The Science of Life

This is an entry in the Basic Statistics Lecture Series which I have realized that I have failed to incorporate into the series so far, and I apologize for that.  This lecture is going to cover the basic calculations required for all of statistical analysis, on a fundamental level. When we collect statistical data, we typically collect it on a small part of the population as a whole.  The population is the entire group for which a sentiment holds true.  This small part of the population as a whole is called the sample of the population, or just sample for short.  The number of data points we collect -- the number of items in the sample -- is called the sample size, which is typically denoted by the letter n. In statistics, we typically calculate the arithmetic mean, which is the sum of all values divided by the sample size.  For the population as a whole, this is denoted by the greek letter μ (mu), and for a sample, it's denoted by x . The sample mean ...

I will begin with a conclusion which is... uncomfortable to say the least.  Then I will walk through how this conclusion was reached.  It is something which will have you call bullshit on me off the bat, but please hear me out (or read me out?).  I have written a theoretical ecology paper last summer which shows that the human population will stop growing no later than 2031, and will drop (not plateau) shortly thereafter.  The cause?  Resource depletion.  Please, read me out. Now, how did I come to this conclusion?  By the power of maths! In ecology, there is a situation where, when a major cause of death for a species is removed, the population of that species goes through what is called exponential growth .  This is where the rate of change (percent change) is constant, and since the population today is more than it was yesterday, the greater the net change.  Let's say the percent change is 1% and we started with $100.  Tomor...

In every physical science, we rely heavily on mathematical models to accomplish further scientific research.  (Yes, even you biologists and organic chemists; you just have the mathematical models hidden.)  Mathematical models are the key to all scientific research.  (And for those reading this from outside of the United States, I will use the word "sciences" in place of the term "physical sciences" from here on out; be prepared for that.) This brings up a key question; what exactly is a mathematical model? It would be good to have an equation fall under a mathematical model.  This can be the case, but more often than not, one equation is insufficient.  It also doesn't have to contain equations; there can also be inequalities, where a value is either less than or greater than a certain quantity. Mathematical models are descriptions of a system with mathematical language , which can be one or many equations or inequalities.  This is more of a...