User blog:Cloudy176/Simulating PEGG

A day or two ago, PsiCubed2 created an ever-growing googolism, or PEGG for short. I think this is a great idea, and I wanted to try out the idea a bit further, and wanted to know what will happen to PEGG in the future. So I decided to simulate it.

Since I don't think I can predict future values of Dow Jones, I slightly modified the definition of PEGG for our simulation purposes. Specifically, rule (a) in the definition is replaced with the following:

(a) We take the (days passed since 2017-05-08)-th integer in the result from the Random Integer Generator by random.org, where the minimum value is 1, the maximum value is 10, and the pregenerated randomization from 2017-05-08 is used (you'll need to switch to Advanced Mode to set this). Call it n.

The first 100 integers produced using the generator are:

10	2	8	8	3 2	9	4	9	5 7	3	8	4	4 8	5	9	3	9 8	2	8	7	2 5	5	4	2	8 2	4	6	4	5 3	4	3	1	5 2	3	5	10	3 7	10	1	8	1 8	3	2	4	2 3	2	10	9	1 7	2	10	2	6 6	6	1	6	6 5	10	5	1	4 8	10	3	2	8 4	2	3	6	3 9	5	7	4	6 6	1	1	6	2 10	6	9	3	9

(The numbers are read from left-to-right, then downwards.)

Using these values, I simulated what happens in the first 100 days in this modified definition of PEGG.

At the beginning, Y = "E", Z = 0.01, and K = 1000. The simulation starts as follows (See this post for the defintion of Letter Notation):

At this point, we should switch to the letter F, and need to find a value m such that Fm = E10.43. Since rule (e-3) only requires us to reach a certain digits of precision after decimal point (currently 3 digits), we can use, say, binary search to determine the value.

Some calculations later, I found:


 * F2.007 = EE(10^0.007) = EE1.0162... = E10.3812...
 * F2.008 = EE(10^0.008) = EE1.0185... = E10.4373...

Therefore F2.007 < E10.43 < F2.008. So the new value for X is 2.007.

The values are updated to Y = "F", Z = 0.007, and K = 10000, and the simulation continues:

(Notice that the simulated PEGG first surpasses a googol on June 4.)

At this point, another switch is required. Since 10.001 is very close to 10, we expect that the new value of X is 2. In fact:


 * G2.0000 = FF1 = F10
 * G2.0001 = FF(10^0.0001) = FF1.00023... = FE(10^0.00023...) = FE1.00053... = F10.01222...

Therefore G2.0000 < F10.001 < G2.0001, and the new value for X is 2.

The values are updated to Y = "G", Z = 0.0049, and K = 100000, and the simulation continues:

This concludes the first 100 days of the simulation of (modified) PEGG. I think the real PEGG would behave similarly, provided that the "Dow Johns rule" indeed produces pseudorandom numbers.