One can say that the image of singularity that I am trying to draw above is an extended version of holographic theory. Holographic Theory offers answers for two main paradoxes, Nature of mind and Non- locality. So it is important for us to investigate it. Dennis Gabor discovered the original optical holography in 1947. He showed that the information pattern of a three-dimensional (3-D) image could be encoded in a beam of light. Later on, discovery of laser helped to put the idea more into experiment.

When light reflects at a mountain at the distance, all the information is restored in a beam of light, which is heading towards us. To a certain extent, it does not matter how narrow you choose that beam of light, when we conjugate the information by using the lens of a camera, you will get the whole picture of the actual mountain. And depending on the strength of your lens, you could recover the information about surface texture or microscopic structures of each point in the mountain. If we had a stronger device we could even extract the atomic or even subatomic structure information of every miniscule of the distant mountain. If you think about it, this is a lot of information for a tiny beam of light to carry. Although the Bekenstein bound put a limit to amount of information that we can get from a screen with a limited area. The number of bits of information available will be less than one quarter of the area of the screen in Planck units. Nevertheless, It is still tremendous amount of information. Let us see how this happens? How do we recognize a spatial object, which exists say about 20 km away from us? You will say the light hit the mountain and part of it gets reflected and travels to our location. A part of the beam of light passes through our eye lenses and hit the retina. From there the action potential transfer the information to our brain and somehow our brain interprets it. In this way we come to realize that there is a mountain twenty kilometer away. Let's investigate it further. Originally the beam of sunlight was just carrying the information about surface of sun. After it hits the distant mountain, it takes the bulk of information from our spatial object and includes it in the light wave. Underneath I use Dr. Jeff Prideaux's interesting description of holography.

The act of converting spatial forms to frequency domain is determined by Fourier transform formula. The Fourier transform (and inverse Fourier transform) consists of convolution integrals, which mathematically smear or de-smear the information. For continuous functions, the Fourier transform and inverse Fourier transform are as follows (for transforms between the time and frequency domain):

The Fourier transform also has meaning between a spatial domain (for instance the position in two dimensional space) and spatial frequency. Mathematically, the two-dimensional spatial Fourier transform is

and the inverse transform is

where x and y are spatial coordinates and a and b are horizontal and vertical frequencies. (Ref 19)

When we put a lens and screen in front of our beam of light we change the frequency nature of information and convert it to a spatial image. We are doing inverse Fourier transform.

Figure 4 Diagram expressing the holographic nature of light incident on the surface of the lens of the eye. (Ref 19)

Please note that the nature of light is electromagnetic energy not spatial. This is exactly the same concept that I am trying to convey about singularity. The proposed singularity contains information and can accommodate the information of four-dimension space just like the beam of light, which accommodate the information of our object, and its space.