Math: When You Need to Feel Superior

Posted on 29 Sep 2017 by Frank Moraes

From as long as I can remember, I’ve been good at math. It was just fun. The same way that Jerry West practiced basketball late into the night, I was the same way about math. Probably as a result, I’ve always hated math used as a substitute for intelligence. And it was in that context that I came upon the image above.

It was for something like joining Mensa or buying some “brain training” course of something. But I like a good math puzzle as much as anyone. So I figured I would solve it. It’s been a while since I’ve posted anything here, and it is as good an excuse as anything.

The thing about it is that it isn’t much of a puzzle. It’s just a math problem. And it takes zero creativity. All you need is to have taken a basic algebra course taught by a reasonably competent teacher. And you must have taken the course seriously enough to learn the material.

That shouldn’t have been hard because math actually is loads of fun. But the fact that someone would use it to construct such a simple, uninspiring problem does sum up everything that makes most people hate math. But without further ado, I guess I will get to it.

Why Someone Thought It Was Interesting

The two equations look similar. It’s just that one is with x and the other with x². And so it looks like there ought to be some clever trick that allows the problem to simply pop out.

Unfortunately, that doesn’t seem to be the case. A mathematician better than I might see something brilliant. But I don’t. There are lots of ways to approach the problem, but they all end in a slog.

Solving the Equations

Sadly, this is a brute force problem. The first equation is just a quadratic that can be solved all by itself, admittedly, with two solutions.

We just multiply both sides of the equation by x, and end up with the following equation:

x² + x – 5 = 0

Oh, how I do wish this were more interesting. There are a bunch of ways to solve this, one way or another, you get that the two values of x are:

x = (5 ± 21^½)/2

If we choose the “plus” case, then x = 4.79. If we choose the “minus” case, then x = 0.209. And through the wonders of mathematics, if you put these two numbers into the second equation, you will get that:

x² + 1/x² = 23

Now an actual mathematical question is why this is so. What we just did was plug numbers into equations. This is a good example of why most people hate math.

Even worse is that some dimrod thought that solving this question indicated any kind of intelligence or, even worse, intellectual creativity.

But trust me: this is the kind of nonsense that your children are being taught in school. This is why the American Empire won’t last the century.

Astronomy Usually Disappoints: Solar Eclipse 2017

Posted on 21 Aug 2017 by Frank Moraes

Where I live in California, the solar eclipse was supposed to start at roughly 9:00 am. It reaches maximum occultation at 10:20 am. And then it ends at roughly 11:40 am. As I write this, it is 10:00 am, and my world is shrouded in clouds.

I got prepared for the event over the last week. I’ve got a set of welder’s glasses. You are supposed to use shade 12 or higher. I’ve got a double-12 set-up. What’s more, my father drilled a circular hole in a board so we could see the shadow of the eclipse as it makes its way across the sky. It would have been fun.

Astronomy Disappoints

When I was in college, I was friends with a number of people who were into astronomy. So I often found myself freezing in the middle of the night while we tried to see this or that. But what’s happening today is pretty typical of those trips. The weather does not cooperate.

Eventually, the fog will burn off. But it is going slow. As we approach full occultation, I can tell that it is much darker than it normally is. In fact, it’s about as dark as it is at 6:30 am. But this is not a lot to get excited about.

If you want to study astronomy, you really need to take a trip to a nice desert somewhere. The truth is that I live in a rotten area for astronomy. But this must also be some corollary of Murphy’s Law: the cloud cover where you are will be directly proportional to your excitement regarding an astronomical event.

Update

At 4:00 pm, I took a walk down to the supermarket. As I came out at 4:30, the cloud cover had just broken up so that I could see the sun to some extent. So only five hours late!

The next time there is an eclipse, I’m going to head for the desert!

Image is in the public domain.

There Is No Dark Side of the Moon

Posted on 12 May 2017 by Frank Moraes

It seems I am constantly been offended with some mention of the dark side of the Moon. This isn’t an attack on Pink Floyd, because at any given time, there is, in fact, a dark side of the Moon. But in Space: 1999, Moonbase Alpha was located on the dark side of the Moon. Now I understand, Space: 1999 was not in love with science. It was 1 part science and 1999 parts fiction. But it isn’t alone. I see this all the time.

There are many things that lead people to think that there is a dark side of Moon. I think that people mistake the outer side of the Moon with the dark side. But anyone who thinks about it for an instant will realize half the Moon is lit up when we are at the quarter Moon. That means the outer side of the Moon must be similarly half-lit. Just the same, the mistake is easy enough to make with our foggy brains.

The Other Side of the Moon

The Moon is tidally locked with the Earth. That means that the same side of it always faces the earth. Until we started sending rockets out into space, we had no idea what the outer side of the moon looked like. Well, we knew it looked a lot like the inner side. It turns out that because of Moon wobbles, we can actually see 59% of the Moon’s surface. That’s not all at once, of course. We have to watch it for a long time. But it’s easiest to say that half of the Moon can’t be seen from the Earth.

Thus, in a sense, the outer side of the Moon is the “dark side of the Moon.” And it is what we people are getting at when they talk about putting Moonbase Alpha on the dark side of the Moon. But it actually doesn’t make any concrete sense. The Moon is between the the Earth and the sun. Compare this to the new Moon (when the Moon is right between the Earth and the sun). That is: when the Moon is “new” — meaning that the dark side of the Moon is facing the earth. The time when the outer Moon is dark is when the Earth is between the sun and the Moon.

The Dark Side of the Moon Is Constantly Changing

Regardless, the outer side of the Moon has a day just like every other part of the moon (unless you want to get technical and talk about the lunar poles): 27.3 Earth days. I think, however, that Pink Floyd is responsible for this error of thought in the song “Brain Damage.” That’s not to say that they were thinking wrong. Waters is a great lover of metaphor. And the song doesn’t even imply that the dark side of the Moon is any particular place.

But people have picked up on it. And “dark side of the Moon” sounds better than “outer side of the Moon.” Although actually, from a metaphorical standpoint “outer” is probably better than “dark” given that we can actually see a great deal of detail in the dark side of the Moon. It is the outer side that we can’t connect with.

The Moon Is Fascinating — We Should Understand It

Regardless, I bristle every time I hear the term used because I know that it is a sign that people are not understanding how the Earth and Moon interact with each other. And this is important to me because learning what caused the phases of the Moon was really important to me. Plus, as I learned when I taught planetary astronomy at college, people really don’t understand this stuff. And it’s so easy and so cool. If there really were a dark side of the Moon, that would be hard to understand.

Dark Side of the Moon Cover via Wikipedia. Licensed under Fair use.

Chaos Theory as it Relates to Rick and Morty

Posted on 29 Apr 2017 by Frank Moraes

It’s weird, but the television show Rick and Morty has given me many ideas for articles. There’s just so much to it. A show like Bob’s Burgers is really all about the characters. But Rick and Morty brings up so many bizarre ideas that I have a hard time not getting lost in them. Most recently, I was thinking of the infinite timelines. This is what explains the Council of Ricks and Jerryboree — the daycare center for Jerrys. Of course, it’s all absurd.

To begin with, if there are infinite timelines, why are there only three thousand Ricks on the Council of Ricks? Well, I do have what might sound like a reasonable explanation: out of the infinite timelines, there are only so many that just happened to have Ricks. This doesn’t work, of course. If there are an infinite number of timelines, there would be an infinite number of timelines with Rick. Infinity is that way. But that doesn’t bother me all that much. What does bother me is this: Rick, Morty, Summer, Beth, Jerry.

Chaos Theory

The issue is this: chaos theory. When I was in my 20s, chaos theory was the thing — even non-nerds were into it. I wasn’t, of course. And that’s because it’s actually a really simple thing. (Research on it, is another matter; but that’s beyond pretty much all but specialists.) It’s just about non-linear systems. Let me explain.

Imagine you are pushing a cart down the road at a fairly constant rate and I’m making measurements of it to figure out how far you’ve gone. That’s a linear system. If I make a small mistake in the measurement of your speed, it will cause me to be wrong in calculating the distance you’ve traveled. But the error will be proportional to the error I made in your speed.

Non-Linear Systems

Now imagine that you are tripling your speed every ten seconds. Then a small error in my speed measurements will lead to a huge error in the distance traveled. In this case, the error will be squared for reasons that I’d love to explain to you, but don’t have the time (nor, admit it, do you the the interest — a fact I know from experience).

Non-linear systems can be highly non-linear, however. To (inappropriately) use the cart example, you could have a situation where a single small error would cause your final answer to be off by a factor of millions. And that’s what chaos theory is all about. And we have an example of that: the weather, which is where this all started. If you want to know more, learn about Edward Lorenz.

Chaos Theory and Time

Think about time. But first, let’s quote Robert Marley from John Dies at the End, “Time is an ocean, not a garden hose.” We have to forget that, even though I think it’s more or less correct. Imagine time as a garden hose — a line. How chaotic is it? Well, we certainly know it is nothing close to linear. Consider the following example:

A woman is going to buy a ticket for the state lottery. She uses the random system. On her way to the store to get it, a squirrel darts in front of her causing her to slow down and get to the store a couple of seconds later. That is the difference between her life going on as usual and her life completely changing because she won a half billion dollars.

That’s one example. So my belief is that time is the most chaotic system imaginable — indeed, infinitely chaotic — the ultimate example of chaos theory. And that brings us back to Rick and Morty. The best estimates are that our universe is 13.8 billion years old. Given that all of the universes in the show are roughly the same, they too must be that old. Time is just stuff happening: it’s a concept to explain why things change; this is why time doesn’t exist without matter. And 13.8 billion years is a lot of time.

A Long Time Coming: 13.8 Billion Years

Even if time were non-chaotic and changes had linear effects — if small changes would have small effects — that’s enough time that there just wouldn’t be multiple Ricks. But even if there were, how is it that they all marry the same woman who has a daughter named Beth, who goes on to marry a man named Jerry with whom she has two children named Morty and Summer.

Okay: infinity. If there are an infinite number of timelines, then literally every possible universe would exist. (It’s still odd that all of those universes start at the same time.) But if that’s the case, where are all the timelines that are exactly like the 3,000 that we know about except that Morty’s sister is named Winter?

I understand: Rick and Morty is just a television show — one I find quite entertaining. But I actually think that it is dangerous to think that time is not chaotic. Politically, it’s the same as believing in an activist God. It justifies kings because they are the result of fate rather than blind chance.

Who You Are Is the Result of Dumb Luck

The more we know about the world, the more we know that luck is everything. Were you born with a good body? Were you born to parents who raised you in a loving and intellectually stimulating environment? Did you inherit billions of dollars? Were you born in the San Francisco rather than Monrovia? Did a squirrel run in front of your car when you went to buy your lottery ticket?

I think that if people can see that their entire success in life is due to nothing but luck (and I cannot escape this conclusion myself), then we will build a more equitable society. Feudalism existed because people believed that God chose how people’s lives should be. Capitalism exists because people believe that the rich have earned what they have — at least to some extent.

Thomas Paine: Computer Program

Thomas Paine was a great rhetorician who was far ahead of his time in terms of social thinking. But that’s just because he was born with the perfect body and environment to make him Thomas Paine. He didn’t choose to be Thomas Paine. Now that’s not to say that we shouldn’t look up to him. The society should pay tribute to people who made the world better, because we want to create an environment that causes people to be better. Thomas Paine’s body born into 1950 Soviet Union would not be the Thomas Paine we all know and love.

But recognizing that Thomas Paine could no more be anything other than what he was than that a computer program can do anything other than what it was programmed to do allows us to see that having great material differences between people is immoral. Thomas Paine should not have had any more comfortable a life than the millions of African slaves that supported the southern colonies’ economies. We are nothing more (or less) than exactly what we have to be.

Immoral Society Based on False Premises

And these are the kinds of things that you can think about if you watch Rick and Morty. Time is the ultimate example of chaos theory. Luck is the only thing that determines who we are. There is no free will. Our unwillingness to see this provides intellectual cover for an immoral system — one that (if we are very lucky) future generations will look back on in horror, just as we look back at the burning of witches and the enslavement of humans.

Top image cropped from Fractal Digital Art by YMF. It is in the public domain. Rick and Morty image cropped from one at Wired. Licensed under Fair Use. Thomas Paine image is in the public domain.

I Don’t Care What You Call Pluto

Posted on 26 Mar 2017 by Frank Moraes

Vox published an article last week that made me want to slam my head against the wall, The Debate Over Pluto Will Never Die. Here’s the Latest Argument for Why It’s a Planet. Astronomer Kirby Runyon has come up with a new definition for a planet. And if we use it, there will be hundreds of planets in our solar system. For example, our Moon would be a planet. And hell, why not?

Remember: the Moon is quite a lot larger than Pluto. In fact, the largest 7 moons in the solar system are bigger than Pluto. So size isn’t the issue. Oh, you think a planet is something that orbits the sun and a moon is something that orbits a planet. Guess what? It ain’t nearly that simple. The Moon doesn’t orbit around the Earth. The two objects orbit around their center of mass. I have discussed this issue before, The Unusual Pluto-Charon Binary Orbit. It turns out that the Earth-Moon center of mass is inside the Earth. But the Pluto-Charon center of mass is way outside Pluto.

Orbits Are More Complex Than They Seem

The same thing is true of the Sun, although Jupiter is the only object large enough to make the Sun wobble. But my point is that if you looked at the Earth-Moon system orbiting around the Sun (the center of mass is effectively the center of the Sun), you would not see the Earth making an ellipse around the sun with the Moon circling it. Instead, you would see the two objects zigzagging around the sun. So if you look at it from a large scale, it looks very much like the Moon is orbiting the Sun. Because it is.

Now look at the Pluto-Charon system. It’s the same, but even more zigzag. So if Pluto is a planet, I sure don’t see why the Moon isn’t. So why not?

A New Planet Definition

Runyon and some other astronomers have suggested this as the definition of a planet:

A planet is a sub-stellar mass body that has never undergone nuclear fusion and that has sufficient self-gravitation to assume a spheroidal shape … regardless of its orbital parameters.

Got a problem with that? All of these objects ultimately orbit the Sun anyway. If the Earth suddenly disappeared, the Moon would continue to orbit the Sun. So there you go: the ultimate definition of a planet that couldn’t possibly be designed just to make Pluto a planet. And I say this knowing that Brian Resnick reported, “Once he’d seen this side of Pluto, Runyon was bothered that it wasn’t a full-fledged planet anymore.”

Here’s the thing: I don’t care. I so don’t care that it’s annoying. Call Pluto whatever you want. And I’ll go further: call the Earth anything you want. I can certainly come up with a definition of planet in which the Sun has only 4 planets, knocking out the four rocky inner “planets.” Because, as Juliet put it:

What’s in a name? That which we call a rose
By any other name would smell as sweet …

Pluto Is Fascinating — Whatever You Call It

I find Pluto fascinating. I don’t need to call it “planet,” “dwarf planet,” or even “rose” to find it fascinating. Is it only the large things that are worth studying — worth caring about? From my perspective, the Earth is the most interesting plant for what I think are obvious reasons.

But here’s the thing: our solar system is amazing. Rather than fight about what category to place Pluto in, why don’t we take a moment to marvel at the fact that Triton orbits Neptune backwards? And speaking of that, how in the universe did Venus get that backwards day (which happens to be longer than its year)? Or how about if you took all the debris of the asteroid belt (including “planet” Ceres), you’d have a “planet” about 1/25th the size of our Moon?

Space Garbage

There is something nice about the current official definition of planets: it creates 8 of them. They divide very nicely into two types: small rocky ones close to the Sun and big gaseous ones far from the Sun. They are completely dominant regarding their moons — all orbit a point inside the planet. I think the Earth has the largest moon relatively speaking, and it is only 1% of the Earth’s mass. (Charon is 12% the mass of Pluto.) But I’m willing to give it all up.

I propose the following definition:

Space garbage is anything that isn’t a star, broadly defined (including black holes, quasars, and so on).

So you say “planet” and I say “space garbage.” And literally nothing about the science of solar systems changes.

Image of Pluto by NASA. It is in the public domain.

Chinese Room Argument

Posted on 25 Feb 2017 by Frank Moraes

The argument and thought-experiment now generally known as the Chinese Room Argument was first published in a paper in 1980 by American philosopher John Searle. It has become one of the best-known arguments in recent philosophy. Searle imagines himself alone in a room following a computer program for responding to Chinese characters slipped under the door. Searle understands nothing of Chinese, and yet, by following the program for manipulating symbols and numerals just as a computer does, he produces appropriate strings of Chinese characters that fool those outside into thinking there is a Chinese speaker in the room. The narrow conclusion of the argument is that programming a digital computer may make it appear to understand language but does not produce real understanding. Hence the “Turing Test” is inadequate. Searle argues that the thought experiment underscores the fact that computers merely use syntactic rules to manipulate symbol strings, but have no understanding of meaning or semantics. The broader conclusion of the argument is that the theory that human minds are computer-like computational or information processing systems is refuted. Instead minds must result from biological processes; computers can at best simulate these biological processes. Thus the argument has large implications for semantics, philosophy of language and mind, theories of consciousness, computer science, and cognitive science generally.

–David Cole
The Chinese Room Argument

John Searle 2015 by FranksValli. Licensed under CC BY-SA 4.0.

Human evolution and the Myth of Control

Posted on 19 Feb 2017 by Frank Moraes

Bone House Wasp - Very Good Mother Mother Nature Network published an interesting little article some time ago, Kooky Cartwheeling Spider Among Bizarre New Species. It seems that 18,000 recently discovered species were given official names this last year. And so the College of Environmental Science and Forestry at State University of New York (SUNY) decided to highlight ten of these creatures. Think about that for a moment. Humans have spent thousands of years cataloging different animal species, yet we can still be discovering tens of thousands of them each year. According to the article, there are still 10 million yet to be discovered. This number is also the estimate of the total number of species on the earth. Thus far, humans have only been able to catalog about 1.5 million species.

The group of creatures include some things that demand a rewrite of Hamlet, “There are more things on earth than are dreamt of in your worst nightmares.” Take the bone house wasp. Although disturbing, we must admit that she is a hell of a good mother. She creates a nest in a hollow stem of a plant. At the bottom, she lays her eggs. On top of it, she puts a dead spider for the hungry baby wasps, once they are born. That’s actually rather nice of the mother in regard to the spider — paralyzing, and having them eaten alive seems a much more common approach in the wild. The creepy part comes when the mother wasp piles dead ants on the very top. This is done to ward off predators because of the smell of the ants. So think about a nursery with rotting corpses piled by the door to keep others away. Effective, loving, and very creepy!

For the creationists out there, there is the Limnonectes larvaepartus. It is a frog from Indonesia that gives birth to live tadpoles. That’s interesting because most frogs lay eggs and a few frogs give birth to baby frogs. This new frog is what we might call “the missing link.” But as we know from creationist apologetics, there will always be “holes” in the diversity of life. Nothing will convince them because they cannot be convinced. They “know” the truth and are only looking for things that justify what they already “know.”

Another of the new species is Torquigener albomaculosu, a kind of pufferfish. The male of this species attract females by creating beautiful designs in the sand. That reminds me of the following “Effective Catcalls” cartoon. Females really do appreciate a man who can provide a nice home.

The sad thing about all the species we are discovering is that plants and animals are going extinct at an even faster rate. Of course, life forms are always going extinct — it is the nature of life. But it is hard not to figure that we are largely responsible for the fast rate. Thus far, we have done this by destroying habitat, but as time goes on, the climate forcing is going to be a much bigger — even catastrophic thing.

Still, the amazing diversity of life on the earth is staggering. At the same time, mama wasps are just like human mothers in all they do to protect their young. And I know that a lot of people will dismiss what the wasp does as just instinct. But our great brains don’t seem to change the overall nature of things. We humans are pre-programmed to think that human babies are cute and worth protecting. We may obscure that with ideas like “feeling” and “choice.” But I think that’s all rubbish. We are all on autopilot, we just have these big brains that trick us into thinking we are in control.

Image of Bone-house Wasp taken from ESF. Cartoon taken from The New Yorker. Both licensed under Fair Use.

Smartphones Have Reduced Us to Goldfish

Posted on 13 Feb 2017 by Frank Moraes

Goldfish The average human’s attention span is… oh look, a bird!

According to scientists, the age of smartphones has left humans with such a short attention span even a goldfish can hold a thought for longer.

Researchers surveyed 2,000 participants in Canada and studied the brain activity of 112 others using electroencephalograms.

The results showed the average human attention span has fallen from 12 seconds in 2000, or around the time the mobile revolution began, to eight seconds.

Goldfish, meanwhile, are believed to have an attention span of nine seconds.

–Leon Watson
Humans Have Shorter Attention Span Than Goldfish, Thanks to Smartphones

Image cropped from Goldfish by AJC1. Licensed under CC BY-SA 2.0.

Forensic Pseudoscience — Oppression of the Poor

Posted on 10 Feb 2017 by Frank Moraes

Two years ago, Radley Balko at The Washington Post wrote a really important article that bears revisting, A Brief History of Forensics. I’ve never been one to watch those forensics dramas on the television. Just the same, I didn’t know just how screwed up the state of forensics was. It seems that many parts of forensics are not settled science, or in fact, science of any kind at all.

Balko is most interested in bite mark analysis. Having managed a dental office for a couple of years, I found it interesting that this is a particularly gloomy area of pseudoscience. “There has yet to be any scientific research to support the notion that the marks we make when we bite with our teeth are unique. But even if we could somehow know that they are, we still wouldn’t know how those unique characteristics are distributed across all of humanity. And even if we knew those things, we still don’t know if human skin is capable of recording and preserving a bite in a way that would allow those markers to be identified.” That last one is the killer as far as I’m concerned: how is it that we could have been relying on such analysis without ever having answered such a fundamental question?

Forensic “Scientists” Don’t Look for Truth

The reason that Balko gives for this state of affairs is that forensic “scientists” are not interested in questioning the basis of their work. As he puts it, they are focused on “solving cases.” I don’t like that phrase. Better would be: “closing cases.” Because it really does seem that no one — not the prosecutors, the police, or the forensic “scientists” — are interested in finding the truth. As far as they are concerned, they already know the truth.

It’s like the line in The Usual Suspects, “To a cop the explanation is never that complicated. It’s always simple. There’s no mystery to the street, no arch-criminal behind it all. If you got a dead body and you think his brother did it, you’re gonna find out you’re right.” And that’s largely true, but it blinds them in cases where things aren’t simple. And it turns forensic “scientists” into little more than apologists, simply arguing for whatever theory the police are pushing.

Forensics Isn’t Science

The actual history of forensics is that of a field developed by people in the criminal justice system. And it has worked just the opposite of the way that science works. When a scientific theory becomes established, scientists have an incentive to beat away at it and find holes in it. That’s how you become a successful scientist. In forensics, once a theory becomes established, no one dares question it. Balko put it this way, “A fingerprint analyst testifying for the defense might disagree with a fingerprint analyst for the prosecution, but he isn’t going to call into question the premises on which the entire field of fingerprint analysis is based.” And in case you were wondering: yes, there are now people outside the field calling into question the reliability of fingerprints — evidence that has sent countless people to their deaths at the hands of the state.

Actual Scientific Forensics

The only kind of forensics that actually did come out of a scientific field and not criminal justice is DNA analysis. And this is really interesting: when forensic analysts are talking about bite marks, for example, they talk about certainty. The same goes for fingerprints, bullet lead composition, voice “prints,” and on and on. “[T]he one area of forensic science in which you will see experts testifying about probability is DNA Testing.” Of course, Balko is careful to note that this doesn’t mean that these other kinds of analyses are useless. But just like with eyewitness testimony, people are often convicted — even killed — because of the word of a single analyst based upon suspect science.

Balko thinks that the solution is to take forensics evidence out of the hands of judges who have no experience that would allow them to determine if these techniques were solid science or just pseudoscience. He wants to put it in the hands of scientific review boards. While I think that would certainly be an improvement, we have a much bigger problem. We have an entire justice system that is inherently unjust.

A Much Bigger Problem

People forget the first federal drug law — Harrison Narcotics Tax Act — was explicitly racist. It was a doctor who testified to the “fact” that, “Most of the attacks upon the white women of the South are the direct result of a cocaine-crazed Negro brain.” Similar things were said about the Chinese with regard to opium, and later, about Mexicans and “marijuana.” There will always be an underclass that the government will always oppress. To me, we need to rethink our harsh sentences in the light that many people convicted are innocent; the laws are unequally applied; and the laws themselves criminalize things that powerless people like to do.

Bearing all these things in mind, the powerful need to let go of their certainty. But that will never happen. Of course, it may also be that in a century, people will still be put to death based upon bad bite mark science. So let’s try to stop that, but we need to push much further.

Image cropped from Radley Balko by Gage Skidmore. Licensed under CC BY-SA 2.0.

Why the Neolithics Did So Much Trepanning

Posted on 24 Jan 2017 by Frank Moraes

More than 1500 trephined skulls have been uncovered throughout the world, from Europe and Scandinavia to North America, from Russia and China to South America (particularly in Peru). Most reported series show that from 5% to 10% of all skulls found from the Neolithic period have been trephined with single or multiple skull openings of various sizes. Many of the skulls show evidence of fractures. In some cases the operations were incomplete, as if the patients suddenly woke up and terminated the procedure. Some skull openings showed evidence of healing, meaning the patients survived the operations; others did not. In these latter cases it is impossible to determine if the patients were already (or recently) dead or whether the patients died soon after the procedure. Trepanations were performed in children as well as adults and in both males and females. The majority of trephinations, though, have been found in adult males…

Neolithic man was a hunter and his life experience revolved around this activity. Cave dwelling paintings also testify to this phenomenon. Consequently, he was very aware of hunting and war injuries. Neolithic man noticed, for example, that penetrating injuries to the chest and abdomen were usually fatal to man and animal. Likewise, massive blunt head injuries were invariably lethal. Nevertheless, blunt injuries to the head, if not massive, were not invariably fatal. With mild blows to the head, man or animal could be knocked down briefly and then get up and run. At other times, a man could be left for “dead” in the back of the cave, but after a period of time, he could “miraculously” recover and become “undead.” It was only with head injuries that primitive man noted that this phenomenon took place — namely suddenly becoming “dead” after an injury and then “undead.” Or, as we would describe it, that a head injury caused a momentary loss of consciousness (LOC), as in a concussion, or a more prolonged LOC, as in a cerebral or brainstem contusion — and then recover as the cerebral edema subsided and neural circuits were reestablished.

Of course, primitive man did not understand the pathophysiology involved. For the Stone Age man, there was also no awareness of the inevitability of death and no recognized mortality as part and parcel of the human condition. Diseases, pain and suffering, and death took place as a result of sorcery, evil spirits, or some other supernaturalistic intervention. People could become gradually “dead” from an illness or injury and then become “undead” because of some phenomenon. In the case of injuries, these conditions were caused by observed specific events, such as penetrating injuries or serious blows. These… did not occur randomly. Such was also the case with becoming “dead” and “undead,” and the primitive surgeon of Neolithic times understandably reasoned that he could also do something to bring back to life those individuals essential to the survival of the group.

Observing that small injuries to the head, more frequently than other injuries, resulted in “dying” and “undying” (ie, spontaneous recovery), they must, according to Prioreschi, come to believe that “something in the head had to do with undying.” More blows would not accomplish the ritual, but an opening in the head, trephination, could be “the activating element,” the act that could allow the demon to leave the body or the good spirit to enter it, for the necessary “undying” process to take place. If deities had to enter or leave the head, the opening had to be sufficiently large.

Prioreschi writes: “It would appear that he was trying to recall to life people who had died (or were dying) without wounds (or with minor ones), in other words, people affected with diseases and people whose small wounds were not so serious as to prevent ‘undying’…” Incomplete trepanations, as mentioned previously, are explained, not because the patients died during the procedure, but because of patients waking up and interrupting the procedure by suddenly becoming “undead.”

–Miguel A Faria
Neolithic Trepanation Decoded — A Unifying Hypothesis

Image cropped from Trepanated Skull, Neolithic by Rama. Licensed under CC BY-SA 2.0 fr.

Human Thought in a Dark Room

Posted on 15 Jan 2017 by Frank Moraes

I’m sure that many of my readers will like this little meme. But to me, it shows such total contempt for the search of knowledge that it makes me really angry. And I don’t know that I have seen a more clear example of the way that much of the atheist community deifies science.

I am, as most of you know, trained as a scientist. I have a PhD in physics. And maybe the fact that I don’t work in the field shows that I have a fundamentally different orientation. But that isn’t my experience. Most scientists I know don’t make a fetish of it. Science is to them what it is to me: a really powerful tool for learning new things of a very specific nature. And that’s it.

A Million Dollars

The whole meme reminds me of my favorite line from Citizen Kane. Bernstein scoffs at Thatcher, Kane’s guardian. The reporter says, “He made an awful lot of money.” And Bernstein replies, “Well, it’s no trick to make a lot of money — if all you want is to make a lot of money.”

The meme presents four ways of gaining knowledge. But the test is rigged. It’s defining knowledge as the kind of knowledge that science excels at. But I’ll come back to that. My point is that people who put these kind of memes together so want to limit the human experience. As Bernstein said in the script (cut from the film), “He [Thatcher] never knew there was anything in the world but money.”

Philosophy

According to the meme, “Philosophy is like being in a dark room and looking for a black cat.” So it’s a way to learn things, but a really bad one.

There are a number of things wrong with this. For one, the search for knowledge isn’t as categorical as this makes out. Work by Kant and Schopenhauer laid intellectual groundwork for Darwin’s discovery. But most people have an extremely childish view of how science actually works.

Perhaps most annoying to me is that math is a branch of philosophy, not science. People get caught up in counting, and think that it is real and thus “Science!” But giving names to quantities is not math. It’s like claiming that knowing the names of different bacteria makes you a microbiologist. It’s so silly.

Metaphysics

The meme claims, “Metaphysics is like being in a dark room and looking for a black cat that isn’t there.” Apparently, the writer doesn’t know what the word “metaphysics” means. From Merriam-Webster, metaphysics is “a division of philosophy that is concerned with the fundamental nature of reality and being and that includes ontology, cosmology, and often epistemology.” That’s right: it really doesn’t have anything to do with Edwardian mysticism.

The cosmology part of this is amusing. Most people think of this as part of science. And it is! In a limited form. But every time I hear some subgenius go on about how cosmology is settled because of the big bang, I think they sound like fundamentalists. Science said it, I believe it, that settles it. Not really.

Don’t get me wrong, the big bang is as established as natural selection. But most people do not find it a satisfying cosmological answer for the same reason they don’t find “God” a satisfying answer. It just raises another question. And that’s fine! But ultimately, cosmology is a metaphysical issue because science isn’t designed to find ultimate answers.

Theology

The meme continues, “Theology is like being in a dark room and looking for a black cat that isn’t there, and shouting, ‘I found it!'” This is probably the most offensive part of the whole thing.

The implication is that theology is the most rigid form of religious belief. It isn’t even religious belief, much less of the “God said it, I believe it, that settles it” variety. There have been many theologians who were atheists and agnostics. It’s only quite recent in the US that theology departments are overrun by theists.

And this part of the meme begs the question. Of course, the point of such simple-minded memes is to preach to the choir. No Christian is going to read it and think, “I’ve been so wrong! I’m an atheist now!”

Science

And so we come to the end of the meme, “Science is like being in a dark room and looking for a black cat using a fucking flashlight.” It’s only at this point in the meme that I wondered, “Why are we looking for a black cat in a dark room?”

I’m not an idiot; I get that it’s an analogy. But as I indicated above, this is a rigged analogy. It all falls apart if you change it to being in a dark room looking for a reason not to kill yourself. Science isn’t all that helpful in gaining that kind of knowledge.

But it’s worse than that, because the example just begs to be criticized on quantum mechanical terms. Once you turn on the flashlight, it isn’t a dark room so you literally can’t find the black cat in a dark room. Consider it on more practical grounds. What if turning on the flashlight caused the black cat to run out of the room before your eyes adjusted?

I suppose I shouldn’t really complain because the kind of people who write these things have a really limited understanding of science — and pretty much everything else. But geez!

Tribalism in Meme Form

This is all about tribalism. You can love and respect science without dismissing other ways of knowing. And it really disturbs me that this is the default position of the New Atheism. It never really bothered me that theists were tribal and awful. But I thought that humans could — if they opened their minds — be more accepting of others. But no. It’s just another “I know the One True Way” of experiencing the world. This is why we will always fight wars.

Image taken from me.me and used under Fair Use because someone has to fight back against arrogant idiocy.

Countable Infinity and Rick and Morty

Posted on 03 Jan 2017 by Frank Moraes

When it comes to math, I think it is best that I assume everyone is really ignorant. So forgive me for going over some really basic ideas about infinity. But I have good reasons for doing this. Some time ago, I wrote, Infinity Is Not a Number. In it, I discuss how the great Christian apologist William Lane Craig used a total misunderstanding of infinity to “prove” that the universe is not eternal. I was pointing out that this brilliant man was ignorant of the fact that infinity is not a number.

I guess I can understand. Mathematicians use infinity (∞) along with a lot of numbers. To understand infinity as a mathematical concept, you really have to study limits. And that isn’t something students get into until college — if then. It’s really when you start to study calculus that you get into limits. And that is done for the opposite reason: to understand the infinitesimal. It’s actually the same thing, but I won’t bore you with it. You either understand what I’m talking about (It’s the reciprocal, stupid!) or you would require a good deal more exposition than I’m willing to expend.

Countable Infinity

But there are some things about infinity that are intuitive to people of this time and place. For example, if you think of the whole numbers (0, 1, 2, 3…), you know that there are an infinity of them. Regardless of what natural number you can come up with, there is always a number that is one unit larger. Let’s combine the whole numbers with all the negative whole numbers (…, -2, -1, 0, 1, 2, …) that infinity space is twice as large. But that doesn’t mean there are twice as many integers as whole numbers. Both sets contain an infinite number of elements. But they are both “countably infinite.”

So what does it mean that they are countably infinite? It means that you can pick any number in the series and count to it. Consider the whole numbers again (because it is easier). You can count from 0 to 15,000,000 or 15,000,000,000 or whatever. It will just take time. If you have an infinite amount of time, I guess you could count all the whole numbers (and, unintuitively, the integers). (Note: this is one reason immortality is so terrifying: eventually you would get to the point of counting all the whole numbers.)

Rational Numbers

Now let’s consider the rational numbers from 0 to 1. These are just the fractions. You can tell that they are countably infinite. You just start counting: 0/1, 1/1, 0/2, 1/2, 2/2, 0/3, 1/3, 2/3, 3/3, etc. It doesn’t matter that many of the numbers of duplicates. The denominators go on forever. Thus, the number series is infinite. And we know it is countable because we are counting it. In theory, we can count all of the numbers. The same is true of all the rational numbers — not just the ones between 0 and 1.

So a countable infinity of countable infinities is a countable infinity. You would think that all infinities would thus be countable. But no.

Irrational numbers are numbers that cannot be represented as a fraction of two integers. You know: numbers like π and e. The set of all these numbers does not represent a countable infinity. Indeed, the irrational numbers between any two numbers are not a countable infinity. Think about it. It’s mind blowing.

Rick and Morty

I was thinking about this because I was watching an episode of Rick and Morty, “Rick Potion No 9.” In it, Rick turns his human world into Cronenberg-world. So in order to fix things, Rick goes looking for another reality, “There’s an infinite number of realities, Morty. And in a few dozen of those, I got lucky and turned everything back to normal. I just had to find one of those realities in which we also happened to both die around this time.” (Note: if there were an infinite number of realities, there would be an infinite number of realities where Rich “got luck,” but I’ll leave that as something to consider on your own time.)

The implication of this episode (and others) is that at every instant, there are an infinite number of realities, and each one creates an infinite reality at that point — and on and on and on. I’ve long thought this is what Planck time must represent: the time at which every possible quantum reality is spawned. But that doesn’t much matter. It’s just a thought. But I like Rick’s idea of an infinite universes (“realities”) constantly spawning an infinite number of universes.

Countably Infinite Universes

As outrageous as this notion is, it would still represent a countably infinite number of universes. I find that vaguely comforting. Of course, there’s all that dark matter and dark energy. Maybe that’s where the non-countably infinite universes exist. I don’t really care. I don’t like thinking about things that can’t be counted. Irrational numbers are as strong a proof of the non-existence of God that I can think of.

But let me leave you with a practical thought. As many of you know, I think memorizing multiplication tables is a waste of time. I think children would be better served watching Rick and Morty. They’d have a chance of thinking about math. And it wouldn’t make them hate math. Finally, it might get them to watch Existenz.

Rick and Morty image cropped from one at Wired. Licensed under Fair Use. Because of course everything has to be copyrighted forever. How else would we have the idyllic world we now live in? Infinity image is in the public domain.