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…


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

Trouble accepting what I have not seen…

I wonder if it is a human trait to reject the experience of others if that said experience is not a part of one’s life.

For example, it has been difficult to persuade my conservative friends that darker skinned males are often seen as “suspect” by the police (example)

I had a brush with being profiled (probably many things, including having a cheap car with Texas plates) and note one of the comments that I got on that post.

It is tough to accept what we haven’t experienced, observed, or been a party to, especially when we don’t want it to be true.

In my case: I have trouble accepting that sexism within the sciences still exists. What caught my eye was this story (from outside of the United States):

In the final months of my physics degree, one of my professors asked me into his office – an exciting prospect, given that I assumed we’d be discussing subjects for my potential honours theses. He closed the door, invited me to sit, and declared he’d fallen in love. He wanted to have an affair, he said, and if I couldn’t share in that plan he couldn’t continue as my advisor – he’d find my presence ‘too distracting’. He was a senior academic, and married; but this was Australia in the late 1970s and the subject of sexual harassment wasn’t on any university radar. It seemed this was just one of life’s inequities, another hurdle facing being a woman in science. So I made the decision to leave physics – a subject I loved – and in the following academic year switched to computer science at a different university.

Now of course, the reasons I resist this claim so strongly is that:

1. I don’t want it to be true.
2. I haven’t seen this in person.
3. I haven’t ever done this to another person.

Note: the degree data I’ve seen in mathematics surprises me. I do know that we’ve had more success in hiring female math professors than we’ve had in the past; is a bad job market part of the reason? I do know that things are better than when I first got my Ph. D., but evidently the numbers have stagnated.

Anyway, I do believe in data and facts though.

Of course, part of what turns me off is the low quality of the arguments that I’ve read. For example, from the article that I quoted from::

Part of what women are up against in science is a continuing widespread attitude that, deep down, we’re not really up to it, which by extension implies that a high rate of attrition is no big loss. That view was startlingly articulated in 2005 by Lawrence Summers, then president of Harvard, when in a conference he mused that if there weren’t more women in top science positions at elite universities it might be in part because women’s mental abilities are different. The ensuing furore led Summers to resign and precipitated a great deal of hand-wringing about academic sexism. Yet here we are, a decade later, with yet more academic sexism.

What surprised me about Summers was not what he thought – in my experience, it’s not an uncommon view among elite academic men – but that he thought he could say it out loud. He didn’t seem to understand the absurdity of stating, in an intellectual forum, that half the Harvard student body might be inherently unsuited for intellectual success.

I see two big problems here. First of all, “he thought he could say it out loud”: this is a hostility to freedom of expression that I find troubling. Also: “that half the Harvard student body might be inherently unsuited for intellectual success”.

The author of this article misses the point badly. For one, Summers remarked that the demands of science at the world class level may be incompatible with family life and it “could be” that women were more interested in the latter. As far as the intellect: remember that Harvard faculty are supposed to be world class; we are talking about the extreme ends of the “bell curve” here. Might it be possible that the variation between men and women are statistically different? Again, I am talking about the “extreme ends”, which is where Harvard STEM faculty would be. That has nothing to do with, say, people like me (ordinary Ph. D. people with a modest publication record) and nothing to do with the student body at Harvard (on the whole.

And, I’ve been turned off by some of the hare brained “sexism!” complaints I’ve seen (e. g. calling an animal part a “penis”).

So yes, some of the “sexism in STEM fields” arguments are bad arguments. But that doesn’t mean that sexism doesn’t exist; I think that I am now convinced that it does.

A bad argument for a position doesn’t invalidate that position (e. g. there are bad pro-evolution arguments out there) , though it does mean that the person making the argument did not make a convincing case for it.

May 31, 2016 Posted by | mathematics, science, social/political | , | Leave a comment

Public Perceptions of Science

Yes, the public, on the whole, doesn’t understand STEM fields. In fact, one economist was briefly detained for questioning when a fellow passenger on an airliner saw what he was writing down and thought it might be something evil (it was a differential equation).

And the results can be difficult to understand. When one attempts to explain them to a non-expert, say via a popular article or a popular book, one has to make simplifications:


Though this meme is probably unnecessarily harsh, it does get across the point that when one is trying to understand something outside of one’s specialty, one is doing a translation of sorts, and we know that information can be lost in translation.

I go through this all the time when I go to mathematics conferences and take in a talk that is outside of my narrow area. I have the advantage that I KNOW that I am missing the nuances and that if I wanted to understand the results or the conjectures, I’d have to engage in intense study in that field..and I still might not be able to understand what is going on.

Aside from that, there is how the media interacts with the science studies themselves, along with the fact that scientists like publicity too. This John Oliver segment (30 minutes) is outstanding and is making the rounds on the various science blogs.

May 13, 2016 Posted by | mathematics, science, social/political | Leave a comment

Human evolution: vestigial traits in the human body

Many of the traits of our body are there because they were useful to our distant ancestors:

There are other traits that wouldn’t make sense if we were intentionally designed; the Vagus nerve is one of them.

I can recommend Neil Shubin’s book Your Inner Fish.

March 20, 2016 Posted by | evolution, science | | Leave a comment

Human evolution and cross breeding

I recently joked about new discoveries on humans mating with other homo species. There is more detail here, including how scientists figure this stuff out. Of interest is that we had mating with other homos both in the “failed migration” out of Africa, and again in the successful one (65 K years ago), and these conclusions are possible because of modern genome sequencing techniques.

On a more mundane (but still fun) level, here is a little video describing an evolutionary trajectory that lead to modern humans.

Science humor: a joke about curved spacetime:


February 19, 2016 Posted by | evolution, human sexuality, physics, science | , , | Leave a comment

Should have been my Valentines Day Post (human evolution)

Hey, you think that you’ve pushed the envelope in seeking romance? Both of us are downright shy compared to what our ancient ancestors did:

The discovery of yet another period of interbreeding between early humans and Neanderthals is adding to the growing sense that sexual encounters among different ancient human species were commonplace throughout their history.

“As more early modern humans and archaic humans are found and sequenced, we’re going to see many more instances of interbreeding,” says Sergi Castellano, a population geneticist at the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany. His team discovered the latest example, which they believe occurred around 100,000 years ago, by analysing traces of Homo sapiens DNA in a Neanderthal genome extracted from a toe bone found in a cave in Siberia.

“There is this joke in the population genetics community — there’s always one more interbreeding event,” Castellano says. So before researchers discover the next one, here’s a rundown of the interbreeding episodes that they have already deduced from studies of ancient DNA.

5 different episodes of inbreeding are discussed, with two different species of homo (based on DNA analysis) Surf to the article to read the rest. The conclusion:

We’re looking at a Lord of the Rings-type world — that there were many hominid populations,” one evolutionary geneticist told Nature when the findings were presented at a conference in 2013.

Kink is nothing new for us; in fact we are tamer than we used to be.

February 18, 2016 Posted by | evolution, human sexuality, nature, science | | Leave a comment

Best intentions waylaid by blogging: Dawkins, Scalia, Clinton and Trump

I had a good morning; long run and a delightful lunch with a dear friend, where we caught up on our personal lives and discussed the events of the day.

So, I figured I’d study some, and yes, it isn’t evening yet. So I might still do that. But for now, some on the events of the day:

Antonin Scalia has been found dead in West Texas. No, I didn’t like his rulings nor his politics nor his social views. But he had friends and loved ones, and there is no doubt that he was a very smart, successful man. I’ll never see anything close to that level of success. So I’ll leave my remarks at that.

Richard Dawkins had a stroke, but his prognosis is excellent. Here he gives a public update.

Politics The uproar over Hillary Clinton’s e-mail is mostly political nonsense. I am NOT saying she handled this optimally (politically speaking) but it really is a non-issue.

Republicans Ok, it is down to Trump, Carson, Cruz, Kasich, Rubio, and Bush. Who will prevail? Right now, Trump is in the driver’s seat. Sam Wang discusses this here, in terms of delegates and how the GOP assigns them after a primary election:

Given the results in Iowa and New Hampshire, as well as national polls, if the Republican front-runner were a more conventional candidate we would be writing about near-inevitability. Donald Trump is in a very similar position to Mitt Romney’s at this point in 2012 – if anything, a somewhat stronger position. In 2012 Romney lagged at various points to other candidates. For Trump, this has not happened since he entered the race.

Nonetheless, what would it take for Trump to fail to get the nomination?

With the Republican field so divided after New Hampshire, the path for anyone other than Trump requires nearly all candidates to drop out. Multiple candidates want that to happen. For example, Ted Cruz thinks it is time to unite around one candidate: Ted Cruz. And so on. However, after getting 3 or 4 convention delegates each on Tuesday, Cruz, John Kasich, Jeb Bush, and Marco Rubio all have reasons to stay in. Under these conditions, Trump wins.

Many political journalists have a wrong understanding of the early-state delegate process. It is not proportional at all, but what I call pseudo-proportional. As suggested by my computational simulation of the delegate process [the code is here], in a field of four candidates, an average-across-states vote share of 30% is enough to get 50% of delegates through Super Tuesday. That’s an average: the winner could get 20% of the vote in Texas and 40% in Georgia, and so on. Donald Trump is well on track for this scenario: he won 24% of the vote in Iowa and 35% in New Hampshire. As of today, he is at 36% in national surveys.

The not-Trump scenario occurs if Republicans cull their field, fast. […]

Surf to the article to read the detailed, but highly readable analysis. It is interesting.

February 13, 2016 Posted by | Friends, political/social, politics, science | , , , | Leave a comment