Let’s look at this idea: There is an eleventh dimension where membranes collide and with every collision another universe breaks out in a big bang. There is an infinite number of parallel universes and new ones are created all the time. Some string theorists today want to create a universe in a lab. We may have our counterparts in other universes. Mine is handsomer, less abrasive, and wiser.
There is a huge incoherence here. It is the obvious that there is no such thing as an infinite number. A number is a limit, while infinity is an indefinite, an unlimited. Something that is an infinite cannot be a determined number and no determined number can be infinite. However, in mathematics, there are many equations that use infinity or approaching infinity in describing physical reality. To speak of an infinite number is to be incoherent or caught in a self-contradiction.
This problem is also extended to a notion of infinite space. Nicholas of Cusa, the Cusanus as he known and a great influence on Giordano Bruno, in Medieval times, postulated that there is an infinite space. In effect, the cosmos is a circle whose center is nowhere and whose circumference is everywhere. But the same problem arises. Space is only space by limitation and because space is not an indefinite it cannot be an infinite.
Similarly, there can’t be anything that is infinitely small. What is small is a measurable entity and thus is determined and not unlimited.
Yet, in modern mathematics, the infinite is used as part of logical operations. While it may be proper to do that in pure math, when it is used to describe the motions and properties of the physical universe, there is something obviously wrong. Let’s take an infinity, N, and let’s take the quantity 1 and let us divide by N. What does 1/N mean? Because infinity is not non-numerical, to give an infinite number or space or size is completely illogical. If we want to give an adequate explanation of the world, how can we include something that is totally illogical in its explanation?
In one of the great works of the last century, Greek Mathematical Thought and the Origin of Algebra, Jacob Klein detailed the monumental change from ancient math to modern math that led to the use of the infinity as it is seen today. “The creation of a formal mathematical language,” Klein writes, “was of decisive significance for the constitution of modern mathematical physics. If the mathematical presentation is regarded as a mere device, preferred only because the insights of natural science can be expressed by ‘symbols’ in the simplest and most exact manner possible the meaning of the symbolism as well as of the special methods of the physical disciplines in general will be misunderstood.” The problem now “it has finally become impossible to separate the content of mathematical physics from its form.”
That means that physics today cannot be expressed in any other way except through modern mathematics, a formal symbolic language. That seems to imply that the universe itself (there is only one universe) has a physical structure that is of modern mathematics. That means the mathematics is not just symbols, but is an integral part of the universe. If there is an infinite space or infinite small or an infinite number, then its illogical construction is built right into the universe itself. The universe is self-contradictory and can’t be explained logically.
Ancient Greek mathematics began with the premise that a number was not an abstraction. A number was always a number of things. A number could not be separated or abstracted from things. It was always three apples, three horses, three women, three triangles. All mathematical operations always related to definite things. Geometry, moreover, related directly to things. A number is simply the operation of counting off things. The universe is cosmos can be counted.
A change occurred at the beginning of the modern period where mathematics was no longer counting off things. It became a system or operations of concepts. For example, the ancient Greek would say 1+2=3, and you would mean three things. Later, mathematicians started to create a kind of rudimentary equation. One could symbolize this process, for example, as 1+n=3. But, again, this is equation is about actual things. However, modern mathematics took the decisive step of writing an equation a+b=c which did not mean anything until values are given to the equation. But Descartes, one of the greatest of modern mathematicians, regarded physics as the symbolical description of extension, i.e., everything that is outside of his mind.
Descartes’ great act was to doubt all pre-scientific knowledge; he doubted everything except his doubting mind. Je pense donc je suis. Cogito ergo sum. I think, therefore I am. The great implication is that intelligence and thought cannot be in a god or outside of man. Moreover, the only things man can truly know is mathematics and what we make, in effect, technology. To top it off, Descartes divided mind and body or what he called extension, a lifeless universe which could be described with a new kind of mathematics, which is the actual mediation of body and mind. “This reconciliation,” writes Klein, “is achieved by means of symbolic figural representation. Everything depends on understanding that the ‘figures’ with which the ‘mathesis universalis’ deals, namely rectilinear and rectangular planes’ as well as ‘straight lines’…have, as far as their mode of being is concerned, no longer anything to do with the ‘figures’ of what had been the ordinary ‘geometry’: We easily conclude: here propositions must just be as much abstracted from those very figures with which geometers deal, if the inquiry involves these, as from any other subject matter; and for this purpose none need be retained besides rectilinear and rectangular plane surfaces, or straight lines, which we also call figures because by means of them we can imagine a subject which is in truth extended [namely in three ‘dimensions’] just as well as by means of a plane surface.'”
Descartes also established a particular form of psychology to establish his purely symbolic mathematics. To get to the simply point directly: To use the kind of math that is being used today to explain the physical universe requires a great change of understanding about man himself and the extended universe. This kind of math assumes that extension has a symbolic character that enables the math to operate and that the physical substance of the world is real. What that became was the “Euclidean space” upon which Newton and classical physics will base all its calculations.
Newton said everything was either in motion or at rest, and he took his entire scheme and did not realize that because he did no have a dynamic space he had essentially made everything in motion or everything at rest. You could not have both motion and rest in such an infinite and empty space. It took Einstein many years later to correct Newton by creating a dynamic space-time. But now that we are in string theory, we come up not with one universe, but an infinite parallel number of them. That infinite number can only exist is the world allows for that symbol of infinity to be a true number and not just a symbol. Yet, as I said in the beginning, to speak of an infinite number is to be illogical. The only way you can have an infinite number is if your mathematics has nothing to do with the real world as it is and is strictly symbolic in character. It is very hard to accept that modern physics is explaining at any reality at all.