depth – Fountain Magazine

Time and Beyond as a Dimension

Louima Cunningham — Fri, 01 May 2009 00:00:00 +0000

Even if we cannot easily grasp the real nature of “time,” we can understand its aspect of being a “dimension.” For example, specifying only a place without specifying a “time’’ for an appointment would not be sufficient. Let us presume that we are on board a space vehicle or a helicopter and we are announcing our present location by giving the ground coordinates, that is, the latitude, the longitude and the height. We have to specify our current time, that is, the date and the hour, in order to make such an announcement meaningful and proper. Space–time is thus a four-dimensional measurement system, the dimensions inseparable from each other, like the nail and the quick of a finger.

We certainly fail if we try to consider time as only a matter of determining the hour. It is, in fact, a dimension like depth, height and length. One reason of our difficulty in perceiving time may be caused by the fact that our optical perception is sensitive only to three dimensions, but no others. Many animals cannot comprehend the dimension of depth. Some animals see their environs in two dimensions as in pictures. We have difficulty perceiving other dimensions just as animals which see the world in two colors live without any awareness of other colors.

Humankind, with the most sophisticated aspects, has a very different and privileged position above all creation. In spite of this, we have limited sight, hearing, and other senses. Many a world that is beyond our senses remains imperceptible to us.

Another aspect of time that supports its dimensional feature is that it is in full conformity with and proportional to other dimensions. In terms of its extent, duration of events increases or decreases in parallel with spatial dimensions. Man lives for around sixty to seventy years, while microscopic animals live around one or two days. The life of the sun and the universe which constitute the macrocosmos is expressed in billions of years. On the other hand, the life of subatomic particles is expressed in billionths of a second. Thus, we assume them as being resonances. There is time reduction together with and compatible with space constriction on the sub-atomic scale, and this fact is yet another proof that time is also a dimension.

How shall we understand the other dimensions of space? What does the fourth dimension of space mean? Let alone describing, it is not easy to even imagine this.

If a is the length, a2 is the area and a3 is the volume of a thing, then what is a4? If we see space as a giant plain sheet of paper, that sheet of paper has no depth but only a surface. If we fold crumple it into the shape of a sphere, we obtain “Riemann space.” Just like we perceive the three-dimensional earth as a two-dimensional surface while we are on it, this 3-dimensional sphere made of 2-dimensional paper will be perceived as 2 dimensional by us. We can only talk about the third dimension after we generate a depth, that is, after we step outside the paper and move above and below it.

The fourth co-ordinate of space is a tunnel. Let us suppose that the universe is two-dimensional, that is, it is like a thin sheet of paper, and let us human beings be like pictures with no thickness over its surface just like the pictures on a newspaper. We are free to move in all directions on this sheet of paper. We can sense four directions. But we will never perceive the terms “up” and “down” (or “upper” and “lower”) since we will never leave the surface of this sheet of paper. Such terms will seem unacceptable to us even we are told of them. Accordingly, we will never hear of a third dimension and our vocabularies will never contain such terms as “up” and “down.”

If a three-dimensional object existed above our fictional paper realm and if this object even slit our paper realm and went away, we still would not see it in three dimensions but only the part of it intersecting our paper realm. If such a thing were a sphere, for instance, we would see its projection in a circular form. Its latitudinal sections would gradually expand starting from the poles, reach their largest on the equator line and its ring-like (circular) shape would gradually decrease and finally disappear at the other pole. That is, we would see it only as its cross section or shade. Such a three-dimensional object would seem two-dimensional to us since we would suddenly see its cross section. The sudden appearance, expansion, decrease and final vanishing of that spherical object in our two-dimensional realm would seem quite amazing to us since our shapes are fixed and immovable.

The three-dimensional shade of an extraterrestrial four-dimensional object overshadows our three-dimensional space. We see the linear tunnels in cross-section, not longitudinally, just as we see the sphere as circular. Though the sphere is a simple object, it amazes us.

Let us now imagine a more complex form. Let us, for instance, reflect the shadow of a vase onto a wall and obtain various shades by turning it repeatedly. A fixed and immovable portrait on the wall would regard the shadow and its variations reflected over the same plane with surprise and fear, since that portrait, or that person without depth, sees only what is reflected on the wall, but not us and the vase. The wall is the only realm for him and there is nothing for him beyond and behind the wall even if we say so.

We humans tend to assess events within the narrow limits of space and within certain dimensions, since we are bound within a single space–time cone. The conceptualization of space with its dimensions of height, length and depth is possible for us. However, the fourth dimension, time, is an abstract and metaphysical measure even though it is studied within physics. The tunnel thus seems to us like an incredible dimension.

Our perceptions with the five senses in the visible universe can be considered as the projections of non-physical and multi-dimensional realities (the eighteen thousand realms) to our domain. Clearly, in order to gain a better understanding of those realms, which we do not see but which we feel exist, with the help of the physics, we need to emancipate ourselves from the narrow patterns of time and space in this world of trial. We need to travel toward the horizon of spirit and develop an all-new scientific language which approaches physics and metaphysics together. Finally, we can say, in Bediüzzaman’s words, that the physical and observable universe which is the domain of research for modern physics is an ornamented curtain veiling the world of the unseen.

Osman Cakmak is a professor of chemistry at Gaziosmanpasa University, Tokat, Turkey.

Pinhole Cameras, Imaging, and The Eye

Louima Cunningham — Sat, 01 Apr 2006 00:00:00 +0000

Cameras, eyes, telescopes, microscopes are various imaging systems. In general, everyone knows that an imaging system has one or multiple lenses. Interestingly, one can also make a camera without using a lens! Such cameras are called “pinhole cameras.”¹ A pinhole camera is actually very simple to make: a box with a pinhole, that is to say, a hole that measures a millimeter or less at the center of one face (Fig. 1). 2 In Fig. 2 (a), a picture taken by a pinhole camera can be seen.³ You might wonder how such a beautiful picture can be taken using a very simple box with a pinhole, considering that thousands of dollars are spent on high-quality cameras. What is more interesting is that there is a sea creature that has a pinhole eye! A nautilus, shown in Fig. 3, has a pinhole eye.⁴ Also, some of the surveillance cameras use pinhole designs with no lenses.⁵ Understanding how a pinhole camera works is very instructive to capture the essence of imaging.

In order to get a sharp image, ideally one point on the image (film) should receive light rays from only one point on the object. In practice, this ideal case can not be achieved in case of a large pinhole. If we have a large pinhole, as seen in Fig. 4, the light rays emerging from one point on the object reaches multiple points on the film. Also, multiple points on the object can arrive at a single point on the film. The result of both cases is a blurry image. For a small pinhole, however, there are light rays emerging from a point on the object in all directions, and only a very small amount of light is received on the film. To produce a decent image on the film, the exposure time needs to be very long, especially when a very small pinhole is used. Of course, we can make the pinhole a little larger to capture more light. But, wait! This would make the image blurry. Therefore, for pinhole photography, the size of the pinhole sets the quality of the image and the minimum exposure time. Also, we can take the picture of a still object, but a moving object cannot be captured easily by a pinhole camera due to the long exposure time. One important question is: Can we make reduce the size of the pinhole size to increase the quality of the image? Well, physics says: “No!” Fig. 5 shows a comparison of the images of a filament taken by a pinhole camera.⁶ As the size of the pinhole gets smaller and smaller, the effects of the diffraction phenomenon are more and more pronounced, and the image becomes blurry again. We also notice that the image is barely formed with a very small pinhole, indicating that very little light is received.

How can we gather more light and still make the image sharp? Can we achieve this with just the pinhole? Apparently not. That is why we mention lenses when talking about any imaging system. This is what a lens basically does. A lens gathers more light, and still preserves the one-to-one correspondence between the points on the object and those on the image. So, a lens is very useful for imaging. Most cameras have one or multiple lenses. Our eyes have lenses. We should remember, though, a pinhole camera takes a picture, but the compromise is the exposure time. Now, we see that a lens solves the exposure time problem, but is there a price to pay? To answer this question, let’s take a look at once again Fig. 2, where we see two pictures, one taken by a pinhole camera, and the other one by a lens camera. Look at the pictures carefully, and try to understand the difference before proceeding. As you probably observed, in the pinhole camera image everything in the picture is in sharp focus, from the close-by plants to the far distant beacon, and the clouds in the sky. However, in the lens camera image, only the closest daisy is in focus, and the other daisies, only a few meters away, are blurry. Indeed, we lose the depth of field in our images when using a lens camera. Depth of field can be defined as “The distance between the nearest and farthest points that appear in acceptably sharp focus in an image.” This is actually something we live with everyday. Try to focus your eyes on a mountain far away; the objects that are very close will not be in focus anymore. So, our eyes, consisting of lenses, also have limited depth of field. A nautilus eye, on the other hand, has an infinite depth of field, as it has a pinhole eye. Therefore, the price paid for gathering more light with a lens is that not everything will be in focus.

We can understand why lens cameras have a limited depth of field while a pinhole camera has nearly infinite depth of field if we consider the focusing mechanism of a lens. Given a pre-determined film position, a lens can only form sharp images of an object at a certain distance from the lens. Other points that are farther from or closer than same section of the object will be out of focus. However, if the size of the object is not large, we usually do not notice this effect. When we want to take pictures of close-by objects, then this effect is clearly seen, as Fig. 2 (b) shows.

Actually, we can correct this problem. The image of the farther points of the object forms at a farther point on the film. So, multiple light rays coming from one point will end up on the film. If we place an aperture next to the lens, then we can block some of these light rays. If we make the size of the aperture sufficiently small, we can get a sharp image of the farther point. Our original question about the lenses can be posed once again at this point: By using the aperture we make the image sharper, but what do we lose? Of course, since we block some of the light rays, we lose the light-gathering ability of the lens. Now, if we make the aperture size smaller and smaller, we finally reach the pinhole, and an almost infinite depth of field!

Our eyes also use similar mechanism of placing an aperture. The amount of light allowed to enter each eye is controlled by the iris, a circular diaphragm that opens wide at low light levels and closes to protect the pupil (the aperture) and retina (light detector of the eye) at very high levels of illumination. As illumination changes, the diameter of the pupil (positioned in front of the crystalline lens) reflexively varies between a size of about 2 to 8 millimeters. When illumination is very bright, the pupil narrows and light rays from the side are excluded from the optical pathway.⁷ The result is a sharper image on the retina. A very narrow pupil (approximately 2 millimeters) produces diffraction artifacts that spread the image of a point source on the retina, similar to the image of the filament captured by a very tiny pinhole (Fig. 5)

In conclusion, a pinhole camera is a very instructive tool for learning about imaging concepts. A pinhole camera has an infinite depth of field and the ability to produce sharp images regardless of the distance of the objects. This comes with a price, though: the small size of the pinhole limits the amount of light received by the film, so long exposure times are needed. A lens helps to gather more light, but compromises the depth of field. These concepts are used in imaging technologies, and can be found in the eyes of living organisms.

Notes

E. Hecht, Optics, 2nd edition, pp. 199. Addison-Wesley Publishing Co.
http://images.encarta.msn.com/xrefmedia/aencmed/targets/illus/ilt/T045986A.gif.
http://www.kosara.net/gallery/.
http://www.eyedesignbook.com/.
http://www.spylife.com/pinholecam.html.
http://www.umiacs.umd.edu/~ramani/cmsc426/Lecture3.pdf
http://www.olympusmicro.com/primer/lightandcolor/humanvisionintro.html.