The Principle Of Sufficient Reason

 

For every fact there must be a sufficient reason why it is so and not otherwise.

From this basic, logical principle, everything in the universe can be worked out.
This is the power of reason. The entire universe can be explained by simply sitting and thinking about it. No experiments need be carried out, no ludicrous amounts of money need to be spent on large hadron colliders or anything like that. All that is required is reason, logic, rationality and mathematics.

If the universe is mathematical in nature, as it patently is, then it must use all of mathematics. Every conceivable number must be used by the universe. There is no sufficient reason for only certain numbers to appear in reality. All of them must. It’s illogical otherwise. Every number must have real existence, or ontology. This includes the greatest number of all – zero.

Zero represents nothing, yet, according to the principle of sufficient reason, it must have ontological existence. Descartes separated the universe into two domains, mind and matter. Matter is everything that can be measured physically, everything that can be experienced by our senses, everything that is physical and can be defined in space and time. Matter is measured using numbers other than zero. Mind, on the other hand, is the opposite. It can not be detected by the senses, can not be measured physically and can not be defined in space and time. Mind, therefore is measured as having the value of zero.

But mind clearly exists. It’s real. “I think therefore I am”, said Descartes. In fact, mind is the only thing we can be certain of existing, as our minds are doing the thinking, therefore that thinking is happening, therefore mind exists. Here we now see that zero has ontological existence. It is the domain of mind.

So zero doesn’t really represent nothing, rather it represents the non-physical i.e. mind. This is fundamental in explaining the universe. Einstein showed (using reason and mathematics rather than experiments) that as objects accelerate towards the speed of light, time and space begin to alter from that object’s frame of reference. The closer the object gets to the speed of light, the more space contracts and time dilates. Space literally begins to shrink and time literally begins to slow down, at least as far as the moving object is concerned.

With this in mind, think of what reality must be like from the frame of reference of a photon, a particle of light. A photon travels at the speed of light. At this speed, space has contracted all the way to zero and time has slowed down all the way to zero. Therefore, the photon does not experience time and space at all. Everything has been reduced to zero. We, as slower moving objects, see the photon as travelling at some immense speed through time and space, but the photon itself experiences no time or space. It doesn’t move at all because there is no time or space through which it can move. The photon exists in the zero domain, outside time and space. Therefore, astoundingly, as per Descartes’s definition, photons i.e. light are mind rather than matter, at least from their own point of view.

Zero is the mind of the universe. Imagine the universe as one giant cartesian co-ordinate system. All of the axes intersect at the same point, the zero point, the origin. This is the mind of the universe from which everything else emerges. The rest of the co-ordinate system represents the physical universe of matter, of time and space.

All of the other numbers must be represented on this cartesian system, as per the principle of sufficient reason which shows that the universe must contain all possible numbers, rather than just a subset. All of these numbers emerge from the zero point, the mind point. All positive numbers flow in one direction from the origin, and all negative numbers flow in the opposite way. These negative numbers have just as much ontological reality as the positive ones.

But are these all of the numbers that can exist? Take a positive number, say 2, and square it i.e. multiply it by itself: 2 x 2 = 4. Now take a negative number, say -2 and perform the same operation: -2 x -2 = 4. Two negatives cancel each other out to make a positive. Therefore any negative number squared will give a positive answer, just as any positive number squared gives a positive answer. This seems to suggest that squaring any number, positive or negative, results in a positive answer.

The opposite of squaring a number is taking the square root. If squaring 2 gives 4 then the square root of 4 is 2. But squaring -2 also gives 4. So 4 actually has two square roots, 2 and -2. All of this seems to suggest that only positive numbers can have square roots, given that squaring any number always gives a positive answer. But this is a violation of mathematical completeness, a violation of symmetry. If positive numbers can have a square root, there is no sufficient reason why negative numbers cannot also have a square root.

So, what is the square root of -4? It is not -2, given that -2 x -2 = 4. So what is the answer? Here we see that we are missing an entire subset of numbers, those that, when squared, give a negative answer.

1 x 1 = 1 and -1 x -1 = 1 also. So, mathematicians ask, what is the square root of -1? To answer this they referred to the square root of -1 as i, meaning imaginary. i is the imaginary constant and the square roots of all negative numbers can be written in terms of i. i x i = -1, therefore we can now find the square root of -4. The answer is 2i, given that 2i x 2i = (2 x 2) x (i x i) = 4 x -1 = -4.

The imaginary constant provides the subset of numbers that allow for negative numbers to have square roots, thereby providing complete mathematics. These so-called imaginary numbers must also have ontological existence, just as the so-called real numbers do. They must also be represented on our giant cartesian co-ordinate system just as the real numbers are. Therefore there must exist an axis for imaginary numbers as well as the axes for real numbers.

The position of any particle in physical space-time must therefore be defined according to where it is along each axis in the cartesian system. There are three axes for the spacial dimensions (the x, y and z axes), all intersecting at the origin, so there must also be an axis for a fourth dimension of imaginary numbers, which can be called the w axis, also intersecting the others at the origin.

Any point in physical space-time must therefore have four co-ordinates, one for each axis. If we have two points in space-time and we know the four co-ordinates for each of them, we can work out the distance between the two points using Pythagoras’s theorem.

In two dimensions, the square of the distance between two points is equal to the square of the change in the x co-ordinate added to the square of the change in the y co-ordinate, i.e. d squared = x squared + y squared.

Adding dimensions has no effect on Pythagoras’s theorem. Therefore, in three dimensions d squared = x squared + y squared + z squared. For four dimensions d squared = x squared + y squared + z squared + w squared. However, the w axis is for imaginary numbers, so any co-ordinate on this axis will be in terms of i, the imaginary constant. Therefore, squaring this co-ordinate will always result in a negative number, as i x i = -1. Therefore, in four dimensions, w squared is always negative.

The presence of a negative when finding the distance between two points is astounding. Our senses have evolved to interpret the physical world in three dimensions, but we know, using reason, that there must exist a dimension for the imaginary numbers, which must have ontological existence. If the negative number happens to equal the sum of the other three numbers used to find the distance between two points, then that distance will actually be zero! We might perceive two points as being separate but there exists the possibility that they might actually be separated by zero distance once the fourth dimension is taken into account.

Thus we have proved, mathematically, that zero can be everywhere, although our senses don’t perceive it. Zero is mind, therefore mind is everywhere, permeating all existence. Given that we all have minds, how does this fourth dimension manifest itself to us? It does so not as space, but as time! We have evolved to experience time completely differently to how we experience space, but, mathematically, we can see that they are both merely mathematical dimensions that work in the same way.

Our senses lie to us about reality. Do not trust them. Trust only in reason, in rationality, in logic, in Mathematics! Only using these things can reality be discerned. Time is nothing but imaginary space. Any object that appears to us to be stationary in space is in fact still moving – through time, through the imaginary dimension.

As per the principle of sufficient reason, imaginary numbers must have ontological existence. Time is how we experience them. But if time is imaginary space, there is no sufficient reason why it would not exactly mirror space. We experience space as having three dimensions, yet I have just described the imaginary space (time) as a fourth dimension. This doesn’t make sense. Why would space have three dimensions and time only one? There is no sufficient reason for this. Therefore, we must conclude that time also has three dimensions. Just as there are three dimensions of space, there must also be three dimensions of time, three dimensions of imaginary numbers to mirror the three dimensions of space.

Therefore, the principle of sufficient reason has showed us that we live in a six dimensional universe. The universe is a giant cartesian co-ordinate system consisting of six axes all intersecting at the origin, three real axes and three imaginary axes. This system allows for every possible number to have ontological existence in the universe, all the positive real numbers, all the negative real numbers, all the positive imaginary numbers, all the negative imaginary numbers, and, most importantly of all, zero, the origin, the domain of mind, from which all matter arises.

Matter is described by all of the non-zero numbers. All of them. What happens if we add all of them together? Take all of the positive real numbers all the way to infinity and add them together. Then take all of the negative real numbers and add them together. Now add the two groups together. The answer is, of course, zero. The same is true of the positive and negative imaginary numbers. Therefore all numbers added together equal zero. Zero is not nothing, as it contains everything. Zero and infinity are basically the same thing. Mind is the domain described by zero and infinity.

This is the mathematical explanation of how mind and matter relate to one another. The problems of cartesian dualism are therefore solved, using mathematics. Mind and matter are both real and intimately linked by mathematics. The universe is mathematics.

“All is number”, said Pythagoras, 2,500 years ago!