The Amateur Society Minutes – September 16, 2014 **Note: these are minutes from the meeting prior to the one this past Tuesday, the notes on cosmology will be up soon*** We introduce this meeting with a minute of silence. This can be spent in prayer, meditation, or simple quiet. The purpose is to refocus our perspective away from the considerations of our day to day affairs and to onto a pursuit of the truth. Motivating topic: How numbers can be misused The group watches a video from Sam Savage on The Flaw of Averages (https://youtube/watch?v=j3zKgAetG5k). The essential point is that summary statistics such as averages don’t capture measures of uncertainty, and in many situations this leads to adverse planning and suboptimal outcomes. Average, or mean, as a measure can be extremely misleading. Steven M: Numerical summaries cannot contain the entire truth for a set of more than one observation. Statistics attempts to analyze numerical information. Numbers contain information in the same way that words do. In fact, often the information content in numbers is much more precise than words. Consider that if an up or down vote on a proposition leads to one alternative winning by one vote, the change of any vote on the winning side would be sufficient to change the outcome. Indeed, every vote for the winning measure was the deciding vote. We have an intuitive sense that numbers make a difference. The precision required of mathematical truths points us to this. Steven M: Probability is both poorly taught and poorly understood in standard parlance and conversation. To say something will probably happen is a vague statement we often make. Consider the flipping of a fair coin, 0.5 likelihood of heads and 0.5 likelihood of tails. For zero flips there is only one possibility. For one flip there are two possibilities. For two flips there are four possibilities. For three flips there are eight possibilities, and so on with 2^n possibilities for n flips. As we increase the number of flips and examine the total number of heads, that number becomes approximately normally distributed. The basic principle of hypothesis testing is assuming a distribution of outcomes, measuring an outcome, and then calculating the probability that the observed outcome could arise from the assumed distribution. If the probability is sufficiently low (typically under 5%), there is reason to reject the assumed distribution of outcomes at that level of confidence. Hypothesis testing, however, doesn’t tell us anything specific about the actual distribution of outcomes. It is possible to flip 20 heads in a row even though it is extremely unlikely. Steven M: Numbers can be puzzling. Consider the ancient paradox: to get from point A to point B you must get to the midpoint. But in order to get to the midpoint B’ you must get to the midpoint between A and B’, and so on and so forth. Thus it appears you need to proceed through an infinite number of these midpoint intervals in order to reach your destination, which cannot be done in a finite period of time. Common sense views this as odd, because it would imply that motion is impossible, yet who would deny the reality of motion? The issue of the paradox was mathematical. Because the ancient Greeks did not have a concept of zero because of their a priori metaphysical rejection of the vacuum, they could not develop limits or calculus of the infinite. It has been conjectured that the ancient Greeks would have developed calculus if they had a notion of zero in their mathematical systems. Steven M: When we approach statistics in everyday life, we typically simply absorb them and fit them into whatever paradigm we like. Instead, we need to recognize the iterative process of statistic that includes postulating assumptions at every turn. Statistics claiming to discover some truth about life are much less cut and dry than their reportage would make them appear. The most dangerous aspect of statistics is that if you have a direct goal in mind, statistically, you can simply run calculations and observations until you find some sort of agreement. Essentially, if you have the time and wherewithal, you can demonstrate anything you like through statistical methods and most observers will view it as an objectively established truth. Steven M: Consider the example of a medical test. If it tells you the test is 95% accurate and you take the test and get a positive reading, should you expect that you actually have whatever is being tested for? Perhaps, yet perhaps not. There are two types of error, false negative and false positive. Proper statistical techniques can help to manage and minimize these errors, but they exist nonetheless. We have to look at various base rates in order to get the complete picture. By the same token, polls and surveys can be subtly manipulated with any conclusion in mind. Opinion surveys measure response and confirmation bias better than they measure opinion. The truth is more often than not more nuanced than a yes/no or a five point scale. Because we have an urgent need to quantify and convince, we assemble numbers rather than appeal to argument and truth. Politicians often appeal to the ‘average voter’ as someone holding to the average opinions of society. It doesn’t matter that on the gradations of issues, there may indeed be no such average voter and that not even one solitary individual would accept the ‘average voter’ policies. Perhaps generalizing, numbers and statistics are ways to subtly siphon off the human element into a form that we can perform simple calculations on. Steven M: We commonly make three kinds of errors. First, we are terrible at understanding summary statistics in that we give them more import than they actually have. Second, we are horrendous at understanding probability intuitively because we don’t engage with the necessary uncertainties deliberately enough. Last, even if we have perfect data, there is no universal standard on how to report it and so we end up making up whatever we wanted to say in the first place. On top of this, we use correlation and causation interchangeably, an egregious error. Causality is impossible to demonstrate with statistics alone, we need a valid argument from true premises to even begin to make a guess at causality. But one wouldn’t know that from the slipshod way statistics are presented in popular culture. Jon M: We typically treat the things we use to determine relationships as causal when we have no standing to. This occurs in all walks of life in all forms. Courtney C: Perhaps there is just an element of sensationalism to the claims. Look at fortune tellers or websites like Buzzfeed that drive traffic off of oblique feelings of user identification. Dan K: When we start to cling to even one assumption there arises a tendency to cling to all assumptions. Jon M: People typically just want to belong, as social considerations outweigh judgments of truth or falsehood. It is frightening because if you are trapped you will not see yourself as trapped and are thereby capable of being misled systematically. Courtney C: Everyone wants to be defined, so where does this leave us. Can we believe in anything if practically all of the messaging we see is deliberately misleading? Jon M: The world is indeed permeated by lies. Dan K: Good mathematicians should be capable of representing math the right way. We need to be cognizant, but there will always be something out of our reach statistically. Steven M: How do we cope? When everyone is in a passive mode we open ourselves up to misleading influences. Indeed, plenty of philosophers claim that truth itself doesn’t have power, rather it is the will to power that creates contextual truths by impacting the world. This is particularly bleak, but the question is… Is it true? There is always an amount of uncertainty, and probability itself comes on a probabilistic scale. How can you tell if you’re being misled? You can do the calculations, or at the very least get a better sense of what flipping a coin is like. Essentially, truth is challenging, but this is why we need to explore a variety of ideas, cross reference, and weed out contradictions. In order to do this we need to be able to interface with both numbers and truth-directed argumentation. If something is logically impossible we know it doesn’t matter what the statistics say.
Posted on: Fri, 03 Oct 2014 19:46:05 +0000