Hausdorff dimension and fractals

Hi, this a part of my work in the course “Measure theory and integration” at the University of Calgary. I discuss the concept of Hausdorff dimension and its application to fractals. You can download the pdf file here

May 13, 2024 Â· 1 min

Resource theories and pieces of cakes

Conversion between objects I would like to begin this article with a question. Is there a way to turn bread into sugar? The answer from biology is yes. $$\textrm{Bread} \xrightarrow{\text{chewing}} \textrm{Smaller pieces of bread}$$ $$\textrm{Smaller pieces of bread} \xrightarrow{\text{enzyme}} \textrm{Sugar}$$ The question of whether or not there is a way is different from the question of whether or not the way is practical. A practicality question may ask whether or not a person can do this. The answer is still yes. A person can chew bread with their teeth and amylose in their saliva can break down the starch in the bread into disaccharide sugar. However, if we ask whether or not a tree can do this, the answer may be different. Obviously, a tree cannot chew bread. A tree might have another way to turn bread into sugar, but it is not the same way as a human does. ...

February 13, 2024 Â· 6 min

Wavefunction: superposition is not the lack of knowledge

A wavefunction is a mathematical object which represents a quantum state. Many would have been introduced to wavefunctions from Schrödinger’s cat or the double-slit experiment. However, there is a more straightforward way to present the concept of wavefunction without resorting to the complex historical development of physics. Often, the wavefunction is introduced by not knowing exactly where a particle is or its state. This is inaccurate because wavefunction is about something other than the lack of knowledge but the nature of quantum state and measurement. ...

January 20, 2024 Â· 5 min