My favourite interest is exactly how can we view the world so what science tells us is intuitive.
Introduction This elaborates some of the claims in my insights article on digital audio. The Sinc Function The first link in my insights article has a section on filters, but I will detail the most critical case. The bit depth is assumed to be so large for all practical purposes that it is infinite, and…
Introduction First, we need some background in Digital Signals. This can be mathematically quite advanced, but since I would like this article to be accessible to as wide an audience as possible, here is a link that explains what is needed (not even Calculus is required): https://brianmcfee.net/dstbook-site/content/intro.html An important point not emphasized in the above…
Introduction I am convinced students learn Calculus far too late. In my view, there has never been a good reason for this. In the US, they go through this sequence of Pre-Algebra, Algebra 1, Geometry, Algebra 2, Precalculus, Calculus 1, and Calculus 2. But is this required? Recently I came across two books that turned…
Introduction When doing mathematics, we usually take for granted what natural numbers, integers, and rationals are. They are pretty intuitive. Going from rational numbers to reals is more complicated. The easiest way at the start is probably infinite decimals. Dedekind Cuts can be used to get a bit more fancy. A Dedekind cut is a…
Introduction When I learned calculus, the intuitive idea of infinitesimal was used. These are real numbers so small that, for all practical purposes (say 1/trillion to the power of a trillion) can be thrown away because they are negligible. That way, when defining the derivative, for example, you do not run into 0/0, but when…
Introduction When I learned calculus, the intuitive idea of infinitesimal was used. These are real numbers so small that, for all practical purposes (say 1/trillion to the power of a trillion) can be thrown away because they are negligible. That way, when defining the derivative, for example, you do not run into 0/0, but when…
Introduction First, for background, here is an overview of the most common video compression standard in use today, H264: https://www.maketecheasier.com/how-video-compression-works/ H265 has improved on this, but for various reasons, it was a bit of a flop. It is in use and will continue to grow, but royalty issues are a problem. To try and address…
Recursion is quite simple. It’s a subroutine calling itself. It’s surprising but some problems that look quite hard can be trivial using recursion – but be wary – as I hope to explain there are traps you need to consider especially if working in a team environment. When I studied Computer Science the first language…
In my paper on renormalisation I mentioned what most who have studied calculations in Quantum Field Theory find, it’s rather complicated and mind-numbing. I am not sure doing these is that illuminating of anything, but every now and then you got to do, what you got to do, so I would like to go through…
Introduction This is a follow on from my paper explaining renormalization. A question was raised – why exactly do we need a cut-off. There is a deep reason to do with dimensional analysis, and the power series expansion used in perturbation theory. Along the way, we will see renormalization in a more general setting, and…
What Is The Issue With Renormalisation If you have an interest in physics you have likely come across renormalisation before, although what it really is would probably have not been explained. Instead, you would read Dirac never accepted it, Feynman called it a ‘dippy process’, and if you look under a quantum theorists rug you…