Investigating Random Properties for Deterministic Constants

The main purpose for the thesis is to identify the random features for pi, e and a comparable pseudo-random number, all of which are deterministic in the sense that they follow a recursive pattern. Despite their deterministic nature, whether these numbers are random or not is an important problem for both science and philosophy. While they are calculable, they remain unpredictable because of any observable pattern. The definition for random is that which proceeds, makes, or occurs without definite aim, reason, or pattern. The statistical significance for random is that of or characterizing a process of selection in which each member of a set has a probability of being chosen. Ehrenfest model is the key part of our work. We use this model to investigate the property of randomness in the above mentioned constants. Every calculation we discuss in the thesis is based on the Ehrenfet model. There are two states in the model. The initial state for all balls is the same. Once a number is picked from the constants, the state for the corresponded ball should be changed. If the number is picked up randomly, according to the statistic explanation for random. The entropy for the model would reach the maximum in a long run. The average quantity of balls in one of the two states would be half of the original quantity. According to the second law of thermodynamics, the entropy would increase rather than decrease in a system before reaching maximum.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Physics

Grantor dc:publisher

University of Akron

Year dc:date

2013

Author dc:creator

• Pang, Wei

Contributors dc:contributor

• Gujrati, Purushottam

• Physics
• random pi

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=akron1362769797

OAI identifier oai:identifier

oai:etd.ohiolink.edu:akron1362769797