Statistics as the Logic of Science
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The Derivation of the Normal Distribution
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Limits, the First Step into Calculus
The concept of a limit is the central idea that underlies calculus and is the unifying mechanism that allows for differentials and integrals to be related. Calculus is used to model real-life phenomena in the language of mathematics. Anything that involves a rate of...
What is an Integral?
The integral is a method to find the area under a curve. It is formulated as a sum of many smaller areas that approximate the area of the curve, all added together to find the total area. We let the number of areas under the curve approach infinity so the...
The Natural Logarithm Rules
The 4 rules of ln
1. ln(ab) = ln(a) + ln(b)
2. ln(a/b) = ln(a) – ln(b)
3. ln(1/x) = -ln(x)
4. ln(a^b)=b ln(a)
The Art of Argumentation-Making: Statistics as Modern Rhetoric
The process of statistical measurement is used to make precise the evaluation of a claim relies upon our assumptions about the sampling measurement process and the empirical phenomena measured. The independence of the sampling measurements leads to the...
Continuous Democracy System
The future of participatory direct democracy, as advocated by Bernie Sander, lies in information systems of coordination that allow deep public opinion to be integrated within a whole reflexive administrative state. The ideal of a fully adaptive and sensitive...
The Bias of 1-D Opinion Polling: Explaining the Low Polling Numbers for Candidate Beto O’Rourke
In Electoral Opinion Sampling, whether of candidates, policies, or values, it is commonplace to ask subjects yes/no questions, where someone either choses one person out of a list of candidates or says whether or not he or she agrees or disagrees with a political...
Quantum Computing Democracy
Consider the binary computer. All bits have one of two states either 0 or 1, symbolic for 'off' and 'on' with reference to a circuit as symbolic of a 'fact of the world' propositionally, A is true or false. In a quantum computer, the states may be occupied in...
The Bias of Underreporting in Experimental Design: Ranked-Choice Voting & The Case of the Latino Vote
The ‘hidden 2nd-place bias’ from my previous blog post <a href=“blog 1”> is due to a bias in the question-asking of political candidate polling, neglecting a necessary ambiguity in the answer when it can’t be precisely known. This ambiguity is essential to the...