Are all three of you there now? I hope so. This letter is more an attempt to try to get back to writing stuff really relevant to the books as well as to my theory and the relevance of time as a geometric variable. We all know that a 3-ball is defined by the equation:
X² + Y² +Z² ≤R²
Note that the equation is a “less than or equal to” statement. An equality would define the two-dimensional cover to the three–dimensional ball. If we add time (T), we can create a 4-ball with time as the fourth dimension.
X² + Y² +Z² + T² ≤R²
However, taking a cue from the fascinating book, “Flatlands” by Edwin Abbot in which he describes a three-dimensional object passing through his two-dimensional world. The spherical object appears as an expanding and then contracting circle. In fact the third dimension has been converted to change, which we can call time. In our case the world is a 3-d ball. The fourth dimension will be converted to time. This can be expressed in an equation:
X² + Y² +Z² ≤ R² – T²
Note that as T approaches R in values the value on the left side of the equation becomes smaller. That is to say the 3-d ball becomes smaller. As T approaches zero, the ball becomes larger. The equation above, with one less variable, would explain Abbot’s example.
However, my theory assumes that that the universe is the 3-d cover of a 4-d ball. Throwing in time, the equation becomes:
W² +X² + Y² +Z² +T² = R²
Moving time to the other side of the equation, we have:
W² +X² + Y² +Z² = R² – T²
Now what we are talking about is a “real” universe, it is obvious we are talking about the Big Bang. Suppose at one time T equalled R. The 4-d sphere that supports our 3-d cover would be non-existent. All would be time. Then suddenly time started to collapse and the universe just as suddenly expand. That would be the Big Bang. It would continue to expand until the value of time reached zero. At that time our universe would have reached its maximum size. If at some point time started to grow, our universe would start to collapse. Eventually T would equal R and the cycle might start all over again.
This equation is much like Jeevra’s except for the sign. She wrote it:
R² = X²+Y² + Z² +W²-T² or R²+T² = X²+Y² + Z² +W²
In her equation time was never zero and neither was the sphere. Her equation did not explain the Big Bang, but it did take steps to explain faster-than-light travel.
As you can see in my first book, “Pygmalion Conspiracy”, there is no reason that many dimensions could not be involved. In the Tovazi’s “Holy Book”, there is the following passage:
6) The Great God Lemma created a mighty void of more
dimensions than one could count. In that void, He created
a sphere of ten dimensions.
7) The other Great Gods were astonished. They watched as
He supplied a spark to the void.
8) There it floated in the void for a long time gathering
strange energy from the void. Finally, it had gathered
more energy than it could hold, and with an unbelievable
bang, it expanded in every direction at nearly infinite
speed, creating a four-dimensioned sphere with a three-dimensioned
The equations below show how a 4-d universe could evolve by the collapse of time and other dimensions producing a Big Bang. Note that in the below equation, Di is an extra dimension.
W² +X² + Y² +Z²+T²+ΣDi²= R²
W² +X² + Y² +Z² = R² –T² –ΣDi²
While looking at spheres and hyperspheres, I discovered an interesting phenomenon that I can not explain. I’ll start with a small example. The volume (area) of a disk is: πR², while the circumference is 2πR. Multiply the two and you get: 2π²R³, which is the volume of the 3-d cover of a 4-d ball. If you multiply 2πR times the volume of a 3-d ball, you get the volume of the 4-d cover of a 5-d ball. Finally, if you multiply 2πR times the cover of a 100-d ball you get the volume of the 101-d cover of a 102-d ball, etc. 2πR appears to be the universal multiplier, but why?
Well, I’ll stop now. I would be excited to be visited by any of you.