Certainty is as unlikely as impossibility?
“The force that created the unimaginable splendors and the unimaginable horrors has taken refuge in us, and it will follow our commands.”
St. Catherine of Siena
“Do I contradict myself? Very well, then I contradict myself, I am large, I contain multitudes.”
Walt Whitman
“we believe that Lateral Gene Transfers (LGTs) are an important form of insertional mutagenesis. Perhaps now that putative bacterial DNA integrations have been identified in cancer, more researchers will look for these mutations in other diseases. A bacterial DNA integration that occurs in a human cell and leads to the expression of a bacterial compound recognized by the human immune system has the potential to trigger autoimmune disease, for example. Further research on the occurrence and consequences of LGT in human cells will likely reveal the phenomenon to be much more common and important than currently appreciated.”
Kelly Robinson and Julia Dunning Hotopp
We rarely portray Neanderthals, our close relatives, as telegenic. Museum exhibits give them wild tangles of hair and Hollywood reduces them to grunting unsophisticates. Their skulls suggest broad faces, tiny chins and jutting brows. But to mock Neanderthals is to mock ourselves: Homo sapiens had lots of sex with Homo neanderthalensis. Neanderthal genes supply between 1 per cent and 4 per cent of the genome in people from homelands on several continents, from Britain to Japan to Colombia.
DNA from another humanlike primate, the Denisovans, lurks in modern genomes, too. A molar and a chip of pinkie bone found in a Siberian cave provide what little information we have about this species. DNA extracted from the fragments previously revealed cross-species breeding. Yet a new study in the journal Cell shows that the ancient hanky-panky did not stop in Siberia: humans who travelled across South Asia mated with a separate group of Denisovans as well.
www.independent.co.uk/...
I myself know nothing, except just a little, enough to extract an argument from another man who is wise and to receive it fairly.
Socrates
Sadly most of us are not as wise as Socrates. One tool we can try to use to increase our wisdom is math. I have spent my life as a mathematical biologist trying to do exactly that. Part of that commitment is that I have taught Summer University and in the Scientists in the School programs of my first Alma Mater, the University of Alberta. These are programs designed to encourage young people to pursue careers in the sciences. Typically students are in Grades 6-10.
Because of my health problems I have been reducing my research work load. I have my own company that uses mathematical modelling to help clients and drive new research we can turn into intellectual property. I used to have a hand in every project, but the math and science soon passed me by. I realized the day would come I would have to walk away. It just came much earlier than I had planned. But I just can’t stop working with the kids.
In terms of science I am left working on just three projects. And I will be writing about each here at much greater length.
1. I am continuing my work on why there is such a difference in the miscarriage rates between populations resident for centuries at high altitude and populations that have moved to high altitude comparatively recently. I have been working on this problem for 45 years and my colleagues, generations of them, have collected immense amounts of data on blood chemistry and DNA that I am trying to find patterns in. I use non-linear large data tools like Functional Data Analysis to look for these patterns.
For those of you who are really interested my interest began with the Quechua of Peru. I got a job taking blood from some Quechua who had come to Edmonton, Alberta so physiologists and doctors could study their adaptations to high altitude. This was in February. It is just shy of forty below and they are wandering around in sandals and socks. But there feet are warm to the touch. As a joke they stood barefoot in a snow drift and the snow melted around their feet.
Anyway, it took a very long time, more than 70 years for the first child to be born to Spanish settlers who lived above 10,000 feet in Peru. The rate of miscarriage (nearly 100%) was stunning. And to this day the female descendants of those first Spanish settlers often still go to the coast once they know they are pregnant. This is because even with modern medicine they still have a far higher miscarriage rate than the Quechua whose rates of miscarriage are quite similar to the average for the world at large.
The Quechua have some very unique adaptations to high altitude living. Though which one leads to their ability to avoid miscarriages is not certain.
The exact same thing is true on the other side of the Andes with the Amaya. But here is the first twist in the tale. The Amaya have different adaptations than the Quechua.
But there is a population that has been resident at altitude for longer than the Quechua. Actually longer than the Quechua and the Amaya combined. These are the people of the Tibetan plateau. For 25,000 years they have lived as high or often higher than the Quechua and Amaya. But we have not yet found any adaptation they have. Their blood work and DNA looks like the average Han and Nakhi who live in the valleys not far away.
40 plus years and we still don’t know the answer to the question. But we have begun to think it has to do with which archaic hominid’s DNA the various populations carry. And we are fairly certain different bacterial DNA within the mitochondria of each population is involved in some way.
2. I am working on building a multi-dimensional model of how ants, bees, wasps (hornets), and termites communicate. They use a few chemicals to communicate immensely complicated things. Things that could not be captured with a simple binary model. This in turn implies maybe even makes necessary the existent of receptors for these chemicals that are analog. This project goes back 40 years and a few days.
This is what is known as a vanity project. I am funding it myself. It turns out to be exceedingly complex because different social insects use the same chemicals in very different ways. Some have also adapted to use sound to communicate. Others use flying dances, ground movements that look like dancing, or even what we believe are directional gestures. Some use all of the above and probably more things we haven’t detected.
Social insects really contain multitudes. They can be the queen, they can be a worker, they can be a soldier, and so on. Which role they end up in depends on the chemical signals they receive. Ants can touch each other with their antenna and instantly know what role each is playing on that occasion.
3. Finally we come to my last project and the one that is probably most relevant to today’s diary. I assume we all realize that some people make smarter decisions than other people. You may also know that a great deal of research has gone into understanding how people make decisions and what goes wrong. There is a great little book for lay people by Joseph T. Hallinan called Why We Make Mistakes (the s is reversed in the actual title but I couldn’t figure out how to do that). For those of you who want a more thorough grounding I would recommend the work of Daniel Kahneman starting with Thinking Fast and Slow. If you like that then you will love his early more scholarly Choices, Values, and Frames and Heuristics and Biases which is actually my favorite book.
Starting 13 years ago I began (well from day one all three of these projects have been team projects so we would be a better word for the project) working on creating algorithms to help people make smarter decisions. Our most commercially successful attempts are used in agricultural commodity trading to help with timing decisions and to help professional scouts in hockey avoid some obvious biases.
I have also continued to teach young people.
So with that background we will move on to the heart of today’s diary. But understand I plan to come back and write about all three of these projects in detail.
Lets begin with a simple thought experiment:
Remember back to your school days (some of you may be living this today). You are taking a test and the subject doesn’t matter. You work your way meticulously through the test from start to finish answering what you can. Then, as all the experts advice you being reviewing your answers. There are some of them you weren’t sure of when you first answered but now in review you think you were spot on the money. You take a shot at the questions you couldn’t answer the first time and then you turn in your paper.
You have made one bad mistake and a second lesser mistake. The bad mistake involves having not changed the answers you gave to the questions that caught your attention in your review. 80 years of studies have shown changing the answer is an equal or usually better decision in every study. What happens is you go from uncertain before you answer to certain when you review. It is harder than most people acknowledge to change our minds. Study after study has told students in advance that changing answers is the better strategy, some have even presented the evidence and yet still students tend to stick to their first answer.
The second lesser mistake is answering the test in order. The correct strategy is to read all the questions and answer one you know you know. As my Human Performance professor Kurt Wilberg was fond of saying it isn’t enough to know you have to know you know. One of the most important tests in his class was multiple choice right minus wrong 100 questions. Dr. Willberg told us in advance that for most of us just not answering any questions would be the best plan. He also told us that the class average was always below zero.
I tried to take his message to heart but I just couldn’t resist, I answered 10 questions. I got 6 right minus 4 wrong for 2 out of 100. I was devastated. Until I learned I was the best student in the class. I answered the fewest question and got the highest mark. Not a single student chose to answer none of the questions, which would have been the third highest mark in a class of over 40 students.
Dr. Willberg explained that it is actually quite hard to know anything with certainty. That is it is hard to know you know. And that things we know a great deal about tend to grow less certain in our minds as we begin to broaden our thinking and try to add to human knowledge which was our job as scholars in his opinion. In order to add something to a field of human knowledge we have to know the unresolved issues and questions in that field and that causes us to be a little less certain of our knowledge even as we learn more and more about it.
The main take home message here is that mathematical approaches to decision making though of obvious value mostly fail because people simply won’t take the advice. We humans are way to certain we are right to ever let math change or minds. Don’t get me wrong we will cite it at length and even misrepresent it to prove we are right but when it proves us wrong we just totally ignore it.
In fact our inability to understand math or accept its conclusions is at the heart of a growing epidemic of fallacy which is known as argument by ignorance. As I said it is hard to know anything for certain but we humans love certainty so we assume we know more than we do. Then we launch an argument or in many cases a lot of arguments based on this faulty knowledge. We don’t know we are wrong but our argument starts out doomed by our ignorance. If you think you’d never do this trust me, you have.
Most often what math proves is that the situation is far more complex than our simplistic view allows for and thus also manages to make use feel stupid. Don’t get me wrong. That isn’t a shot at humans in general or anybody in particular. Our ability to make smartish decisions quickly has been vital in our evolutionary success.
The problem is we don’t live in a simple world any more and we are struggling to fundamentally change how we think.
With that in mind here comes some math, I apologize if I make your eyes glaze over.
Math typically starts with definitions and here are some that are associated with all probability formulas;
Experiment: Any situation or phenomena and the method you chose to explore that situation or phenomena.
Outcome: The observed result of your experiment but also what you learn in the process of conducting the experiment.
Event: The combination of all possible outcomes of an experiment.
Sample space: The set of all possible outcomes or results.
Probability function: This is the tool we use to figure out the odds of each and every outcome happening or not happening.
The probability of the event is given by
Probability of Event = The number of wanted outcomes/The total possible number of outcomes
Let me pause here and say I will get to what you do when not all wanted outcomes are equally desirable and not all possible remaining outcomes are equally bad. But for that I will have to present some algebra and what is known as algebraic logic, particularly propositional algebraic logic and we will get there though probably not in this post. Research shows us that the more material we try to present the less likely humans are to change behaviours.
What is the probability to get a 6 when you roll a die?
A die has 6 sides, 1 side contain the number 6 that give us 1 wanted outcome in 6 possible outcomes.
Using the formula above the answer is 1/6.
So you can have independent events and dependent events.
One independent event has no effect on the other.
Now you need to know that if there are two independent events and you want to know the probability of both occuring your simply multiply the probabilities of each.
P(X and Y) = P(X)*P(Y)
So Imagine you are playing the kids game Yahtzee. The game is played with five dice and the total of the dice is used to create a score for a number of common poker hands and one that wouldn’t occur unless someone was cheating, five of a kind which is automatically 50 points even though a maximum score, five sixes would be 30 points.
You are trying to fill a full house and you have three sixes. So you need two fives if you want the maximum possible score. If you keep the three sixes (and why wouldn’t you since you can’t do any better) then you have two dice to roll. What is the probability you will roll two fives?
P(5 and 5) = P(5)*P(5) = 1/6*1/6 = 1/36
Now try something trickier. What is the chance of rolling a Yahtzee, getting five of a kind?
P(5 and 5 and 5 and 5 and 5) = P(5)*P(5)*P(5)*P(5)*P(5) = 1/6*1/6*1/6*1/6*1/6 = 1/7776
But wait surely we need to do this for 1,2,3,4,and 6 as well. Absolutely thus the chances of getting a Yahtzee on your first role with five dice is 6/7776.
And now it is going to get really tricky in Yahtzee you have three roles so what is the chance of coming up with a Yahtzee in three rolls rather than one. We are no longer dealing with independent variables and suddenly your decisions matter. The optimal answer if you make the right decision is 4.603% or roughly 1/22.
You can get here by using nothing more than a pencil and paper and what I have already told you. Though there are much more powerful tools which I will teach you in future diaries.
And now for bonus points how many times do you have to roll the dice to get a 95% certainty of getting a yahtzee. Again, I will give you the answer which is 23. But how do you get there?
By now you have probably figured out this is what I have quite recently been teaching aspiring young scientists. You are looking at the beginnings of game theory. I am going to skip over a ton of fun games and jump to where we ended up.
I am a fan of Bruce Bueno de Mesquita. Bruce is a master of game theory and one of its pioneers. Game theory is a fancy label for a simple idea: People compete, and they always do what they think is in their own best interest. Bruce wrote a truly great book, The Predictioneer’s Game, in 2009 that explains game theory and details how to play the Predictioneer’s Game. Which is where I end my introduction to Game Theory with my students.
So I gave this group of young people a number of options for questions and from that long list they picked a doozy.
Will climate change mean the end of humans?
In the end they decided no was the most probable outcome. Yup, they figure 5.4% of humans will survive +/- 3%, 95 times out of 100. Though of course those may be the ones with the most Denisovan, Neanderthal, archaic homonid, and Bacterial DNA, so not necessarily Homo sapiens or even human as we think of it. Maybe they will be better at decision making than we are.
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