Illusion of the moon and biomathematics of consciousness

21 октября, 2021 от Kinok Выкл

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B of the previous part of the post

In the continuation of our story, we will now change the point of view with high-level abstraction to the most close to the reality of specifics. We will look at two specific and very important PES-based theories, illustrating the applied aspects of this fundamental principle.

This pair of theories, most important to understand the phenomena of knowledge through the PSE prism, will be

Our goal will be understood with the help of PSE,

«… an astronomer is not able to prevent that the moon seems to be at sunrise, although astronomer is not deceived by this visibility.»

The enlightened model of the surrounding world is the basis of perception, mind and actions of any biological forms, without which their survival and reproduction is impossible. The two components of this model are space and time, are key elements of the ideas about the world of any living being, its perception of the world and awareness of their own location in it.

This model of the world is formed and is constantly updated as a result of integral perception by different senses, the roles of which in this process in different animals are very different. For example, Dolphins have a major role in working with the model of their water world, the senses working with sound and echolocation are played. People are the same model of the world and his perception, first of all, are determined by vision.

Vision, through which people get the greatest part of the information (approximately 80%), is the most important tool for the formation and clarification of our cognitive painting of the world. This is a very complex and multidimensional tool.

At the junction of the last two of the listed aspects, the oldest and most famous, most poetic and most interdisciplinary, the most scientifically defiant and most unresolved problem called

It doesn’t matter whether the moon looks out because of the mountain, rises from the sea, boil over the city or hangs over the forest, — everywhere at the horizon it seems, approximately twice as much (although an average illusion an increase is 50-70%). Although in fact, the true size of the moon does not change, because the angle under which we sees the upper and lower points of the Moon diameter remains the same and when the moon at the horizon, and when it rises to Zenit.

And it seems to. For with any check (the most coarse-pose next to the moon, the thumb stretched forward and comparing its size with a nail, or more accurate — with measuring the angular degrees of the moon image boundaries) It is found that the size of the moon visible by us does not change and remains the same That the horizon is that in the zenith.

And you can also check that there is no increase in the size of the moon at the horizon, using photos. In the pictures with constant settings of the camera, the moon does not change its size all over the path from the horizon to the zenith.

You can also look at the moon through the tube, simply turning it out of the paper sheet. And about the miracle — the illusion will disappear. But what looks like absolutely mockery, the illusion is significantly reduced, if you turn to the moon and, lowering the head between the legs, look at the moon from such interesting postures.

Finally, it is possible using a special device to measure the size of the light spot formed by the reflected moonlight with sunlight on the retina. We obtain a stain with a diameter of about 0.15 mm. That for the moon at the horizon, that in the zenith.

So this, for sure, the illusion is a fraudulent trick, which is conscious of the brain. He seems to insist that the moon at the horizon is greater.

Throughout the millennium, the mystery of the illusion of the Moon fascinated and puzzled the greatest philosophers, mathematicians, physicists, astronomers and psychologists. For the first time, it was mentioned in clinox inscriptions on clay signs from the Royal Library in Nineveia in the 7th century BC. And since then many great minds are Aristotle, Ptolemy, Da Vinci, Kepler, Descartes, Galilee, Newton and dozens of others, — tried to solve this scientific puzzle.

At first, the researchers assumed that the moon in reality is more near the horizon. When it turned out the opposite, began to try to explain this illusion of optical effects. But then it became clear that it was not. Finally, it became clear that the apparent increase in the size of the moon at the horizon is a pure illusion constructed by the brain. But that for the title forces us to see what is not in reality, and remained incomprehensible. Moreover, the distortion of the perception of reality is not limited to the Moon, the same thing happens and with the way we see the sun and constellation. And as shown by the experience of American astronauts on the moon, while on its surface, people see the similar «illusion of the Earth» — an increase in the size of the Earth at the horizon.

That finally confuses, — the presence of the horizon for illusion is not strictly necessary, because it all depends on the perspective of the scene perceived by our consciousness. For example, what tells you your (albeit not exact, but leading you in life) a sense of proportion in the world — which of the figures below closer to the real world? Which of the pictures of the moon seems to you «aesthetically correct»?

Most people «aesthetically correct» seems to be the size on the right picture. Then, as actually correct is the left image. From which it follows that the illusion of the moon changes not only our ideas about the environment of us, but also our aesthetic reality assessments —

3A Three thousand years old to explain the illusion of the Moon, a lot of hypotheses were proposed, the basis for various concepts and theories. You can chase in 4 minutes in the most famous versions of the explanation of the moon’s illusion:

You can try to delve deeper into the problem and, having spent an hour, read several sensible scientific and popular articles — for example, shorter and easier [

And it is possible for many hours, days and even the week to immerse yourself in reading hundreds of pages of scientific articles, monographs, and metaanalyzes. As a starting base, you can walk on hundreds of references from work

The result is that at viewing the four-minute roller, which has a long study of hundreds of scientific articles, there will be the same — a discouraging conclusion, honestly formulated by NASA professionals:

The inability of modern science give a full-fledged and verifiable explanation for only one (although the most famous) phenomenon of our perception is the best illustration of the limited and affect of existing theories of reason, perception and consciousness. All, except for one — active withdrawal within the framework of PSE Carl frets (what will be told on)

In the meantime, let’s see if, despite the abundance of a variety of theories, claiming the mystery of the mystery of the moon, «there is still no satisfactory scientific explanation for why we see it.»


If you are not interested in «exposure», go directly to the «dry residue» — section «Conclusion».


Most explanatory hypotheses of all three named groups are based on

A. External



Among the hypothesis there are quite primitive (because it is easily refuted), and very complex (as a result, their refutation is not a simple matter). Here are two examples of not the most common hypotheses in the media:

To refute the simplest hypothesis that the moon at the horizon is simply closer to the moon in the zenith, it is enough of this picture.

As can be seen from the picture, the moon on the horizon is further from the observer. And if the illusion depended on this, the moon should seem less at the horizon than in the zenith. In reality, the same way is on the contrary.

«No object can be simultaneously two-dimensional and three-dimensional. And we see the paintings that way … the pictures are impossible objects «

At the same time, from the point of view of perception, two-dimensional and three-dimensional components of paintings in general are equal. And therefore we are able to see the plane and space in the same and the same, although it is absolutely contrary

That this is not the case, first in 1764 suspected the Scottish philosopher



It would seem, a hurray — an explanation of the illusion of the moon was obtained. But alas, not yet received. For, as A.M. Kovlev writes,

And also, as Donald E. Symannek writes in essay

And until answers to each of these questions, the explanation of the illusion of the moon anisotropy of the hyperbolic visual space remains only not to the end of the proven hypothesis.

We have led the examples of two, so to speak, marginal hypotheses that did not reach popularity: the first — due to the easily proven error, the second — because of the unverified (at the current level of scientific knowledge) of complexity. There are even more dozens of other hypotheses trying to explain the illusion of the moon with three classes of reasons: physical, optical and perceptual causes. As shown in the famous monograph Helen Ross and Cornelis Plow «

Two classes such hypotheses are considered classic to this day are found in many textbooks:



Each of the two classes includes a set of close, but something different options for hypotheses, designed to explain the causes of the appearance and mechanisms of the illusion of the moon. Consider not engaged in details, pros and cons of the most popular hypotheses options in each of the named classes.

Theory of remote accounting (

Then the perceived size of the object s is equal to the product of the tangent of the optic angle α



Practical experience spoke to researchers the following.

This contradiction was necessary to somehow resolve

Consider both options.

We are intuitively perceive the sky as located at some final distance from us, and the moon (as well as the sun and the stars) we perceive the closer to us towards the sky (it is as it were against the sky). In fact, the distance to the moon is significantly further than «to the sky.» And in order to somehow correct this contradiction, the human brain is trying to compensate him in our perception, representing our consciousness, as if the Moon disk at the horizon is greater. In such a model of the world, the brain represents the sky not as a hemisphere, which it is, but as a flattened (bleached) dome, such as an inverted bowl (see Fig. Below).

That’s just the plusion of the sky and did not receive scientific confirmation. If only do not rely on the hypothesis about the inherent visual space

The logic of resolution of the contradiction can be as follows.

And everything in this logic was good. After all

Consequently, the second method of resolution of the contradiction turns into a dead end. And we do not have anything else, how to recognize — we are dealing with the illusion of the erroneous perception of the size of the subject as a result of some computing fit of this size of the brain. And the theory of accounting for remoteness, unfortunately, does not give an explanation, why this happens.

Those. The result of the illusion of the moon is obtained by such

And in the next picture it can be seen even better, because there is a real image. You see how tiles on the wall are becoming less and less with increasing distance. And if the neighbor to us the red segment is approximately equal to the altitude of one tile, to the far equal to the height of five tiles.

What is a pure illusion — the deception of our consciousness as a result of the work of the same brain, where this consciousness will be born — it can be seen from the figure below, on which two cuts from the top drawing are compared. At both segments there are almost the same length (although they are still slightly different due to problems with the resolution of the image, but not as much as the brain is deceived in the case of the first drawing).

With the illusion of the Moon, it turns out similarly: we are on them that this is an illusion; We understand that this illusion is the result of the recalculation of the brain size of the light spot display of the subject on the retina of the eye …
But here

Last of trying

To resolve this contradiction, the brain distorts the projections of the moon in each of the eyes and thereby increase the binocular inconsistency. And this leads to an increase in the perceived size of the moon. The degree of distortion depends on the visible distance to the sky, which affects the surrounding items and the state of the sky.

On the horizon, the visible distance to the sky is minimal, since there are many other items on the way of view that you can judge the distance. When the moon in the zenith, vision simply is simply not to be attached when evaluating the distance, which makes it difficult to estimate the distance and weakens the illusion.

Such is the essence of the hypothesis, which since 2013 wrote almost all scientific and popular media, as a new explanation of the reasons forcing people to see the illusion of the Moon. But unfortunately, almost no one wrote that, as well as with the previous hypothesis, a reliable and checked explanation of the illusion of the moon in the new hypothesis. And there are all the same principal disadvantages, as in many previous hypotheses.

Not to mention the «crown destroyer» of all hypotheses based on TAD models, — the new hypothesis does not explain in any way, why the illusion disappears, if you become a back to the moon, bend down and look at it with your head, lowered between the legs.

As a result, science was not able to give a convincing explanation of the Illusion of the Moon based on the theory of remote accounting. Well, that the brain is able to twist our perception also more abruptly than the illusion of the moon, we know on convincing examples. For example, the change in the apparent size of many fixed images simultaneously with them in motion (as in the «moving» figure below).

We finish a review of the hypotheses applying for the explanation of the Illusion of the Moon, the most popular and simplest (both in explanation and refutation) the theory of relative size.

According to this theory, the perceived size of the object L depends not only on the size of its light print on the retina, but also on the size of the prints of other objects in the immediate vicinity of the object L. in the case of the illusion of the Moon, these are objects near the horizon located next to Luno (trees, houses, etc.)

The effect of influence on the perception of the size of the object of its environment is illustrated by the classical illusion of Ebbighaus, where the circle seems more, surrounded by smaller circles, and less, surrounded by large circles.

The horizon of the moon surrounds relatively small objects. After all, even the skyscraper, standing near the horizon line, is the observer, at least several kilometers. When the moon is high in the sky, there are simply no items for comparison. And therefore, she does not see the lack of in the field of view, less than it.

With the refutation of this theory, everything is completely simple.

So the reference objects of the known size — cannot be an exhaustive explanation of this illusion. Well, to top it all, according to tradition, of course, the «corona destroyer». He works here at its best. There are reference objects or not, but the illusion of the Moon disappears as soon as you lean and look at it from an interesting posture.

All, you can lower the curtain over the pantheon of the outstanding hypotheses that have tried to reveal the widest scientific secret during the 27th centuries. None of the hypothesis could not be reliably prove,

B Lookage for the 507th volume of the world’s edition on theoretical biology «The Journal of theoretical Biology» was published by David Rudraufa (David Rudrauf), Kenneh Williford, Daniel Bennequin (Daniel Bennequin) and Kenneth of Wilford (Kenneth Williford), entitled

This work has a fundamental difference from all previous attempts to explain the Illusion of the Moon.

New explanation of the illusion of the Moon:

What allowed the authors to receive such breakthrough results, at once solved all the problems of explaining the illusions of the Moon, irresistible for many centuries for the most prominent scientific minds of the past and present?

The answer to this question is just as amazing, however, we expect —

Here is this chain:

✔️ The basis of everything is

✔️ on the conceptual base and mathematical apparatus of PSE constructed the mathematical model of the embodied consciousness called by the authors

✔️ on the conceptual base and mathematical apparatus of PMS built a new and most complete today

As you probably guess, even for a brief description of each of these theories, a separate Longride is needed. Here we will try to give only an abstraction of the top level of generalizations of new theories, as was done (in the form of a helicopter location of the area) for the submission of the PSE in

Recall the key position formulated in

The mathematical representation of the integral process of minimizing free energy based on the «Bayesian theory of the brain» is based on two processes:

✔️ Brain designs

✔ process

✔ process

Mathematical model of embodied consciousness (A Mathematical Model of Embodied Consciousness [

FOC in PCM combines incoming multisensor data with previous convictions in memory and forms new beliefs, choosing points of view and prospects in accordance with preferences. The choice of projective framework determines how expectations are transformed by consciousness. Waiting disorders are encoded as free energy. The minimization of free energy stimulates the perception of the perspective and controls the switching between perception, imagination and action. In PCM, consciousness functions as an algorithm for maximizing sustainability, using the projective perception of perspective and imagination to avoid local minima of free energy.

This infographics is a top-level abstraction — a schematic representation

In Figure A shows the following

Life space S (blue spheres): subjective experience of the space and its content, both perceived (solid funnels in the figure) and imaginary (dashed funnels). S is imagined and perceived by experience as a 3-dimensional projective view of the model of the world R (x, T) associated with the distribution of free energy (Fe) in space. S is also associated with a cognitive and affective personal accessory (different colors of figures / doors and a disc with a color gradient). The definition of the perspective and the choice of the corresponding projective transformations T is controlled by a free energy gradient in the space Δfe. The circuit with the arrows in a circle represents possible transitions of states: from the state of perception, to imagination and actions in the Consciousness field (FOC). These transitions are partially controlled by sensory data (when the field of consciousness is focused on the perception of the conditions of the area). It is completely controlled by priors in memory and modeling capabilities (when it is focused on the imagination of nonlocal spaces), for example, when we are at work, we present yourself at home in the present, past or future (after all, such a representation cannot be based on direct sensory testimonies ). FE free energy defining the optimal perspective at the moment is globally minimized through the cycles of perception, imagination and action in time. The histogram represents FE as a function of time and various perspectives and processing modes (P: perception or I: (nonlocal) imagination).

Figure in shown

I understand perfectly, how difficult it is to state such complex scientific abstractions in a simple and understandable language. And therefore I do not feel illusions that the above schematic description of the RSM can serve as a big rather than the visual card of the essence of RSM. However, I believe that a 47-minute professionally made film with the story of the authors of the RSM, what it is and how it works can help make the first steps to understand this most important and absolutely breakthrough theory.

In conclusion of this section, I would like to fix three of the most important points in the context of PCM.

RSM postulates that

The possession of consciousness, which includes a virtual, transformable projective space, is a highly efficient method for the body to track its own location and navigate in a variety of real spaces — including social spaces and time. In addition, projective geometry is necessary for the body in order to be able to create three-dimensional promising maps of significance that are necessary to modulate attention, assessment, motivation and orientation.

RSM unites and unifies the basic ideas of the main modern approaches to consciousness. The fact that PCM adds to already existing theories is geometry: the thesis that projective transformations and projective frameworks necessarily submit themselves the processes of the emergence and work of consciousness.

According to the principles of the projective model of consciousness (RCM), the illusion of the moon may result from optimizing the three-dimensional projective geometric structure in the process of minimizing free energy.

This is how it can be portrayed schematically.

Explanation to the drawing.

a) Consciousness fields (FOC) for the moon high in the sky (at the top) and on the horizon (below) are determined by the corresponding projective framework F and F ‘. The moon is in projective infinity and at the same time it seems less, being high in the sky, and more at the horizon.

b) Conditions for observation and influence on frames and their metrics. The observer (man) looks at the moon M high in the sky and M ‘around the horizon at the height θ and azimuth φ. Visual angle A remains the same. The minimization of free energy gives frame F (respectively f ‘) with projective transformations for a plane at infinity t (respectively, T’), which uses the information as possible. Point I in the projective frame F involves a wider projective region, and I ‘in frame F’ is less, which calibrates the internal metrics of the invariant projective plane on infinity inside the focus and induces the illusion.

The mathematical explanation of the illusion of the Moon is the proof that the projective framework F and F ‘, which minimize the free energy in both situations, entail that the apparent diameter D of the rising moon is less than the seeming diameter D’ of the moon near the horizon. Based on this, we can expect most observers to conclude that the distance D is greater than the distance d ‘, and will perceive the moon as a big and closest in the projective frame F’. However, on the basis of the same model, some observers can conclude from other privities that the moon is at the same time more and further (as confirmed in practice).

The above mathematical justification looks heavy. Here is an example of 9 out of 64 equations.

But since Daniel Bennekin was responsible for mathematics in this work — a famous French mathematician, one of the founders of the contact topology, who invented the number of Truston — Benneckin, — no error in any of the 64 equations was not yet found.

Napomnia — Our goal was to understand with the help of PSE, how space and time are designed in our consciousness so as to optimize our survival and satisfying the preferences in the reality around us.

In relation to space, we did it.

The logic of this is approximately such.

As a practical super-test of the projective model of consciousness, as well as the principle of free energy underlying the principle of free energy, the permit is shown on their basis of the entire spectrum of problems around the explanation of the illusion of the Moon, with whom Science was not able to cope for almost 3 thousand years. And as showing the results of the work «The Moon Illusion Explained by The Projective Consciousness Model», the projective model of consciousness is able to resolve all these problems.


Why (why) the brain is deceiving us, increasing the moon at the horizon


What can conclude that

Two great secrets — how the illusion of the moon is born and how the biomathematics of consciousness works — help reveal each other.

✔️ Biomathematics of consciousness (described by the principle of free energy and the projective model of consciousness) helped reveal the mechanism of the illusion of the Moon, which remained an intractable mystery of science during the 28th centuries.

✔️ Solution of the mystery of the Illusion of the Moon helps us make sure that the biomathematics of consciousness based on the PSE is not just another theory, applying to be called the «theory of all», and it is possible that that will become.

It remains for us (as I promised it in the 1st part of the post) to conduct a similar super test for checking the explanatory and evidence capabilities of the PSE with respect to the phenomenon of time.

How time is constructed in our consciousness so as to optimize our survival and satisfying the preferences in the surrounding world, will be told in the final 3rd part of the post about the constitution of biomathematics.

Thanks for watching! Put husky I.