Yin & Yang Logarithmic Spirals


The figure depicts the well-known black and white symbol of Yin and Yang. The dots of different color in the area delimited by each force symbolize the fact that each force bears the seed of its counterpart within itself. According to the principle of Yin and Yang outlined above, neither Yin nor Yang can be observed directly. Both Yin and Yang are intertwined forces always occurring in pairs, rather than being isolated forces independent from each other. In Chinese philosophy, Yin and Yang assume the form of spirals. Let us now show that the net force in

K = −p(K ) ∗ ln(1 − p(K )/p(K))

the performance of a given confidence value K always matches exactly the expectation, i.e. in other words E = p(K), is a spiral too. In order to do so, let us introduce the general definition of the logarithmic spiral before illustrating the similarity to the famous Yin/Yang symbol.

A logarithmic spiral is a special type of spiral curve, which plays an important role in nature. It occurs in all different kinds of objects and processes, such as mollusk shells, hurricanes, galaxies, etc. In polar coordinates (r, θ), the general definition of a logarithmic spiral is

r = ae

Parameter a is a scale factor determining the size of the spiral, while parameter b con- trols the direction and tightness of the wrapping. For a logarithmic spiral, the distances between the turnings increase. This distinguishes the logarithmic spiral from the Archimedean spiral, which features constant distances between turnings. The figure below  depicts a typical example of a logarithmic spiral.


Resolving r = ae for θ leads to the following general form of logarithmic spirals:

θ = 1/b ln (r/a)

In order to show that the net force in

K = −p(K ) ∗ ln(1 − p(K )/p(K))

defines a logarithmic spiral, and for the sake of easier illustration, let us look at the negative version of the net force in the above equation for net force and look at the polar coordinates (r, θ) it defines, namely:

θ = −p(K) ∗ ln(p(K)/(1−p(K)))


r = (1−p(K)) ∗ e−θ/p(K)

A comparison of θ = −p(K) ∗ ln(p(K)/(1−p(K))), r = (1−p(K)) ∗ e−θ/p(K) with the general form of logarithmic spirals in θ = 1/b ln (r/a) shows that the net force does indeed describe a spiral. Both of these equations match when we set the parameters a and b to the following values:

a = 1−p(K)


b = − 1/p(K)

In particular, we can check that a and b are identical when p(K) equals the golden ratio, which happens to be

φ ≈ 1.618 ∨ −0.618

If we let p(K) run from 0 to 1, and mirror the resulting spiral along both axes, we receive two spirals. Figure 8 shows both spirals plotted in a Cartesian coordinate system. Both spirals are, of course, symmetrical and their turnings approach the unit circle. A comparison of the Yin/Yang symbol with the spirals in the figure below shows the strong similarities between both figures.


A simple mirror operation transforms the spirals in the above figure into the Yin/Yang symbol. The addition of a time dimension to the above figure generates a three-dimensional object.


The above is an informational universe. Note that the use of performance as time is reasonable because the exponential distribution is typically used to model dynamic time processes and the expectation value is thus typically associated with time.

Yin and Yang with deep roots in Chinese philosophy, stand for two principles that are opposites of each other, and which are constantly trying to gain the upper hand over each other. However, neither one will ever succeed in doing so, though one principle may temporarily dominate the other one. Both principles cannot exist without each other. It is rather the constant struggle between both principles that defines our world and produces the rhythm of life. According to Chinese philosophy, Yin and Yang are the foundation of our entire universe. They flow through, and thus affect, every being. Typical examples of Yin/Yang opposites are, for example, night/day, cold/hot, rest/activity, etc. Chinese philosophy does not confine itself to a mere description of Yin and Yang. It also provides guidelines on how to live in accordance with Yin and Yang. The central statement is that Yin and Yang need to be in harmony. Any imbalance of an economical, biological, physical, or chemical system can be directly attributed to a distorted equilibrium between Yin and Yang.


Nobel Prize in Economics and Crimino(logy)/(genic). How Contracts Work? Note Quote.


How has the Swedish Central Bank’s committee that awards prizes in Economics in honor of Nobel responded to the field’s abject failures regarding the recent financial crisis and the Great Recession?  A lesser group would display humility, acknowledge its failures, and promise a fundamental rethink of the field.  Neoclassical economists, however, are made of sterner stuff.  The committee’s response is to praise the discipline for its theoretical advances and proposed policies related to finance, regulation, and corporate governance. Oliver Hart, and Bengt Holmström exemplify this pattern.

The economics prize is a bit different. It was created by Sweden’s Central Bank in 1969, nearly 75 years later. The award’s real name is the “Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.” It was not established by Nobel, but supposedly in memory of Nobel. It’s a ruse and a PR trick, and I mean that literally. And it was done completely against the wishes of the Nobel family.

Sweden’s Central Bank quietly snuck it in with all the other Nobel Prizes to give free-market economics for the 1% credibility. One of the Federal Reserve banks explained it succinctly, “Few realize, especially outside of economists, that the prize in economics is not an “official” Nobel. . . . The award for economics came almost 70 years later—bootstrapped to the Nobel in 1968 as a bit of a marketing ploy to celebrate the Bank of Sweden’s 300th anniversary.” Yes, you read that right: “a marketing ploy.”

The Economics Prize has nestled itself in and is awarded as if it were a Nobel Prize. But it’s a PR coup by economists to improve their reputation,” Nobel’s great great nephew Peter Nobel told AFP in 2005, adding that “It’s most often awarded to stock market speculators …. There is nothing to indicate that [Alfred Nobel] would have wanted such a prize.

Members of the Nobel family are among the harshest, most persistent critics of the economics prize, and members of the family have repeatedly called for the prize to be abolished or renamed. In 2001, on the 100th anniversery of the Nobel Prizes, four family members published a letter in the Swedish paper Svenska Dagbladet, arguing that the economics prize degrades and cheapens the real Nobel Prizes. They aren’t the only ones.

Scientists never had much respect for the new economic Nobel prize. In fact, a scientist who headed Nixon’s Science Advisory Committee in 1969, was shocked to learn that economists were even allowed on stage to accept their award with the real Nobel laureates. He was incredulous: “You mean they sat on the platform with you?”

Why economics? To answer that question we have to go back to Sweden in the 1960s.

Around the time the prize was created, Sweden’s banking and business interests were busy trying to ram through various so-called “free-market” economic reforms. Their big objective at the time was to loosen political oversight and control over the country’s central bank. According to Philip Mirowski, a professor at the University of Notre Dame who specializes in the history of economics, the

Bank of Sweden was trying to become more independent of democratic accountability in the late 60s, and there was a big political dispute in Sweden as to whether the bank could have effective political independence. In order to support that position, the bank needed to claim that it had a kind of scientific credibility that was not grounded in political support.

Promoters of central bank independence couched their arguments in the obscure language of neoclassical economic theory of market efficiency. The problem was that few people in Sweden took their neoclassical babble very seriously, and saw their plan for central bank independence for what it was: an attempt to transfer control over economic matters from democratically elected government and place into the hands of big business interests, giving them a free hand in running Sweden’s economy without pesky interference from labor unions, voters and elected officials.

For the first few years, the Swedish Central Bank Prize in Economics went to fairly mainstream and maybe even semi-respectable economists. But after establishing the award as credible and serious, the prizes took a hard turn to the right. Over the next decade, the prize was awarded to the most fanatical supporters of theories that concentrated wealth among the top 1% of industrialized society of our time. At the time of the prizes, neoclassical economics were not fully accepted by the media and political establishment. But the Nobel Prize changed all that. What started as a project to help the Bank of Sweden achieve political independence, ended up boosting the credibility of the most regressive strains of free-market economics, and paving the way for widespread acceptance of libertarian ideology.

The Swedish Riksbank awarded this year’s Nobel prize for economic sciences to Oliver Hart, a British economist at Harvard University, and Bengt Holmstrom, a Finnish economist at MIT, for their work improving our understanding of how and why contracts work, and when they can be made to work better.

Their work focuses attention on the necessity of trade-offs in setting contract terms; it is yet another in a series of recent prizes which explores the unavoidable imperfections in many critical markets. Mr Holmstrom’s analyses of insurance contracts describe the inevitable trade-off between the completeness of an insurance contract and the extent to which that contract encourages moral hazard. From an insurance perspective, the co-payments that patients must sometimes make when receiving treatment are a waste; it would be better for people to be able to insure fully. Yet because insurers cannot know that all patients are receiving only the treatment they need and no more, they employ co-payments as a way to lean against the problem of moral hazard: that some people will choose to use much more health care than they need when the pool of all those being insured picks up the bill. A common and important thread in work by Messrs Hart and Holmstrom is the role of power in planning co-operative ventures. Individuals or firms with the ability to hold up arrangements – by withholding their service or the use of a resource they own – wield economic power. That power allows them to capture more of the value generated by a co-operative effort, and potentially to sink it entirely, even if the venture would yield big gains for all participants and society as a whole. Contracts exist to shape power relationships. In some cases, they are there to limit the exercise of hold-up power so that a venture can go forward. In others, they are intended to create or protect certain power relationships in order to encourage good behaviour: workers or firms with the right to exit a relationship, for instance, force other parties to that relationship to take their interests into account. The broader lesson – that power matters – is one economics too often neglects.

The theory holds that the contracting costs between economic units are shaped by the nature of the interaction between them. These costs are not operational costs, such as commission fees or transportation costs. Instead, they stem from the lack of clarity and enforceability of the terms of the interaction and each unit’s dependence on the interaction. And, in the words of today’s prize winners, they cause contracts to be incomplete. 

Difficulties in Negotiating a Transaction

Difficulties in Monitoring an Ongoing Transaction

Difficulties in Enforcing an Agreement

When managers spot these sorts of problems on the horizon, a deal that potentially will create value may not get done because the contract is bound to be incomplete. The danger is that the contract will not specify how to resolve conflicts in the future. This is because the agreement between the parties does not cover all contingencies, all issues, or all possible states of the world. To govern a partnership successfully, then, you need to manage the gaps in the contract. Traditional management techniques call for command and control in these situations, to respond quickly and decisively to new conditions. But this solution is missing from typical partnerships, most of which are characterized by a sharing of control. It may be a formal joint venture with shared ownership or a looser arrangement whereby one party controls certain parts of the joint project and the other party controls others. So, each partner’s control in these combinations is also incomplete.

Neoclassical economic dogma is that money is the “high power” incentive.  Normal humans know that this is preposterous.  The highest power incentives are rarely monetary.  People give up their lives for others.  Some of them do so nominally for “duty, honor, country,” but actually because of the effects of “small unit cohesion.” A second neoclassical dogma is ignoring fraud and predation.  The 2016 prizes show how, despite their knowledge of the falsity of the implicit assumption, neoclassical economists repeatedly ignore the manners in which CEOs shape perverse incentives and render the Laureates’ compensation and governance policies criminogenic.  A third neoclassical dogma is, implicitly, to assume that perverse incentives do not influence CEOs and those they suborn.  Holmström and Steven N. Kaplan’s article about corporate governance in light of the Enron-era frauds unintentionally displayed this third neoclassical dogma about incentives. The fourth dogma is that regulation cannot succeed because it lacks “high power” incentives. Criminologists’ understanding of incentives and how CEOs set and pervert incentives is far more sophisticated than neoclassical economists’ myths about incentives.  Criminologists provide the content to how CEOs that predate “rig the system.”  Criminologists agree that perverse financial incentives are important contributors to white-collar crime.



Gravity has often been suggested as playing a role in quantum theory, principally as a mechanism that induces quantum state vector collapse. However, at an ontological level, the Invariant Set Postulate does not require superposed states and hence does not require a collapse mechanism, gravitational or otherwise.


On the other hand, the order-of-magnitude estimates provided by Penrose, that gravitational processes can be locally significant when a quantum sub-system and a measuring apparatus interact, seem persuasive. Here, we would interpret these estimates as supporting the notion that gravity plays a key role in defining the state space geometry of the invariant set, in particular in defining the regions of relative stability (small local Lyapunov exponents) and relative instability (large local Lyapunov exponents). Black-hole thermodynamics may additionally provide the mechanism which leads to the dimensional reduction of the invariant set compared with that of the embedding state space.

Indeed this leads to the following rather radical suggestion. If the geometry of invariant set I is to be considered primitive, then the geometric properties of the invariant set which lead to certain regions being relatively stable and other regions unstable should be considered a generalization of the notion introduced by Einstein that the phenomenon we call ‘gravity’ is merely a manifestation of some more primitive notion of geometry—here the geometry of a dynamically invariant subset of state space. As such, a challenge will be to try to unify the notions of pseudo-Riemannian geometry for space–time, and fractal geometry for state space. This is a very different perspective on ‘quantum gravity’. 

From this we can make two gravitationally relevant predictions. Firstly, since gravitational processes are not needed to collapse the quantum state vector, experiments to detect gravitational decoherence may fail. By contrast with Objective Reduction, I could be seen as providing the preferred basis, with respect to which conventional non-gravitational decoherent processes operate. Secondly, if gravity should be seen as a manifestation of the heterogeneity in the geometry of the invariant set, then attempts to quantize gravity with the framework of standard quantum theory will also fail. As such, it is misguided to assume that ‘theories of everything’ can be formulated within conventional quantum theory.