The holographic principle

A) A teapot of bits

1. While drinking a cup of tea we can think of many things, but usually we forget the cup of tea itself. We also often ignore that we are thinking. It would have been completely boring, and also exhausting, to think about any move we made, preparing the tea, finding a cup, making the tea, holding the cup in our hands, drinking the tea, thinking that we are drinking the tea, thinking about what thought is, and so on. However some people do this all the time…

B) This is an explanation:

2. Is the (previous) picture worth a thousand words? According to the Holographic Principle, the most information you can get from this image is about 3x10⁶⁵ bits for a normal sized computer monitor. The Holographic Principle, yet unproven, states that there is a maximum amount of information content held by regions adjacent to any surface. Therefore, counter-intuitively, the information content inside a room depends not on the volume of the room but on the area of the bounding walls. The principle derives from the idea that Planck length, the length scale where quantum mechanics begins to dominate classical gravity, is one side of an area that can hold only about one bit of information. The limit was first postulated by physicist Gerard ‘t Hooft in 1993. It can arise from generalizations from seemingly distant speculation that the information held by a black hole is determined not by its enclosed volume but by the surface area of its event horizon. The term ‘holographic’ arises from a hologram analogy where three-dimension images are created by projecting light through a flat screen. Beware, other people looking at the featured image may not claim to see 3x10⁶⁵ bits- they might claim to see a teapot. [1]

C) A little bit of thought

3. Whether we like it or not, our mind functions in such a way that most information is processed unconsciously (imagine for example that we had to remember how to breath each time we took a breath). Furthermore our own brain ‘thinks’ very differently than we think. Our thought (in fact everything we can think of) consists of images, or ‘ideas.’ Even a color or a sound which we can reproduce in our mind comes about as an ‘image,’ either with a definite or indefinite shape.

4. But while we perceive everything around us in the form of ‘perfect images,’ our own brain in the background reconstructs these images from ‘scrap,’ choosing a certain combination of bits, with ‘on’ and ‘off’ values. The way we perceive such a series of bits (a ‘string’) as a ‘landscape,’ some ‘holidays,’ ‘the person we love,’ or ‘an image of ourselves’ is still a great mystery and at the same time a great miracle.

5. Having some idea about such a process, which in fact is the process of thought, and trying to decode it, becoming thus aware of our own awareness, is what distinguishes us from computers.

D) A spoonful of brain

6. How many bits of information does the brain consists of? Most computational neuroscientists tend to estimate human storage capacity somewhere between 10 terabytes and 100 terabytes, though the full spectrum of guesses ranges from 1 terabyte to 2.5 petabytes. [2]

7. However it seems to be a great disagreement between the last estimation (10¹⁵ bytes≈ 10¹⁶ bits, if 1 byte= 8 bits, thus 1 byte≈ 10¹ bits) and the number of bits in a teacup (3x10⁶⁵≈ 10⁶⁵). Is it possible that a teacup is smarter than a brain?

E) The spirit in the teacup

8. Imagine that all information available in a room can be found on the surface of its walls. Even if we can be certain that there is furniture in the room (together with us sitting on some furniture, drinking a cup of tea), we can also imagine that everything in the room (as well as ourselves) is an image inside our minds. I don’t say ‘brain’ but ‘mind’ because the mind is much larger than the brain: It includes the brain as a physical object, but it also has an idea about the brain as an image in an area of space and time that the mind considers its own.

F) The holographic principle

9. In fact all the information stored in the mind (what we can also call consciousness) could be concentrated at a point, a singularity, while the information is projected outwards onto a surface like a hologram. In the last example it was a room whose contents were projected on the surface of its surrounding walls (including the roof and the floor). But, expanding the example, such a room could be the whole universe, including everything, from a chair to a galaxy, from us to all living creatures.

10. Simply put the holographic principle states that the information found in a black hole is stored on its surface. In mathematical terms the entropy S (content of information) of the black hole is analogous to its surface area A: 

where k is a constant (Boltzmann constant), and here Planck length l_P was set equal to 1.

11. According to the holographic principle, the maximum information needed to perfectly recreate an average human brain down to the quantum level will be 2.6x10⁴² bits. [3]

12. Still it seems that the original teacup is smarter than ‘an average human brain down to the quantum level…’

G) How many qubits of information does the universe consist of?

13.  If the Planck area can hold one qubit of information according to the holographic principle, then we have:

- Planck length is 1.6x10^-35 m.

- Planck area will be (assuming a square with size equal to Planck length) 2.6x10^-70 m².

- The radius of the observable universe is 13.8 billion light-years (ignoring the expansion).

- One light year is 9.461x10¹⁵ m.

- Thus the radius of the observable universe is about 1.3x10²⁶ m.

- Approximating the universe with a sphere of that radius R, the area A of its surface will be (A=4πR²) 2.1x10⁵³ m².

- If an area equal to Planck area consists of one qubit of information, then the surface area of the observable universe will consist of about 10¹²³) qubits.

H) Can the brain hold as much information as the universe itself?

14. I will not do the same calculation for the human brain, but since the brain (as a physical object with definite boundaries) is much smaller than the universe, it will contain much less information. The problem however is that a balloon can be of similar size to a brain but not of similar intelligence. An important notion is the degrees of freedom available to a system (either a teapot, a balloon, the brain or the universe itself), thus the number of possible combinations between its distinct elements. While a teapot knows nothing about its contents, the human brain knows what to make out of these contents and how to deal with them.

15. Is therefore something missing from the holographic principle, in order to account for the rise of consciousness? What is relationship between the contents which consciousness projects on a holographic surface, and that surface? Is that surface part of consciousness itself?

16. Can all the information stored on a holographic surface be identified with the content of consciousness?

Appendix:

Is Consciousness information?

Formally, the information I of a system is given as the logarithm of the states (degrees of freedom) n,

(where here it was chosen that the base of the logarithm is e).

For simplicity we will suppose that the information can be defined as the logarithm of the energy instead,

where t is the time.

We can also assume an energy of the form

This energy is associated with the damped harmonic oscillator, so that γ is the damping factor.

The states n of the system can appear by setting

Now setting

we have

The constant of integration which appears in the last equation

represents the total energy E₀ of the system, for all states γt=n, and since it is equal to the logarithm of the energy, it is a dimensionless quantity.

In that sense, the constant 𝒞,

will stand for the total amount of information available to the system.

This is why I call this constant 𝒞 for Consciousness.

A more compact form of the energy equation can be taken by using the following substitution,

so that the equation for the total energy, including the factor Γ, can be written in the equivalent forms,

Since the factor Γ is related to how fast information is absorbed (‘damped’), I will call the factor Γ, Factor of Free Will.

A final note can be made with respect to the difference in the energy,

The difference ΔE in the energy can be identified with the kinetic energy K, in the sense that the total initial energy E₀ is transformed into the motion of an object. 

We may call the process by which the total potential energy E₀ of the system is transformed into the kinetic energy K of an object, ‘Displacement of Consciousness.’ [4]

This is an example of how the available energy, in the form of implicit information, transforms into the kinetic energy of a material object moving in spacetime, if this object is Consciousness itself.

[1]: [https://apod.nasa.gov/apod/ap170423.html]

[2]: [https://www.quora.com/How-much-data-can-the-human-brain-store-Is-there-any-limit-to-it-Can-humans-keep-storing-information-as-much-as-they-want-If-so-how]

[3]: [https://en.wikipedia.org/wiki/Bekenstein_bound]

[4]: [https://archive.org/details/CrossingTheBrachistochrone_201804]

9/7/2018

Image: [https://apod.nasa.gov/apod/ap170423.html]