Tag Archives: crackpottery

The Gravitational Force of Rubbish

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Imagine, for just a moment, that you were one a group of scientists that had proven the most important, the most profound, the most utterly amazing scientific discovery of all time. Where would you publish it?

Maybe Nature? Science? Or maybe you’d prefer to go open-access, and go with PLOS ONE? Or more mainstream, and send a press release to the NYT?

Well, in the case of today’s crackpots, they bypassed all of those boring journals. They couldn’t be bothered with a pompous rag like the Times. No, they went for the really serious press: America Now with Leeza Gibbons.

What did they go to this amazing media outlet to announce? The most amazing scientific discovery of all time: gravity is an illusion! There’s no gravity. In fact, not just is there no gravity, but all of that quantum physics stuff? It’s utter rubbish. You don’t need any of that complicated stuff! No – you need only one thing: the solar wind.

A new theory on the forces that control planetary orbit refutes the 400-year old assumptions currently held by the scientific community. Scientific and engineering experts Gerhard and Kevin Neumaier have established a relationship between solar winds and a quantized order in both the position and velocity of the solar system’s planets, and movement at an atomic level, with both governed by the same set of physics.

The observations made bring into question the Big Bang Theory, the concept of black holes, gravitational waves and gravitons. The Neumaiers’ paper, More Than Gravity, is available for review at MoreThanGravity.com

Pretty damned impressive, huh? So let’s follow their instructions, and go over to their website.

Ever since humankind discovered that the Earth and the planets revolved around the Sun, there was a question about what force was responsible for this. Since the days of Newton, science has held onto the notion that an invisible force, which we have never been able to detect, controls planetary motion. There are complicated theories about black holes that have never been seen, densities of planets that have never been measured, and subatomic particles that have never been detected.

However, it is simpler than all of that and right in front of us. The Sun and the solar wind are the most powerful forces in our solar system. They are physically moving the planets. In fact, the solar wind spins outward in a spiral at over a million miles per hour that controls the velocity and distances that planets revolve around the Sun. The Sun via the solar wind quantizes the orbits of the planets – their position and speed.

The solar wind also leads to the natural log and other phenomenon from the very large scale down to the atomic level. This is clearly a different idea than the current view that has been held for over 400 years. We have been working on this for close 50 years and thanks to satellite explorations of space have data that just was not available when theories long ago were developed. We think that we have many of the pieces but there are certainly many more to be found. We set this up as a web site, rather as some authoritative book so that there would be plenty of opportunity for dialog. The name for this web site, www.MorethanGravity.com was chosen because we believe there is far more to this subject than is commonly understood. Whether you are a scientific expert in your field or just have a general interest in how our solar system works, we appreciate your comments.

See, it’s all about the solar wind. There’s no such thing as gravity – that’s just nonsense. The sun produces the solar wind, which does absolutely everything. The wind comes out of the sun, and spirals out from the sun. That spiral motion has eddies in it an quantized intervals, and that’s where the planets are. Amazing, huh?

Remember my mantra: the worst math is no math. This is a beautiful demonstration
of that.

Of course… why does the solar wind move in a spiral? Everything we know says that in the absence of a force, things move in a straight line. It can’t be spiraling because of gravity, because there is no gravity. So why does it spiral? Our brilliant authors don’t bother to say. What makes it spiral, instead of just move straight? Mathematically, spiral motion is very complicated. It requires a centripetal force which is smaller than the force that would produce an orbit. Where’s that force in this framework? There isn’t any. They just say that that’s how the solar wind works, period. There are many possible spirals, with different radial velocities – which one does the solar wind follow according to this, and why? Again, no answer from the authors.

Or… why is the sun producing the solar wind at all? According to those old, stupid theories that this work of brilliance supercedes, the sun produces a solar wind because it’s fusing hydrogen atoms into helium. That’s happening because gravity is causing the atoms of the sun to be compressed together until they fuse. Without gravity, why is fusion happening at all? And given that it’s happening, why does the sun not just explode into a supernova? We know, from direct observation, that the energy produced by fusion creates an outward force. But gravity can’t be holding the sun together – so why is the sun there at all? Still, no answers.

They do, eventually, do some math. One of the big “results” of this hypothesis is about the “quantization” of the orbits of planets around the sun. They were able to develop a simple equation which predicts the locations where planets could exist in their “solar wind” system.

Let’s start with the distance between the planets and the Sun. We guessed that if the solar system was like an atom, that planetary distance would be quantized. This is to say that we thought that the planets would have definite positions and that they would be either in the position or it would be empty. In a mathematical sense, this would be represented by a numerical integer ordering (0,1,2,3,…). If the first planet, Mercury was in the 0 orbital, how would the rest of the planets line up? Amazingly well we found.

If we predict the distance from the surface of the Sun to each planet in this quantized approach, the results are astounding. If D equals the mean distance to the surface of the Sun, and d0 as the distance to Mercury, we can describe the relationship that orders the planets mathematically as:

D=d_0 S^n

Each planetary position can be predicted from this equation in a simple calculation as we increase the integer (or planet number) n. S is the solar factor, which equals 1.387. The solar factor is found in the differential rotation of the Sun and the profile of the solar wind which we will discuss later.

Similar to the quantized orbits that exist within an atom, the planetary bodies are either there or not. Mercury is in the zero orbital. The next orbital is missing a planet. The second, third, and fourth orbitals are occupied by Venus, Earth, and Mars respectively. The fifth orbital is missing. The sixth orbital is filled with Ceres. Ceres is described as either the largest of all asteroids or a minor planet (with a diameter a little less than half that of Pluto), depending on who describes it. Ceres was discovered in 1801 as astronomers searched for the missing planets that the Titius-Bode Law predicted would exist.

So. What they found was an exponential equation which products very approximate versions of the size of first 8 planets’ orbits, as well as a couple of missing ones.

This is, in its way, interesting. Not because they found anything, but rather because they think that this is somehow profound.

We’ve got 8 data points (or 9, counting the asteroid belt). More precisely, we have 9 ranges, because all of the orbits are elliptical,but the authors of this junk are producing a single number for the size of the orbits, and they can declare success if their number falls anywherewithin the range from perihelion to aphelion in each of the orbits.

It would be shocking if there weren’t any number of simple equations that described exactly the 9 data points of the planet’s orbits.

But they couldn’t even make that work directly. They only manage to get a partial hit – getting an equation that hits the right points, but which also generates a bunch of misses. There’s nothing remotely impressive about that.

From there, they move on to the strawmen. For example, they claim that their “solar wind” hypothesis explains why the planets all orbit in the same direction on the same plane. According to them, if orbits were really gravitational, then planets would orbit in random directions on random planes around the sun. But their theory is better than gravity, because it says why the planets are in the same plane, and why they’re all orbiting in the same direction.

The thing is, this is a really stupid argument. Why are the planets in the same plane, orbiting in the same direction? Because the solar system was formed out of a rotating gas cloud. There’s a really good, solid, well-supported explanation of why the planets exist, and why they orbit the sun the way they do. Gravity doesn’t explain all of it, but gravity is a key piece of it.

What they don’t seem to understand is how amazingly powerful the theory of gravity is as a predictive tool. We’ve sent probes to the outer edges of the solar system. To do that, we didn’t just aim a rocket towards Jupiter and fire it off. We’ve done things like the Cassini probe, where we launched a rocket towards Venus. It used the gravitational field of Venus twice to accelerate it with a double-slingshot maneuver, and send it back towards earth, using the earth’s gravity to slingshot it again, to give it the speed it needed to get to Jupiter.

This wasn’t a simple thing to do. It required an extremely deep understanding of gravity, with extremely accurate predictions of exactly how gravity behaves.

How do our brilliant authors answer this? By handwaving. The extend of their response is:

Gravitational theory works for things like space travel because it empirically measures the force of a planet, rather than predicting it.

That’s a pathetic handwave, and it’s not even close to true. The gravitational slingshot is a perfect answer to it. A slingshot doesn’t just use some “empirically measured” force of a planet. It’s a very precise prediction of what the forces will be at different distances, how that force will vary, and what effects that force will have.

They do a whole lot more handwaving of very much the same order. Pure rubbish.

A Bad Mathematical Refutation of Atheism

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At some point a few months ago, someone (sadly I lost their name and email) sent me a link to yet another Cantor crank. At the time, I didn’t feel like writing another Cantor crankery post, so I put it aside. Now, having lost it, I was using Google to try to find the crank in question. I didn’t, but I found something really quite remarkably idiotic.

(As a quick side-comment, my queue of bad-math-crankery is, sadly, empty. If you’ve got any links to something yummy, please shoot it to me at markcc@gmail.com.)

The item in question is this beauty. It’s short, so I’ll quote the whole beast.

MYTH: Cantor’s Set Theorem disproves divine omniscience

God is omniscient in the sense that He knows all that is not impossible to know. God knows Himself, He knows and does, knows every creature ideally, knows evil, knows changing things, and knows all possibilites. His knowledge allows free will.

Cantor’s set theorem is often used to argue against the possibility of divine omniscience and therefore against the existence of God. It can be stated:

  1. If God exists, then God is omniscient.
  2. If God is omniscient, then, by definition, God knows the set of all truths.
  3. If Cantor’s theorem is true, then there is no set of all truths.
  4. But Cantor’s theorem is true.
  5. Therefore, God does not exist.

However, this argument is false. The non-existence of a set of all truths does not entail that it is impossible for God to know all truths. The consistency of a plausible theistic position can be established relative to a widely accepted understanding of the standard model of Cantorian set theorem. The metaphysical Cantorian premises imply that Cantor’s theorem is inapplicable to the things that God knows. A set of all truths, if it exists, must be non-Cantorian.

The attempted disproof of God’s omniscience is, from a meta-mathematical standpoint, is inadequate to the extent that it doesn’t explain well-known mathematical contexts in which Cantor’s theorem is invalid. The “disproof” doesn’t acknowledge standard meta-mathematical conceptions that can analogically be used to establish the relative consistency of certain theistic positions. The metaphysical assertions concerning a set of all truths in the atheistic argument above imply that Cantor’s theorem is inapplicable to a set of all truths.

This is an absolute masterwork of crankery! It’s remarkably silly argument on so many levels.

  1. The first problem is just figuring out what the heck he’s talking about! When you say “Cantor’s theorem”, what I think of is one of Cantor’s actual theorems: “For any set S, the powerset of S is larger than S.” But that is clearly not what he’s referring to. I did a bit of searching to make sure that this wasn’t my error, but I can’t find anything else called Cantor’s theorem.

  2. So what the heck does he mean by “Cantor’s set theorem”? From his text, it appears to be a statement something like: “there is no set of all truths”. The closest actual mathematical statement that I can come up with to match that is Gödel’s incompleteness theorem. If that’s what he means, then he’s messed it up pretty badly. The closest I can come to stating incompleteness informally is: “In any formal mathematical system that’s powerful enough to express Peano arithmetic, there will be statements that are true, but which cannot be proven”. It’s long, complex, not particularly intuitive, and it’s still not a particularly good statement of incompleteness.

    Incompleteness is a difficult concept, and as I’ve written about before, it’s almost impossible to state incompleteness in an informal way. When you try to do that, it’s inevitable that you’re going to miss some of its subtleties. When you try to take an informal statement of incompleteness, and reason from it, the results are pretty much guaranteed to be garbage – as he’s done. He’s using a mis-statement of incompleteness,and trying to reason from it. It doesn’t matter what he says: he’s trying to show how “Cantor’s set theorem” doesn’t disprove his notion of theism. Whether it does or not doesn’t matter: for any statement X, no matter what X is, you can’t prove that “Cantor’s set theorem” or Gödel’s incompleteness theorem, or anything else disproves X if you’re arguing against something that isn’t X.

  3. Ignoring his mis-identification of the supposed theorem, the way that he stated it is actually meaningless. When we talk about sets, we’re using the word set in the sense of either ZFC or NBG set theory. Mathematical set theory defines what a set is, using first order predicate logic. His version of “Cantor’s set theorem” talks about a set which cannot be a set!

    He wants to create a set of truths. In set theory terms, that’s something you’d define with the axiom of specification: you’d use a predicate ranging over your objects to select the ones in the set. What’s your predicate? Truth. At best, that’s going to be a second-order predicate. You can’t form sets using second-order predicates! The entire idea of “the set of truths” isn’t something that can be expressed in set theory.

  4. Let’s ignore the problems with his “Cantor’s theorem” for the moment. Let’s pretend that the “set of all truths” was well-defined and meaningful. How does his argument stand up? It doesn’t: it’s a terrible argument. It’s ultimately nothing more than “Because I say so!” hidden behind a collection of impressive-sounding words. The argument, ultimately, is that the set of all truths as understood in set theory isn’t the same thing as the set of all truths in theology (because he says that they’re different), therefore you can’t use a statement about the set of all truths from set theory to talk about the set of all truths in theology.
  5. I’ve saved what I think is the worst for last. The entire thing is a strawman. As a religious science blogger, I get almost as much mail from atheists trying to convince me that my religion is wrong as I do from Christians trying to convert me. After doing this blogging thing for six years, I’m pretty sure that I’ve been pestered with every argument, both pro- and anti-theistic that you’ll find anywhere. But I’ve never actually seen this argument used anywhere except in articles like this one, which purport to show why it’s wrong. The entire argument being refuted is a total fake: no one actually argues that you should be an atheist using this piece of crap. It only exists in the minds of crusading religious folk who prop it up and then knock it down to show how smart they supposedly are, and how stupid the dirty rotten atheists are.

Audiophiles and the Need to be Special

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I love laughing at audiophiles.

If you’re not familiar with the term, audiophiles are people who are really into top-end audio equipment. In itself, that’s fine. But there’s a very active and vocal subset of the audiophile community that’s built up their self-image around the idea that they’re special. They don’t just have better audio equipment than you do, but they have better appreciation of sound quality than you do. In fact, their hearing is better than yours. They can hear nuances in sound quality that you can’t, because they’re so very, very special. They’ve developed this ability, you see, because they care more about music than you do.

It’s a very human thing. We all really want to be special. And when there’s something that’s really important to us – like music is for many people – there’s a very natural desire to want to be able to appreciate it on a deep level, a special level reserved only for people who really value it. But what happens when you take that desire, and convince yourself that it’s not just a desire? You wind up turning into a sucker who’s easy to fleece for huge quantities of money on useless equipment that can’t possibly work.

I first learned about these people from my old friend John Vlissides. John died of brain cancer about 5 years ago, which was incredibly sad. But back in the day, when we both worked at IBM Research, he and I were part of a group that ate lunch together every day. John was a reformed audiophile, and used to love talking about the crazy stuff he used to do.

Audiophiles get really nutty about things like cables. For example, John used to have the cables linking his speakers to his amp suspended from the ceiling using non-conductive cord. The idea behind that is that electrical signals are carried, primarily, on the outer surface of the wire. If the cable was sitting on the ground, it would deform slighly, and that would degrade the signal. Now, of course, there’s no perceptible difference, but a dedicated audiophile can convince themselves that they can hear it. In fact, this is what convinced John that it was all craziness: he was trained as an electrical engineer, and he sat down and worked out how much the signal should change as a result of the deformation of the copper wire-core, and seeing the real numbers, realized that there was no way in hell that he was actually hearing that tiny difference. Right there, that’s an example of the math aspect of this silliness: when you actually do the math, and see what’s going on, even when there’s a plausible explanation, the real magnitude of the supposed effect is so small that there’s absolutely no way that it’s perceptible. In the case of wire deformation, the magnitude of the effect on the sound produced by the signal carried by the wire is so small that it’s essentially zero – we’re talking about something smaller than the deformation of the sound waves caused by the motion of a mosquito’s wings somewhere in the room.

John’s epiphany was something like 20 years ago. But the crazy part of the audiophile community hasn’t changed. I encountered two instances of it this week that reminded me of this silliness and inspired me to write this post. One was purely accidental: I just noticed it while going about my business. The other, I noticed on boing-boing because the first example was already in my mind.

First, I was looking for an HDMI video cable for my TV. At the moment, we’ve got both an AppleTV and a cable box hooked up to our TV set. We recently found out that under our cable contract, we could get a free upgrade of the cable box, and the new box has HDMI output – so we’d need a new cable to use it.

HDMI is a relatively new standard video cable for carrying digital signals. Instead of old-fashioned analog signals that emulate the signal recieved by a good-old TV antenna like we used to use, HDMI uses a digital stream for both audio and video. Compared to old-fashioned analog, the quality of both audio and video on a TV using HDMI is dramatically improved. Analog signals were designed way, way back in the ’50s and ’60s for the televisions that they were producing then – they’re very low fidelity signals, which are designed to produce images on old TVs, which had exceedingly low resolution by modern standards.

The other really great thing about a digital system like HDMI is that digital signals don’t degrade. A digital system takes a signal, and reduces it to a series of bits – signals that can be interpreted as 1s and 0s. That series of bits is divided into bundles called packets. Each packet is transmitted with a checksum – an additional number that allows the receiver to check that it received the packet correctly. So for a given packet of information, you’ve either received it correctly, or you didn’t. If you didn’t, you request the sender to re-send it. So you either got it, or you didn’t. There’s no in-between. In terms of video quality, what that means is that the cable really doesn’t matter very much. It’s either getting the signal there, or it isn’t. If the cable is really terrible, then it just won’t work – you’ll get gaps in the signal where the bad packets dropped out – which will produce a gap in the audio or video.

In analog systems, you can have a lot of fuzz. The amplitude of the signal at any time is the signal – so noise effects that change the amplitude are changing the signal. There’s a very real possibility that interference will create real changes in the signal, and that those changes will produce a perceptible result when the signal is turned into sound or video. For example, if you listen to AM radio during a thunderstorm, you’ll hear a burst of noise whenever there’s a bolt of lightning nearby.

But digital systems like HDMI don’t have varying degrees of degradation. Because the signal is reduced to 1s and 0s – if you change the amplitude of a 1, it’s still pretty much going to look like a one. And if the noise is severe enough to make a 1 look like a 0, the error will be detected because the checksum will be wrong. There’s no gradual degradation.

But audiophiles… ah, audiophiles.

I was looking at these cables. A basic six-foot-long HDMI cable sells for between 15 and 25 dollars. But on the best-buy website, there’s a clearance cable for just $12. Great! And right next to it, there’s another cable. Also six feet long. For $240 dollars! 20-times higher, for a friggin’ digital cable! I’ve heard, on various websites, the rants about these crazies, but I hadn’t actually paid any attention. But now, I got to see it for myself, and I just about fell out of my chair laughing.

To prolong the entertainment, I went and looked at the reviews of this oh-so-amazing cable.

People who say there is NO difference between HDMI cables are just trying to justify to themselves to go cheap. Now it does depend on what you are connecting the cable between. If you put this Carbon HDMI on a Cable or Satellite box, you probably won’t see that much of a difference compared to some middle grade cables.

I connected this cable from my PS3 to my Samsung to first test it, then to my receiver. It was a nice upgrade from my previous Cinnamon cable, which is already a great cable in it’s own right. The picture’s motion was a bit smoother with gaming and faster action, but I still want to check the link to the guide about gaming monitors my fried sent me. I also noticed that film grain looked a little cleaner, not sure why though.

The biggest upgrade was with my audio though. Everything sounded a little crisper with more detail. I also noticed that the sound fields were more distinct. Again not sure exactly why, but I will take the upgrade.

All and all if you want the best quality, go Audio Quest and specifically a Carbon HDMI. You never have to upgrade your HDMI again with one of these guys. Downfall though is that it is a little pricey.

What’s great about it: Smooth motion and a little more definition in the picture

What’s not so great: Price

It’s a digital cable. The signal that it delivers to your TV and stereo is not the slightest bit different from the signal delivered by the $12 clearance cable. It’s been reduced by the signal producing system to a string of 1s and 0s – the identical string of 1s and 0s on both cables – and that string of bits is getting interpreted by exactly the same equipment on the receiver, producing exactly the same audio and video. There’s no difference. It has nothing to do with how good your ears are, or how perceptive you are. There is no difference.

But that’s nothing. The same brand sells a $700 cable. From the reviews:

I really just bought 3 of these. So if you would like an honest review, here it is. Compared to other Audio Quest cables, like the Vodka, you do not see a difference unless you know what to look for and have the equipment that can actually show the difference. Everyone can see the difference in a standard HDMI to an HDMI with Silver in it if you compare, but the difference between higher level cables is more subtle. Audio is the night and day difference with these cables. My bluray has 2 HDMI outs and I put one directly to the TV and one to my processor. My cable box also goes directly to my TV and I use Optical out of the TV because broadcast audio is aweful. The DBS systems keeps the cable ready for anything and I can tell that my audio is clean instantly and my picture is always flawless. They are not cheap cables, they are 100% needed if you want the best quality. I am considering stepping up to Diamond cables for my theater room when I update it. Hope this helps!

And they even have a “professional quality” HDMI cable that sells for well over $1000. And the audiophiles are all going crazy, swearing that it really makes a difference.

Around the time I started writing this, I also saw a post on BoingBoing about another audiophile fraud. See, when you’re dealing with this breed of twit who’s so convinced of their own great superiority, you can sell them almost anything if you can cobble together a pseudoscientific explanation for why it will make things sound better.

This post talks about a very similar shtick to the superexpensive cable: it’s a magic box which… well, let’s let the manufacturer explain.

The Blackbody ambient field conditioner enhances audio playback quality by modifying the interaction of your gear’s circuitry with the ambient electromagnetic field. The Blackbody eliminates sonic smearing of high frequencies and lowers the noise floor, thus clarifying the stereo image.

This thing is particularly fascinating because it doesn’t even pretend to hook in to your audio system. You just position it close to your system, and it magically knows what equipment it’s close to and “harmonizes” everything. It’s just… magic! But if you’re really special, you’ll be able to tell that it works!

Hydrinos: Impressive Free Energy Crackpottery

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Back when I wrote about the whole negative energy rubbish, a reader wrote to me, and asked me to write something about hydrinos.

For those who are lucky enough not to know about them, hydrinos are part of another free energy scam. In this case, a medical doctor named Randell Mills claims to have discovered that hydrogen atoms can have multiple states beyond the typical, familiar ground state of hydrogen. Under the right conditions, so claims Dr. Mills, the electron shell around a hydrogen atom will compact into a tighter orbit, releasing a burst of energy in the process. And, in fact, it’s (supposedly) really, really easy to make hydrogen turn into hydrinos – if you let a bunch of hydrogen atoms bump in to a bunch of Argon atoms, then presto! some of the hydrogen will shrink into hydrino form, and give you a bunch of energy.

Wonderful, right? Just let a bunch of gas bounce around in a balloon, and out comes energy!

Oh, but it’s better than that. There are multiple hydrino forms: you can just keep compressing and compressing the hydrogen atom, pushing out more and more energy each time. The more you compress it, the more energy you get – and you don’t really need to compress it. You just bump it up against another atom, and poof! energy.

To explain all of this, Dr. Mills further claims to have invented a new
form of quantum mechanics, called “grand unified theory of classical quantum mechanics” (CQM for short) which provides the unification between relativity and quantum mechanics that people have been looking for. And, even better, CQM is fully deterministic – all of that ugly probabilistic stuff from quantum mechanics goes away!

The problem is, it doesn’t work. None of it.

What makes hydrinos interesting as a piece of crankery is that there’s a lot more depth to it than to most crap. Dr. Mills hasn’t just handwaved that these hydrino things exist – he’s got a very elaborate detailed theory – with a lot of non-trivial math – to back it up. Alas, the math is garbage, but it’s garbage-ness isn’t obvious. To see the problems, we’ll need to get deeper into math than we usually do.

Let’s start with a couple of examples of the claims about hydrinos, and the kind of favorable clueless press they’ve received.

Here is an example of how hydrino supporters explain them:

In 1986 Randell Mills MD developed a theory that hydrogen atoms could shrink, and release lots of energy in the process. He called the resultant entity a “Hydrino” (little Hydrogen), and started a company called Blacklight Power, Inc. to commercialize his process. He published his theory in a book he wrote, which is available in PDF format on his website. Unfortunately, the book contains so much mathematics that many people won’t bother with it. On this page I will try to present the energy related aspect of his theory in language that I hope will be accessible to many.

According to Dr. Mills, when a hydrogen atom collides with certain other atoms or ions, it can sometimes transfer a quantity of energy to the other atom, and shrink at the same time, becoming a Hydrino in the process. The atom that it collided with is called the “catalyst”, because it helps the Hydrino shrink. Once a Hydrino has formed, it can shrink even further through collisions with other catalyst atoms. Each collision potentially resulting in another shrinkage.

Each successive level of shrinkage releases even more energy than the previous level. In other words, the smaller the Hydrino gets, the more energy it releases each time it shrinks another level.

To get an idea of the amounts of energy involved, I now need to introduce the concept of the “electron volt” (eV). An eV is the amount of energy that a single electron gains when it passes through a voltage drop of one volt. Since a volt isn’t much (a “dry cell” is about 1.5 volts), and the electric charge on an electron is utterly minuscule, an eV is a very tiny amount of energy. Nevertheless, it is a very representative measure of the energy involved in chemical reactions. e.g. when Hydrogen and Oxygen combine to form a water molecule, about 2.5 eV of energy is released per water molecule formed.

When Hydrogen shrinks to form a second level Hydrino (Hydrogen itself is considered to be the first level Hydrino), about 41 eV of energy is released. This is already about 16 times more than when Hydrogen and Oxygen combine to form water. And it gets better from there. If that newly formed Hydrino collides with another catalyst atom, and shrinks again, to the third level, then an additional 68 eV is released. This can go on for quite a way, and the amount gets bigger each time. Here is a table of some level numbers, and the energy released in dropping to that level from the previous level, IOW when you go from e.g. level 4 to level 5, 122 eV is released. (BTW larger level numbers represent smaller Hydrinos).

And some of the press:

Notice a pattern?

The short version of the problem with hydrinos is really, really simple.

The most fundamental fact of nature that we’ve observed is that everything tends to move towards its lowest energy state. The whole theory of hydrinos basically says that that’s not true: everything except hydrogen tends to move towards its lowest energy state, but hydrogen doesn’t. It’s got a dozen or so lower energy states, but none of the abundant quantities of hydrogen on earth are ever observed in any of those states unless they’re manipulated by Mills magical machine.

The whole basis of hydrino theory is Mills CQM. CQM is rubbish – but it’s impressive looking rubbish. I’m not going to go deep into detail; you can see a detailed explanation of the problems here; I’ll run through a short version.

To start, how is Mills claiming that hydrinos work? In CQM, he posits the existence of electron shell levels closer to the nucleus than the ground state of hydrogen. Based on his calculations, he comes up with an energy figure for the difference between the ground state and the hydrino state. Then he finds other substances that have the property that boosting one electron into a higher energy state would cost the same amount of energy. When a hydrogen atom collides with an atom that has a matching electron transition, the hydrogen can get bumped into the hydrino state, while kicking an electron into a higher orbital. That electron will supposedly, in due time, fall back to its original level, releasing the energy differential as a photon.

On this level, it sort-of looks correct. It doesn’t violate conservation of energy: the collision between the two atoms doesn’t produce anything magical. It’s just a simple transfer of energy. That much is fine.

It’s when you get into the details that it gets seriously fudgy.

Right from the start, if you know what you’re doing, CQM goes off the rails. For example, CQM claims that you can describe the dynamics of an electron in terms of a classical wave charge-density function equation. Mills actually gives that function, and asserts that it respects Lorentz invariance. That’s crucial – Lorentz invariance is critical for relativity: it’s the fundamental mathematical symmetry that’s the basis of relativity. But his equation doesn’t actually respect Lorentz invariance. Or, rather, it does – but only if the electron is moving at the speed of light. Which it can’t do.

Mills goes on to describe the supposed physics of hydrinos. If you work through his model, the only state that is consistent with both his equations, and his claim that the electrons orbit in a spherical shell above the atom – well, if you do that, you’ll find that according to his own equations, there is only one possible state for a hydrogen atom – the conventional ground state.

It goes on in that vein for quite a while. He’s got an elaborate system, with an elaborate mathematical framework… but none of the math actually says what he says it says. The Lorentz invariance example that I cited above – that’s typical. Print an equation, say that it says X, even though the equation doesn’t say anything like X.

But we can go a bit further. The fundamental state of atoms is something that we understand pretty well, because we’ve got so many observations, and so much math describing it. And the thing is, that math is pretty damned convincing. That doesn’t mean that it’s correct, but it does mean that any theory that wants to replace it must be able to describe everything that we’ve observed at least as well as the current theory.

Why do atoms have the shape that they do? Why are the size that they are? It’s not a super easy thing to understand, because electrons aren’t really particles. They’re something strange. We don’t often think about that, but it’s true. They’re deeply bizarre things. They’re not really particles. Under many conditions, they behave more like waves than like particles. And that’s true of the atom.

The reason that atoms are the size that they are is because the electron “orbitals” have sizes and shapes that are determined by resonant frequencies of the wave-like aspects of electrons. What Mills is suggesting is that there are a range of never-before observed resonant frequencies of electrons. But the math that he uses to support that claim just doesn’t work.

Now, I’ll be honest here. I’m not nearly enough of a physics whiz to be competent to judge the accuracy of his purported quantum mechanical system. But I’m still pretty darn confident that he’s full of crap. Why?

I’m from New Jersey – pretty much right up the road from where his lab is. Going to college right up the road from him, I’ve been hearing about his for a long time. He’s been running this company for quite a while – going on two decades. And all that time, the company has been constantly issuing press releases promising that it’s just a year away from being commercialized! It’s always one step away. But never, never, has he released enough information to let someone truly independent verify or reproduce his results. And he’s been very deceptive about that: he’s made various claims about independent verification on several occasions.

For example, he once cited that his work had been verified by a researcher at Harvard. In fact, he’d had one of his associates rent a piece of equipment at Harvard, and use it for a test. So yes, it was tested by a researcher – if you count his associate as a legitimate researcher. And it was tested at Harvard. But the claim that it was tested by a researcher at Harvard is clearly meant to imply that it was tested by a Harvard professor, when it wasn’t.

For something around 20 years, he’s been making promises, giving very tightly controlled demos, refusing to give any real details, refusing to actually explain how to reproduce his “results”, and promising that it’s just one year away from being commercialized!

And yet… hydrogen is the most common substance in the universe. If it really had a lower energy state that what we call it’s ground state, and that lower energy state was really as miraculous as he claims – why wouldn’t we see it? Why hasn’t it ever been observed? Substances like Argon are rare – but they’re not that rare. Argon has been exposed to hydrogen under laboratory conditions plenty of times – and yet, nothing anamalous has even been observed. All of the supposed hydrino catalysts have been observed so often under so many conditions – and yet, no anamolous energy has even been noticed before. But according to Mills, we should be seeing tons of it.

And that’s not all. Mills also claims that you can create all sorts of compounds with hydrinos – and naturally, every single one of those compounds is positively miraculous! Bonded with silicon, you get better semiconductors! Substitute hydrinos for regular hydrogen in a battery electrolyte, and you get a miracle battery! Use it in rocket fuel instead of common hydrogen, and you get a ten-fold improvement in the performance of a rocket! Make a laser from it, and you can create higher-density data storage and communication systems. Everything that hydrinos touch is amazing

But… not one of these miraculous substances has ever been observed before. We work with silicon all the time – but we’ve never seen the magic silicon hydrino compound. And he’s never been willing to actually show anyone any of these miracle substances.

He claims that he doesn’t show it because he’s protecting his intellectual property. But that’s silly. If hydrinos existed, then just telling us that these compounds exist and have interesting properties should be enough for other labs to go ahead and experiment with producing them. But no one has. Whether he shows the supposed miracle compounds or not doesn’t change anyone else’s ability to produce those. Even if he’s keeping his magic hydrino factory secret, so that no one else has access to hydrinos, by telling us that these compounds exist, he’s given away the secret. He’s not protecting anything anymore: by publically talking about these things, he’s given up his right to patent the substances. It’s true that he still hasn’t given up the rights to the process of producing them – but publicly demonstrating these alleged miracle substances wouldn’t take away any legal rights that he hasn’t already given up. So, why doesn’t he show them to you?

Because they don’t exist.

Second Law Silliness from Sewell

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So, via Panda’s Thumb, I hear that Granville Sewell is up to his old hijinks. Sewell is a classic creationist crackpot, who’s known for two things.

First, he’s known for chronically recycling the old “second law of thermodynamics” garbage. And second, he’s known for building arguments based on “thought experiments” – where instead of doing experiments, he just makes up the experiments and the results.

The second-law crankery is really annoying. It’s one of the oldest creationist pseudo-scientific schticks around, and it’s such a terrible argument. It’s also a sort-of pet peeve of mine, because I hate the way that people generally respond to it. It’s not that the common response is wrong – but rather that the common responses focus on one error, while neglecting to point out that there are many deeper issues with it.

In case you’ve been hiding under a rock, the creationist argument is basically:

  1. The second law of thermodynamics says that disorder always increases.
  2. Evolution produces highly-ordered complexity via a natural process.
  3. Therefore, evolution must be impossible, because you can’t create order.

The first problem with this argument is very simple. The second law of thermodynamics does not say that disorder always increases. It’s a classic example of my old maxim: the worst math is no math. The second law of thermodynamics doesn’t say anything as fuzzy as “you can’t create order”. It’s a precise, mathematical statement. The second law of thermodynamics says that in a closed system:

Delta S geq int frac{delta Q}{T}

where:

  1. S is the entropy in a system,
  2. Q is the amount of heat transferred in an interaction, and
  3. T is the temperature of the system.

Translated into english, that basically says that in any interaction that involves the
transfer of heat, the entropy of the system cannot possible be reduced. Other ways of saying it include “There is no possible process whose sole result is the transfer of heat from a cooler body to a warmer one”; or “No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.”

Note well – there is no mention of “chaos” or “disorder” in these statements: The second law is a statement about the way that energy can be used. It basically says that when
you try to use energy, some of that energy is inevitably lost in the process of using it.

Talking about “chaos”, “order”, “disorder” – those are all metaphors. Entropy is a difficult concept. It doesn’t really have a particularly good intuitive meaning. It means something like “energy lost into forms that can’t be used to do work” – but that’s still a poor attempt to capture it in metaphor. The reason that people use order and disorder comes from a way of thinking about energy: if I can extract energy from burning gasoline to spin the wheels of my car, the process of spinning my wheels is very organized – it’s something that I can see as a structured application of energy – or, stretching the metaphor a bit, the energy that spins the wheels in structured. On the other hand, the “waste” from burning the gas – the heating of the engine parts, the energy caught in the warmth of the exhaust – that’s just random and useless. It’s “chaotic”.

So when a creationist says that the second law of thermodynamics says you can’t create order, they’re full of shit. The second law doesn’t say that – not in any shape or form. You don’t need to get into the whole “open system/closed system” stuff to dispute it; it simply doesn’t say what they claim it says.

But let’s not stop there. Even if you accept that the mathematical statement of the second law really did say that chaos always increases, that still has nothing to do with evolution. Look back at the equation. What it says is that in a closed system, in any interaction, the total entropy must increase. Even if you accept that entropy means chaos, all that it says is that in any interaction, the total entropy must increase.

It doesn’t say that you can’t create order. It says that the cumulative end result of any interaction must increase entropy. Want to build a house? Of course you can do it without violating the second law. But to build that house, you need to cut down trees, dig holes, lay foundations, cut wood, pour concrete, put things together. All of those things use a lot of energy. And in each minute interaction, you’re expending energy in ways that increase entropy. If the creationist interpretation of the second law were true, you couldn’t build a house, because building a house involves creating something structured – creating order.

Similarly, if you look at a living cell, it does a whole lot of highly ordered, highly structured things. In order to do those things, it uses energy. And in the process of using that energy, it creates entropy. In terms of order and chaos, the cell uses energy to create order, but in the process of doing so it creates wastes – waste heat, and waste chemicals. It converts high-energy structured molecules into lower-energy molecules, converting things with energetic structure to things without. Look at all of the waste that’s produced by a living cell, and you’ll find that it does produce a net increase in entropy. Once again, if the creationists were right, then you wouldn’t need to worry about whether evolution was possible under thermodynamics – because life wouldn’t be possible.

In fact, if the creationists were right, the existence of planets, stars, and galaxies wouldn’t be possible – because a galaxy full of stars with planets is far less chaotic than loose cloud of hydrogen.

Once again, we don’t even need to consider the whole closed system/open system distinction, because even if we treat earth as a closed system, their arguments are wrong. Life doesn’t really defy the laws of thermodynamics – it produces entropy exactly as it should.

But the creationist second-law argument is even worse than that.

The second-law argument is that the fact that DNA “encodes information”, and that the amount of information “encoded” in DNA increases as a result of the evolutionary process means that evolution violates the second law.

This absolutely doesn’t require bringing in any open/closed system discussions. Doing that is just a distraction which allows the creationist to sneak their real argument underneath.

The real point is: DNA is a highly structured molecule. No disagreement there. But so what? In the life of an organism, there are virtually un-countable numbers of energetic interactions, all of which result in a net increase in the amount of entropy. Why on earth would adding a bunch of links to a DNA chain completely outweigh those? In fact, changing the DNA of an organism is just another entropy increasing event. The chemical processes in the cell that create DNA strands consume energy, and use that energy to produce molecules like DNA, producing entropy along the way, just like pretty much every other chemical process in the universe.

The creationist argument relies on a bunch of sloppy handwaves: “entropy” is disorder; “you can’t create order”, “DNA is ordered”. In fact, evolution has no problem with respect to entropy: one way of viewing evolution is that it’s a process of creating ever more effective entropy-generators.

Now we can get to Sewell and his arguments, and you can see how perfectly they match what I’ve been talking about.

Imagine a high school science teacher renting a video showing a tornado sweeping through a town, turning houses and cars into rubble. When she attempts to show it to her students, she accidentally runs the video backward. As Ford predicts, the students laugh and say, the video is going backwards! The teacher doesn’t want to admit her mistake, so she says: “No, the video is not really going backward. It only looks like it is because it appears that the second law is being violated. And of course entropy is decreasing in this video, but tornados derive their power from the sun, and the increase in entropy on the sun is far greater than the decrease seen on this video, so there is no conflict with the second law.” “In fact,” the teacher continues, “meteorologists can explain everything that is happening in this video,” and she proceeds to give some long, detailed, hastily improvised scientific theories on how tornados, under the right conditions, really can construct houses and cars. At the end of the explanation, one student says, “I don’t want to argue with scientists, but wouldn’t it be a lot easier to explain if you ran the video the other way?”

Now imagine a professor describing the final project for students in his evolutionary biology class. “Here are two pictures,” he says.

“One is a drawing of what the Earth must have looked like soon after it formed. The other is a picture of New York City today, with tall buildings full of intelligent humans, computers, TV sets and telephones, with libraries full of science texts and novels, and jet airplanes flying overhead. Your assignment is to explain how we got from picture one to picture two, and why this did not violate the second law of thermodynamics. You should explain that 3 or 4 billion years ago a collection of atoms formed by pure chance that was able to duplicate itself, and these complex collections of atoms were able to pass their complex structures on to their descendants generation after generation, even correcting errors. Explain how, over a very long time, the accumulation of genetic accidents resulted in greater and greater information content in the DNA of these more and more complicated collections of atoms, and how eventually something called “intelligence” allowed some of these collections of atoms to design buildings and computers and TV sets, and write encyclopedias and science texts. But be sure to point out that while none of this would have been possible in an isolated system, the Earth is an open system, and entropy can decrease in an open system as long as the decreases are compensated by increases outside the system. Energy from the sun is what made all of this possible, and while the origin and evolution of life may have resulted in some small decrease in entropy here, the increase in entropy on the sun easily compensates this tiny decrease. The sun should play a central role in your essay.”

When one student turns in his essay some days later, he has written,

“A few years after picture one was taken, the sun exploded into a supernova, all humans and other animals died, their bodies decayed, and their cells decomposed into simple organic and inorganic compounds. Most of the buildings collapsed immediately into rubble, those that didn’t, crumbled eventually. Most of the computers and TV sets inside were smashed into scrap metal, even those that weren’t, gradually turned into piles of rust, most of the books in the libraries burned up, the rest rotted over time, and you can see see the result in picture two.”

The professor says, “You have switched the pictures!” “I know,” says the student. “But it was so much easier to explain that way.”

Evolution is a movie running backward, that is what makes it so different from other phenomena in our universe, and why it demands a very different sort of explanation.

This is a perfect example of both of Sewell’s usual techniques.

First, the essential argument here is rubbish. It’s the usual “second-law means that you can’t create order”, even though that’s not what it says, followed by a rather shallow and pointless response to the open/closed system stuff.

And the second part is what makes Sewell Sewell. He can’t actually make his own arguments. No, that’s much too hard. So he creates fake people, and plays out a story using his fake people and having them make fake arguments, and then uses the people in his story to illustrate his argument. It’s a technique that I haven’t seen used so consistency since I read Ayn Rand in high school.

Yet Another Cantor Crank

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I get a fair bit of mail from crackpots. The category that I find most annoying is the Cantor cranks. Over and over and over again, these losers send me their “proofs”.

What bugs me so much about this is how shallowly wrong they are.

What Cantor did was remarkably elegant. He showed that given anything that is claimed to be a one-to-one mapping between the set of integers and the set of real numbers (also sometimes described as an enumeration of the real numbers – the two terms are functionally equivalent), then here’s a simple procedure which will produce a real number that isn’t in included in that mapping – which shows that the mapping isn’t one-to-one.

The problem with the run-of-the-mill Cantor crank is that they never even try to actually address Cantor’s proof. They just say “look, here’s a mapping that works!”

So the entire disproof of their “refutation” of Cantor’s proof is… Cantor’s proof. They completely ignore the thing that they’re claiming to disprove.

I got another one of these this morning. It’s particularly annoying because he makes the same mistake as just about every other Cantor crank – but he also specifically points to one of my old posts where I rant about people who make exactly the same mistake as him.

To add insult to injury, the twit insisted on sending me PDF – and not just a PDF, but a bitmapped PDF – meaning that I can’t even copy text out of it. So I can’t give you a link; I’m not going to waste Scientopia’s bandwidth by putting it here for download; and I’m not going to re-type his complete text. But I’ll explain, in my own compact form, what he did.

It’s an old trick; for example, it’s ultimately not that different from what John Gabriel did. The only real novelty is that he does it in binary – which isn’t much of a novelty. This author calls it the “mirror method”. The idea is, in one column, write a list of the integers greater than 0. In the opposite column, write the mirror of that number, with the decimal (or, technically, binary) point in front of it:

Integer Real
0 0.0
1 0.1
10 0.01
11 0.11
100 0.001
101 0.101
110 0.011
111 0.111
1000 0.0001
… …

Extend that out to infinity, and, according to the author, the second column it’s a sequence of every possible real number, and the table is a complete mapping.

The problem is, it doesn’t work, for a remarkably simple reason.

There is no such thing as an integer whose representation requires an infinite number of digits. For every possible integer, its representation in binary has a fixed number of bits: for any integer N, it’s representation is no longer that lceil log_2(n) rceil. That’s always a finite integer.

But… we know that the set of real numbers includes numbers whose representation is infinitely long. so this enumeration won’t include them. Where does the square root of two fall in this list? It doesn’t: it can’t be written as a finite string in binary. Where is π? It’s nowhere; there’s no finite representation of π in binary.

The author claims that the novel property of his method is:

Cantor proved the impossibility of both our enumerations as follows: for any given enumeration like ours Cantor proposed his famous diagonal method to build the contra-sample, i.e., an element which is quasi omitted in this enumeration. Before now, everyone agreed that this element was really omitted as he couldn’t tell the ordinal number of this element in the give enumeration: now he can. So Cantor’s contra-sample doesn’t work.

This is, to put it mildly, bullshit.

First of all – he pretends that he’s actually addressing Cantor’s proof – only he really isn’t. Remember – what Cantor’s proof did was show you that, given any purported enumeration of the real numbers, that you could construct a real number that isn’t in that enumeration. So what our intrepid author did was say “Yeah, so, if you do Cantor’s procedure, and produce a number which isn’t in my enumeration, then I’ll tell you where that number actually occurred in our mapping. So Cantor is wrong.”

But that doesn’t actually address Cantor. Cantor’s construction specifically shows that the number it constructs can’t be in the enumeration – because the procedure specifically guarantees that it differs from every number in the enumeration in at least one digit. So it can’t be in the enumeration. If you can’t show a logical problem with Cantor’s construction, then any argument like the authors is, simply, a priori rubbish. It’s just handwaving.

But as I mentioned earlier, there’s an even deeper problem. Cantor’s method produces a number which has an infinitely long representation. So the earlier problem – that all integers have a finite representation – means that you don’t even need to resort to anything as complicated as Cantor to defeat this. If your enumeration doesn’t include any infinitely long fractional values, then it’s absolutely trivial to produce values that aren’t included: 1/3, 1/7, 1/9.

In short: stupid, dull, pointless; absolutely typical Cantor crankery.

Hold on tight: the world ends next saturday!

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(For some idiot reason, I was absolutely certain that today was the 12th. It’s not. It’s the tenth. D’oh. There’s a freakin’ time&date widget on my screen! Thanks to the commenter who pointed this out.)

A bit over a year ago, before the big move to Scientopia, I wrote about a loonie named Harold Camping. Camping is the guy behind the uber-christian “Family Radio”. He predicted that the world is going to end on May 21st, 2011. I first heard about this when it got written up in January of 2010 in the San Francisco Chronicle.

And now, we’re less than two weeks away from the end of the world according to Mr. Camping! So I thought hey, it’s my last chance to make sure that I’m one of the damned!

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An Open Letter to Glen Beck from a non-Orthodox Jew

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Hey, Glen.

Look, I know we don’t get along. We don’t agree on much of anything. But still, we really need to talk.

The other day, you said some really stupid, really offensive, and really ignorant things about Jews. I know you’re insulted – after all, four hundred Rabbis from across the spectrum came together to call you out for being an antisemitic asshole, and that’s gotta hurt.

But that’s no excuse for being a pig-ignorant jackass.

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Another Crank comes to visit: The Cognitive Theoretic Model of the Universe

When an author of one of the pieces that I mock shows up, I try to bump them up to the top of the queue. No matter how crackpotty they are, I think that if they’ve gone to the trouble to come and defend their theories, they deserve a modicum of respect, and giving them a fair chance to get people to see their defense is the least I can do.

A couple of years ago, I wrote about the Cognitive Theoretic Model of the Universe. Yesterday, the author of that piece showed up in the comments. It’s a two-year-old post, which was originally written back at ScienceBlogs – so a discussion in the comments there isn’t going to get noticed by anyone. So I’m reposting it here, with some revisions.

Stripped down to its basics, the CTMU is just yet another postmodern “perception defines the universe” idea. Nothing unusual about it on that level. What makes it interesting is that it tries to take a set-theoretic approach to doing it. (Although, to be a tiny bit fair, he claims that he’s not taking a set theoretic approach, but rather demonstrating why a set theoretic approach won’t work. Either way, I’d argue that it’s more of a word-game than a real theory, but whatever…)

The real universe has always been theoretically treated as an object, and specifically as the composite type of object known as a set. But an object or set exists in space and time, and reality does not. Because the real universe by definition contains all that is real, there is no “external reality” (or space, or time) in which it can exist or have been “created”. We can talk about lesser regions of the real universe in such a light, but not about the real universe as a whole. Nor, for identical reasons, can we think of the universe as the sum of its parts, for these parts exist solely within a spacetime manifold identified with the whole and cannot explain the manifold itself. This rules out pluralistic explanations of reality, forcing us to seek an explanation at once monic (because nonpluralistic) and holistic (because the basic conditions for existence are embodied in the manifold, which equals the whole). Obviously, the first step towards such an explanation is to bring monism and holism into coincidence.

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E. E. Escultura and the Field Axioms

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As you may have noticed, E. E. Escultura has shown up in the comments to this blog. In one comment, he made an interesting (but unsupported) claim, and I thought it was worth promoting up to a proper discussion of its own, rather than letting it rage in the comments of an unrelated post.

What he said was:

You really have no choice friends. The real number system is ill-defined, does not exist, because its field axioms are inconsistent!!!

This is a really bizarre claim. The field axioms are inconsistent?

I’ll run through a quick review, because I know that many/most people don’t have the field axioms memorized. But the field axioms are, basically, an extremely simple set of rules describing the behavior of an algebraic structure. The real numbers are the canonical example of a field, but you can define other fields; for example, the rational numbers form a field; if you allow the values to be a class rather than a set, the surreal numbers form a field.

So: a field is a collection of values F with two operations, “+” and “*”, such that:

  1. Closure: ∀ a, b ∈ F: a + b in F ∧ a * b ∈ f
  2. Associativity: ∀ a, b, c ∈ F: a + (b + c) = (a + b) + c ∧ a * (b * c) = (a * b) * c
  3. Commutativity: ∀ a, b ∈ F: a + b = b + a ∧ a * b = b * a
  4. Identity: there exist distinct elements 0 and 1 in F such that ∀ a ∈ F: a + 0 = a, ∀ b ∈ F: b*1=b
  5. Additive inverses: ∀ a ∈ F, there exists an additive inverse -a ∈ F such that a + -a = 0.
  6. Multiplicative Inverse: For all a ∈ F where a != 0, there a multiplicative inverse a-1 such that a * a-1 = 1.
  7. Distributivity: ∀ a, b, c ∈ F: a * (b+c) = (a*b) + (a*c)

So, our friend Professor Escultura claims that this set of axioms is inconsistent, and that therefore the real numbers are ill-defined. One of the things that makes the field axioms so beautiful is how simple they are. They’re a nice, minimal illustration of how we expect numbers to behave.

So, Professor Escultura: to claim that that the field axioms are inconsistent, what you’re saying is that this set of axioms leads to an inevitable contradiction. So, what exactly about the field axioms is inconsistent? Where’s the contradiction?