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Confusing the individual with the aggregate

One of the things that fascinated me was radioactive decay. If you were given a certain amount of a radioactive isotope, you can deduce how much will be left (not decayed) after a certain amount of time. In fact, you can do this so accurately that you can base a precision clock on it.

However, it is impossible to determine WHICH atom will decay, no matter how much information you have about it. I don’t mean that it is practically impossible but rather that it is literally impossible. And the individual atoms will decay at different times.

In short, you have information about the aggregate but not about the individual. Of course, in this example, we are in the range of quantum phenomena.

But this principle, (aggregate vs. the individual) applies when one attempts to make inferences about what will happen with a population in which there is a high level of variance within the said population, and people often get confused.

Example: suppose you have two groups of students who are, say, starting a program of study in engineering. One group is the group of students whose math ACT scores are 22, and the other group has math ACT scores of 30. The harsh reality is that the group of students with a score of 22 will have very little success; there may well be a few individuals who make it, but the vast majority won’t. And yes, the group with a score of 30 will have some failures, but they will have many more successes.

So, the ACT score matters and has predictive value. But if you bring this up, someone will remember the person with a 30 who flunked out, and someone with a 22 who made it and claim that means that the “ACT is meaningless”. Psst: that isn’t true.

So yes, there are smokers who live a long time, there are those who drive while texting who don’t get into accidents, etc. But smoking does harm longevity and driving while texting increases one’s risk of having an accident.

Application to Illinois Football Illinois football is starting MANY true freshmen and, well, the record so far is grim (2 wins over weaker non-conference opposition, followed by 5 straight losses against “power 5” caliber opposition (USF isn’t “power 5” but they are an undefeated, ranked team). And prospects for another win this season are grim, with 2 Top 10 teams (Wisconsin, Ohio State) and 3 improved teams (Indiana, Purdue, Northwestern) left to play.

So the PR department is playing this “the future is bright” angle:

And yes, the team is playing a lot of freshmen.

But: how good is that class? I went on ESPN and looked at how the Big Ten 2017 recruiting classes were ranked:

Top 10: Ohio State, Michigan
10-25: Penn State, Maryland, Nebraska
26-39: Michigan State
40-49: Wisconsin, Iowa, Northwestern
50-59: Rutgers, Illinois, Indiana, Minnesota, Purdue.

So, based on talent, we *might* be able to hang with Rutgers, Indiana, Minnesota and Purdue, youth or no youth.

Now yes, measuring recruiting is tough to do, and there is always that individual “lightly regarded” recruit who blossoms into an NFL player. It does happen..individually. But a team composed of lightly regarded recruits is rarely, if ever, successful.

Workout notes: yesterday, wet 10K walk (untimed). today: weights. Pull ups were a struggle, so I did a couple of 5-5 sets then 2 sets of 10, one of 7-3 (50 total). (switched grip), usual PT, incline presses: 10 x 135, 4 x 160, 6 x 150, military (dumbbell: 10 x 50, 10 x 45) 10 x 180 machine (90 each arm), rows: 3 sets of 10 x 110. Then a chilly 5K walk outside.

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October 25, 2017 Posted by | college football, education, football, science, statistics, walking, weight training | , , | Leave a comment

It isn’t that simple…

Ah, I remember when I was a kid.

I was in grade school and was introduced to a table top model of the solar system.

Then I remembered reading that solar eclipses were rare..and happened every time the moon passed between the sun and earth.
I looked at the model and asked my teacher: “if this model is accurate, why don’t we get a solar eclipse every orbit?”

Of course, she didn’t know.

By the time I got into high school, I found an astronomy book that explained why (short answer: the orbits are not in the same 2 dimensional plane).

But the moral: the solar system was vastly more complicated than a table top model can model.

I also read up on “how we might go to Mars” and wondered why the scientists just didn’t go in a straight line path; things like momentum, fuel considerations, etc. just did not compute in my little pea brain.

It was more complicated that I realized at the time.

Now of course, I was a kid. But the “simple answer to a complex problem lives on..and we see that when, say, Trump supporters, Sanders supporters and libertarians try to discuss a topic like healthcare. That trying to get something that works from where we are right now is hideously complicated …well, that is just lost on many.

August 1, 2017 Posted by | science, social/political | Leave a comment

I’ve never seen anything like President Trump but…

It is weird. On one hand, I see President Trump as being a disaster. But, at least for NOW, my personal life is going well…for NOW…there are potential land mines ahead. But enough about that.

I work in education (mathematics) and Trump is a potential distaster at many levels. His nominee for Secretary of Education doesn’t even know the basics:

and yet is likely to be confirmed. I sure hope that the Democrats are united in opposing her, though if it looks like she will win anyway, I can see giving a few red state Senators a pass for local political reasons.

Higher education will not be spared; a creationist is being appointed to lead a task force in higher education.

And do not think that our lead in science/engineering/mathematics research is a “given” either; remember that in the 1930’s, Germany lead the world. They ran many of their top people out and the US took command.

Even worse, Trump appears to have no grasp of reality. He thinks that Islamic terrorism is being under reported and provided the media with a list of 78 “under reported” events…(and yes, the list had egregious misspellings in it, including of the word “attacker” in places!”

And just read some of President Trump’s tweets: do these sound presidential to you?

As someone pointed out, Trump is like a “boy’s idea of a man”. Oh sure, there are times when I have fantasies about being well off enough to tell anyone to “f*ck off” without having to worry about the consequences, but I realize that my having those fantasies are the result of my incomplete growth as a mature human being; it is my goal to get to the point where I don’t have those thoughts. I certainly do not admire someone who acts that way…especially the President of the United States.

What to do about it:

https://www.theatlantic.com/politics/archive/2017/02/how-to-beat-trump/515736/

February 7, 2017 Posted by | education, political/social, politics, politics/social, science, social/political | , | Leave a comment

Weather aches, hypocrisy and football

Paul Krugman noted that economic conditions are different (no longer zero interest rates..and companies are interested in borrowing and employment is up) and so we should look at deficits differently. Yes, public investment should be done, but not upper end tax breaks. OF COURSE, the right wing is calling him a hypocrite. And OF COURSE, they are wrong.

The idea that the best thing to do often depends on the situation is not a subtle concept. Why do conservatives have so much trouble with it?

Think of it this way: ask ANY football fan “what is the best play for a team to run” and they will tell you: “it depends on: down, distance, field conditions, time in the game, the score, the defense, the strengths and weaknesses of the respective teams, etc. Obviously, 3’rd and goal from the 1 with 1 minute to go in the game is different from 2’nd and 15 from your own 20 in the middle of the second quarter.

Of course, there are different philosophies; some teams are option teams, some are running teams, others are passing teams, and the play call also depends on the philosophy of the team (pass on 3’rd and 1 vs. run on 3’rd and 1). But the call is very situational. No one disputes that.

So why is this hard when it comes to economic policy?

Speaking of hypocrisy, why is hypocrisy bad? After all, if a coach has a good reputation for developing an athlete, I won’t call the coach a hypocrite for being a bad athlete and a workout slacker himself.

The article I linked to offers the following answer: those who say one thing and do another often use their moralizing to bring credit to themselves; a kind of PR. So when they don’t live up to their preaching, we get angry for them for putting up a false front. In the “out of shape coach” case, the coach is NOT billing himself as a good athlete when he coaches you. The moral scold who is themselves immoral IS billing themselves as a moral person, and that is where the resentment comes in.

Weather Yes, at one time, I bought into this “knee aches with weather changes” stuff. But more studies have been done…and I’ve come to understand I’ve run reasonably well during some very rainy days. It turns out there is no solid evidence that weather changes causes joint pain.
runtoremembercrop1

January 14, 2017 Posted by | economics, economy, science, social/political, Uncategorized | , , | Leave a comment

Trump, “Real America” and all sorts of “Political Correctness”

I am on the road and we stopped near Columbus, Ohio for the evening. We are about 6 hours out of Peoria.

I have time for some political posting.

So, Donald J. Trump will be President. Oh yes, there might be a “faithless elector” or two, but that won’t stop him. We need to engage in very basic politics to stop him. That doesn’t mean that we take Russian interference lying down; Sen. Lindsey Gram offers some good suggestions.

Paul Krugman offers suggestions on how to channel that “cool anger”. I agree: we should really make the case that Trump really represents wealthy interests and little else; he won’t help improve the normal lives of the “rank and file” nor will he level the playing field so as to empower the rank and file to improve their own live (which is what most really want anyway).

Though America is NOT the GOP, America is NOT a liberal college campus either. The average American is not going to get the vapors if Trump doesn’t speak according to some approved “PC” script. We can show that Trump is making the playing field more unequal though…he is lying about big manufacturing coming back, he is going to try to take away people’s health insurance and he will do nothing to “Make America Great Again.”

We have to make him pay a political price for that, and that means nominating those with the political skill to do it.

About political correctness: Yeah, I get tired of all of this nonsense that says that “rural, Trump voting” people are the “real Americans” and that the rest of us (close to 3 million more!) are, what?

But, I will continue to call out liberal political correctness, which sometimes can be so pervasive that it actually attacks well established scientific results.

Workout notes: easy 3.1 mile walk (5K) on the treadmill yesterday; 39:10.

December 15, 2016 Posted by | political/social, politics, politics/social, science, social/political, travel, walking | , , | Leave a comment

Thinking about thinking: critical thinking, empathy (and its limitations), faulty memories, etc.

Memories: yeah, our minds fill in the gaps, and so some of our vivid memories…never happened, or didn’t happen the way that we remember them. That is one reason I keep this blog; I often revisit what I did..and once in a while, find that I didn’t do what I thought that I did.

I still “remember” an epic workout that I once did: 8 x 400 in 75 each..back in 1982. Trouble is: I never did that. When I read my old logs, I did one workout where my LAST 400 was in 78 (others were 82-83) and I did a few 10-12 x 200 in 37-38…very different. I had written that 8 x 400 in 75 was my GOAL. Goals are not facts. 🙂

Empathy Yes, compassion for other humans is a good thing. But sometimes empathy for an individual can override doing greater good for more people. So empathy for individuals might lead to policy that might actually be harmful for more people (or do less good than it might otherwise). This book is on my reading list.

Critical thinking: Yes, I am for it, but effective critical thinking requires a context and a detailed knowledge of the facts and principles for the context. So teach history, teach physics, teach chemistry. But forget this “course on critical thinking” stuff.

Challenging beliefs and the “regressive academic left”. This article has given me something to chew on. Some of it is very good: one can’t challenge absurd beliefs without talking about underlying assumptions:

Malhar Mali: What in your opinion is the best way of fostering critical thinking when it comes to religious and supernatural beliefs?

Peter Boghossian: I think the whole way we’ve taught critical thinking is wrong from day one. We’ve taught, “Formulate your beliefs on the basis of evidence.” But the problem with that is people already believe they’ve formulated their beliefs on evidence — that’s why they believe what they believe. Instead, what we should focus on is teaching people to seek out and identify defeaters.

What is a defeater? A defeater is:

IF A, THEN B, UNLESS C.
C is the defeater. We should teach people to identify conditions under which their beliefs could be false. This is profound for a number of reasons. If I’m correct, then it would be the holy grail of critical thinking. The problem with traditional notions of critical thinking is that most people believe what they want to believe anyway. They only look in their epistemic landscape for pieces of evidence which enforce the beliefs they hold — thus entrenching them in their view of reality. Eli Pariser has a vaguely related notion and talks about a technological mechanism that traps us in a “filter bubble.”

There are attitudinal dispositions that help one become a good critical thinker and there are skill-sets. If you don’t possess the attitudinal disposition then what’s the point of the skill set? A skill set could actually make it worse because, as Michael Shermer says, you become better at rationalizing bad ideas.

By teaching people to identify defeaters, which is a skill set, we may be able to help them shift their attitudes toward responsible belief formation. We may be able to help them habituate themselves to constantly readjusting and realigning their beliefs with reality. In the philosophy literature there’s a related notion called doxastic responsibility, which basically means responsible belief formation.

MM: So if you had put that formula into action with “If A, Then B, Unless C” what would that look like?

PB: A pedestrian example could be when someone thinks they see a goldfinch in their backyard. The traditional route here is to say, “Formulate your beliefs on evidence. What evidence do you have to believe that’s a goldfinch?” and they say: “Well I see the bird is yellow. I know there’s a high incidence of goldfinches in this area, so by induction I can see that it’s probably a goldfinch.” But unbeknownst to them it’s not a goldfinch but a canary.

So instead of saying, “formulate your beliefs on the basis of evidence,” we should say: “how could that belief be wrong? Give me three possibilities how the belief that it could be a goldfinch might be in error.” This type of questioning — applied to any belief — helps engender a critical thinking and an attitude of doxastic responsibility.

The author then goes on to lose his way when he discusses the “regressive academic left” later in the article. Yes, they exist. Yes, some are nasty people. And yes, they are a threat to free speech and the free exchange of ideas. Yes, they are a threat to critical thinking skills.

He says:

Here’s what is surprising: with very few exceptions, and there are exceptions, Christians are very kind decent people all over the world. I do talks and we go out afterwards for drinks etc., and we talk with civility.

The far Left in contemporary academia is not like this. These are viciously ideological and nasty people whose goal it is to shut down discourse and indoctrinate students. I think we’ve spent too much time on Creationism. The problem is less with creationism and more with radical Leftism. For example, if you’re a professor who teaches in the biological sciences, creationists have substantive disagreements with your work and they’ll try to demean it. But they’re not going to harass you or your family. They’re not going to try and get you fired. They’re not going to call you a racist, a sexist, a bigot, a homophobe.

That may well be true, but creationists get on school boards and have seats of political power. Climate change denialists have seats in Congress:
inhofesnowball

You really can’t compare the power and money behind the right wing variety of nonsense.

Sure the idiots in academia are annoying. But they aren’t the threat to science that the science denialists are, and they have nowhere near the degree of institutional support.

December 10, 2016 Posted by | education, science, social/political | | Leave a comment

A bit of statistics

Ok, how can we draw statistical inference when we cannot run a controlled experiments? After all, correlation and causation are not the same. This is a useful guide as to the how and when. Basically: is the correlation strong, and is there some “plausible reason” for such a correlation? This paper lists 7 points.

Simpson’s paradox You can see a discussion here.

Think of it this way: say 1000 women and 1000 men apply for admission to graduate school. 656 men get admitted, whereas only 260 women get admitted. Does this mean that things are biased against women?

But then we see that there are two very different graduate programs. The very selective graduate program admitted 8 percent of all male applicants but 10 percent of all women applicants. The other graduate program..the “easy to get into” program admitted 90 percent of female applicants and 80 percent of all male applicants. So: we see that the women outdid the men in both programs. Yet, we also see that 800 women applied to the “difficult to get into program” and only 200 men did. On the other hand, 800 men applied to the easy program but only 200 women did.

Check it out: women: 800*.1 =80 admits to the hard program, 200*.9 = 180 admits to the easy program, so 260 total admits. Men: 200*.08 = 16 admits to the hard program, 800*.8 = 640 admits to the easy program, or 656 total admits.

This isn’t just some “trick” either. When social scientists analysed the “stand your ground” defense law in Florida, they found that whites were more likely to be convicted than non-whites. BUT this was because whites were more likely to be accused of assaulting a white victim; it turns out that the probability of prosecution was higher if the victim was white than if the victim was non-white. You can see the details here.

workout notes: 4 mile walk after weights: rotator cuff, 5 sets of 10 pull ups, bench press: 10 x 135, 5 x 185 (strong), 10 x 170, incline: 10 x 135 (very easy), military: 10 x 50 standing, 20 x 50 seated supported, 10 x 200 machine, rows: 3 sets of 10 x 50 single arm. head stand, 2 sets each of 10 yoga leg lifts, 12 twist crunch.

November 29, 2016 Posted by | science, social/political, statistics, walking, weight training | Leave a comment

They are good at it

Workout notes: though the weather was great, I went inside for my “faster” running segment:
treadmill: 5 min at 5.2, 5 at 5.3, 10 min at 6.7, 6.8 to 2 miles (28:xx), 6.9 to 35 minutes, and 7.0 3.75 and 7.1 for the final .25 (37:35 for 4), then 15 minutes at 15 mpm to get to 5 miles in 52:35.
Then 1 more mile of walking outside.

Weight: 191 on the gym scale prior to running. I don’t think that my weight training is helping my marathon prospects. 🙂

Science: Three physics Nobel Prizes were awarded, and these physicists used topology to help them understand what they were studying:

David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz were awarded the Nobel Prize in Physics on Tuesday for discoveries in condensed-matter physics that have transformed the understanding of matter that assumes strange shapes. All three were born in Britain but work in the United States.

Using advanced mathematical models, the three scientists studied unusual phases, or states, of matter, such as superconductors, superfluids or thin magnetic films. Their findings have relevance for materials science and electronics.

Dr. Thouless of the University of Washington, Dr. Haldane of Princeton University and Dr. Kosterlitz of Brown University were honored by the Royal Swedish Academy of Sciences in Stockholm for “theoretical discoveries of topological phase transitions and topological phases of matter.”

Topology is a branch of mathematics that describes properties that change only in increments. In the early 1970s, Dr. Kosterlitz and Dr. Thouless “demonstrated that superconductivity could occur at low temperatures and also explained the mechanism, phase transition, that makes superconductivity disappear at higher temperatures,” the academy found.

In the 1980s, Dr. Thouless showed that the integers by which the conductivity of electricity could be measured were topological in their nature. Around that time, Dr. Haldane discovered how topological concepts could be used to understand the properties of chains of small magnets found in some materials.

“We now know of many topological phases, not only in thin layers and threads, but also in ordinary three-dimensional materials,” the academy said. “Over the last decade, this area has boosted front-line research in condensed matter physics, not least because of the hope that topological materials could be used in new generations of electronics and superconductors, or in future quantum computers.”

I think that “Topology is a branch of mathematics that describes properties that change only in increments.” refers to “continuous functions”. Of course, analysis and geometry uses continuity also, therefore I find this statement puzzling.

But to the reader who might wonder “what doesn’t change in increments”, consider electron orbitals (you studied these in chemistry). The electron energy levels are in discrete units and change in a quantum manner (“jump between discrete levels”).

October 4, 2016 Posted by | physics, running, science, walking | , | Leave a comment

The Dunning-Kruger club…

dkclub

Upshot: it takes a bit of intelligence, awareness and humility to be aware of your own intellectual limitations. If you think that your “common sense” overrides the opinion of experts who are talking about their field of expertise, you belong to the Dunning-Kruger club.

That might sound snarky, but there are times when I find myself as being too close to being in that club. Here is one such example:

Pass the sick bag. A device that allows people to empty a portion of their stomach contents into a toilet after a meal has just got the go-ahead from the US Food and Drug Administration. The device is approved for use by people who are severely obese, defined as having a body mass index of over 35 kg/m2.

The stomach-churning device, which is already available in some European countries, involves a tube being placed into the stomach in a short surgical procedure. The end of the tube contains a valve that lies flush against the skin.

Normally it is kept closed, but after meals, the person can connect the valve to another tube to drain about a third of their partially digested food into the toilet. It cannot remove more food than this, because the end of the internal tube is positioned higher than most of the stomach’s contents.

Manufacturer Aspire Bariatrics, based in Pennsylvania, says users need to chew their food well and eat more slowly to stop the 6 millimetre tube from getting blocked, and that this in itself helps reduce overeating.

“You get some solid chunks,” says Kathy Crothall, head of Aspire Bariatrics. “If a patient doesn’t chew their food very carefully they won’t get anything out of this device.”

The link contains a video and a description of the experimental results.

Now my emotional reaction is YUCK…THAT CAN”T BE GOOD FOR YOU (disclaimer: I used to weigh 320 pounds so this arouses some emotions in me). But I am not an expert in medicine and …IF this actually helps some people lead healthier lives…well, that is a good thing, despite my “yuck reaction”.

June 17, 2016 Posted by | obesity, science, social/political | , | Leave a comment

How I try to determine what is “right”….

Here is what I am talking about: there is a major issue (say, vaccines, climate change,GMOs, or perhaps a claim from Keynesian economics, or a claim made in the social sciences) and I want to decide: where IS the truth? It is absolute or statistical? The problem is, of course, that many of these claims require a technical background to evaluate properly; one’s “common sense” is woefully insufficient. And, given that my training is narrow (mathematics; in particular, topology) I often do not have the professional background to properly evaluate such claims. Yes, I am subject to being fooled, especially if the conclusion is what I want to hear, or what “feels right” to me, or even, “makes sense” to me. “Figure it out for yourself” has some serious limitations, though there IS a place for it.

Here is an example of a popular math video which, while interesting, valuable and well done, does make an error:

The value is that it shows how something which, while involving infinity, can lead to something practical when one takes a finite approximation. Note: Fourier series is also like that.

The error is technical. Yes, “space filling curves” exist, but it can be shown that they can never be “one to one”.

For the experts: an onto continuous function from a compact space to a Hausdorff space is a homeomorphism (topological equivalence) if and only if the function is one to one. To prove this, note that the continuous image of a compact set is compact and compact sets in a Hausdorff space are closed, hence one to one implies that one has a one to one closed map which makes the inverse map continuous as well.

So: the limit function described in the video cannot have an inverse, though all of the approximating curves can, and these approximating curves can come as close to “filling” the square as one pleases, in terms of running them through a given finite lattice of points.

And the discussion of the “serpentine” curves is excellent; very well done. I’ll used that the next time I teach topology or analysis.

But, most non-mathematicians wouldn’t be able to evaluate this properly and realize that the presentation was just a tiny bit flawed, and yet very good and valuable.

And so, when I read an article on GMOs (appears to be a good article to me) which makes the point that organic foods may well use worse pesticides than GMO ones, among many, many other excellent points (e. g. organic foods could have had deliberately induced mutations via radiation) I really can’t do a technical evaluation of the article.

The same goes for this article on why poor people make so many bad decisions in life (basically, basic survival uses up most of their thought processing abilities).

So, this is how I go about deciding:

1. WHO is writing the article? Is it a journalist (who often will misunderstand technical details) or a specialist? If it is a journalist, I might go see if the the specialists have anything to say.
2. Where die the article appear? Is is in Scientific American? The New York Times? Natural News? (lol).
3. If the author is a specialist:
a. What are the author’s credentials?
b. Is the author STILL respected within the community? Yes, even Nobel laureates in science can go “off of the rails” and go crackpot, but this is usually picked up by the rest of the community.
c. Does the result conform to current consensus? Is there currently a debate within the community? Or is the result really an exciting new conjecture that is still being vetted by the other top guns within the community? Most new conjectures are false, but a few past the test of peer vetting.
4, Who are the critics? Are they themselves specialists or people who just don’t like the results for social or political reasons? (think: some of the criticisms of Steven Pinker’s stuff)

And yes, even with all of this, I am going to get things wrong from time to time.

June 10, 2016 Posted by | politics/social, science, social/political, Uncategorized | Leave a comment