this view, the role of philosophy is not to stitch ourselves a metaphysical comfort blanket, in an attempt to reconcile scientific rationality with our subjective experience of the world, but rather to unify the natural sciences.
This should not amount to beating the drum for scientism, so much as delimiting the contours of empirical enquiry, tracing its incapacity to unify experience in order to spur philosophical research. In what follows, I attempt to apply such a method to the physics of information, as a means of reconciling an information-theoretic version of structural realism with the principle of infinite precision.
Indeed, a recourse to metaphysics will be required if we are to clear a path out of this antinomy that does not simply dispense with scientific realism altogether. If we take the doctrine of scientific realism to assert that the laws of physics constitute a compression of real patterns, and structural realism to assert that all matter is derived from such patterns, we are left with some definitional work to do on the nature of pattern-governed regularities and their contents.
This precipitates a state of affairs in which the Higgs field can be hypothesized decades prior to a suitable experiment being devised to verify the theory. Strings and fields may be unobservable in themselves, but most physicists do not regard these as twenty-first century aether, rather an admission that fundamental models capable of unification necessarily require an appeal to theoretical structures.
Traces of a basal idea of pattern in physics are to be found in the logical notion of degrees of freedom, and this echoes the framing of information as freedom of choice originally presented by Weaver. Freedom of choice casts pattern as the negation of entropy, whereby information, in the sense defined by Shannon, does not correspond to signal, but rather the degree of surprisal presented by any given structure.
As Malaspina notes, the converse of information is not noise but redundancy, information instead corresponds to the modal notion of possibility, it is intricately bound up in this condition of freedom. Surprisal is precisely the idea that our capacity to learn is grounded in an attempt to absorb new forms of entropy as information, and that the negation of intelligence is a reversion to pattern. Here, encoding is an in-situ theory of knowledge in formation, an ontogenesis founded in the tension between freedom and constraint, not so much a dialectics as an informatics of pattern and surprisal.
Towards An Epistemics of Surprisal The cognitive science of attention shows a growing body of experimental evidence for the central role of surprisal in both perception and knowledge acquisition. This renders perception a mode of prediction, echoing negentropy in its attempt to describe the capacity for organisms to maintain internal states far from thermodynamic equilibrium.
Such models speak to the efficacy of perception as predictive error and are to some extent reinforced by experimental evidence. This is demonstrated, for example, by studies in which dopamine neurons are seen to act as regulators of attention under varying conditions of uncertainty linked to rewards. Here we can charge the machine learning industrial complex, in its relentless pursuit of deep learning, of sidelining modes of surprisal as the drivers of intelligence, in favour of an inductive encoding of the past as ground truth.
As Patricia Reed has noted, Turing was perhaps the first to identify the notion of interference as an integral aspect of learning, proposing it as a key principle for the project of AI. Thinking of going to the next pattern in a sequence causes a cascading prediction of what you should experience next.
As the cascading prediction unfolds, it generates the motor commands necessary to fulfill the prediction. Thinking, predicting, and doing are all part of the same unfolding of sequences moving down the cortical hierarchy. But to model counterfactuals, indeed to engage in simulation, where the latter represents an isomorphism between model and world, one is entirely dependent on causal reasoning as a means of generalization.
For Pearl, this is what it means for a theory to bear the property of explanation; patterning alone is insufficient, an asymmetric causal structure must be presented. Here learning, as a locus of intelligence, is constituted by error and uncertainty, but an epistemics of surprisal should not be interpreted as a fully-fledged expression of Humean skepticism.
Indeed, the path from contingency to possibility and finally necessity is mediated by acts of encoding which engage in the realizability of invariants I call truths, but these truths are forged in the cognition of unbound variation from existing pattern, not simply in the association of phenomena treated as givens.
The distinction rests on the notion of epistemic construction as the generator of modes of surprisal, the latter not merely signalling an active form of perception, but the outcome of nomological acts rooted in time-bound inferential processes. This casts reason not so much as a generative prediction of the given, but the construction of worlds as the surprisal of form, a dynamics of adaptive models in continuous formation.
Spontaneous Collapse Surprisal is a distinct treatment of uncertainty grasped in the context of communication, namely the capacity for a recipient to predict a message. What it shares with theories of computation, and distances it from axiomatic forms of logic, is its rootedness in time. This notion of time is not to be found in the block universe of Einstein, but rather, as Gisin suggests, in a tensed universe, yielding a certain ontological commitment to information.
There are many reasons to endorse asymmetry, most notably the causal patterns which underpin the entirety of the special sciences. Combined with the second law of thermodynamics, these make a stronger case for a tensed universe than fundamental physics does for the converse, the latter conspicuously ambivalent on the issue. From this view, logical expressions must provide the means for their own realizability, manifested as denumerable procedures we can call programs, in the broadest sense of the term.
Here we see an imbrication of epistemic and ontic claims under the rubric of structural realism, whereby the unreasonable effectiveness of mathematics and a commitment to real patterns suggests a Platonist attitude to form. But being a realist about information, as Gisin evidently is, compels its own challenge to Platonism on constructive grounds—those structures which present themselves as a priori, patterns which science compresses into physical laws, are not deemed intelligible in the last instance, they can only be constructed from one moment to the next.
From this view, the continuum is beyond the grasp of statistical randomness, real numbers tail off into pure indeterminacy, and time is presented as a medium of contingency. It follows that information is not a measure which is conserved, but rather an encoding of entropy, to be created and destroyed via the dissipation of energy precipitated by certain kinds of interactions, the precise identity of which are open to interpretation. We should pause here to consider these claims in light of the black hole information paradox, a key debate in contemporary physics, wherein radiation from black holes is posited as a means of conserving information in the universe that would otherwise seem to disappear into a dark void.
Implicitly at play here is another fundamental open problem in physics, namely the quantum measurement problem, canonical interpretations of which are supplied by Bohr and Heisenberg, instigating an uncertainty principle with an ambiguous role for the act of observation. Everett and Bohm, in turn, have supplied views of measurement which instead support a deterministic universe. Objective collapse theories of this sort are desirable insofar as they are broadly compatible with both ontic structural realism and asymmetry, although the role of information in them can vary.
Advocates of quantum information theory characterize quantum states as entirely informational, representing probability distributions over potential measurement. In adopting a theory of collapse, one need not speculate on the content of quantum states however, the commitment is only to a realist treatment of collapse, which we can subsume within an account of real patterns as information. This allows for a view in which encoding is the dynamic means by which a basal notion of pattern, such as that offered by quantum fields, gives rise to individual particles; encoding and mattering are inextricably bound by an informational account of structure.
This recourse to metaphysics is needed in order to reconcile information as a real entity with the principle of infinite precision, leading in turn to an abandonment of the principle of conservation—the aforementioned paradox is dismissed in favour of an entropic view of time as the agent of spontaneous collapse.
It is this interplay which leads to the emergence of intelligence as such, conceived as a locus of learning manifested by acts of encoding predictive, normative, etc , arising from an energetic process of individuation. Here we can follow Simondon in observing that individuation and information are two aspects of ontogenesis, a process he calls transduction. On this point, cybernetics can be accused of seeding a conflation of the two concepts, whereas it is more accurate to render the interplay of negentropy and surprisal as an informatics preceding any dialectical relation.
How can one countenance an ontological move to a physical theory of information shorn from perspectival subjectivity? An ontic emphasis on the dynamics of surprisal compels a commitment to a tensed universe, extending a process-oriented account of number, which yields a treatment of the continuum following from a constructive view of mathematics. This in turn leads Gisin to a metaphysical principle I call the irreducibility of contingency IOC , a law following from a process ontology ultimately rooted in information.
As such, compatibility between the two positions is not assured and tentative at best. The suggestion here is that encoding be considered a basal operation which yields a fundamental dynamics, providing a supplementary rather than conflicting theory. The IOC, which can be traced back to C.
However, as Wilkins cautions, we should not take this as a fetishization of noise, but rather the means by which statistical inference is grounded. At stake in such debates is the politics of simulation, most recently that of the metaverse, and its capacity to impinge on notions of freedom and agency, in manifesting a pervasive world presented as reality.
For Chalmers, Bostrom, and others, who hold the simulation hypothesis to be highly probable, a shift to virtual environments should not concern us in the long run, as such developments will theoretically converge on what we call reality today. For these thinkers, we may as well be living in a simulation, we would not be able to tell either way. Critics of such positions are hasty to charge their advocates with Cartesian dualism, while I take this to be an insufficient riposte.
There are three critiques worth outlining, however, which go beyond the usual emphasis on embodied cognition, and these are by turns ontic, energetic and normative. As Gisin suggests, the broader issue here is the determinism of physics, or its inadmissibility thereof, and the ensuing repercussions for a theory of computational reason. Information-theoretic structural realism, interpreted via Gisin as an ontology of information, presents a more compelling critique of metaversal realities in the long run, while an epistemics of surprisal inextricably grounds knowledge in the indeterminacy of physics encapsulated by the IOC.
Ultimately, field theories are not able to ground subnuclear interactions in the standard model without recourse to experimental data, which is subject to the principle of infinite precision, and as such exposed to the IOC. Furthermore, the energetics of computation posits an entropic cost to simulation.
Earlier I presented a view of information as a theory of optimal encoding rooted in an inferential dynamics, where optimality is defined by an appeal to algorithmic complexity. This subsumed information within a computational definition provided by Chaitin, as the length of the shortest program able to output an expression, reducible to a probability distribution. In this view, real pattern comes to resemble a compressed encoding with no redundancies, which finds expression in scientific models.
This raises the question of how to assess computational reason, and ontologically inflationary claims made on its behalf, such as those presented by pan-computationalists. Contra to the machinis universalis posited by Chaitin, Wolfram, Deutsch, and others, I take computational explanation to be a form of inference, whereby information offers a purely syntactic theory for encoding uncertainty, while computation acts as a broader epistemic theory of encoding.
This leaves us with an apparent inconsistency—if information is real, and identified as a form of encoding, this appears to conflict with the notion that computation is intrinsically inferential and thus intentional. If computation and information are unified under a theory of encoding, a metaphysical principle of encoding is needed to bridge the ontic and epistemic divide, and this comes without justification.
Elsewhere, I have argued for such a principle on purely epistemic grounds, and in this essay I have only just begun to assess the ontic prospects of encoding.
The math behind this is detailed a bit more extensively in Figure 1 and can be better conceptually visualized through the graph in Figure 2 below. Would that change your long-term return expectations? Intuitively, most people would not think so. The coin-flip game has a zero expected return, and cash has a zero expected return at least in this example , so how would this change things? Well, it changes things quite a bit, because it converts two zero-expectancy return streams into a wealth generating machine.
Well, we can actually simulate this randomness using a computer. More specifically, we can tell a computer to randomly choose between heads and tails 1, times to simulate 1, randomized coin flips. We can see that there is a fair amount of dispersion lots of winners and lots of losers , but in aggregate they are all essentially centered around the zero line i.
The new rebalanced results are presented in Figure 6 below. As we can see in Figure 6, even with random coin flips, the expectancy of every single simulation is now consistently positive. We have just created a return producing portfolio from two assets that have zero expected returns and zero wealth generation capabilities on their own. Now, obviously this is just a simple example illustrated by a hypothetical coin-flip game, and it is not likely something in which we would be able to invest our hard-earned money in real life.
That being said, the main concepts still very much apply to real world investing and optimizing investment portfolios through time — albeit with a bit more complexity and sophisticated computations to account for changing market dynamics. Moreover, the greater the size of these return swings i. For instance, our simple coin-flip example above actually has an arithmetic average expected return of roughly 8.
So, what causes the difference between our 8. Where does all of that return go? Next, picture an alternative investment of true paper cash that pays no interest at all. Option B also tracks sideways with no expected return.
If one were to invest in both option A and B and let them each do their thing with no interference, the long term return is clearly zero. The name is dual nod to the man who first uncovered it and a similar thought problem in thermodynamics where an unseen force creates unexpected outcomes. How the rebalancing bonus works Luckily, while the outcome may be unintuitive the source of the unexpected return is mathematically very simple.
While the compounded expected return is zero, the average return is decidedly positive. They were eroded away by the volatility. The standard deviation of the returns in the charted series is a very high But it should be pretty close without going overboard with the calculations. The most important thing to note is that while the arithmetic average return is clearly the starting point of the geometric compound return, it is reduced by the square of the standard deviation.
That means that the volatility has a much greater effect than you might normally think, and it always reduces the return you experience in real life. It looks like we found our demon. Because of the square in the equation, halving the volatility has a greater positive effect on the compound return than the negative effect of halving the average. The end result is a positive return from two assets that, on their own, have zero expected return. And the outcome is only possible through the act of periodic rebalancing.
You know when people talk about the benefits of buying low and selling high?
Shannon's demon (which, by the way, either loses 50%, or gains % each tick, not 50%) exploits the fact that if you already know that the market is moving sideways, it is easy to . Jun 16, · In the s, the great genius conducted an experiment also known as Shannon’s Demon and it proved that it is possible to yield a profit from the random market conditions, but . The general idea behind Shannon’s Demon is that two uncorrelated assets, each with zero expected long-term returns, can actually produce a combined portfolio that consistently generates positive returns if intelligently balanced and rebalanced at regular intervals. Sounds too good to be true, we know.