Originally posted by ranyart
This paper is really thought provoking in its reasoning behind the HUP and how it imposes upon Maths and Physics.
http://uk.arxiv.org/PS_cache/quant-ph/pdf/0402/0402197.pdf
Originally posted by selfAdjoint
The paper is not about determinism, but completeness, specifically algortihmic completeness a la Chaitin.
Uncertainty in mathematics and physics refers to the unpredictability or lack of certainty in the outcome of a mathematical or physical phenomenon. It is the result of incomplete information or limitations in measurement and observation.
Uncertainty and randomness are often used interchangeably, but they are not the same concept. Randomness refers to the lack of a pattern or predictability in a sequence of events or outcomes. Uncertainty, on the other hand, can be the result of randomness but can also be caused by other factors such as incomplete knowledge or inherent variability.
Yes, uncertainty can be quantified and represented mathematically. In mathematics, it is often represented by a range or margin of error in a calculation or measurement. In physics, uncertainty is often expressed as the standard deviation or error in a measurement or experimental result.
Uncertainty plays a significant role in scientific research and experimentation. It is a crucial factor in determining the validity and reliability of results. Scientists must consider and account for uncertainty in their methods and interpretations to ensure the accuracy and credibility of their findings.
No, uncertainty cannot be completely eliminated in mathematics and physics. It is an inherent part of these fields due to the limitations of human knowledge and measurement. However, scientists and mathematicians continue to develop methods and techniques to minimize and manage uncertainty in their work.