The fundamental “stuff” of the Universe is the same and the differences arise only due to the manner of their accumulation and reduction – magnitude and sequential arrangement. Since number is a property of all particles, physical phenomena have some associated mathematical basis. However, the perceptible structures and processes of the physical world are not the same as their mathematical formulations, many of which are neither perceptible nor feasible. Thus the relationship between physics and mathematics is that of the map and the territory. Map facilitates study of territory, but it does not tell all about territory. Knowing all about the territory from the map is impossible. This creates the difficulty. Science is increasingly becoming less objective. The scientists are presenting data as if it is absolute truth merely liberated by their able hands for the benefit of lesser mortals. Thus, it has to be presented to the lesser mortals in a language that they do not understand – thus do not question. This leads to misinterpretations to the extent that some classic experiments become dogma even when they are fatally flawed. One example is the Olber’s paradox.
In order to understand our environment and interact effectively with it, we engage in the activities of counting the total effect of each of the systems. Such counting is called mathematics. It covers all aspects of life. We are central to everything in a mathematical way. As Barrow points out; “While Copernicus’s idea that our position in the universe should not be special in every sense is sound, it is not true that it cannot be special in any sense”. If we consider our positioning as opposed to our position in the Universe, we will find our special place. For example, if we plot a graph with mass of the star relative to the Sun (with Sun at 1) and radius of orbit relative to Earth (with Earth at 1) and consider scale of the planets, its distance from the Sun, its surface conditions, the positioning of the neighboring planets etc; and consider these variables in a mathematical space, we will find that the Earth’s positioning is very special indeed. It is in a narrow band called the Habitable zone (For details, please refer to Wikipedia on planetary habitability hypothesis).
If we imagine the complex structure of the Mandelbrot Set as representative of the Universe (since it is self similar), then we could say that we are right in the border region of the fractal structure. If we consider the relationship between different dimensions of space or a (bubble), then we find their exponential nature. If we consider the center of the bubble as 0 and the edge as 1 and map it in a logarithmic scale, we will find an interesting zone at 0.5. Starting for the Galaxy, to the Sun to Earth to the atoms, everything comes in this zone. For example, we can consider the galactic core as the equivalent of the S orbital of the atom, the bars as equivalent of the P orbital, the spiral arms as equivalent of the D orbital and apply the logarithmic scale, we will find the Sun at 0.5 position. The same is true for Earth. It is known that both fusion and fission push atoms towards iron. The element finds itself in the middle group of the middle period of the periodic table; again 0.5. Thus, there can be no doubt that Nature is mathematical. But the structures and the processes of the world are not the same as mathematical formulations. The map is not the territory. Hence there are various ways of representing Nature. Mathematics is one of them. However, only mathematics cannot describe Nature in any meaningful way.
Even the modern mathematician and physicists do not agree on many concepts. Mathematicians insist that zero has existence, but no dimension, whereas the physicists insist that since the minimum possible length is the Planck scale; the concept of zero has vanished! The Lie algebra corresponding to SU (n) is a real and not a complex Lie algebra. The physicists introduce the imaginary unit i, to make it complex. This is different from the convention of the mathematicians. Mathematicians treat any operation involving infinity is void as it does not change by addition or subtraction of or multiplication or division by any number. History of development of science shows that whenever infinity appears in an equation, it points to some novel phenomenon or some missing parameters. Yet, physicists use renormalization by manipulation to generate another infinity in the other side of the equation and then cancel both! Certainly it is not mathematics!
Often the physicists apply the “brute force approach”, in which many parameters are arbitrarily reduced to zero or unity to get the desired result. One example is the mathematics for solving the equations for the libration points. But such arbitrary reduction changes the nature of the system under examination (The modern values are slightly different from our computation). This aspect is overlooked by the physicists. We can cite many such instances, where the conventions of mathematicians are different from those of physicists. The famous Cambridge coconut puzzle is a clear representation of the differences between physics and mathematics. Yet, the physicists insist that unless a theory is presented in a mathematical form, they will not even look at it. We do not accept that the laws of physics break down at singularity. At singularity only the rules of the game change and the mathematics of infinities takes over.
Modern scientists claim to depend solely on mathematics. But most of what is called as “mathematics” in modern science fails the test of logical consistency that is a corner stone for judging the truth content of a mathematical statement. For example, mathematics for a multi-body system like a lithium or higher atom is done by treating the atom as a number of two body systems. Similarly, the Schrödinger equation in so-called one dimension (it is a second order equation as it contains a term x2, which is in two dimensions and mathematically implies area) is converted to three dimensional by addition of two similar factors for y and z axis. Three dimensions mathematically imply volume. Addition of three areas does not generate volume and x2+y2+z2 ≠ (x.y.z). Similarly, mathematically all operations involving infinity is void. Hence renormalization is not mathematical. Thus, the so called mathematics of modern physicists is not mathematical at all!
In fact, some recent studies appear to hint that perception is mathematically impossible. Imagine a black-and-white line drawing of a cube on a sheet of paper. Although this drawing looks to us like a picture of a cube, there are actually infinite numbers of other three-dimensional objects that could have produced the same set of lines when collapsed on the page. But we don’t notice any of these alternatives. The reason for the same is that, our visual systems have more to go on than just bare perceptual input. They are said to use heuristics and short cuts, based on the physics and statistics of the natural world, to make the “best guesses” about the nature of reality. Just as we interpret a two-dimensional drawing as representing a three-dimensional object, we interpret the two-dimensional visual input of a real scene as indicating a three-dimensional world. Our perceptual system makes this inference automatically, using educated guesses to fill in the gaps and make perception possible. Our brains use the same intelligent guessing process to reconstruct the past and help in perceiving the world.
Memory functions differently than a video-recording with a moment-by-moment sensory image. In fact, it’s more like a puzzle: we piece together our memories, based on both what we actually remember and what seems most likely given our knowledge of the world. Just as we make educated guesses – inferences – in perception, our minds’ best inferences help “fill in the gaps” of memory, reconstructing the most plausible picture of what happened in our past. The most striking demonstration of the minds’ guessing game occurs when we find ways to fool the system into guessing wrong. When we trick the visual system, we see a “visual illusion” – a static image might appear as if it’s moving, or a concave surface will look convex. When we fool the memory system, we form a false memory – a phenomenon made famous by researcher Elizabeth Loftus, who showed that it is relatively easy to make people remember events that never occurred. As long as the falsely remembered event could plausibly have occurred, all it takes is a bit of suggestion or even exposure to a related idea to create a false memory.
Earlier, visual illusions and false memories were studied separately. After all, they seem qualitatively different: visual illusions are immediate, whereas false memories seemed to develop over an extended period of time. A recent study blurs the line between these two phenomena. The study reveals an example of false memory occurring within 42 milliseconds – about half the amount of time it takes to blink your eye. It relied upon a phenomenon known as “boundary extension”, an example of false memory found when recalling pictures. When we see a picture of a location – say, a yard with a garbage can in front of a fence – we tend to remember the scene as though more of the fence were visible surrounding the garbage can. In other words, we extend the boundaries of the image, believing that we saw more fence than was actually present. This phenomenon is usually interpreted as a constructive memory error – our memory system extrapolates the view of the scene to a wider angle than was actually present. The new study, published in the November 2008 issue of the journal Psychological Science, asked how quickly this boundary extension happens.
The researchers showed subjects a picture, erased it for a very short period of time by overlaying a new image, and then showed a new picture that was either the same as the first image or a slightly zoomed-out view of the same place. They found that when people saw the exact same picture again, they thought the second picture was more zoomed-in than the first one they had seen. When they saw a slightly zoomed-out version of the picture they had seen before, however, they thought this picture matched the first one. This experience is the classic boundary extension effect. However, the gap between the first and second picture was less than 1/20th of a second. In less than the blink of an eye, people remembered a systematically modified version of pictures they had seen. This modification is, by far, the fastest false memory ever found.
Although it is still possible that boundary extension is purely a result of our memory system, the incredible speed of this phenomenon suggests a more parsimonious explanation: that boundary extension may in part be caused by the guesses of our visual system itself. The new dataset thus blurs the boundaries between the initial representation of a picture (via the visual system) and the storage of that picture in memory. This raises the question: is boundary extension a visual illusion or a false memory? Perhaps these two phenomena are not as different as previously thought. False memories and visual illusions both occur quickly and easily, and both seem to rely on the same cognitive mechanism: the fundamental property of perception and memory to fill in gaps with educated guesses, information that seems most plausible given the context. The work adds to a growing movement that suggests that memory and perception may be simply two sides of the same coin. This, in turn, implies that mathematics, which is based on perception of numbers and other visual imagery, could be misleading for developing theories of physics.