Summary below - full article at (PDF) BUSY BEAVER’S FUTURE - Unravelling the Big Bang and Bypassing the Speed of Light in Infinite Space and Eternal Time
ABSTRACT
The theory of Special Relativity is credited to Albert Einstein. But months before Einstein published his work, the French mathematician Jules Henri Poincare published his results on the theory, and they were the same. However, Poincare’s work was purely mathematical while Einstein put things in a physical context. Poincare insisted that Einstein be given credit for discovering Special Relativity because he made it practical by incorporating physics. In the same spirit, the Busy Beaver function should not be restricted to maths but scientists ought to seek its application to the physical universe. The Busy Beaver (BB) function can be defined as “finding the smallest program that outputs as much data as possible and eventually halts” and consists of extraordinarily fast-growing numbers, representing the upper limit to how quickly things can grow eg the first BB(n) or Busy Beaver number is 1, the second number in the series is 6, and the fifth is 47,176,870. It’s a situation similar to the rapidity of the speed of light (claimed to be the greatest possible velocity at 299,792,458 metres per second). The fantastic fast growth of BB(n) also brings to mind the possibility of space, and its partner time, being literally infinite. The lower limit to how slowly BB(n) can grow is called the Sleepy Sloth (SS) function by Toby Ord at England’s Oxford University. It grows extraordinarily slowly. Like light’s speed, BB and SS may well exist in the reference frame used by humans but they might have no reality in the universal frame that considers all space-time as a unity. If everything in space and time is viewed as a singularity - a single entity - all periods of time would be united and concepts such as “quickly” and “slowly” would be irrelevant, belonging only to time that isn’t unified but is divided into past, present, and future. At the end of the article is a brief outline of an “imaginary computer” that is a program that outputs as much data as possible and eventually halts by making use of imaginary numbers, Wick rotation, time dilation, and space-time warping.