Trailblazing Research
   Home      Mathematics of Infinity

Dr. Allen Klein developed two major systems of mathematics.  The first is called Multi-dimensional mathematics, and the second is called Infinimatics, or the Infinimatic Theory

Multi-dimensional Mathematics

In conventional analytic geometry, equations are used to describe deiferent dimensions.  In multi-dimensional mathematics, the equations themselves are in different dimensions.  Thus, a multi-level dimensional system can be created to model our multi-dimensional real universe.  In this system, some equations can be put in one level or dimension to describe or govern the events at that  one level or dimension, and different equations can be put into a different level or dimension to describe or govern the events in that level or dimension. 

The Infinimatic Theory

The Infinimatic Theory is based on the fundamental premise “that the universe is infinite in time and space, matter and energy.”  In his Infinimatic Theory, Dr. Klein postulates “the universe is not only infinite, it is absolutely infinite.  Thus, there exist higher order infinities.”  The Infinimatic Theory includes “infinimatics,” which is a whole new system of mathematics that describes rules, processes, and principles for manipulating infinite quantities, and higher order infinites. 

The Infinimatic Theory also includes a model of the universe that corresponds with Infinimatics. Dr. Klein was able to solve some of the problems encountered in his other theories using concepts and processes from Infinimatics.

The following are a few of the concepts described in the Infinimatic Theory.

Infinite Inference.  If a certain quantity of something, n, exists in nature, and if n is greater than one, and if n may be attached to an infinity, then by “infinite inference’, n is also an infinity (or infinite quantity).

The two infinites may not equal each other (see inequality of infinites).  Thus, if the number of stars is an infinity (an infinite number), and for each star, there are approximately 10 planets, then by infinite inference, the number of planets is also an infinity.

Thus, for example, if we find that for every one hundred billion to one trillion stars are grouped together into a galaxy, then by infinite inference, the number of galaxies is also an infinity.

Inequality of infinities.   Just because two quantities are infinite does not mean they are equal.  Two infinities (two infinite quantities) can be different or not equal each other, but still be infinite.  For example, the number of stars in the universe is an infinity (an infinite number).  If there are approximately 100 moons for each star, then the number of moons is also an infinity (an infinite number), but the number of moons is not equal to the number of stars.

The inverse infinity Absolute Zero.   Absolute zero may be thought  of as an inverse infinity.  Just as a line is infinite in one direction and we cannot reach the end of a line, we cannot reach absolute zero temperature, absolute zero pressure,  or absolute zero energy.  We may be able to reach one-millionth of one degree K.  This is a very small number, but not the smallest.  There is no smallest number.  For we can take one divided by larger and larger numbers to get smaller and smaller numbers without limit.  Thus, we cannot reach absolute zero temperature.  Since it is like the reciprocal of larger and larger numbers, it may be thought of as an inverse infinity.

Higher order infinities.   Higher order infinities include infinity squared, infinity cubed, infinity to the fourth power, infinity to the fifth power, etc.  These higher order infinities may represent two dimensional space, three dimensional space, four dimensional space, five dimensional space, etc. respectively.

The human mind can usually only comprehend three dimensions at a time,. This does not mean  higher or more dimensions do not  exist—we just have a hard time comprehending them.   In essence, we are like an ant on a staircase.  An ant on one step can only see the floor and wall of that step he is on.   The ant cannot see the steps above or below him.  If the ant crawls to a higher step, he can only see that step,   He loses sight of his previous step.

Similarly, for us to comprehend higher order infinities (higher dimensions),  we must let go of the previous dimensions.  Thus, for us to see through a telescope, we have to let go of our present world to see things on a larger scale.

Likewise, to see smaller or lower dimensions, as we look into a microscope, we also must let go of our present world.  To see things on a subatomic scale, we need to let go of even the microscopic scale.  There are many higher order infinities (higher dimensions) above and below our own, we just may have to climb several steps to get there.   

Infinite conversion.   Sometimes, we encounter infinitely complex problems.  To solve such problems, we may be able to use infinite conversion to convert the infinitely complex problem into a finite number of infinities.  We may then use other processes of infinimatics to manipulate these finite number of infinities into a form where we can solve the problem.

Crossing an infinity.   Crossing an infinity is a mental leap into a higher level  of consciousness to solve a complex problem or go to a higher dimension to solve a problem.

Einstein once said, “The problems encountered in this level of consciousness cannot be solved in this level of consciousness.”  In essence, we must go to a higher level of consciousness.

For example, if the problem  is on a two dimensional level (a plane), we must go to a three dimensional level to go above the problem to see the solution.  Sometimes, we may need to go to the fifth, sixth, or even higher dimension to solve a problem.

Another example:  to go from non-life to life, we must cross an infinity.