According to a Gallup poll, about 6% of Americans believe that man never went to the moon; they endorse conspiracy theories in which these landings were supposedly staged in a studio. This post is not about such conspiracy theories. I will discuss why we cannot go to the moon, although we can have the experience of going to the moon, based on a fractal space in which there is a ‘moon’ within earth (because the whole is represented in the part), but it is not the real moon. I will discuss how fractal space is evidenced in Sāńkhya when space is described as a tree rather than a box. Since modern science treats space as a box rather than a tree, we can interpret the arrival on the earthly moon to be the arrival on the real moon—assuming such a journey is undertaken. Thus, regardless of whether the moon landings were staged or not, we cannot go to the real moon, but we could go to the moon within the earth space. To understand the real moon, we will have to revise the model of space from a box into a tree.

Fractal Geometry

A fractal is a picture in which the parts are self-similar to the whole. Therefore, as you zoom into the picture, you rediscover the same whole through a scaling transformation. However, clearly, the picture you see by zooming in, is not the same as the picture you see as you zoom out.

Such pictures were originally discovered in the study of non-linear systems in which a variable is referenced in the computation of that very same variable. A classic example of such a computation is the Mandelbrot Set which is computed by using the following equation:

Z = Z2 + C

Clearly, you cannot solve this equation as a polynomial. However, you can use discrete mathematics to solve such equations, which means that these are always solved via incremental steps.

Z N+1 = Z N 2 + C

The incremental process is that the N+1th iteration of the variable Z is computed based on the Nth iteration. The result of such a process can be compared to an artist who draws an outline and then fills in the details. The details are within the outline, and yet they mimic the outline itself. To count the points in this space you cannot go from left to right, top to bottom, as if the space were linear. You have to rather count hierarchically such that the whole picture is the first object, which is then subdivided into parts, and each part is then further subdivided into subparts. This process of counting constitutes a hierarchical geometry because the whole is counted ahead of the parts. However, given the legacy of reductionism in modern science, we don’t call this hierarchical; we call it a fractal.

Examples of Fractal Geometry

Our everyday world is replete with the use of fractal geometry, which is quite counterintuitive because modern science treats space linearly. For instance, our ordinary notions of space are hierarchical; when you send a letter to a person, the address includes a country, a state, a city, a street, a building, and then a person. When the mail is routed to the destination, it is first forwarded to the country, then a state, then a city, then a street, then a building, and finally the person. The mail service zooms out from the sender (from person to building to street to city to state to nation) and then zooms into the receiver (nation to state to city to street to building to person). This is quite unlike ordinary motion in linear space in which we suppose that the object goes directly from one place to another.

Of course, even when a letter is sent from a source to destination, it goes hop by hop, and therefore it has a trajectory. However, the individual locations on this trajectory are not in the linear space. For instance, there is a post box in a building which is ‘lower’ than the city post office, which is ‘lower’ than the state post office, which is ‘lower’ than the national post office, and so forth. Thus, from a physical viewpoint, the letter appears to move in a linear space, however, the points in that space have higher or lower designations relative to each other, and the letter first goes upward and then downward.

Similarly, when you send an email to [email protected] the email server first finds a registry for all .com addresses. This registry then forwards the mail to acme.com, and when the email reaches the acme.com email server, this server will resolve a sub-domain called doe.acme.com. When the mail reaches doe.acme.com server, it will locate the mail box of john and post it into that mail box. The email goes hop by hop, but it starts at the top (.com) and descends downward (to [email protected]). When John responds to this email, his email server will append the name ‘doe’, create the ‘from’ address as [email protected], and forward it to the mail server for acme.com which will append its name and create the full address of [email protected]. Now, the email is moving upward before it will go downward.

This hop by hop forwarding is quite like a post office stamping the mail on receipt. Typically, on international mail you can see multiple stamps on the envelope through which you can know the succession of post offices the letter passed through.

Internet addresses are also defined hierarchically. An IPv4 address for instance involves a hierarchy of 4 numbers—A.B.C.D—in which A is the highest level designator and D is the lowest level. With IPv6 addressing (which has 128 bits instead of 32 bits for IPv4 addresses) the number of levels increases. When packets are forwarded on the internet, the packet routers summarize the routes; in other words, they send the packet upward toward a router that advertises the route for A.0.0.0/8 (meaning that only the first digit of 8-bits is considered significant) and then downward to A.B.C.D.

Note that in these cases, it is possible to have an address A.A.A.A which means that each digit in the address can be repeated at any level of addressing. Therefore, it is not sufficient to know a single digit—e.g. A—in order to route the packet; we have to rather know the number’s position in the hierarchy, and this position is itself defined hierarchically. Thus, A maybe the first, second, third, or fourth byte in the address. If you don’t know the position of the byte, you cannot forward the packet.

Fractal geometry is thus all pervasive in our world. I just gave examples of snail mail, email, and internet addressing. It constitutes a very efficient system of motion because each building only needs to know the city post office rather than all the post offices in the world. The city post office similarly needs to only know the state post office, and the national post offices only need to know other national post offices. Hierarchy makes motion every efficient which is why everyone uses it.

However, modern science doesn’t treat motion in this manner because particles move directly from one destination to another, kind of like people carrying packages to each other in a village where they don’t need the assistance of a post office because the package can be carried directly. The model of motion in modern science is the extension of the model of communication in a village. When the system gets very large this communication model fails, and a hierarchical model has to be adopted.

Hierarchy Produces a Tree

All hierarchical addressing systems are organized like a tree. Below is an example of the internet domain name hierarchy. This is not a novel idea because all systems of classification are organized as trees.

The novelty is that when hierarchy is used for addressing then motion doesn’t occur directly between the leaves of the tree. Rather, the moving object has to go up and down the tree. For example, if an email is sent from MIT to Google, then it will find the lowest node in the hierarchy that connects to Google. In this case, it might be the mit.edu server sending to a root server, which then forwards it to the .com server, which then forwards it to the google.com server.

Straight line motion is forbidden in a tree. Which means that if light were a particle moving according to hierarchical addressing, then it will not go directly between leaves of the tree. It will rather go up and then down the tree. The path of light would seem to be curved (as we now understand through relativistic space-time bending) but the reason of this bending would be entirely different. In particular, the cause of this bending would not be matter (as we postulate right now) but the hierarchical nature of space itself in which light doesn’t move linearly because space is itself hierarchical.

Our Brain is a Fractal

Using this understanding of light and space, we can now formulate a theory of perception in which light from an object goes up and down a tree (whose higher nodes are not always known to us) but when the light is received by an observer, a new leaf is added to the tree that looks just like the object outside but this time it is actually in the brain. Cognitive scientists call this the mental representation of reality in which there is a real object outside but its representation is created within the brain.

Clearly, the mental representation is contextualized against your prior beliefs, which means that the higher branches in the tree constitute prior acquired information, which you already believe to be true, while the new reality is added as a leaf to the existing knowledge. Accordingly, if the new information is inconsistent with previous knowledge, then this leaf would be shed from the tree as an illusion or mistake. If, instead, the new knowledge is consistent with the previous knowledge, then the leaf would be assimilated as part of the growing tree.

The addition and removal of knowledge will constitute the ‘change’ of the brain where additional neurons are added or older neurons are removed. As the person gets older, or under degenerative diseases like Parkinson’s, new neurons are not created while the older neurons are lost. As a result, the person loses their long-term memory gradually (because the old neurons are being destroyed) and has a difficulty in forming new memories (because new neurons are not being created). We can liken it to a tree in autumn that is gradually shedding its leaves.

Clearly, when we form a picture of the world in our brain, the picture is not as detailed as the reality, but that abstract picture is created as a detail of our brain. Thus, physically the picture is detailed, but semantically it is an abstraction of the reality. Everything we have ever experienced and which we remember exists as a memory in our brain, but obviously the brain is much smaller than the world we have seen. Thus, the world outside is also real inside, but these two worlds are different.

The Representation of Reality

If you were an electron microscope looking at a brain which is in turn perceiving an apple, you will see the representation of the apple inside the brain, but you won’t be seeing the apple itself. And if you simply look at the individual molecule that represents the apple in the brain then you will find no similarity to the real apple because you will only see a molecule. To convert that molecule into the perception of an apple, you have to traverse the entire hierarchy up and down. In other words, you have to correlate the individual molecule corresponding to the perception of the apple to practically every other molecule even to understand that the molecule denotes an apple.

If you simply look at an individual neuron or molecule you can never know what it means. The meaning is created by correlations to the other branches and leaves on the tree. If we don’t perform that correlation, then we will only see a neuron or molecule but it cannot be interpreted as an apple. You can say that you have the sense perception of the brain molecule but you have no grasp of what the molecule means.

The net effect of the interaction between the apple and the brain is that there is a representation of the apple in the brain. Similarly, there is a representation of the brain in the apple. My looking at the apple not only changes my brain, but it objectively alters the apple itself. The act of looking is an act of impregnating the apple with a representation of myself, while the apple has been impregnated in me. Thus, in the act of knowing, both knower and known are modified. This fact is commonly experienced when people realize that they are being stared at even though they are not looking at each other directly. It is because both objects are modified in the act of seeing.

Understanding Fractal Cosmology

We have so far discussed the hierarchical nature of fractal geometry. We saw its application in everyday notions of motion—e.g. in sending letters, emails, or packets over the internet. We saw how perception has to be modeled in the same manner. In different ways we are simply talking about the structure of space which gives us the necessary background to understand the travel to the moon.

The moon and the earth are interacting objects. Due to their interaction, there is a part of earth that represents the moon, and there is a part of the moon that represents the earth, quite like there is an apple representation in me and there is a representation of the self in the apple.

If we try to observe the effects of the existence of the apple from within the brain, we can study the apple representation in the brain. It won’t be the real apple, and yet there will be something which corresponds to the apple that we can observe. An electron microscope can thus ‘go’ to the apple inside the brain, but it won’t be going to the real apple. Similarly, when it sees the representation it won’t interpret it as an apple unless the representation is correlated to everything else in the brain.

Our landing on the moon is like the electron microscope seeing the apple representation in the brain. It is not the real moon, and yet it looks like the moon as its representation. Loosely speaking, we could say that the moon we see is the ‘ambassador’ of the real moon. It appears to have the qualities of the real moon, and yet it is not the moon.

The Meaning of the Earth Planet

We normally think that the earth planet is just the land and water surface of a globe. But in fractal geometry, the earth is much bigger; apart from the surface of the globe that we can perceive, it includes every other planet, galaxy, and star that we can see from the earthly viewpoint. If earth is a trunk of the tree, then all these planets from earthly perception are branches, twigs, and leaves of earth.

The real planets and stars are different; we have no access to them through our sense perception. However, if we correlate and understand everything in the sky then we can understand that the earthly moon is actually a representation of the real moon, like an external apple is represented in the brain. Thus, by ‘earth’ we don’t mean the surface of land and water. We rather mean everything that can be experienced using this body and all the instruments that we can build on this planet. In short, ‘earth’ is to be defined as a collection of possible experiences, of which land and water are parts.

Sāńkhya and Vedic Cosmology

Vedic cosmology provides this type of description of the universe in which space is modeled as a tree rather than a box. An individual planet has a ‘size’ from the most zoomed out view. But, given that the entire universe is represented in each part of the universe, you can keep zooming in within that space and discover the entire universe from that perspective. It won’t be the real universe, but it will be an impression of that universe which you can see. Indeed, the universe exists inside each body as a representation. Thus, living entities on different planets can see the entire universe from their planet, but it’s all within the ‘space’ of that planet. They are looking downward from their vantage point on the inverted universal tree where they see other planets as twigs and leaves of their planet rather than branches and trunks of the tree emanating above their planet.

Each planet therefore has a sense of self and others. The surface of the earth constitutes the ‘self’ of the earth, and all the planets that we can see from earth constitute the ‘other’. This idea is described in Sāńkhya as ādiatmika or self and ādibhautika or other. The planets such as the moon and the sun that we see from our earthly vantage point are not the real planets; they are just the ādibhautika representations of the real sun and moon.

Similarly, in the brain, there is a core part called the amygdala which constitutes the emotional center of the brain because it denotes the sense of self; if this self is ‘attacked’ then fear is created and it is responsible for the fight or flight responses in the body. Similarly, happiness is created when this ‘self’ is mollified. The rest of the cortical brain holds the representations of the external world—visual, auditory, tactile, etc. Thus even within the brain there is a self-center and places for ‘others’. Descartes, while formulating the mind-body interaction postulated that the pineal gland (which also lies in the center of the brain like the amygdala) was the seat of the soul. He was right in a sense because the center of the brain represents the ‘self’ although it is not the soul; similarly, the parts of the brain surrounding it represent the ‘other’.

The Model of the Atom

The same fractal approach to space can be used to understand the nature of atoms such as oxygen, carbon, etc. The nucleus of the atom is the real atom or the self which we can call the ādiatmika. The electrons surrounding this nucleus are ādibhautika or representations of other realities in the ‘world’ of the atom. These electrons correspond to the other nuclei and the nucleus sees the effects of other atoms through such electrons. It knows it’s ‘world’ through the representations of the ‘external reality’ that exist within its own space.

In one sense the atom is only the nucleus. But, the ‘world’ of the atom is significantly larger than the nucleus as it contains the electrons too. Typically, the atoms (including the electrons) are 100,000 times larger than the nucleus. If this were used to estimate the size of the earth space relative to the earth globe then the earth space would be 100,000 larger than the earth globe. The diameter of the earth globe is about 8000 miles, and by such an estimate, the earth space will be 800 million miles in diameter.

We might note that the diameter of the earth space is a measure of the size of the fractal space, not linear space. The diameter of the circle is a circle limit such that the circle is bound but you still can never reach the boundary. The extremities of this circle represent the farthest galaxies and stars we can perceive. They are not that far if we look at the earth space from the outside, and yet they appear to be very far from within the earth space. A satellite sent to the extremities will take billions of years to reach its destination, giving the impression that these are very far, although they are within earthly space.

When we view the electrons of an atom representing an external reality, then the addition or removal of electrons becomes a counterpart of our perception. Thus, more electrons (which create a negative ion) correspond to an interaction with more nuclei. Similarly, fewer electrons (which create a positive ion) correspond to an interaction with fewer nuclei. The ‘electrovalent bond’ between two atoms is then the counterpart of a unilateral perception—i.e. one nucleus ‘sees’ the second nucleus, but the second nucleus doesn’t. The ‘covalent bond’ between atoms is similarly a counterpart of both nuclei seeing each other as a result of which atomic theory models them as ‘sharing’ electrons. If we understand the deeper levels of perception in Sāńkhya then we can also understand why these chemical bonding models are useful in some cases but inadequate in others.

The Universe of Virtual Realities

If we understand space linearly as we do right now in modern science, then the moon we see is the real moon, and if we happen to go to this moon then we have to gone to the real moon. If however we understand space hierarchically according to Sāńkhya, then the moon we see is simply a representation of the real moon, and even if we go to this ‘moon’ we haven’t truly gone to the moon.

The question of lunar travel therefore is a scientific question, but not quite the current science, which is based on a model of communication suitable to a small village. When this model is extended to the entire universe we arrive at erroneous conclusions. Similarly, when the understanding of matter is divorced from the understanding of the observer we make erroneous conclusions.

Each planet has to be treated as a combination of reality and virtual reality. What we can see, touch, taste, smell, and hear on this planet is reality. But the things in the sky are virtual reality. We can know about the reality outside the earth space by looking at this virtual reality. This virtual reality also exists, like the apple exists in the brain as a representation. And yet, it is not reality itself. Therefore, we cannot go to the real moon through moon expeditions because the moon we will go to is within the earthly space. To treat the objects in the sky as virtual reality, we need to understand how matter becomes a symbol that references some reality but it is not the object being represented.