Magnets, how do they work? (part 1)

Subtitle: Basic derivation of Ampere’s Law from the Biot-Savart equation.

Know your meme.

It’s been a while since this became a thing, but I think it’s actually a really good question. Truly, the original meme exploded from an unlikely source who wanted to relish in appreciating those things that seem magical without really appreciating how mind-bending and thought-expanding the explanation to this seemingly earnest question actually is.

As I got on in this writing, I realized that the scope of the topic is bigger than can be tackled in a single post. What is presented here will only be the first part (though I haven’t yet had a chance to write later parts!) The succeeding posts may end up being as mathematical as this, but perhaps less so. Moveover, as I got to writing, I realized that I haven’t posted a good bit of math here in a while: what good is the the mathematical poetry of physics if nobody sees it?

Magnets do not get less magical when you understand how they work: they get more compelling.

magnet-stem-cell-therapy

This image, taken from a website that sells quackery, highlights the intriguing properties of magnets. A solid object with apparently no moving parts has this manner of influencing the world around it. How can that not be magical? Lodestones have been magic forever and they do not get less magical with the explanation.

Truthfully, I’ve been thinking about the question of how they work for a couple days now. When I started out, I realized that I couldn’t just answer this out of hand, even though I would like to think that I’ve got a working understanding of magnetic fields –this is actually significant to me because the typical response to the Insane Clown Posse’s somewhat vacuous pondering is not really as simple as “Well, duh, magnetic fields you dope!” Someone really can explain how magnets work, but the explanation is really not trivial. That I got to a level in asking how they work where I said, “Well, um, I don’t really know this,” got my attention. How the details fit together gets deep in a hurry. What makes a bar magnet like the one in the picture above special? You don’t put batteries in it. You don’t flick a switch. It just works.

For most every person, that pattern above is the depth of how it works. How does it work? Well, it has a magnetic field. And, everybody has played with magnets at some point, so we sort of all know what they do, if not how they do it.

KONICA MINOLTA DIGITAL CAMERA

In this picture from penguin labs, these magnets are exerting sufficient force on one another that many of them apparently defy gravity. Here, the rod simply keeps the magnets confined so that they can’t change orientations with respect to one another and they exert sufficient repulsive force to climb up the rod as if they have no weight.

It’s definitely cool, no denying. There is definitely a quality to this that is magical and awe inspiring.

But, is it better knowing how they work, or just blindly appreciating them because it’s too hard to fill in the blank?

The central feature of how magnets work is quite effortlessly explained by the physics of Electromagnetism. Or, maybe it’s better to say that the details are laboriously and completely explained. People rebel against how hard it is to understand the details, but no true explanation is required to be easily explicable.

The forces which hold those little pieces of metal apart are relatively understandable.

Lorentz force

Here’s the Lorentz force law. It says that the force (F) on an object with a charge is equal to sum of the electric force on the object (qE) plus the magnetic force (qvB). Magnets interact solely by magnetic force, the second term.

2000px-lorentz_force-svg

In this picture from Wikipedia, if a charge (q) moving with speed (v) passes into a region containing this thing we call a “magnetic field,” it will tend to curve in its trajectory depending on whether the charge is negative or positive. We can ‘see’ this magnetic field thing in the image above with the bar magnet and iron filings. What is it, how is it produced?

The fundamental observation of magnetic fields is tied up into a phenomenological equation called the Biot-Savart law.

Biotsavart1

This equation is immediately intimidating. I’ve written it in all of it’s horrifying Jacksonian glory. You can read this equation like a sentence. It says that all the magnetic field (B) you can find at a location in space (r) is proportional to a sum of all the electric currents (J) at all possible locations where you can find any current (r’) and inversely proportional to the square of the distance between where you’re looking for the magnetic field and where all the electrical currents are –it may say ‘inverse cube’ in the equation, but it’s actually an inverse square since there’s a full power of length in the numerator. Yikes, what a sentence! Additionally, the equation says that the direction of the magnetic field is at right angles to both the direction that the current is traveling and the direction given by the line between where you’re looking for magnetic field and where the current is located. These directions are all wrapped up in the arrow scripts on every quantity in the equation and are determined by the cross-product as denoted by the ‘x’. The difference between the two ‘r’ vectors in the numerator creates a pure direction between the location of a particular current element and where you’re looking for magnetic field. The ‘d’ at the end is the differential volume that confines the electric currents and simply means that you’re adding up locations in 3D space. The scaling constants outside the integral sign are geometrical and control strength; the 4 and Pi relate to the dimensionality of the field source radiated out into a full solid angle (it covers a singularity in the field due to the location of the field source) and the ‘μ’ essentially tells how space broadcasts magnetic field… where the constant ‘μ’ is closely tied to the speed of light. This equation has the structure of a propagator: it takes an electric current located at r’ and propagates it into a field at r.

It may also be confusing to you that I’m calling current ‘J’ when nearly every basic physics class calls it ‘I’… well, get used to it. ‘Current vector’ is a subtle variation of current.

I looked for some diagrams to help depict Biot-Savart’s components, but I wasn’t satisfied with what Google coughed up. Here’s a rendering of my own with all the important vectors labeled.

biotsavart diagram

Now, I showed the crazy Biot-Savart equation, but I can tell you right now that it is a pain in the ass to work with. Very few people wake up in the morning and say “Boy oh boy, Biot-Savart for me today!” For most physics students this equation comes with a note of dread. Directly using it to analytically calculate magnetic fields is not easy. That cross product and all the crazy vectors pointing in every which direction make this equation a monster. There are some basic feature here which are common to many fields, particularly the inverse square, which you can find in the Newtonian gravity formula or Coulomb’s law for electrostatics, and the field being proportional to some source, in this case an electric current, where gravity has mass and electrostatics have charge.

Magnetic field becomes extraordinary because of that flipping (God damned, effing…) cross product, which means that it points in counter-intuitive directions. With electrostatics and gravity, the field is usually going toward or away from the source, while magnetism has the field seems to be going ‘around’ the source. Moreover, unlike electrostatics and gravity, the source isn’t exactly a something, like a charge or a mass, it’s dynamic… as in a change in state; electric charges are present in a current, but if you have those charges sitting stationary, even though they are still present, they can’t produce a magnetic field. Moreover, if you neutralize the charge, a magnetic field can still be present if those now invisible charges are moving to produce a current: current flowing in a copper wire is electric charges that are moving along the wire and this produces a magnetic field around the wire, but the presence of positive charges fixed to the metal atoms of the wire neutralizes the negative charges of the moving electrons, resulting in a state of otherwise net neutral charge. So, no electrostatic field, even though you have a magnetic field. It might surprise you to know that neutron stars have powerful magnetic fields, even though there are no electrons or protons present in order give any actual electric currents at all. The requirement for moving charges to produce a magnetic field is not inconsistent with the moving charge required to feel force from a magnetic field as well. Admittedly, there’s more to it than just ‘currents’ but I’ll get to that in another post.

With a little bit of algebraic shenanigans, Biot-Savart can be twisted around into a slightly more tractable form called Ampere’s Law, which is one of the four Maxwell’s equations that define electromagnetism. I had originally not intended to show this derivation, but I had a change of heart when I realized that I’d forgotten the details myself. So, I worked through them again just to see that I could. Keep in mind that this is really just a speed bump along the direction toward learning how magnets work.

For your viewing pleasure, the derivation of the Maxwell-Ampere law from the Biot-Savart equation.

In starting to set up for this, there are a couple fairly useful vector identities.

Useful identities 1

This trio contains several basic differential identities which can be very useful in this particular derivation. Here, the variables r are actually vectors in three dimensions. For those of you who don’t know these things, all it means is this:

vectors

These can be diagrammed like this:

vector example

This little diagram just treats the origin like the corner of a 3D box and each distance is a length along one of the three edges emanating from the corner.

I’ll try not to get too far afield with this quick vector tutorial, but it helps to understand that this is just a way to wrap up a 3D representation inside a simple symbol. The hatted symbols of x,y and z are all unit vectors that point in the relevant three dimensional directions where the un-hatted symbols just mean a variable distance along x or y or z. The prime (r’) means that the coordinate is used to tell where the electric current is located while the unprime (r) means that this is the coordinate for the magnetic field. The upside down triangle is an operator called ‘del’… you may know it from my hydrogen wave function post. What I’m doing here is quite similar to what I did over there before. For the uninitiated, here are gradient, divergence and curl:

gradivcurl

Gradient works on a scalar function to produce a vector, divergence works on a vector to produce a scalar function and curl works on a vector to produce a vector. I will assume that the reader can take derivatives and not go any further back than this. The operations on the right of the equal sign are wrapped up inside the symbols on the left.

One final useful bit of notation here is the length operation. Length operation just finds the length of a vector and is denoted by flat braces as an absolute value. Everywhere I’ve used it, I’ve been applying it to a vector obtained by finding the distance between where two different vectors point:

lengthoperation

As you can see, notation is all about compressing operations away until they are very compact. The equations I’ve used to this point all contain a great deal of math lying underneath what is written, but you can muddle through by the examples here.

Getting back to my identity trio:

Useful identities 1

The first identity here (I1) takes the vector object written on the left and produces a gradient from it… the thing in the quotient of that function is the length of the difference between those two vectors, which is simply a scalar number without a direction as shown in the length operation as written above.

The second identity (I2) here takes the divergence of the gradient and reveals that it’s the same thing as a Dirac delta (incredibly easy way to kill an integral!). I’ve not written the operation as divergence on a gradient, but instead wrapped it up in the ‘square’ on the del… you can know it’s a divergence of a gradient because the function inside the parenthesis is a scalar, meaning that the first operation has to be a gradient, which produces a vector, which automatically necessitates the second operation to be a divergence, since that only works on vectors to produce scalars.

The third identity (I3) shows that the gradient with respect to the unprimed vector coordinate system is actually equal to a negative sign times the primed coordinate system… which is a very easy way to switch from a derivative with respect to the first r and the same form of derivative with respect to the second r’.

To be clear, these identities are tailor-made to this problem (and similar electrodynamics problems) and you probably will never ever see them anywhere but the *cough cough* Jackson book. The first identity can be proven by working the gradient operation and taking derivatives. The second identity can be proven by using the vector divergence theorem in a spherical polar coordinate system and is the source of the 4*Pi that you see everywhere in electromagnetism. The third identity can also be proven by the same method as the first.

There are two additional helpful vector identities that I used which I produced in the process of working this derivation. I will create them here because, why not! If the math scares you, you’re on the wrong blog. To produce these identities, I used the component decomposition of the cross product and a useful Levi-Civita kroenecker delta identity –I’m really bad at remembering vector identities, so I put a great deal of effort into learning how to construct them myself: my Levi-Civita is ghetto, but it works well enough. For those of you who don’t know the ol’ Levi-Civita symbol, it’s a pretty nice tool for constructing things in a component-wise fashion: εijk . To make this work, you just have to remember it as I just wrote it… if any indices are equal, the symbol is zero, if they are all different, they are 1 or -1. If you take it as ijk, with the indices all different as I wrote, it equals 1 and becomes -1 if you reverse two of the indices: ijk=1, jik=-1, jki=1, kji=-1 and so on and so forth. Here are the useful Levi-Civita identities as they relate to cross product:

levicivita

Using these small tools, the first vector identity that I need is a curl of a curl. I derive it here:

vector id 1

Let’s see how this works. I’ve used colors to show the major substitutions and tried to draw arrows where they belong. If you follow the math, you’ll note that the Kroenecker deltas have the intriguing property of trading out indices in these sums. Kroenecker delta works on a finite sum the same way a Dirac delta works on an integral, which is nothing more than an infinite sum. Also, the index convention says that if you see duplicated indices, but without a sum on that index, you associate a sum with that index… this is how I located the divergences in that last step. This identity is a soft stopping point for the double curl: I could have used the derivative produce rule to expand it further, but that isn’t needed (if you want to see it get really complex, go ahead and try it! It’s do-able.) One will note that I have double del applied on a vector here… I said that it only applies on scalars above… in this form, it would only act on the scalar portion of each vector component, meaning that you would end up with a sum of three terms multiplied by unit vectors! Double del only ever acts on scalars, but you actually don’t need to know that in the derivation below.

This first vector identity I’ve produced I’ll call I4:

useful vector id 1

Here’s a second useful identity that I’ll need to develop:

useful vector id 2

This identity I’ll call I5:

vector id 2

*Pant Pant* I’ve collected all the identities I need to make this work. If you don’t immediately know something off the top of your head, you can develop the pieces you need. I will use I1, I2, I3, I4 and I5 together to derive the Maxwell-Ampere Law from Biot-Savart. Most of the following derivation comes from Jackson Electrodynamics, with a few small embellishments of my own.

first line amp devIn this first line of the derivation, I’ve rewritten Biot-Savart with the constants outside the integral and everything variable inside. Inside the integral, I’ve split the meat so that the different vector and scalar elements are clear. In what follows, it’s very important to remember that unprimed del operators are in a different space from the primed del operators: a value (like J) that is dependent on the primed position variable is essentially a constant with respect to the unprimed operator and will render a zero in a derivative by the unprimed del. Moreover, unprimed del can be moved into or out of the integral, which is with respect to the primed position coordinates. This observation is profoundly important to this derivation.

BS to amp 1

The usage of the first two identities here manages to extract the cross product from the midst of the function and puts it into a manipulable position where the del is unprimed while the integral is primed, letting me move it out of the integrand if I want.

BS to amp 2

This intermediate contains another very important magnetic quantity in the form of the vector potential (A) –“A” here not to be confused with the alphabetical placeholder I used while deriving my vector identities. I may come back to vector potential later, but this is simply an interesting stop-over for now. From here, we press on toward the Maxwell-Ampere law by acting in from the left with a curl onto the magnetic field…

BS to amp 3

The Dirac delta I end with in the final term allows me to collapse r’ into r at the expense of that last integral. At this point, I’ve actually produced the magnetostatic Ampere’s law if I feel like claiming that the current has no divergence, but I will talk about this later…

BS to amp 4

This substitution switches del from being unprimed to primed, putting it in the same terms as the current vector J. I use integration by parts next to switch which element of the first term the primed del is acting on.

BS to amp 5

Were I being really careful about how I depicted the integration by parts, there would be a unit vector dotted into the J in order to turn it into a scalar sum in that first term ahead of the integral… this is a little sloppy on my part, but nobody ever cares about that term anyway because it’s presupposed to vanish at the limits where it’s being evaluated. This is a physicist trick similar to pulling a rug over a mess on the floor –I’ve seen it performed in many contexts.

BS to amp 6

This substitution is not one of the mathematical identities I created above, this is purely physics. In this case, I’ve used conservation of charge to connect the divergence of the current vector to the change in charge density over time. If you don’t recognize the epic nature of this particular substitution, take my word for it… I’ve essentially inverted magnetostatics into electrodynamics, assuring that a ‘current’ is actually a form of moving charge.

BS to amp 75

In this line, I’ve switched the order of the derivatives again. Nothing in the integral is dependent on time except the charge density, so almost everything can pass through the derivative with respect to time. On the other hand, only the distance is dependent on the unprimed r, meaning that the unprimed del can pass inward through everything in the opposite direction.

BS to amp 8

At this point something amazing has emerged from the math. Pardon the pun; I’m feeling punchy. The quantity I’ve highlighted blue is a form of Coulomb’s law! If that name doesn’t tickle you at the base of your spine, what you’re looking at is the electrostatic version of the Biot-Savart law, which makes electric fields from electric charges. This is one of the reasons I like this derivation and why I decided to go ahead and detail the whole thing. This shows explicitly a connection between magnetism and electrostatics where such connection was not previously clear.

BS to amp 9

And thus ends the derivation. In this casting, the curl of the magnetic field is dependent both on the electric field and on currents. If there is no time varying electric field, that first term vanishes and you get the plain old magnetostatic Ampere’s law:

Ampere's law

This says simply that the curl of the magnetic field is equal to the current. There are some interesting qualities to this equation because of how the derivation leaves only a single positional dependence. As you can see, there is no separate position coordinate to describe magnetic field independently from its source. And, really, it isn’t describing the magnetic field as ‘generated’ by the current, but rather that a deformation to the linearity of the magnetic field is due to the presence of a current at that location… which is an interesting way to relate the two.

This relationship tends to cause magnetic lines to orbit around the current vector.

magcur

This image from hyperphysics sums up the whole situation –I realize I’ve been saying something similar from way up, but this equation is proof. If you have current passing along a wire, magnetic field will tend to wrap around the wire in a right handed sense. For all intents and purposes, this is all the Ampere’s law says, neglecting that you can manipulate the geometry of the situation to make the field do some interesting things. But, this is all.

Well, so what? I did a lot of math. What, if anything, have I gained from it? How does this help me along the path to understanding magnets?

The Ampere Law is useful in generating very simple magnetic field configurations that can be used in the Lorentz force law, ultimately showing a direct dynamical connection between moving currents and magnetic fields. I have it in mind to show a freshman level example of how this is done in the next part of this series. Given the length of this post, I will do more math in a different post.

This is a big step in the direction of learning how magnets work, but it should leave you feeling a little unsatisfied. How exactly do the forces work? In physics, it is widely known that magnetic fields do no work, so why is it that bar magnets can drag each other across the counter? That sure looks like work to me! And if electric currents are necessary to drive magnets, why is it that bar magnets and horseshoe magnets don’t require batteries? Where are the electric currents that animate a bar magnet and how is it that they seem to be unlimited or unpowered? These questions remain to be addressed.

Until the next post…

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Revoke Shaquille’s Doctorate in Education… he doesn’t deserve it.

We are in a world where truth doesn’t matter.

Read this and weep. These men are apparently the authorities of truth in our world.

Everywhere you look, truth itself is under assault. It doesn’t really matter whether you believe, it really doesn’t matter what you want it to say. Truth is not beholden to human whims. We can’t ultimately change it by manipulating it with cellphone apps. We can’t reinterpret it if we wanted to. One of these days, in however great of importance we hold ourselves, the truth will catch up. And we will deserve what happens to us after that point in time.

“It’s true. The Earth is flat. The Earth is flat. Yes, it is. Listen, there are three ways to manipulate the mind — what you read, what you see and what you hear. In school, first thing they teach us is, ‘Oh, Columbus discovered America,’ but when he got there, there were some fair-skinned people with the long hair smoking on the peace pipes. So, what does that tell you? Columbus didn’t discover America. So, listen, I drive from coast to coast, and this s*** is flat to me. I’m just saying. I drive from Florida to California all the time, and it’s flat to me. I do not go up and down at a 360-degree angle, and all that stuff about gravity, have you looked outside Atlanta lately and seen all these buildings? You mean to tell me that China is under us? China is under us? It’s not. The world is flat.”

This spoken by a man with a public platform and a Doctorate in Education. This is the paragon of teachers!

{Edit: 3-20-17 since I’m thinking better about this now, I will rebut his meaningless points.

First, arguments about whether or not Columbus discovered America are a non-sequitur as to whether or not the Earth is round.

Second, driving coast to coast can tell you very little about the overall roundness of the Earth, especially if you aren’t paying attention to the things that do. The curvature of the earth is extremely small: only about 8 inches per mile. This means that on the scale of feet, the curvature is in thousandths of an inch, so that you can’t measure it to not be flat at the dimensions that a human being can meaningfully experience standing directly on the surface. Can you see the couple feet of curvature at a distance of fifty miles looking off a sky scraper in the middle of Atlanta, or distinguish the deviation from the same direction of ‘up’ of two sky scrapers separated by ten miles? You can’t resolve tens of feet with your eyes at a distance of miles. That said, you actually can see Pikes Peak emerge over the horizon as you come out of Kansas into Colorado, but I suppose you would explain that away by some sort of giant conspiracy theory elevator device. To actually start to directly see the curvature at a meaningful degree with your eyes, you need to be at an altitude of hundreds of thousands of feet above the surface… which you could actually do as somebody with ridiculous wealth.

Third, how would you know that China is not ‘under?’ How would you know where China isn’t when you wouldn’t be able to see that distance along a flat surface no matter which direction you look? Can you explain the phase factor that you pick up to your day that causes your damn jet lag every time your wealthy, ignorant ass travels to places like China? By your logic, you should be able to use your colossal wealth to travel to where the globe of the sun pops out of the plane of the Earth in the east every morning. Hasn’t it once occurred to you that if you’re truly right, you should test a hypothesis first before making an assertion that can be easily shown to be wrong?}

You made a mint of money on the backs of a lot of people who made it possible for you to be internationally known, all because of the truth that they determined for you! You do not respect them, you do not understand the depth of their efforts, you do not know how hard they worked. You do not deserve the soapbox they built for you.

For everyone who values the truth, take a moment to share a little about it. Read other things in my blog to see what else I have to say. I have very little I can say right this second; I’m aghast and I feel the need to cry. My hard work is rendered essentially meaningless by morons like Shaquille O’Neal… men of no particular intellect or real skill dictating what reality ‘actually is’ while having no particular capacity to judge it for themselves.

From a time before cellphone apps and computer graphics manipulation, I leave you with one of the greatest pinnacles of truth ever to be achieved by the human species:

moon_and_earth_lroearthrise_frame_0

Like it or not, that’s Earth.

If you care to, I ask you to go and hug the scientist or engineer in your life. Tell them that you care about what they do and that you value their hard work. The flame of enlightenment kindled in our world is precious and at dire risk of guttering out.

Edit:

An open letter to the Shaq:

Dear Shaquille O’Neal,

I’m incredibly dismayed by your use of your public personae to endorse an intellectually bankrupt idea like flat earth conspiracy theories particularly in light of your Doctorate Degree in Education. If you are truly educated, and value truth, you should know that holding this stance devalues the hard work of generations of physicists and engineers and jeopardizes the standing of actual scientific truth in the public arena. The purpose of an educator is to educate, not to misinform… the difference is in whether you spread the truth or not.

There is so much evidence of the round earth available in the world around us without appeal to digital media, the cycle of the seasons, scheduled passages of the moon and the planets, observations of Coriolis forces in the weather patterns and simple ballistics, the capacity to jump in an airplane heading west and continue to head west until you get back to where you started, the passage of satellites and spacecraft visible from the surface of the Earth over our heads, the very existence of GPS available on your goddamn smart phone, to the common shapes of objects like the moon and planets visible through telescopes in the night skies around us, that appeals to flat earth conspiracies show a breathtaking lack of capacity to understand how the world fits together. That it comes from a figure who is ostensibly a force of truth –an educator– is truly deeply hurtful to those of us who developed that truth… modern scientists and engineers.

Since you are so profoundly wealthy, you among all people are singularly in a position to prove to yourself the roundness of our world. I bet you 50 million dollars that I don’t even have and will spend my entire life trying to repay, that you can rent an airliner with an honest pilot of your choice and fly west along a route also of your choice, and come back to the airport you originally departed from without any significant eastward travel. Heck, you can do the same exercise heading north or south if you want. And, if that experiment isn’t enough, use your celebrity to talk to Elon Musk: I hear he’s selling tickets now to rich people for flights around the moon. I bet he would build you a specially-sized two-person-converted-to-one berth in his Dragon capsule to give you a ride high enough to take a look for yourself at the shape of the world, if your eyes are the only thing you’ll believe. If you lose, you pay a 49 million dollar endowment to the University of Colorado Department of Physics for the support of Physics Education –and a million to me for the heartache you caused making a mockery of my education and profession by use of your ill-gotten public soapbox and mindlessly open mouth. Moreover, if you lose, you relinquish your Doctorate and make a public apology for standing for exactly the opposite of what that degree means.

Sincerely,

Foolish Physicist
of Poetry in Physics

Edit 4-5-17:

So, Shaq walked back his comments.

O’Neal: “The first part of the theory is, I’m joking, you idiots. That’s the first part of the theory. The second part is, I said jokingly that when I’m in my bus and I drive from Florida to California, which I do every summer, it seems to be flat. When I’m in my plane, and we’re getting ready to land, and I open up the window, and I’m looking at all the land that we’re flying over, it seems to be flat.”

“This world we live in, people take things too seriously, but I’m going to give the people answers to my test,” he said. “Knowing that I’m a funny guy, if something seems controversial or boom, boom, boom, you’ve got to have my funny points on, right? So now, once you have my funny points on, that should eradicate and get rid of all your negative thoughts, right? That’s what you should do when you hear a Shaquille O’Neal statement, OK? You should know that he has funny points right over here, and what did he say? Boom, boom, boom, add the funny points. You either laugh or you don’t laugh, but don’t take me seriously. When I want you to take me seriously, you will know by the tone of my voice that I’m being serious.”

“No, I don’t think that,” O’Neal told Harbinger of a flat Earth. “It was a joke, OK? So know that when Shaquille O’Neal says something, 80 percent of the time I’m being humorous, and it is a joke. And 20 percent of the time, I’m being serious, but when I’m being serious, you’ll know. You want to see me, seriously? See me and Charles Barkley going back and forth on TNT. That’s when I’m mad and when I’m serious. Other than that, you’re not going to get that out of me, so I was just joking people. The Earth is not round, it’s flat. I mean, the Earth is not flat, it’s round.”

One thing that should be added to these statements is this: there are people who are actively spreading misinformation about the state of the world, for instance that the earth is flat. The internet, Youtube, blogs, you name it, has given these people a soapbox that they would not otherwise have. Given that there is a blatant antiscientific thread in the United States which is attacking accepted, settled science as a big cover-up designed to destroy the rights of the everyday man, it is the duty of scientists and educators to take the truth seriously. In a world where Theory of Evolution, Climatology and Vaccine science are all actively politicized, we have to stand up for the truth.

Where real scientists are about studying and doing our work, the antiscientific activists are solely about spreading their belief… they don’t study, they don’t question, they spend their time actively lobbying the government and appealing to legislators, running for and getting onto school boards where they have an opportunity to pick which books are presented to school districts and various places where they can actively undercut what students are told about the truth of the world. They aren’t spending their energy studying, they are spending their energy solely on tinkering with the social mechanisms which provide our society with the next generation of scientists. As such, their efforts are more directed at undercutting the mechanisms that preserve the truth rather than on evaluating the truth… as scientists do. These people can do huge damage to us all. Every screwball coming out of a diploma mill “Quantum University” with a useless, unaccredited ‘PhD’… who goes off to promote woo-bong herbalist healthcare as an alternative to science based medicine, does damage to us all by undercutting what it means to get healthcare and by putting crankery and quackery in all seriousness at the same level as scientific truth when there should be no comparison.

If everybody understood that there is no ‘alternative’ to the truth, joking about what is true would mean something totally different to me. But, we live in a world where ‘alternative facts’ are a real thing and where everyone with a soapbox can say whatever they wish without fear of reprisal. Lying is a protected right! But someone has to stand up for truth. That someone should be scientists and educators. That should include an ‘education doctorate’ like the Shaq. If he were an NBA numbskull without the doctorate, I would care less: Kyrie Irving is a joke. But he isn’t; he’s got a doctorate and he has a responsibility to uphold what that degree means! The only reason humor in irony can work is if it can be clear that one is being ironic instead of serious… and that is never completely clear in this world.

Nuclear Toxins

A physicist from Lawrence Livermore Labs has been restoring old nuclear bomb detonation footage. This seems to me to be an incredibly valuable task because all of the original footage was shot on film, which is currently in the process of decaying and falling apart. There have been no open air nuclear bomb detonations on planet Earth since probably the 1960s, which is good… except that people are in the process of forgetting exactly how bad a nuclear weapon is. The effort of saving this footage makes it possible for people to know something about this world-changing technology that wasn’t previously declassified. Nukes are sort of mythical to a body like me who wasn’t even born until about the time that testing went underground: to everybody younger than me, I suspect that nukes are an old-people thing, a less important weapon than computers. That Lawrence Livermore Labs has posted this footage to Youtube is an amazing public service, I think.

As I was reading an article on Gizmodo about this piece of news, I happened to wander into the comment threads to see what the echo chamber had to say about all this. I should know better. Admittedly, I actually didn’t post any comments castigating anyone, but there was a particular comment that got me thinking… and calculating.

Here is the comment:

Nuclear explosions produce radioactive substances that are rare in nature — like carbon-14, a radioactive form of the carbon atom that forms the chemical basis of all life on earth.

Once released into the atmosphere, carbon-14 enters the food chain and gets bound up in the cells of most living things. There’s still enough floating around for researchers to detect in the DNA of humans born in 2016. If you’re reading this, it’s inside you.

This is fear mongering. If you’ve never seen fear mongering before, this is what it looks like. The comment is intended to deliberately inspire fear not just in nuclear weapons, but in the prospect of radionuclides present in the environment. The last sentence is pure body terror. Dear godz, the radionuclides, they’re inside me and there’s no way to clean them out! I thought for a time about responding to this comment. I decided not to because there is enough truth here that anyone should probably stop and think about it.

For anyone curious, the wikipedia article on the subject has some nice details and seems thorough.

It is true the C-14 is fairly rare in nature. The natural abundance is 1 part per trillion of carbon. It is also true that the atmospheric test detonations of nuclear bombs created a spike in the C-14 present in the environment. And, while it’s true that C-14 is rare, it is actually not technically unnatural since it is formed by cosmic rays impinging on the upper atmosphere. For the astute reader, C-14 produced by cosmic rays forms the basis of radiocarbon dating since C-14 is present at a particular known, constant proportion in living things right up until you die and stop uptaking it from the environment –a scientist can then determine the date when living matter died based on the radioactive decay curve for C-14.

Since it’s not unnatural, the real question here is whether the spike of radionuclides created by nuclear testing significantly increases the health hazard posed by excess C-14 above and beyond what it would normally be. You have it in your body anyway, is there greater hazard due to the extra amount released? This puzzle is actually a somewhat intriguing one to me because I worked for a time with radionuclides and it is kind of chilling all the protective equipment that you need to use and all the safety measures that are required. The risk is a non-trivial one.

But, what is the real risk? Does having a detectable amount of radionuclide in your body that can be ascribed to atomic air tests constitute an increased health threat?

To begin with, what is the health threat? For the particular case of C-14, one of a handful of radionuclides that can be incorporated into your normal body structures, the health threat would obviously come from the radioactivity of the atom. In this particular case, C-14 is a beta-emitter. This means that C-14 radiates electrons; specifically, one of the neutrons in the atom’s nucleus converts into a proton by giving off an electron and a neutrino, resulting in the carbon turning into nitrogen. The neutrino basically doesn’t interact with anything, but the radiated electron can travel with energies of 156 keV (or about 2.4×10^-14 Joules). This will do damage to the human body in two routes, either by direct collision of the radiated electron with the body, or by a structurally important carbon atom converting into a nitrogen atom during the decay process if the C-14 was part of your body already. Obviously, if a carbon atom turns suddenly into nitrogen, that’s conducive to organic chemistry occurring since nitrogen can’t maintain the same number of valence interactions as carbon without taking on a charge. So, energy deposition by particle collision, or spontaneous chemistry is the potential cause of the health threat.

In normal terms, the carbon-nitrogen chemistry routes for damage are not accounted for in radiation damage health effects simply because of how radiation is usually encountered: you need a lot of radiation in order to have a health effect, and this is usually from an exogenous source, that is, provided by a radiation source that is outside the body rather than incorporated with it, like endogenous C-14. This would be radiation much like the UV radiation which causes a sunburn. Heath effects due to radiation exposure are measured on a scale by a dose unit called a ‘rem.’ A rem expresses an amount of radiation energy deposited into body mass, where 1 rem is equal to 1.0×10^-5 Joules of radiation energy deposited into 1 gram of body mass. Here is a table giving the general scale of rem doses which causes health effects. People who work around radiation as part of their job are limited to a full-body yearly dose of 5 rem, while the general public is limited to 0.1 rem per year. Everybody is expected to have an environmental radiation dose exposure of about 0.3 rem per year and there’s an allowance of 0.05 rem per year for medical x-rays. It’s noteworthy that not all radiation doses are created equal and that the target body tissue matters; this is manifest by different radiation doses being allowed to occur to the eyes (15 rem) or the extremities, like the skin (50 rem). A sunburn would be like a dose of 100 to 600 rem to the skin.

What part of an organism must the damage affect in order to cause a health problem? Really, only one is truly significant, and that’s your DNA. Easy to guess. Pretty much everything else is replaceable to the extent that even a single cell dying from critical damage is totally expendable in the context of an organism built of a trillion cells. The problem of C-14 being located in your DNA directly is numerically a rather minor problem: DNA actually only accounts for about 3% of the dry mass of your cells, meaning that only about 3% of the C-14 incorporated into your body is directly incorporated into your DNA, so that most of the damage to your DNA is due to C-14 not directly incorporated in that molecule. This is not to say that chemistry doesn’t cause the damage, merely that most of the chemical damage is probably due to energy deposition in molecules around the DNA which then react with the DNA, say by generation of superoxides or similar paths. This may surprise you, but DNA damage isn’t always a complete all-or-nothing proposition either: to an extent, the cell has machinery which is able to repair damaged DNA… the bacterium Dienococcus radiodurans is able to repair its DNA so efficiently that it’s able to subsist indefinitely inside a nuclear reactor. Humans have some repair mechanisms as well.

Cells handling radiation damage in humans have about two levels of response. For minor damage, the cell repairs its DNA. If the DNA damage is too great to fix, a mechanism triggers in the cell to cause it to commit suicide. You can see the effect of this in a sunburn: critically radiation damaged skin cells commit suicide en mass in the substratum of your skin, ultimately sacrificing the structural integrity of your skin, causing the external layer to sough off. This is why your skin peels due to a sunburn. If the damage is somewhere in between, matters are a little murkier… your immune system has a way of tracking down damaged cells and destroying them, but those screwed up cells sometimes slip through the cracks to cause serious disease. Inevitably cancer. Affects like these emerge for ~20 rem full body doses. People love to worry about superpowers and three-arm, three-eye type heritable mutations due to radiation exposure, but congenital mutations are a less frequent outcome simply because your gonads are such a small proportion of your body; you’re more likely to have other things screwed up first.

One important trick in all of this to notice is that to start having serious health effects that can be clearly ascribed to radiation damage, you must absorb a dose of greater than about 5 rem.

Now, what kind of a radiation dose do you acquire on a yearly basis from body-incorporated C-14 and how much did that dose change in people due to atmospheric nuclear testing?

I did my calculations on the supposition of a 70 kg person (which is 154 lbs). I also adjusted rem into a more easily used physical quantity of Joules/gram (1 rem = 1×10^-5 J/g, see above.)  One rem of exposure for a 70 kg person works out to an absorbed dose of 0.7 J/year. An exposure sufficient to hit 5 rems is 3.5 J/year while 20 rem is 14 J/year. Beta-electrons from c-14 maximally hit with 2.4×10^-14 J/strike (150 keV) with about 0.8×10^-14 J/hit on average (50 keV).

In the following part of the calculation, I use radioactive decay and half-life in order to determine the rate of energy transference to the human body on the assumption that all the beta-electron energy emitted by radiation is absorbed by the human body. Radiation rates are a purely probabilistic event where the likelihood of seeing a radiated electron is proportional to the size of the radioactive atom population. The differential equation is a simple one and looks like this:

decay rate differential equation

This just means that the rate of decay (and therefore electron production rate) is proportional to the size of the decaying population where the k variable is a rate constant that can be determined from the half-life. The decay differential equation is solved by the following function:

exponential decay

This is just a simple exponential decay which takes an initial population of some number of objects and reduces it over time. You can solve for the decay constant by plugging the half-life into the time and simply asserting that you have 1/2 of your original quantity of objects at that time. The above exponential rearranges to find the decay constant:

decay constant

Here, Tau is the half-life in seconds (I could have used my time as years, but I’m pretty thoroughly trained to stick with SI units) and I’ve already substituted 1/2 for the population change. With k from half-life, I just need the population of radiation emitters present in the body in order to know the rate given in the first equation above… where I would simply multiply k by N.

To do this calculation, the half-life of C-14 is known to be 5730 years, which I then converted into seconds (ick; if I only care about years, next time I only calculate in years). This gives a decay constant of 3.836×10^-12 emissions/sec. In order to get the decay rate, I also need the population of C-14 emitters present in the human body. We know that C-14 has a natural prevalence of 1 per trillion and also that a 70 kg human body is 16 kg carbon after a little google searching, which gives me 1.6×10^-8 g of C-14. With C-14’s mass of 14 g/mole and Avagadro’s number, this gives about 6.88×10^14 C-14 atoms present in a 154 lb person. This population together with the rate constant gives me the decay rate by the first equation above, which is 2.639×10^3 decays per second. Energy per beta-electron absorbed times the decay rate gives the rate of energy deposited into the body per second on the assumption that all beta-decay energy is absorbed by the target: 2.639×10^3 decays/sec * 2.4×10^-14 Joules/decay = 6.33 x 10^-11 J/s. For the course of an entire year, the amount of energy works out to about 0.002 Joules/year.

This gets me to a place where I can start making comparisons. The exposure limit for any old member of the general public to ‘artificial’ radiation is 0.1 rem, or 0.07 J/year. The maximum… maximum… contribution due to endogenous C-14 is 35 times smaller than the allowed public exposure limits (for mean energy, it’s more like 100 times smaller). On average, endogenous C-14 gives 1/100th of the allowed permitted artificial radiation dose.

But, I’ve actually fudged here. Note that I said above that humans normally get a yearly environmental radiation dose of about 0.3 rem (0.21 J/year)… meaning that endogenous C-14 only provides about 1/300th of your natural dose. Other radiation sources that you encounter on a daily basis provide radiation exposure that is 300 times stronger than C-14 directly incorporated into the structure of your body. And, keep in mind that this is way lower than the 5 rem where health effects due to radiation exposure begin to emerge.

How does C-14 produced by atmospheric nuclear testing figure into all of this?

The wikipedia article I cited above has a nice histogram of detected changes in the environmental C-14 levels due to atmospheric nuclear testing. At the time of such testing, C-14 prevalence spiked in the environment by about 2 fold and has decayed over the intervening years to be less than 1.1-fold. This has an effect on C-14 exposure specifically of changing it from 1/300th of your natural dose to 1/150th, or about 0.5%, which then tapers to less than a tenth of a percent above natural prevalence in less than fifty years. Detectable, yes. Significant? No. Responsible for health effects…… not above the noise!

This is not to say that a nuclear war wouldn’t be bad. It would be very bad. But, don’t exaggerate environmental toxins. We have radionuclides present in our bodies no matter what and the ones put there by 1950s nuclear testing are only a negligible part, even at the time –what’s 100% next to 100.5%? A big nuclear war might be much worse than this, but this is basically a forgettable amount of radiation.

For anybody who is worried about environmental radiation, I draw your attention back to a really simple fact:

depositphotos_9985842_s-199x300

The woman depicted in the picture above has received a 100 to 600 rem dose of very (very very) soft X-rays by deliberately sitting out in front of a nuclear furnace. You can even see the nuclear shadow on her back left by her scant clothing. Do you think I’m kidding? UV light, which is lower energy than x-rays, but not by that much… about 3 eV versus maybe 500 eV, is ionizing radiation which is absorbed directly by skin DNA to produce real radiation damage, which your body treats indistinguishably from how it treats damage from particle radiation of radionuclides or X-rays or gamma-rays. The dose which produced this affect is something like two to twelve times higher than the federally permitted dose that radiation workers are allowed to receive in their skin over the course of an entire year… and she did it to herself deliberately in a matter of hours!

Here’s a hint, don’t worry about the boogieman under the bed when what you just happily did to yourself over the weekend among friends is much much worse.

What is a qubit?

I was trolling around in the comments of a news article presented on Yahoo the other day. What I saw there has sort of stuck with me and I’ve decided I should write about it. The article in question, which may have been by an outfit other than Yahoo itself, was about the recent decision by IBM to direct a division of people toward the task of learning how to program a quantum computer.

Using the word ‘quantum’ in the title of a news article is a sure fire way to incite click-bait. People flock in awe to quantum-ness even if they don’t understand what the hell they’re reading. This article was a prime example. All the article really talked about was that IBM has decided that quantum computers are now a promising enough technology that they’re going to start devoting themselves to the task of figuring out how to compute with them. Note, the article spent a lot of time kind of masturbating over how marvelous quantum computers will be, but it really actually didn’t say anything new. Another tech company deciding to pretend to be in quantum computing by figuring out how to program an imaginary computer is not an advance in our technology… digital quantum computers are generally agreed to be at least a few years off yet and they’ve been a few years off for a while now. There’s no guarantee that the technology will suddenly emerge into the mainstream –and I’m neglecting the DSpace quantum computer because it is generally agreed among experts that DSpace hasn’t even managed to prove that their qubits remain coherent through a calculation to actually be a useful quantum computer, let alone that they achieved anything at all by scaling it up.

The title of this article was a prime example of media quantum click-bait. The title boldly declared that “IBM is planning to build a quantum computer millions of times faster than a normal computer.” Now, that title was based on an extrapolation in the midst of the article where a quantum computer containing a mere 1000 qubits suddenly becomes the fastest computing machine imaginable. We’re very used to computers that contain gigabytes of RAM now, which is actually several billion on-off switches on the chip, so a mere 1,000 qubits seems like a really tiny number. This should be underwritten with the general concerns of the physics community that an array of 100 entangled qubits may exceed what’s physically possible… and it neglects that the difficulty of dealing with entangled systems increases exponentially with the number of qubits to be entangled. Scaling up normal bits doesn’t bump into the same difficulty. I don’t know if it’s physically possible or not, but I am aware that IBM’s declaration isn’t a major break-through so much as splashing around a bit of tech gism to keep the stockholders happy. All the article really said was that IBM has happily decided to hop on the quantum train because that seems to be the thing to do right now.

I really should understand that trolling around in the comments on such articles is a lost cause. There are so many misconceptions about quantum mechanics running around in popular culture that there’s almost no hope of finding the truth in such threads.

All this background gets us to what I was hoping to talk about. One big misconception that seemed to be somewhat common among commenters on this article is that two identical things in two places actually constitute only one thing magically in two places. This may stem from a conflation of what a wave function is versus what a qubit is and it may also be a big misunderstanding of the information that can be encoded in a qubit.

In a normal computer we all know that pretty much every calculation is built around representing numbers using binary. As everybody knows, a digital computer switch has two positions: we say that one position is 0 and the other is 1. An array of two digital on-off switches then can produce four distinct states: in binary, to represent the on-off settings of these states, we have 00, 01, 10 and 11. You could easily map those four settings to mean 1, 2, 3 and 4.

Suppose we switch now to talk about a quantum computer where the array is not bits anymore, but qubits. A very common qubit to talk about is the spin of an atom or an electron. This atom can be in two spin states: spin-up and spin-down. We could easily map the state spin-up to be 1, and call it ‘on,’ while spin-down is 0, or ‘off.’ For two qubits, we then get the states 00, 01, 10 and 11 that we had before, where we know about what states the bits are in, but we also can turn around and invoke entanglement. Entanglement is a situation where we create a wave function that contains multiple distinct particles at the same time such that the states those particles are in are interdependent on one another based upon what we can’t know about the system as a whole. Note, these two particles are separate objects, but they are both present in the wave function as separate objects. For two spin-up/spin-down type particles, this can give access to the so-called singlet and triplet states in addition to the normal binary states that the usual digital register can explore.

The quantum mechanics works like this. For the system of spin-up and spin-down, the usual way to look at this is in increments of spinning angular momentum: spin-up is a 1/2 unit of angular momentum pointed up while spin-down is -1/2 unit of angular moment, but pointed the opposite direction because of the negative sign. For the entangled system of two such particles, you can get three different values of entangled angular momentum: 1, 0 and -1. Spin 1 has both spins pointing up, but not ‘observed,’ meaning that it is completely degenerate with the 11 state of the digital register since it can’t fall into anything but 11 when the wave function collapses. Spin -1 is the same way: both spins are down, meaning that they have 100% probability of dropping into 00. The spin 0 state, on the other hand, is kind of screwy, and this is where the extra information encoding space of quantum computing emerges. The 0 states could be the symmetric combination of spin-up with spin-down or the anti-symmetric combination of the same thing. Now, these are distinct states, meaning that the size of your register just expanded from (00, 01, 10 and 11) to (00, 01, 10, 11 plus anti-symmetric 10-01 and symmetric 10+01). So, the two qubit register can encode 6 possible values instead of just 4. I’m still trying to decide if the spin 1 and -1 states could be considered different from 11 and 00, but I don’t think they can since they lack the indeterminacy present in the different spin 0 states. I’m also somewhat uncertain whether you have two extra states to give a capacity in the register of 6 or just 5 since I’m not certain what the field has to say about the practicality of determining the phase constant between the two mixed spin-up/spin-down eigenstates, since this is the only way to determine the difference between the symmetric and anti-symmetric combinations of spin.

As I was writing here, I realized also that I made a mistake myself in the interpretation of the qubit as I was writing my comment last night. At the very unentangled minimum, an array of two qubits contains the same number of states as an array of two normal bits. If I consider only the states possible by entangled qubits, without considering the phasing constant between 10+01 and 10-01, this gives only three states, or at most four states with the phase constant. I wrote my comment without including the four purely unentangled cases, giving fewer total states accessible to the device, or at most the same number.

Now, the thing that makes this incredibly special is that the number of extra states available to a register of qubits grows exponentially with the number of qubits present in the register. This means that a register of 10 qubits can encode many more numbers than a register of ten bits! Further, this means that fewer bits can be used to make much bigger calculations, which ultimately translates to a much faster computer if the speed of turning over the register is comparable to that of a more conventional computer –which is actually somewhat doubtful since a quantum computer would need to repeat calculations potentially many times in order to build up quantum statistics.

One of the big things that is limiting the size of quantum computers at this point is maintaining coherence. Maintaining coherence is very difficult and proving that the computer maintains all the entanglements that you create 100% of the time is exceptionally non-trivial. This comes back to the old cat-in-the-box difficulty of truly isolating the quantum system from the rest of the universe. And, it becomes more non-trivial the more qubits you include. I saw a seminar recently where the presenting professor was expressing optimism about creating a register of 100 Josephson junction type qubits, but was forced to admit that he didn’t know for sure whether it would work because of the difficulties that emerge in trying to maintain coherence across a register of that size.

I personally think it likely that we’ll have real digital quantum computers in the relatively near future, but I think the jury is still out as to exactly how powerful they’ll be when compared to conventional computers. There are simply too many variables yet which could influence the power and speed of a quantum computer in meaningful ways.

Coming back to my outrage at reading comments in that thread, I’m still at ‘dear god.’ Quantum computers do not work by teleportation: they do not have any way of magically putting a single object in multiple places. The structure of a wave function is defined simply by what you consider to be a collection of objects that are simultaneously isolated from the rest of the universe at a given time. A wave function quite easily spans many objects all at once since it is merely a statistical description of the disposition of that system as seen from the outside, and nothing more. It is not exactly a ‘thing’ in and of itself insomuch as collections of indescribably simple objects tend to behave in absolutely consistent ways among themselves. Where it becomes wave-like and weird is that we have definable limits to how precisely we can understand what’s going on at this basic level and that our inability to directly ‘interact’ with that level more or less assures that we can’t ever know everything about that level or how it behaves. Quantum mechanics follows from there. It really is all about what’s knowable; building a situation where certain things are selectively knowable is what it means to build a quantum computer.

That’s admittedly pretty weird if you stop and think about it, but not crazy or magical in that wide-eyed new agey smack-babbling way.

Calculating Molarity part 2: Vaccine structure

I’ve continued to think about this post at Respectful Insolence. You may already have read my previous post on this subject. I had a short conversation with Orac by email about the previous post; he had asked me what I thought about the alterations he made after thinking about my objections. One thing I answered that I thought he might add has sort of stuck with me and I think is worthy of a post of its own. What do you know, two posts in one week! This one may not be tremendously long, but it’s important and it bolsters the thesis written in that post on Respectful Insolence. They are about minimizing the contamination; this is true, but I would actually modify it by saying that you have to know what you’re looking at before you claim it’s a problem.

My previous writing here has been directed at my fellow skeptics and could be used by antivaccine advocates to attack people whose efforts I normally support. I would rather my efforts be focused at the greater good: namely to support vaccines. I don’t write often about my specific research expertise, but I’m mainly a soft matter researcher and I have a great deal of experience with colloids, nanoparticles and liquid crystals. This paper they’re talking about is my cup of tea! More than that, I’ve spent time at the university electron microscopy lab using SEM and elemental analysis in the form of EDS, shooting electron beams at precipitates obtained from colloidal suspensions.

I feel that the strategy of showing that vaccine contaminants are extraordinarily minor and not nearly as large as the antivaccine efforts try to claim is a good effort, but might also be the wrong strategy for tackling this science, particularly when screwing up the math. A part of my reason for feeling this way is that the argument is actually hinging on the existence, or not, of particulate objects in the preparations that the antivaxxers are examining. The paper that Orac (and, in a quotation, Skeptical Raptor) are looking at, is focusing on the spurious occurrence of a small particle content revealed in vaccine samples under SEM examination. The antivaxxers are counting and reporting particles found in SEM, of which they are reporting highly dispersive values: very few in some, many in others. They are also reporting instances where EDS shows unexpected metal content, like gold and others. Here, Orac notes that the particles are typically so few that they should be considered negligible and that’s fair… question is, what is the nature of these particles? And, should we take the antivaxxer EDS results seriously? It seems poor form for me to criticize my fellow skeptics and to not turn my attention against the subject that are analyzing –to allay my own conscience, I have to open my mouth! I therefore spent a bit of time of my own looking at the paper they were analyzing “New Quality-Control Investigations on Vaccines: Micro- and Nanocontamination.” I won’t link to it directly because I have no respect for it.

I’ll deal with the EDS first.

edsschematic

This picture is from https://s32.postimg.org/yryuggo1x/EDSschematic.gif

EDS is another spectroscopy technique that is sometimes called electron fluorescence. You shoot an electron beam (or X-ray) at a sample with the deliberate intent of knocking a deep orbital electron out of the atom. A higher energy shell electron will then drop down into the vacant orbital and emit an X-ray at the transition energy between the two orbitals. The spectrometer then detects the emitted X-rays. Because atoms have differing transition energies due to the depth of their shells, you can identify the element based on the X-ray frequencies emitted. A precondition for seeing this X-ray spectrum is that your impinging electron beam must be at sufficiently high energy to knock a deep shell electron up into the continuum, ionizing the atom and that energy might actually be considerable. There is also a confounder in that a lot of atoms have EDS peaks at fairly similar energies, meaning that it can be hard sometimes to distinguish them.

Here is a periodic table containing EDS peaks from Jeol:

energy-20table-20for-20eds-20analysis-1

Now, when you perform SEM, you spread your sample onto a conductive substrate and observe it in a fair vacuum. To generate an SEM image, the electron beam is rastered in a point across an area in the sample and an off-angle detector detects electron scatter. You’re literally trying to puff electrons up into the space over the sample by bombarding the surface. The substrate is usually conductive in order to replenish ejected electrons. The direction the ejection puff travels depends on the topography of the surface and the off-angle positioning of the detector means that some surfaces face the detector and give bright puffs while surfaces facing away do not. This gives the dimensionality to SEM images. Many SEM samples are sputtered with a layer of gold to improve contrast by introducing a material that is electron dense, but a system with the intent to use EDS would actually be directed at naked samples. With SEM, you always have to remember that the electron beam is intrinsically erosive and damaging. The beam doesn’t just bounce off the surface, it penetrates into the sample to a depth that I’ve heard called the interaction volume. The interaction volume is regulated by the accelerating voltage of the electron beam: higher accelerating voltages means deeper interacting volumes. Crisp SEM images that show clear surface features are usually obtained with low accelerating voltages which limit the interacting volume to only surface features of the sample. SEM images obtained at higher accelerating voltages take on a sort of translucent cast because the beam penetrates into the sample and interacts with an interior volume.

The combination of EDS with SEM is a little tricky. In SEM, EDS gains its excitation from the imaging electron beam of the system. Now, what makes this tricky is that samples like protein antigens in a vaccine are predominantly carbon and have low electron density, making them low contrast. You hit the sample at low accelerating voltages to see surface features. If you try to do EDS, you must hit the sample with electrons at energies sufficient to eject deep orbital electrons: it depends on the depth of that atom’s potential and on which electron is ejected, but atoms like gold can have deeper orbitals than atoms like carbon, meaning larger energies are needed to resolve deeper gold atom orbital transitions. Energies favorable to SEM imaging are sometimes very low compared to the energies needed to hit the EDS ejection energies. When you switch to EDS from imaging, you must be aware that you’re gaining a deeper penetration depth from the larger interaction volume of the beam. If your sample is thin and has low electron density, like carbonaceous biological molecules, you can easily be shooting through the sample and hitting the substrate, whatever that might be.

This can be a serious confounder because you don’t necessarily know where your signal is coming from. In the article commented on by Orac, the authors mention that they’re using an aluminum stub as an SEM mount, but they also talk about aluminum hydroxide and aluminum phosphate. The EDS aluminum signal is sensitive only to the aluminum atoms: you can’t know if the signal is coming from the mount or the sample! How do they know that the phosphate signal isn’t from phosphate buffered saline? That’s a common medical buffer that shows up in vaccine preparation. You can’t know if the material you’re looking at is aluminum phosphate from EDS or SEM.

As I mentioned, you also have to contend with close spacing of EDS peaks: if you look at that periodic table linked above, there’s a lot of overlap. To know gold, for certain, you really need to hit a couple of its EDS peaks to make certain you aren’t misreading the signal (all the peaks you get will have a gaussian width, meaning that you might have a broad signal that covers a number of peaks.) And, at least in the figure presented by Orac, they’re making their calls based on single peak identifications. This in addition to the other potential confounders Orac brought up: exogenous grit and the possibility that they’re reusing their SEM stub for other experiments. How can they be certain they aren’t getting spurious signals?

For EDS, I would be careful about making calls without having some means of independent analysis… like knowing what materials are supposed to be present and possibly hiring out elemental analysis of the sample. Will the gold or zirconium appear in the second analysis? Remember, science depends on being able to reproduce a result… if it was always spurious, a good tale is not being able to make it dance the second time around! Reporting everything doesn’t always mean that you know what you’re looking at. When I was doing EDS more routinely, I had a devil of a time hitting Titanium over Silicon and Gold signals… I knew titanium was present because I put it there, but I had trouble hitting it or ascribing it to specific particles in the SEM image. The EDS would not routinely allow me to reproduce an observation before the sample simply exploded while I was pounding high energy electrons into it.

Referring directly to the crank paper myself and I note that they make some extremely complicated mineral calls in their tables from the EDS data. Again, be aware that EDS is only sensitive to atoms specifically: you can’t know if Aluminum signals are aluminum phosphate or aluminum hydroxide or aluminum from the SEM stub. To know mineral crystals, you need precision ratios of the contents or X-ray diffraction or maybe Raman analysis of the mineral’s crystal lattice.

From their SEM imagery, it looks to me like they’re using a very strong voltage, which is confirmed in their methods section. They claim to be using voltages between 10 kV and 30 kV. These are very high voltages. For good surface resolution of a proteinaceous sample, I restricted myself to around 1 kV to 5 kV and sometimes below 1 kV and found that I was cutting holes through the specimen for much higher than that. Let me actually quote a piece of their methods for sample mounting:

A drop of about 20 microliter of vaccine is released from
the syringe on a 25-mm-diameter cellulose filter (Millipore,
USA), inside a flow cabinet. The filter is then deposited on an
Aluminum stub covered with an adhesive carbon disc.

They put a cellulose filter from Millipore into this SEM. I would have dried directly onto a clean silicon substrate. Here are the appropriate specimen mounts from Ted Pella. Note that the specimen mounts are not cellulose. Cellulose filters are used for a completely different purpose from normal SEM specimen mounts and, really importantly, you can’t efficiently clean a cellulose filter before putting your sample onto it. And, since these filters are actually designed to easily collect dust and grit as a part of their function, it is actually kind of difficult to get crap off of them. Without a control showing that their filters are clean of dust, there’s no way to be certain that this article isn’t actually a long survey examining the dust and foreign crap that can be found impregnating cellulose filters since the SEM acceleration voltages are unquestionably high enough to be cutting through a thin, low contrast biological layer on the top.

I won’t say more about the EDS.

So, I wanted also to address the particulate discussion a bit more directly too.

First off, from the paper directly, there is no real effort at reproduction or control. The source of the particles mentioned could be the carbon adhesive, the cellulose membrane or the vaccine sample. Having thought about it, I personally would bet on that cellulose: you don’t use them this way! They claim to be making preparations in a flow hood to keep dust out, but that doesn’t mean the dust isn’t already on any of the components being brought into the hood.

I stand by my original criticism of Orac’s post that these particles can’t be effectively quantified by molarity: those shown in the paper are all clearly micron scale objects, meaning that they have relatively large mass in and of themselves and constitute significant quantities of material. A better concentration unit for describing them would be mg/mL. I repeat that we don’t know the source of these objects for certain because the experiment is performed without true replication! If the vaccines are the source, the authors should have been able to perform a simple filtration of a vaccine specimen by a 0.22 um or 0.1 um filter and show that this drastically reduces contamination because many of their micrographs are of objects that should not have passed through such a filter… but they did no comparable experiment.

As I’ve been thinking about it, there are a couple potential different particles that could be observed under these conditions. The first is dust, as already detailed. The second possible source is vaccine components, but from a non-contaminating perspective. Orac used a quote by Skeptical Raptor who was rebutting the idea of Aluminum hydroxide being a strong contaminant by again mistaking particles for molecules. I won’t get into his difficulty calculating concentration since it was similar to what happened to Orac, but he was speaking about Aluminum hydroxide being a chemical that is a tiny fraction of a nanogram in a vaccine and therefore much less than environmental exposure to aluminum. I know I probably annoyed Orac with my thoughts about this as I was thinking out loud, but Aluminum hydroxide is not any sort of contaminant in the Cervarix vaccine friend Raptor was talking about: it’s the Adjuvant! Here’s a product insert for a Cervarix vaccine.

cervarix-pi-pil

In this vaccine, I found that there is approximately 500 ug of Aluminum hydroxide adjuvant added per 0.5 mL vaccine dose. If you look in the Aluminum hydroxide MSDS, there is no LD50 for this compound, no cancinogen warnings and no other special health precautions from chronic exposure –it irritates your eyes from contact, but what doesn’t? It got a 1 as a chemical hazard. Antivaxxers are crazy about being anti-aluminum based upon more decades old information that has since been rebutted, but for all intents and purposes, this material is pretty harmless. One special thing about it is that it’s actually very insoluble unless you drop an acid or a strong base on it, meaning that it should be no surprise if it’s a particulate in a neutral physiological pH vaccine (Ksp = 3×10^-34)! In vaccine design, and I haven’t spent a huge amount of time looking, but the main point of the adjuvant is to cause the antigen to be retained at the site of injection for a prolonged time so that the body can be exposed to it for a longer period. The adjuvant adheres the vaccine antigen and, by being an insoluble particle, it lodges in your tissues upon injection and stays there, holding the antigen with it. I found immunology papers on pubmed calling this establishment of a ‘immune depot’ for stimulating immune cells. Over a prolonged period, the insoluble Ksp will allow this compound to gradually dissolve and release the antigen out of the injection site, but Aluminum hydroxide will never have a very high concentration in the body as a whole: that’s what Ksp says, that the soluble phase of the salt components can be no greater than about 2.4 nM, which is well below established exposure limits recommended in the MSDS of between 30 nM and 100 nM (by my calculation).

But, if you look at vaccine adjuvant under SEM, it will be a colloidal particle with a core of Aluminum in the EDS! You can even see examples of this in the target paper itself: the SEM in figure 1 looks like a colloid fractal (they call it a ‘crystals’, but it looks like a precipitate deposition fractal), and the colloids are probably aluminum hydroxide particles caked with antigen protein (again, EDS can’t distinguish between  aluminum hydroxide mixed with PBS and aluminum phosphate, contrary to what the caption says). And, these colloids are INTENDED TO BE THERE by the manufacture of the vaccine. Note, this is a structure designed into the vaccine to help prolong the immune response.

I’ve been debating the source of the singleton particles that the authors of this paper take many SEM pictures of in the remainder of their work. They are mostly not regular enough to be designed nanoparticles or precipitate colloids and they often look like dust (Orac mentions as much). I’ve been skeptical of the sample preparation practices outlined in the paper: I think adding the cellulose membrane to the sample is asking for trouble. You use substrates in SEM to avoid contaminant issues and to provide surfaces that are easily cleaned prior to use. The cellulose polymer and vaccine antigens are all low contrast… at 30 kV accelerating voltage, the SEM could actually be interacting down into the volume of the filter (as I mentioned above). If this isn’t dust sitting on the filter prior to dropping the vaccine onto it, it might also be dust dropped randomly into the cellulose monomer during the manufacturing process and trapped there while polymerizing the membrane. The filter won’t care about most of this sort of contamination because the polymer will immobilize it. Another possibility, but the paper tests almost no hypotheses for purposes of error checking, so we’ll never know.

Overall, I found that paper incompetent. There’s no reason to take it seriously. I hope that my writing this blog post will help balance the previous post which attacked science advocates for misusing the science.

Calculating Molarity (mole/L)

As a preface to this post, I want to make doubly clear my stance on vaccines. There is no good scientific evidence to support the notion that vaccination is in any way an unsafe practice or that it is responsible for any manner of health problem above and beyond the diseases that vaccines protect against. Vaccination is the single most powerful health intervention created in the last 150 years of medicine. There is, in my opinion, some potential for this post to be used to damage the credibility of a person who I believe to be a necessary positive force in the Healthcare scene and I want to make it clear that this was not the intention of my writing here. Orac is a tireless advocate for science and for clear, skeptical thought in general and I respect him quite deeply for the time he puts in and for putting up with the static he puts up with.

That said, I believe that science advocacy is a double edged sword: if you didn’t get it right, it can come back to bite you.

I love Respectful Insolence, but I’ve got to ding Orac for failing to calculate molarity correctly. He is profoundly educated, but I think he’s a surgeon and not a physicist. We all have our weak points! (Thank heaven above I’m not ever in the operating room with the knife!)

In this post, which he may now have edited for correctness (and it seems he has), he makes the following statement:

More importantly, look at the numbers of precipitates found per sample. It ranges from two to 1,821.

O.M.G.! 1,821 particles! Holy crap! That’s horrible! The antivaxers are right that vaccines are hopelessly contaminated!

No. They. Are. Not.

Look at it this way. This is what was found in 20 μl (that’s microliters) of liquid. That’s 0.00002 liters. That means, in a theoretical liter of the vaccine, the most that one would find is 91,050,000 (9.105 x 107) particles! Holy hell! That’s a lot. We should be scared, shouldn’t we? well, no. Let’s go back to our homeopathy knowledge and look at Avogadro’s number. One mole of particles = 6.023 x 1023. So divide 91,050,000 by Avogadro’s number, and you’ll get the molarity of a solution of 91,050,000 particle in a liter, as a 1 M solution would contain 6.023 x 1023 particles. So what’s the concentration:

1.512 x 10-16 M. that’s 0.15 femtomolar (fM) (or 150 altomolar), an incredibly low concentration. And that’s the highest amount the investigators found.

Anybody see the mistake? Let’s start here: Avogadro’s number is a scaling constant for a linear relationship and it has a unit! The units on this number are atoms(or molecules) per mole. It converts a number of atoms or molecules into a number of moles.

‘Moles’ is a convenient person-sized number that is standardized around ‘molecular weight,’ which is a weight unit that arbitrarily says that a single carbon atom has a weight of ’12’ and results in atomic hydrogen having a weight of ‘1.’ That’s atomic mass units (or AMU), which is usually very convenient for calculating relative weights of molecules by adding up all the AMU of their atomic constituents. To use molarity, we usually need a molecular weight in the form of Daltons, or grams/mole. Grams per mole says that it takes this many grams in mass of a substance for that substance to contain a single mole’s worth of molecules (or atoms) where it is then implicit that the number of molecules or atoms is Avogadro’s number.

‘Mole’ is extremely special. It refers to a collection of objects that are atomically identical! If you have a mole of a kind of protein, it means that you have 6.02 x 10^23 number of this kind of identical object. If you make a comparison between two proteins, the same molar number of each with a different molecular weight is a different overall mass. Consider Insulin (5808 g/mole) compared to the 70S Ribosome (2,500,000 g/mole)… one mole of Insulin would weigh 5.8 kg while one mole of 70S Ribosome would weigh 2.5 metric tons!!! If they have roughly the average density of proteins, what would be the volume of 1 mole of 70S ribosome as compared to 1 mole of Insulin? It would be 430 times greater for the Ribosome; 2900 L for 70S Ribosome while Insulin is about 6 L!

Notice something here: an object with a big molecular weight occupies a bigger volume than the same object of a smaller molecular weight… regardless of the fact that they are at the same molarity. Molarity as a number depends strongly on the molecular weight of the substance in question in order to mean anything at all. For the Ribosome, the same molar concentration as for Insulin means a solution containing a much larger amount of solute.

In the post in question on Respectful Insolence, Orac is talking about a paper which observes particulate matter derived from vaccine specimens in an SEM. It is clear from the authorship and publication of the paper that the intent is to find fault in vaccines based upon the contents of materials examined by this probing… from what little I know about the paper, it does not seem to be producing any information that is truly that informative. But, you can’t fault a paper on a point that may not actually be as flawed as an initial interpretation would imply. The paper reports number of particles observed per 20 uL of a solvent. They find as many as 1,821 particles per 20 uL. We are not told for certain what these particles are composed of except that the investigators aren’t sure and shot an overpower EDS at everything and reported even the spurious results. Orac scales up this number to 1L to get 90.1 x 10^7 particles and then divides by Avogadro’s number to find what proportion this is of one mole of these particles, never mind that we don’t know how big the particles are in terms of molecular weight or how dense in volume per mass. He declares it to be a tenth of a femtomole and runs on with how tiny the concentration is. As I initially wrote this, I focused on the gleeful way in which Orac does his deconstruction in large part because it really isn’t a valid thing to laugh at when the deconstruction is not properly done.

Here is how someone of my background approaches the same series of observations. I can see from the micrograph in the blog post that the scale bar is something like 2 mm (2000 microns)… the objects in question are maybe tens to hundreds of microns in size. Let’s make a physicist supposition here and think about it: pulling this out of my ass, I’ll claim these are 1,821 approximately spherical identical particles of sodium chloride, each of 40 microns diameter. That gives a volume of 4/3*Pi*20^3 um^3 or 1.9 x 10^-12 m^3 per particle and 3.5 x 10^-9 m^3 for the whole collection of particles. Now, density usually is given in terms of g/cm^3 or g/mL… there are 100 cm per meter and you must convert three times to cube it, so 3.5 x 10^-9 x 100^3 = 3.5 x 10^-3 cm^3. Wait a minute, we’re now at a volume of 3.5 uL!!! Did you see that? A cubic centimeter is a mL and 0.0035 mL is 3.5 uL, or 17% of the original 20 uL sample volume! What molarity is this? The density of sodium chloride is 2.16 g/mL or 2.16 mg/uL… which is 7.56 mg. That’s 7.56 mg of salt dissolved in 20 uL. The molecular weight of sodium chloride is 58.44 g/mole or 58.44 mg/mmole, which gives .129 mmole. From this .129 mmole in .02 mL is 6.47 mmole/mL.

That’s 6.47 mole/L……. 6.47 M!!!!

Let’s pause for a second. Is that femtomolar?

Orac missed the science here! I initially wrote that he should be apologizing for it, but I’ve revised this so that my respect for his work is more apparent. The volume of these particles and their composition is everything. A single particle with a molecular weight in the gigadaltons or teradaltons range is suddenly a very substantial mass in low particle number. If these particles are as I specified and composed of simple salt, they are at a molarity that is abruptly appreciable. If we make these into tiny balls of Ricin, that’s unquestionably a fatally toxic quantity!

As with all things, dose makes the poison and there’s no Ricin in evidence, but this argument Orac has made about concentration, in this particular case is catastrophically wrong. A femtomole of a big particle that can be dissolved could be a large dose!

I forgive him and I love his blog, but let this be a lesson… you don’t just divide by Avogadro’s number in order to get meaningful concentrations!

The Difference Between Trees and Rocks

This post is in response to a Flat Earther youtube video entitled “There are no forests on Flat Earth Wake Up.” I won’t link directly to this video because I refuse to help provide it with traffic.

I first happened across a description of this video in an article from The Atlantic. At the time, I sort of sat there and fulminated as I read it. That article in and of itself was not enough to stimulate a response from me because there’s really not much to say. Flat Earth believers are a train wreck of misconception and arrogance. They do not deserve acknowledgement for their ideas except to say that they are not merely wrong, but willfully contrarian to reality.

There is no arguing with a Flat Earther.

Fact is that such a person is so invested in a bad idea that they cannot be dissuaded from it. There are so many things that happen or are happening around you all the time that provide evidence against the flat earth that you need only open your eyes to see them. It takes a willful investment in the avoidance of reality to believe in a flat earth. You can look back at my response to a set of flat earth claims to know my general thoughts.

The video I mentioned above goes a step beyond the usual flat earth nonsense and makes the rather extravagant claim that there used to be forests on earth where the trees are miles tall and that land features like mesas or volcanic plugs like Devil’s Tower are stumps left from these huge trees. And, further, at some point those trees were all toppled and that the ‘man’ has a conspiracy going to cover up that they ever existed. Scientists are apparently actively complicit in hiding ‘the truth’ by distorting findings about fossils.

devils_tower_in_autumn__wyoming

Devil’s Tower is a striking piece of landscape. I’ve seen it for myself and it is visceral and impressive. The structure is sort of biological after a fashion, I will admit. It does look like a tree stump. However, making the claim that an object has a biological form is not the same as claiming the object is biological. Nature has an incredible repertoire of mechanisms for producing complicated patterns that are absolutely not biological.

How was the following pattern constructed?

stripey-weird-thing-nematic014

Tell me what you think this is! I know what it is, but I’m not going to identify it right away. Is it biological? Is this in an art museum? What do you think? More than that, how would you go about figuring out what this is? Think about it while you read.

The video I mentioned above goes on and on about things looking like other things actually being the other thing. That video is an hour and a half of blanket assertion. I admittedly could only stomach about 20 minutes of the video before it became completely clear that I wasn’t about to encounter anything resembling reality at any point along the way. Watching it all the way through is a waste of time… it should chill one to the bone that the number of ‘likes’ on this video is in the hundreds of thousands. Do that many people really get stuck on this topic?

The first thing you’ll note about that video is that the narrator very frequently says “This is bullshit” or “That’s bullshit!” Does an assertion of falsehood uproot a truth? He characterizes claims made by scientists using the words “Contrary to all laws of Physics, Chemistry and Biology.” What are those laws? What does science actually say? How do you know when a scientist is contradicting the ‘laws of science?’ You have to know what the science is, right? He goes on at length showing goofy pictures of apparently inept scientists while attacking the notion of fossilization, that a biological relic can be subsumed into a route of decomposition where the carbon structure is replaced by a long-term silicon structure.

Of course, in order to justify his mile-tall trees, he needs to completely throw out the window basically everything known about geology. His mile-tall trees weren’t actually carbon, but silicon (never mind that his entire treatise started out on the assertion that everything that’s left of these trees is carbon trapped in ice: carbon, silicon, carbon, iron, apparently self-consistency isn’t required in the rarefied atmosphere he inhabits)… and that relics of these huge trees are stumps formed by mesa-like mountains or that fossil trees from petrified forests are actually branches from some huge silicon tree. Early on, he makes the claim that trees produce a constant current of electricity (which is false) and that there was a silicon era (never mind that there is no such thing as silicon based life… that we know of on Earth. And, no, diatoms are not silicon based).

Coming back to Devil’s tower, he spends a huge amount of time claiming that there’s no way the structure of the tower could be naturally occurring without the patterning provided by life because it’s far too regular. If you look closely at the tower, it has this fascinating hexagonal columnar structure that almost looks built rather than deposited.

adventure-11-1728007

As he was marveling at Devil’s Tower and how the structure is inexplicable, I turned him off…

Let’s consider this one particular claim and distinguish how an actual scientist thinks in contrast to the nonsense put forth by this crank. The claim is that there’s no way a non-biological process can produce regular hexagonal column structures of the size seen at Devil’s tower. Claims by geologists that these structures are rock formed from lava are therefore ‘bullshit.’ I do hear scientists use the word ‘bullshit’ once in a while, but here’s the difference. The crank says ‘the structures are too big and too regular, therefore they had to have been made from a tree.’ On the other hand, a scientist would say this: ‘These structures are very big and very regular, I do not accept that they were made without the patterning provided by life, but I would change my mind about this if I could find an example of this kind of structure where I know the patterning is by a non-living process.’

Jumping to the money shot, one obvious candidate is crystallization. This process is well known to make geometrical inorganic shapes and it is understood that it happens spontaneously. Crystallization has a hefty contact to physics, chemistry and biology and there is huge literature of it outside of scientific fields. This is, of course, where gemstones come from. The objects in Devil’s Tower look very much like crystals. Can crystals become that large? Can they bend like the fluting of a tree trunk?

With Devil’s Tower in mind, I went to Google and performed an image search looking for ‘large industrially produced crystals.’ How big can crystals be made? This turned up a company by the name of Cleveland Crystals which produces large crystals:

ccboules

So, first off, crystals can be made that are ‘big.’ How big is big enough? Can it be scaled up without limit? There’s no reason to think not. The website for the company says pretty clearly that there is a correlation between the size of the crystal and the time it took to form.

Now, second, if crystals are ‘made’ by a company, does that mean that nature can’t also make crystals? Certainly a valid question since humans almost certainly caused the structures in the picture above to exist. Maybe nature can’t make them that big.

I therefore did an image search for ‘large natural crystals.’ Which produced this:

crystal11191341899

This is found in a mine in Mexico.

Do I believe that crystals can be big? Clearly they can be. But, are those things in Devil’s Tower crystals?

I then started to search for natural crystals that are hexagonal in cross section that look like rocks:

aqum413-aquamarine-crystal

This is a mineral called aquamarine. One rapidly descends into mineralogy at some point, necessitating at least some cursory respect for geology.

Now, I have big hexagonal crystals. But do they bend like the gentle curvature seen in Devil’s Tower? I mean, crystals are renown for their geometric straightness, so maybe the failure would be if crystals don’t bend.

A quick search gave me this example in Quartz:

curved300

As it turns out, crystal lattices do have the ability to deform their dimensions over long distances.

What I have now is this. There’s a process called ‘crystallization’ which is totally non-living that produces big, patterned objects that can have hexagonal, geometric cross sections that can be slightly bent all while still looking like rock. Crystallization is well known to be spontaneous and to not depend on the presence of life, even if it can occur in a factory. ‘Crystallization’ is a bit of a leap because I was simply fishing for non-living processes that can produce large, geometrically patterned objects. A bundle of crystals could conceivably be piled together into a formation like a tree stump.

So then, is Devil’s Tower a crystal formation? If it’s from a living thing, you should be able to walk over to it and break off a piece to look for biological cells… in reality, if you look at a piece of Devil’s Tower under the microscope, you would find no cells and if you put it into a mass spectrometer, you would find minerals, maybe like the ones above. There is even a testable model for how a structure like Devil’s Tower might form… it would be like a much longer term version of the conditions that happen in the factory at Cleveland Crystals, but just sitting out in the world. You could melt rock of similar chemical composition to Devil’s Tower in a crucible shaped like a tree stump and then set the crucible in conditions that support crystallization. Would it then spontaneously crystallize so that the crystals filled a volume shaped like a stump?

Notice, there are details that can be chased as long as you keep asking logical questions. A scientist will say, “I know this and this and this, but I’m not quite sure about that.”

Here’s the big difference between the scientist and the crank. The crank decided ahead of time that the formation was too *whatever* to have occurred by any means other than his preferred crankery. The scientist may start with a similar idea to the crank, but he’s got to include ‘falsification’ in his process (either directly by his own hand, or by peer review). Falsification is a loop hole that you must always add which gives you some way of being able to change your mind if better evidence or explanations come along. What evidence would I have to find in order to prove this theory wrong? A big part of the scientific method is deliberately trying to knock a theory down, to falsify it. In the case of Devil’s Tower, a crystal forming process might well have created the observed pattern, so the Tower isn’t necessarily a biological product. Since other processes exist which can produce the same outcome, the “huge tree” hypothesis is in immediate jeopardy as one among competing theories –Occam’s razor would give an adequate coup de gras to finish the argument right here since the “huge tree” theory can’t support all the evidence that the full field of geology can throw at it. But, if you’re stubborn and absolutely certain that the Tower is biological in origin, you would have to look and see if it has a biological fabric… if it has no fundamental biological structure, like evidence of cells, then it can’t be a living product and the hypothesis that it’s the stump of some huge tree must be discarded. Eventually, the combined weights of Biology and Geology would crush this fanciful little pet theory.

This may confuse some people. I’m saying that a necessary core of the scientific method is that you must go out and look for evidence that disproves your thesis. With a lot of science, it doesn’t look like this is happening anymore, which is why certain science is called ‘settled.’ The creationist will say “I’m trying to attack a hypothesis: I’m offering evidence that shows that Evolution is wrong.” The Flat Earther who made the video will say “Everything in geology is bullshit: don’t you see all the explanations I’m offering?” Even an antivaxxer will say “If you’re so confident in vaccines, why aren’t you still testing to see if they cause autism?” To many cranks, science looks like this united party who thoughtlessly discards every challenge to the hallowed orthodoxy. If science is based on tearing down accepted theories, why won’t they test my version?

In some ways, certain parts of science take on the aura of a hallowed ground. This is the result of the last generation of active theories weathering all the assaults waged against them… scientists have tried for decades to knock old theories down and offered modifications to strengthen those theories wherever an attack succeeded. As a result, the old theories became the modern theories and their weaknesses vanished. The fights occurring between scientists to falsify modern theories happen at a level above where most of the public and laymen are competent to contribute. You have to pick your fights, and if you’re smart, you understand not to pick a losing fight! In most cases, cranks are not seeing that the relevant fights have already been long since fought. The young earth creationist is typically attacking science where the fight was settled about a hundred years ago: any scientifically justifiable modification to the modern theories that would work better than Darwin’s evolution inevitably still looks too much like evolution to do anything but offend creationist sensibilities, making it a losing fight. The Flat Earther in the video needs literally to throw out the entire geology textbook and the last five hundred years of human history to get to where he has a competent fight, which means he may as well be headbutting a 10 ton granite rock. Antivaxxers are fighting a science that is more recently settled, ten years or twenty years, but settled –at some point, you can’t keep testing a discarded hypothesis. The climatology that global warming deniers question is very fresh and still contains questions, but certain parts are as settled as heliocentricism.

To contribute to science, you must be at the level of the science! Crankery often hinges on not merely willful ignorance, but on someone not understanding the limits of what they understand.

What did you think that pattern was in the mystery picture I posted above? The material depicted is also a kind of crystal, but its a type of cholesteric liquid crystal, meaning that the pattern formed spontaneously and is not biological in nature. Did you guess what it was? How easy is it to look at a pattern and be wrong about what you’re seeing? Human perception is fragile and easily fooled.