Bethel McGrew, Homeschool Graduate and Mathematics Ph.D. Student

The universe is inherently mathematical. Many scientists have come to this realization, but one of the first was Galileo Galilei. In his book, The Assayer, he wrote:

[The universe] cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it.

I have always been intrigued by people who dedicate themselves to learning this language, and I had the privilege of interviewing one such person last week: Mathematics Ph.D. student Bethel McGrew.

Bethel McGrew

Bethel was homeschooled K-12, and her experience produced a lifelong love of learning, whether the topic was literature, science, music, or chess (she has been a competitive tournament player but can now proudly say she is no longer the highest-rated among her siblings!) She didn’t do much with co-ops or group activities, and in some ways, I would say that her experience was that of a “classic” homeschooler. Her family used curriculum when it fit their needs, and when it didn’t, they found some other way to get the job done. For example, she said that her family couldn’t find a good course for geometry, so she just read Euclid.

In case you don’t know who that is, he’s the father of geometry. His treatise, Elements, was written around 300 BC and is considered one of the most important works of mathematics to this day. That was her primary reference for learning high school geometry! This was common in her homeschooling, perhaps because her parents (each has a Ph.D.) were so academically inclined. She read many primary sources as a part of her secondary education. For example, she read the works of Josephus (a first-century Jewish historian) to learn more about the history of New Testament times.

While her homeschooling experience was quite classic, her higher education was more modern. She started with distance-learning courses from Christian universities like Patrick Henry College and Bryan College. She then transferred to Western Michigan University in her home town of Kalamazoo and continued living at home while she finished her undergraduate degree. She originally thought she would pursue a career in philosophy (the field of her father’s Ph.D. and her mother’s main professional research focus) but decided to double major in philosophy and mathematics, discovering an unexpected love for the latter when some professors helped her see the beauty of math. She was offered and accepted a teaching assistantship to pursue a Ph.D. there. As a TA, she has taught everything from algebra to applied calculus, adding occasional long-distance tutoring work on the side with Asian ESL (English as a second language) students. She has earned her master’s degree en route and is currently beginning work on her dissertation in graph theory.

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Did The 2016 Election Actually Cause Psychological Stress?

A woman screams when she hears who won the 2016 election that Donald Trump has been sworn in as President of the United States (click for video)

**** PLEASE NOTE **** This is NOT a political post, and political comments will NOT be tolerated.

One of the many problems associated with doing scientific studies on the psychology of people is that you have to ask them how they are feeling and what they are thinking. The problem, of course, is aptly pointed out by fictional character Dr. Gregory House: “Everbody lies.” How can scientists determine whether or not people are actually telling the truth in these studies? There are some techniques. For example, if the study is based on a survey, the survey can ask the same question in many different ways, and a model can compare a person’s answers to those slightly-different questions to see if there is a consistent pattern. However, I recently ran across a study that did something radically different, and I found it very interesting.

The scientists noted that many people said the results of the 2016 presidential election here in the U.S. caused them a great deal of stress and anxiety. As the authors of the study put it:

One therapist, Inger Burnett-Zeigler, wrote in Time, “In the weeks since the election, many of my patients have come to therapy with anxiety, fear, and worry…It’s obvious to me that this highly contested election is already having real mental health consequences.”…A full 72% of Democrats reported that the presidential election outcome was “a significant source of stress,” as compared to 26% of Republicans. (references removed for clarity)

The researchers wanted to see if this was really the case, so they decided to do something interesting: They studied how people searched the internet after the election. After all, in a survey, you are either responding to a person or filling out a form that you know a person will read. The fact that you know someone else is going to evaluate your responses might lead you to say things that aren’t really true, so as to look better to that person or to make a point. However, your internet searches are (supposedly, not really) private, so people might be more “honest” with Google (or in this case, Bing) than they are with people. As a result, if you really want to know how people are feeling, look at their internet searches.

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A Classic Example of Misleading “Journalism”

View of Arkhangelsk, Russia at night (click for credit)

The headline at MSN is ominous:

It was 84 degrees near the Arctic Ocean this weekend as carbon dioxide hit its highest level in human history

Oh no! It’s sweltering in (or at least near) the Arctic! To emphasize the dire nature of this horrible news, the article goes on to say:

Over the weekend, the climate system sounded simultaneous alarms. Near the entrance to the Arctic Ocean in northwest Russia, the temperature surged to 84 degrees Fahrenheit (29 Celsius). Meanwhile, the concentration of carbon dioxide in the atmosphere eclipsed 415 parts per million for the first time in human history.

To the average American, who was given a very poor education in both geography and critical thinking, that sounds so bad. It shouldn’t be that warm near the Arctic Ocean, should it? Of course it should! All you have to do is look at a compilation of the weather statistics for the city being discussed (Arkhangelsk, Russia). As you can see, since 1940, the highest temperature recorded at Arkhangelsk was 93.9 F (34.4 C). During that same time period, the highest May temperature was 86.4 F (30.2 C). Both of those are higher than the “alarming” temperature being discussed in the article.

Now these results are for all years since 1940. The recent, “abnormally warm” temperatures caused by global warming are setting those records, right? Wrong. You can click on various years, and you will find that the highest temperature on record (34.4 C) occurred sometime between 1960 and 1980. As you can see, then, there is nothing unusual about it being 84 F near the Arctic Ocean at this time of year. Most people don’t know that, and most people (especially those who blindly accept what the High Priests of Science proclaim) aren’t willing to do any investigation on their own to find out.

Of course, that’s what the author of this article is counting on.

Even Eyes Contain Bacteria!

Mouse eyes were studied in the article being discussed, but the results are probably applicable to many mammal eyes.

Writing about coral in the Journal Science, paleontologist Dr. George D. Stanley noted:

Symbiosis is the most relevant and enduring biological theme in the history of our planet.

If you aren’t familiar with the term, “symbiosis” refers to organisms of different species living together. There are three general forms:

(1) Parasitic symbiosis, in which one organism benefits and the other is harmed

(2) Commensal symbiosis, in which one organism might benefit but neither is harmed

(3) Mutualistic symbiosis, in which all organisms in the relationship benefit

I have written extensively on mutualistic symbiosis (see here, here, here, here, here, here, here, here, here, and here, for example). Not only does it fascinate me, but it was also the major scientific issue that led me away from atheism. When one sees the amazing mutualistic relationships that exist all over nature, it becomes clear that these organisms were designed to work together.

Bacteria tend to develop a lot of mutualistic relationships. Indeed, you would not be nearly as healthy as you are if it weren’t for the many mutualistic bacteria that live in and on your body. And while it is widely-known that you can find mutualistic bacteria in many parts of a mammal’s body, it was thought that you would never find them living in the eye for any extended period of time. That’s because mammal eyes contain an enzyme called lysosyme, which kills bacteria. However, new research indicates that at least one species of bacterium, Corynebacterium mastitidis, makes its home in at least some mammal eyes.

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What Is the Function of a Narwhal’s Tusk?

Three Narwhals swimming close to the surface of the ocean. The lead narwhal’s tusk is easy to see.
(credit: Dr. Kristin Laidre, Polar Science Center, UW NOAA/OAR/OER)

Back in April, I spoke at the Ohio Homeschool Convention. It is part of the Great Homeschool Conventions, at which I have been fortunate to be a regular speaker. This year, the convention graciously allowed me to do my favorite kind of presentation: A Question/Answer Session. I have done them at other conventions (see here, here, and here), and I always enjoy them, usually because I learn something. I open these sessions by simply asking for questions, and I tell the audience that the questions can be about anything. If I can’t answer a question, I am happy say the three words any scientist should be totally comfortable saying, “I don’t know.” I also tell them that if I have to say those words, I will try to find the answer later and post it on my blog.

That’s what happened at the Ohio Homeschool convention. One of the audience members asked me what a narwhal (Monodon monoceros) does with its horn. I had to tell him that I don’t know. I did tell him that it isn’t really a horn. In fact, it is an elongated tooth. I speculated about a couple of possibilities, but I couldn’t say anything for sure. That was a few weeks ago, and I have been pretty busy since then. However, I have wrapped up both the Thermodynamics course I was teaching at Anderson University, and the online classes I have been teaching this year, so I finally got around to investigating narwhals.

The short answer is that we still don’t know what a narwhal does with its tusk. The long answer, however, is much more interesting.

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Ignorant People Acting Intellectually Superior

Screenshot from the video being discussed.

We live in a nation that is shockingly ignorant of basic science. Yet, at the same time, some of the most ignorant people on the planet act as if they can speak for science. Take, for example, Bill Nye. Many people view him as today’s spokesperson for science, despite the fact that he displays his scientific ignorance time and time again (see here, here, here, here, and here, for example). I just ran across another example of ignorant people claiming to speak for science. It comes from the Jimmy Kimmel Live show.

It’s one of those fake public service announcements (PSAs) which attempts to demonstrate the intelligence of the people making the announcement while at the same time displaying the stupidity of those who disagree with them. This is a form of what is now called virtue signaling – the attempt to show others how virtuous you are, often by making fun of people who disagree with you. A screenshot from the fake PSA is given above. The spokesperson, “actor, director, and two-time sexiest man alive George Clooney,” is promoting an organization that attempts to educate ignorant people to give up their foolish beliefs. In the segment from which the screenshot is taken, Mr. Clooney says that your donation of $200 will “…teach ten @*!x&^ knuckle-draggers that dinosaurs existed, but not at the same time as people.”

Now, of course, anyone with a modicum of scientific knowledge should immediately see what is wrong with the graphic being shown. Those who believe that dinosaurs and people did not live at the same time cannot use carbon dating as a way of supporting their claim. Because of the relatively “short” half-life of carbon-14, carbon dating can only be used on carbon-containing items that are less than 60,000 years old. Given that the generally-accepted timescale has dinosaurs going extinct 65 million years ago and the earliest humans appearing about 200,000 years ago, “Basic F**king Carbon Dating” cannot tell us anything about whether or not humans and dinosaurs existed at the same time.

In fact, if one truly believes carbon dating, one has to believe that people and dinosaurs did, indeed, coexist. That’s because multiple dinosaur fossils have been carbon dated to between 23,000 and 41,000 years old (see here, here, and here). All of those values are well within the timeframe that the scientific consensus tells us modern humans existed.

Now, of course, those who desperately want to believe in the generally-accepted timescale will make up excuses for why you can believe most carbon dates, but not the ones done on dinosaur bones. Interestingly enough, however, at least some of those people don’t want to do further tests to see if their excuses work. But that’s not my point. To some extent, all scientists make up “just so” stories to prop up their hypotheses, so it’s understandable that those who are committed to the scientific consensus do so as well.

My point is much simpler than that. The makers of this fake PSA wanted to show that they are well-educated and intelligent because they simply accept what the High Priests of Science proclaim without investigating the evidence in any way. At the same time, they wanted to show that those who believe dinosaurs and people lived at the same time are stupid. Instead, they ended up demonstrating their own ignorance of the scientific data related to the issue. Unfortunately, because the High Priests are doing such a great job at keeping the general public ignorant of science, most people will have no idea!

Dr. Winston Ewert, Homeschool Graduate and Software Engineer

Dr. Winston Ewert

Back in July of last year, I wrote about what might be one of the most important genetic studies of the decade. It treated an organism’s genome like a large computer program that was put together using specific groups of genes as programming “modules.” The study showed that this view of the genome made more sense of the genetic similarities between certain animals than an evolutionary view. When I read the study and blogged about it, I did not recognize the author’s name and had no idea who he was. Later on, he contacted me and thanked me for blogging about his study. He also informed me that he is a homeschool graduate and used my courses in his education. I recently contacted him to see if he would be willing to be a part of my homeschool graduate project, and he graciously agreed.

Dr. Ewert was homeschooled K-12, as were his four siblings. Like many homeschoolers, his parents’ primary motivation was to school their children using a Christian worldview. However, unlike most of the homeschool graduates I have talked with and written about, he was homeschooled in British Columbia, Canada. This actually made access to university a bit more difficult for him. Most British Columbia universities weren’t “homeschool friendly” like U.S. universities, so when he graduated from homeschooling, he started his higher education at Kwantlen University College, which was pretty much the Canadian equivalent of a community college. After two semesters, he transferred to Trinity Western University to finish his degree.

He said he had developed a computer obsession by the age of 10, so he knew he wanted to study computers. At Kwantlen, he started studying computer information systems. He transferred to Trinity when he realized he should be studying computer science instead. Had he started out in computer science at Trinity, this would have made graduating in four years a bit easier. That’s the only real negative aspect he could think of regarding his homeschooling.

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You Just Never Know What Will Inspire a Student

Spoons used as resistors in series (left) and in parallel (right).

In my high school physics course designed for homeschooling, I cover the standard topics that are considered important in preparing a student for university-level physics. One of those topics is resistance in electrical circuits. Unless you are dealing with exotic substances at very low temperatures (superconductors), all materials that conduct electricity resist the flow of electrons to some extent. A good conductor has a low resistance; a poor conductor has a high resistance. The amount of resistance in an electrical circuit and the voltage of the power source determine the amount of current flowing through the circuit, so it is important to be able to calculate a circuit’s overall resistance.

When resistors are connected so that the electricity must flow through each one of them, we say that the resistors are hooked in series. Notice how the spoons are connected in the left-hand photograph above. If I hook a battery up to the handle of the right-hand spoon and the head of the left-hand spoon, electricity would have to flow through both spoons to get from the negative side of the battery to the positive side. That tells you the spoons are hooked together in series.

When resistors are connected so that electricity has a “choice” about which resistor to travel through, we say that the resistors are hooked up in parallel. Notice how the spoons are connected in the right-hand photo above. If I were to hook a battery to the handle and head of the bottom spoon, the electricity would only have to travel through one of the two spoons to go from the negative side of the battery to the positive side. That tells you the spoons are hooked together in parallel.

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No, Scientists Did Not “Partially Revive” Pig Brains!

One conception of a pig’s brain being kept alive outside the body. (modified from the linked image)

As anyone who reads my blog knows, I have a rather low opinion of science “journalism.” In my experience, most science “journalists” know little about journalism and even less about science. As a result, what they publish is often so misleading that it just adds to the level of scientific ignorance that is already shockingly prevalent in today’s society.

As a result, I was pleased to find that two different readers sent me two different articles about a recent experiment involving dead pig brains. They were both justifiably skeptical of what the articles were saying, and they asked my opinion. I am happy to oblige. The worst of the two articles can be found at Big Think. It is entitled “Yale scientists restore brain function to 32 clinically dead pigs.” It then goes on to say:

The image of an undead brain coming back to live again is the stuff of science fiction…But like any good science fiction, it’s only a matter of time before some manner of it seeps into our reality. This week’s Nature published the findings of researchers who managed to restore function to pigs’ brains that were clinically dead. At least, what we once thought of as dead.

None of this is true. The researchers have accomplished something that overturns the current scientific consensus about the survivability of neurons (the “workhorse” cells of the brain). They also might have developed a technology that will significantly improve drug testing, but they haven’t even come close to restoring brain function!

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Best Evidence Yet for a Black Hole!

Four images of the center of M87 constructed from data collected by eight radio telescopes on four different days. The bar represents an angle of roughly 14 billionths of a degree, and the circle represents the resolution of the system.
(click for credit)

In 1796, Simon Pierre LaPlace predicted that there are objects in the universe which are so massive that light cannot escape them. As a result, they would be “invisible” to us. These objects have become known as black holes. More than 100 years later, Einstein published one of the most successful theories of modern science: General Relativity. A year later, Karl Schwartzchild used Einstein’s equation to define a black hole and calculate its radius, which is now known as the Schwarzschild radius. While black holes captured the imagination of many scientists, Einstein himself did not like them. In fact, in 1939, he published a paper that attempted to show they cannot exist.

Over the years, however, several lines of indirect evidence have supported the existence of black holes. For example, astronomers can measure the speed of objects in orbit around other objects. The speed of the orbiting object indicates the mass of the object being orbited. In the center of a nearby galaxy charmingly named “M87,” there is a disc of hot gas that is orbiting so quickly that the mass of what is being orbited must be three billion times the mass of our sun. However, the size of the object is, at most, the size of our solar system. Those measurements are consistent with Schwartzchild’s description of a black hole.

Of course, it’s always possible that the speed measurements are wrong, or that there is a very massive object that is consistent with what we think a black hole might be but isn’t actually a black hole. Thus, we need some other means by which to analyze the object. That’s where the Event Horizon Telescope (EHT) comes in. Despite it’s name, it is not a single telescope. It is a combination of eight different telescopes that are found in different geographic locations. Those telescopes examined the center of M87 for several days, and their data were combined together to produce the images seen at the top of this post. They are exactly what one expects those telescopes to detect if the center of M87 is a black hole. Thus, as the title of this post indicates, they represent the best evidence to date for the existence of a black hole!

Now while these images are excellent evidence for a black hole at the center of M87, it is important to know what they are and what they are not.

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