My Notes from "Calling Bullshit: The Art of Skepticism in a Data-Driven World"

Calling Bullshit: The Art of Skepticism in a Data-Driven World by Carl T. Bergstrom
My rating: 5 of 5 stars

A good review, for scientists and engineers, and probably news to the liberal arts culture (reference C. P. Snow's "The Two Cultures"), of the current use of numbers, statistics and charts to mislead readers.

The final chapter "Refuting Bullshit" is the best chapter of the book. Read this chapter first if you are in a hurry. Then fill any gaps in understanding by reviewing the previous chapters and sections as needed.

Page 232 says, "A single study doesn't tell you much about what the world is like. It has little value unless you know the rest of the literature and have a sense about how to integrate these findings with previous ones. Researchers weigh the evidence across multiple studies and try to understand why multiple studies often produce seemingly inconsistent results."

They quote Jonathan Swift, "Falsehood flies, and truth comes limping after it."


In chapter 9 he explains a principle called the "base rate fallacy" based on the statistical concept of "p-value."

He uses several examples, one is a suspect whose finger print matches the finger print on file with the police. The reported odds of this are one in 10 million. But the probability that the suspect is guilty requires that we know how many other peoples have the matching finger print. It turns out that in a database of 50 million, 5 other people are a match also.

Therefore the odds of the person being guilty are one in five, not one in 50 million!

When the suspect comes up with a matching finger print then the probability must evaluated agains all the others who also have a matching finger print.

He provides more examples, Lyme disease testing, testing for ESP with playing cards, why so many "proven" science results cannot be duplicated by other scientists. If you come up positive on a Lyme disease test the probability of your having Lyme disease must be based on the population of positive results. How many false positives for Lyme exist? At the time of this book, it was a surprisingly large percentage.

My take away is the the "p-value" error may be like finding theories to fit the data. About as bad as selecting data to fit the theory. For theories based on research of huge amounts of data, data can always be found to support many spurious correlations.

[Please note that they say matching finger print, distinct from the same finger print.]
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Self Awareness through Literature

Wonderworks: The 25 Most Powerful Inventions in the History of Literature by Angus Fletcher
My rating: 5 of 5 stars

I have not read Wonderworks since May 25th, 2022. I asked myself why I was putting it off. I realized that the underlying idea that most of what we do is driven by how we feel is a little bit depressing. It is like I am a puppet on biochemical strings, endorphins, adrenaline, oxytocin, dopamine. On the other hand I have enhanced awareness of how my body feels and how it is affected by my thoughts, food, and exercise. Intellectually I have known about this for a long time, but I am becoming aware of it at a deeper, more direct level than before.

For years I have puzzled over the difference between awareness, attention and knowing. In summary, awareness is direct perception of what is happening in my body. It is wordless, knowledge that does not come through ideas or perception. I found this discussion and distinction in Mortimer Adler’s theory of language presented in his small book “Some Questions about Language” page 99 in chapter 4, question number six. I found that going to any one section of this book and trying to read it for a quick answer to my questions is incomprehensible without first studying the intellectual scaffold of all the preceding pages. I had to be very patient to get to page 99 and I found that I could not read this book in anything but short doses each day. Almost as difficult as studying my mathematics books.

So back to Wonderworks, I immediately see that what I get from books I also get from my own thoughts and memories. In a sense every thought or memory is a potential story and produces its own feeling in me. I was surprised to recognize that the first thing I do when I wake up in the morning is to find thoughts and possibilities that inspire me to get up and get things done, until this new awareness I just thought it was a result of habit and my good character, ;).

What it really is, is using my imagination to manage my body chemistry to excite myself into action. What a great tool that I didn’t even know I was using automatically. If anyone had asked me prior to starting to read Wonderworks, I would have said that I can call on my imagination to manage my feelings, but I don’t do it except on rare occasions when I feel in need of a little extra grit or happiness. Now I see it happens all the time, I am a continuous flow of feelings driven by my behavior and diet. But I am more than this in a way that I can’t yet describe yet.

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Notes from "Twilight of Democracy" by Anne Applebaum

Twilight of Democracy: The Seductive Lure of Authoritarianism by Anne Applebaum
My rating: 3 of 5 stars

I gained several valuable insights from this book:

On page 16 she cites the work of Karen Stenner (https://www.karenstenner.com), a behavioral economist, who argued that about a third of the population in any country has what she calls an authoritarian predisposition, a word that is more useful than personality, because it is less rigid. Authoritarianism appeals to people who cannot tolerate complexity.

On page 29 she says "If you are someone who believes that you deserve to rule, then your motivation to attack the elite, pack the courts, and warp the press to achieve you ambitions is strong. Resentment, envy and above all the belief that the "system" is unfair--not just to the country but to you--these are important sentiments among the nativist ideologues of the Polish right, so much so that it is not easy to pick apart their personal and political motives.
Then she goes on to delve into a case study of this phenomena by looking at two brothers who went in opposite ways. Very interesting.

On page 38 she distinguishes between the "Big Lie" and the "Medium-Size Lie" use in propaganda. The effort to avoid the facts of reality, but still have the lies believed, lead to these lies.

On page 45 she continues a specific discussion of conspiracy theory in Polish politics by generalizing that "The emotional appeal of a conspiracy theory is in its simplicity. It explains away complex phenomena, accounts for chance and accidents, offers the believer the satisfying sense of having special, privileged access to the truth."

On page 144, she quotes others from de Tocqueville to Reagan "... that American patriotism is unique, both then and later, was the fact that it was never explicitly connected to a single ethnic identity with a single origin in a single ethnic identity with a single origin in a single space." {To me this seems like common sense, but apparently not if someone needs to emphasize it.}



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Mathematics, Why am I studying my college textbooks?

First I want to have a better understanding of what my mind does in the process of solving mathematical problems, proving theorems and general propositions in mathematics.  Why do I want this? Because I plan to develop a deeper understanding of Objectivist epistemology compared to the one presented by Mortimer J. Adler’s “The Four Dimensions of Philosophy” and “Ten Philosophical Mistakes”.  Adler’s “object of thought” vs Rand’s “mental entity.” 

A second reason for deepening my knowledge of calculus and related topics in topology and abstract algebra is to be able to read Penrose’s “The Road to Reality.”   Penrose suggests in his preface to the book that by working through the exercises he presents, an interested reader can gain better knowledge of the mathematics that powers quantum physics.  His exercises  worked fine for me up to about chapter 5 where he asks for proof of his expansion of exponentials in radial coordinates as an exercise for the interested reader.  I recognized the process, but I don’t think I ever mastered in the first time around in my calculus, or physics, courses.  Then he goes way deeper into Complex Analysis than I ever did.  I disposed of my Complex Analysis book when we were paring down our possessions.  Fortunately Penrose recommended a complex analysis textbook  by one of his students. It is available for free on-line, and I am excited for the chance to study it.

Third, my high school assessment of psychology let to math as the “perfection” of human thinking, thus the pinnacle of psychological study.  Inspired by Isaac Asimov’s “Second Foundation” novel.

My reading Feynman’s biography by James Gleick “Genius” clarified the distinction for me that Penrose had alluded to, understanding more than just manipulating symbols but grasping the meanings of the equations in as near a sensory manner as possible.  Rand speaks of this in her essays about rationality, but never dives deep into it the way the physicists do.

Coincidentally, I am reading a history of economic thought in “Hayek’s Challenge” by Bruce Caldwell.  The history cites epistemological errors in the use of abstract concepts by brilliant people in the early 1900’s.  Sadly I still run across many of these same kinds of errors in current social, economic, news, and other reporting.  

My best guess is that many of these people come from a literary background and have no hands on appreciation for the role of abstract concepts used as tools to understand reality.  It as if I told them about a the concept of a circle, they would want to see empirical proof that it exists, else what good is it?  How many studies have we heard about over the years that dig into the causes of poverty, and they always come up with the same answer.  I can remember at least three that I have listened to, while commuting to work, over the decades.  It is reassuring that they all get the same answer, but does the endless accumulation of data ever going to give something essentially new?  It is like going out and gather data on all the examples of circles in the world in an attempt to prove the concept of circle.  Each area of knowledge has its own modes of investigation, and proof.  History is not the same as mathematics, chemistry is not the same as economics.  The problem with economic research is trying to meet the demand for forecasting in order to support state policy.  

Politics motivated the money spent in educating economists, hence economists doe the best they can to support providing the desires of politicians to “control” the economy for the benefit of the “common good,” e.g. more votes, more money for politicians.  I believe this phenomena explains I. Kant’s theories of reason, and ethics.  To support his Prussian King.

Example of learning, the definition of a function:

My initial steps were a cursory review of material that I “thought I knew.”  Well maybe I missed some of the nuances, such as. the definition of supply set, that I glossed over because it seemed pretty trivial.  The contents of the domain are drawn from the supply set.

The resistance to learning the formal definition of a function was that I had an intrinsic preference for curves instead of ordered pairs.  Because I feel very bored with infinite series, number theory, set theory, fields, all the algebraic reasoning that goes into this stuff.  

As I continue to study math, I make more and more connections between fields of math that I had not appreciated before.  Algebra (abstract algebra), matrices, calculus, series, polynomials, the limits of what may be calculated.

As I observe the back and forth of imagination and logic I develop a much greater personal appreciation for imagination.  Some how this study has also allowed me to recognize the allusions to this imagination-logic process by all sorts of people.  Allusions that I would have not and did not notice in the past.

Even current debate in mathematical theory about teaching and understanding calculus, a geometrical, image based (imaginative) approach or a more formal abstract explanation based in proven number theory,  delta-epsilon proofs.  The debate is still current and driving other lines of mathematical investigation.  

What would make this discussion more interesting would be the demonstration of the various findings and writings of these uses and discussions of imagination and logic.  Imagination comes before logic in our thinking, both developmentally and functionally, but many people stop at imagination because it moves so quickly and feels so satisfying, but really it is a short cut to thinking by skipping verification of imagination by the use of logic and establishing consistency with prior knowledge.  Even Kant mentions the importance of confirming imagination by logic unless it is his special intuition.  

[TODO: Quote Kant on above comments about verification of imagination]

Quotes from "The New Tsar: The Rise and Reign of Vladimir Putin"

 

The New Tsar: The Rise and Reign of Vladimir Putin by Steven Lee Myers
My rating: 5 of 5 stars

This book is very timely for today's events.
Quote from page 474 describes events in 2014 with war in Crimea, Eastern Ukraine and just after Malaysian Airlines Flight 17 was shot down over eastern Ukraine:

"Entire sections of the [Russian] economy, including banking and energy, now faced sanctions, not just the officials and friends close to Putin. By the middle of 2014, capital flight had reached $75 billion for the year as those with cash sought safe harbors offshore; by the end of the year $150 billion had fled the country. The economy, already slowing, slumped badly as investments withered. The value of the ruble crashed, despite efforts by the central bank to shore it up. The prices of oil slumped--which Putin blamed on a conspiracy between the United States and Saudi Arabia--and that strained the budget, depleting the reserves that Putin had steadfastly built up throughout his years in power. Russia plunged into an economic crisis as bad as the one in 1998 and 2009. Putin’s tactics had backfired. Many in the West cheered, seeing the economic crisis as evidence of the self-inflicted pain of Putin’s actions, but the isolation also fed Putin’s view that the crises confronting Russia economically and diplomatically were part of a vast conspiracy effort to weaken Russia—to weaken his rule.”

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Notes from Godel's Proof by Nagel and Newman

Gödel's Proof by Ernest Nagel
My rating: 5 of 5 stars

I have discovered recently, the last month or so, that when I read, I only read and recall what interests me at the time of me reading. Hence my reading of this book is skewed by my current fascination with imagination and conceptualization. I am not willing not to invest the time it would take me to assess the mathematical value of this apparently exceptional summary of Godel's Proof.

This book greatly extended my mathematical horizons. The questions that it evoked and the effort I took to dig into these questions were very useful. I discovered that mathematics was developed as an imaginative effort through history until the expression of Euclid's geometry in terms of algebra was done by Descartes' analytic geometry. The frequent references to "The Principles of Mathematics" by Russell, Whitehead, inspired me to find out the contents of this famous work. I was surprised and pleased to see that my book on Advance Calculus by Hans Sagan follows an outline that was probably inspired by the Principles.

Useful quotes from this book:
Page 10. "It was not until the 19th century, chiefly though the work of Gauss, Bolyai, Lobachevsky, and Riemann, that the impossibility of deducing the parallel axiom from the other was demonstrated. ... The traditional belief that the axioms of geometry (or for that matter, the axioms of any discipline) can be established by their apparent self-evidence was the radically undermined. ... the proper business of the pure mathematician is to derive theorems from postulated assumptions, and that it is not his concern as a mathematician to decide whether the axioms he assumes are actually true. ... Axiomatic foundations were eventually supplied for fields of inquiry that had hitherto been cultivated only in a more or less intuitive manner. (In 1899 the arithmetic of cardinal numbers was axiomatized by Giuseppe Peano.)” {Note: cardinal numbers denote quantities.}

Page 11. Hence mathematics is not just the "science of quantity." "... mathematics is simply the discipline par excellence that draws conclusions logically implied by any given set of axioms or postulates.”

Page 12, David Hilbert published his axioms of geometry in 1899. Hilbert states that the connotations of primitive terms ignored, their meaning depends only on the axioms. (Primitive terms are “point”, “line”, “lies on”, and “between.”)

My comment: In this sense mathematical formalization, logic, frees our minds from the limits of our imagination. Examples are ’n’ dimensional spaces, negative numbers, complex numbers.

My understanding is that intuition is a kind of imagination. Imagination gave us the earliest geometry, and imagination continues to be a powerful tool to leap across the unimaginable valleys of logic. Arithmetic moved from domain of imagination to logic in 1899, thanks to Peano. Ditto for geometry by Hilbert.

Page 14, “Moreover, as we all know, intuition is not a safe guide: it cannot be used as a criterion of either truth or fruitfulness in scientific explorations.”

My comment, ditto for philosophical opinions, e.g. I. Kant’s
“But in order to ascertain to what given intuitions objects, external me, really correspond, in other words, what intuitions belong to the external sense and not to imagination, I must have recourse, in every particular case, to those rules according to which experience in general (even internal experience) is distinguished from imagination, and which are always based on the proposition that there really is an external experience.”

Kant, Immanuel. Complete Woks of Immanuel Kant (p. 29). Minerva Classics. Kindle Edition.

Page 23, Another example of the failure of “clear” and “distinct” intuitive notions is the notion of “class” or “aggregate.” Bertrand Russell’s antinomy, paradox, “Classes seem to be of two kinds: those which do not contain themselves as members, and those which do. A class will be called ‘normal’ if, and only if, it does not contain itself as a member; otherwise it will be called ‘non-normal.” Then what is the class ’N’ that stands for the class of all normal classes? If ’N’ is normal it is a member of itself because by definition ’N’ is all normal classes, but if it includes itself, but then it would not be normal.

My comment: Epistemologically this looks like shifting the level of abstraction without noticing the shift. A class of all normal classes is a higher level abstraction that a “class.” On page 28, Hilbert’s solution to this issue is “meta-mathematical” statements, a language that is about mathematics. Hence meta-mathematics is a different level of abstraction.

Page 34, an analogy to meta-mathematics is made with the game of chess. The pieces have no meaning but they must be moved according to the rules of the game. The chess pieces correspond to the elementary signs of a formalized mathematical calculus, the legal positions of the pieces, to the formulas derived from the axioms (i.e. theorems); and the rules of the game to the rules of inference for the calculus. A theory of meta-chess can tell us about the number of possible moves that White can make at any point in the game. A theory of meta-mathematics may be able to tell us if contradictory formulas may be derived from a given mathematical calculus.

Page 83, distinguishes signifiers from concepts using the difference between numerals and numbers. “A numeral is a sign, a linguistic expressions, something which one can write down, erase, copy, and so on. A number, on the other hand, is something which a numeral names or designates and which cannot literally be written down erased, copied, and so on. … A number is a property of classes (and is sometimes said to be a concept), not something we can put on paper.
My comment: I need to read Adler’s book Some Questions About Language: A Theory of Human Discourse and Its Objects (1976)

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Goals at 67

 My perspective has certainly changed in the last 4 years of my retirement.  I tend to get “addicted” to my goals, and neglect other parts of my life that are not part of a goal. I thought I would live “goal free” as Harry mentions below, but I found my body began to rebel.  I was getting physically out of shape, my belly was getting bigger.  I have found that a certain minimum structure for my days is valuable for keeping fit and healthy, and to keep moving toward my current interests.  As long as I stick to my daily routine, determined by my weekly/monthly plans, everything works well and I feel happy with my life.

My current interests, (but not goals) are:

• to have a better understanding why people behave the way they do, so many people are their own worst enemies and they don’t seem to know it.
• To learn the mathematics that I need to know to understand modern physics books, i.e. number theory, analytic geometry and n-dimensional vector calculus.  These are topics that I covered in college, but I have found it very rewarding to revisit them.  
• To understand the role of concepts in my thinking by watching how my mind works when I work math problems out imaginatively and then formalize them via concepts.  I am amazed to find out how large the role of imagination is in thinking and understanding.
• To read good stories and essays, learn to appreciate good drama on TV or in books and improve my senses of smell and taste.  Compared to Amanda I am almost blind when it comes to smell, taste, appreciating drama, or listening to music.  I am beginning to desire to enhance my experience in these artistic arenas. 

My biggest distraction is the local library system.  I am limiting the number of books I check out at a time, so that I can get more of my own studies and home projects done.  Home projects are to clean out old files, photographs, floppy disks, and emails, (like this one).

My worst bad habit is not asserting myself in conversation with others.  I have an underlying fear I won’t be liked.

When I look back on my working life, I realize other things could have been accomplished if I had dedicated myself to those goals, but when I read my old files, and emails from those time periods of my life, I see that I made the best possible choices for who I was at the time.  So no regrets.  

Goals are given to us by the possibilities that we commit to.  We all have possibility via imagination, what is missing willingness commit. If I am not working toward my goals, I ask myself “what is stopping me?”  I write down the answers for clarity and post them on my bathroom mirror.

Mathematics and Imagination Lessons

I had the opportunity this morning to review some of the notes I made about Immanuel Kant’s Critique of Pure Reason.  I realize on second reading of my highlights in the Kindle book, that I failed to understand what Kant was trying to say, my bad.  Of particular interest to me today was in the preface where Kant says

"A philosophical system cannot come forward armed at all points like a mathematical treatise, and hence it may be quite possible to take objection to particular passages, …”  He goes on to say that he is 64 years old and does not have the time to make his writing free of all mistakes and inconsistencies, he depends upon future generations to smooth the “rough edges” of his exposition.

              Kant, Immanuel. Complete Woks of Immanuel Kant (p. 30). Minerva Classics. Kindle Edition. 

I have been collecting evidence for imagination from other writers, to learn if what they have to say is the same as my own conclusions.  This has led me down some interesting side paths.  Most notably the lecture by Richard Feynman "The Relation of Mathematics to Physics" and a small book “Godel’s Proof” by Ernst Nagel and James R. Newman.  As a former math major this book really expanded my horizons and showed me connections that I had never contemplated.  

I haven’t found anyone that contradicts what I am thinking.  What surprises me is that imagination is such a common theme among mathematicians, scientists and engineers. I see now that all my reading of the past was always in search of an answer to a question, and if what I read didn’t seem to apply to my question, I would ignore it, or at least give it no attention.

I suspect that if I attempt to give you quick answers, I may find myself contradicting what I have to say at later date.

First, I define imagination as mental images, models of what is not before my senses.  Imagination includes memory, planning, what I have in mind to create (write, draw, say).  Intuition is a form of imagination.  I see a car, and my imagination using memories and logic tells me it is a 3 dimensional object with an internal combustion engine and wheels. My imagination may be wrong, it may be running on a battery, it may be clever picture of a car painted on the wall of a barn.  Similarly, we don’t “know” the person we are talking to, we only know our imagination of them.  

In Math, the number two is an abstraction from pairs of items that exist either in the world of in our imagination. The number two is a concept, perhaps it represents a process of pairing.  But you will never find the number 2 in the objective world, certainly not the number “-2”, nor the square root of "-2".

The awakening moment for me was realizing that the number line is pure imagination!  This insight came when I was working on a series of proofs about ordered fields.  Since I am interested in learning the difference between imagination and conceptual thinking I would write each proof imaginatively, drawing diagrams as needed to prove the point.  Then I would work to write a formal proof based on prior axioms, definitions, and previously proved theorems.

Example: If “a” is a member of an order field, numbers are an ordered field, and “a” > 0 then prove 1/a >0.

Imaginatively this is drop dead obvious, 

I imagine a number line: 

<——————————|————|—————————> positive direction

negative                        0             a

I imagine “a” some number >0 on the right hand side of the 0 in the drawing above.

I imagine 1/a as a point on the line that clearly is >0.  Taking the reciprocal of a number cannot be negative.

Notice that for a complete imaginative proof, I would need two diagrams, one for a < 1, another for a >= 1.

Formally, i.e. logically, it takes more thinking.  (The fringe benefit of formal methods is that they come closer to what may be programmed into a computer.)

1. Suppose that 1/a < 0 and “a” > 0, contrary to initial assumptions.  // I am thinking of proof by contradiction
2. Then a * 1/a = 1 > 0 by axiom of multiplicative inverse.
3. But a positive number times a negative number is < 0 (i.e. negative), by previously proved rule that -a=a(-1). // I did this in an earlier exercise, so I can build on the result.
4. Hence supposing that 1/a < 0 leads to a contradiction, that a negative times a positive is > 0, 
5. Therefore 1/a > 0.   QED

Comments, the power of abstraction (conceptualization) is that “a” stands for any number.  The number line is pure imagination, formally this number line represents the mathematical definition of an ordered field.  The image gives our minds something to “hang onto” in order to use the concept of “ordered field.”

Notice that I am using my imagination to manipulate abstract symbols, number line, zero, positive and negatived.  This is a step away from using my imagination to manipulate a pencil and paper to draw a picture.

With practice I have learned that the imaginative proof is frequently in incomplete, as seen above, and sometimes it is just plain wrong.  What seems clear and intuitive is not always correct.  A good example is the “Russell Paradox” of set theory.  

The incentive for creating things, (diagrams, paintings, essays, science, machines, tools, music, etc.), is that it brings my imaginations to life and embodiment.  At the same time creations make my imagination more detailed, complete, and accurate to the domain that I am imagining in.