This is a repost from GM/BMs old home; the original article appeared
[here][old]. I’m reposting because someone is attempting to respond to this
article, and I’d rather keep all of the ongoing discussions in one place. I also
think it’s a pretty good article, which some of the newer readers here may not
have seen. As usual for my reposts, I’ve fixed the formatting and made a few
minor changes. This article was originally posted on May 29.
I’ve been looking at PEAR again. I know it may seem sort of like beating a dead
horse, but PEAR is, I think, something special in its way: it’s a group of
people who pretend to use science and mathematics in order to support all sorts
of altie-woo gibberish. This makes them, to me, particularly important targets
for skeptics: if they were legit, and they were getting the kinds of results
that they present, they’d be demonstrating something fascinating and important.
But they’re not: they’re trying to use the appearance of science to undermine
science. And they’re incredibly popular among various kinds of crackpottery:
what led me back to them this time is the fact that I found them cited as a
supporting reference in numerous places:
1. Two different “UFOlogy” websites;
2. Eric Julien’s dream-prophecy of a disastrous comet impact on earth (which was supposed to have happened back in May; he’s since taken credit for *averting* said comet strike by raising consciousness);
3. Three different websites where psychics take money in exchange for psychic predictions or psychic healing;
4. Two homeopathy information sites;
5. The house of thoth, a general clearinghouse site for everything wacky.
Anyway, while looking at the stuff that all of these wacko sites cited from
PEAR, I came across some PEAR work which isn’t just a rehash of the random
number generator nonsense, but instead an attempt to define, in mathematical
terms, what “paranormal” events are, and what they mean.
It’s quite different from their other junk; and it’s a really great example of
one of the common ways that pseudo-scientists misuse math. The paper is called
“M^* : Vector Representation of the Subliminal Seed Regime of M⁵“, and you can
find it [here][pear-thoth].
The abstract gives you a pretty good idea of what’s coming:
>A supplement to the M⁵ model of mind/matter interactions is proposed
>wherein the subliminal seed space that undergirds tangible reality and
>conscious experience is characterized by an array of complex vectors whose
>components embody the pre-objective and pre-subjective aspects of their
>interactions. Elementary algebraic arguments then predict that the degree of
>anomalous correlation between the emergent conscious experiences and the
>corresponding tangible events depends only on the alignment of these
>interacting vectors, i. e., on the correspondence of the ratios of their
>individual ”hard” and ”soft” coordinates. This in turn suggests a
>subconscious alignment strategy based on strong need, desire, or shared purpose
>that is consistent with empirical experience. More sophisticated versions of
>the model could readily be pursued, but the essence of the correlation process
>seems rudimentary.
So, if we strip out the obfuscation, what does this actually say?
Umm… “*babble babble* complex vectors *babble babble babble* algebra *babble babble* ratios *babble babble* correlation *babble babble*.”
Seriously: that’s a pretty good paraphrase. That entire paragraph is *meaningless*. It’s a bunch of nonsense mixed in with a couple of pseudo-mathematical terms in order to make it sound scientific. There is *no* actual content in that abstract. It reads like a computer-generated paper from
[SCIgen][scigen] .
(For contrast, here’s a SCIgen-generated abstract: “The simulation of randomized algorithms has deployed model checking, and current trends suggest that the evaluation of SMPs will soon emerge. In fact, few statisticians would disagree with the refinement of Byzantine fault tolerance. We confirm that although multicast systems [16] can be made homogeneous, omniscient, and autonomous, the acclaimed low-energy algorithm for the improvement of DHCP [34] is recursively enumerable.”)
Ok, so the abstract is the pits. To be honest, a *lot* of decent technical papers have really lousy abstracts. So let’s dive in, and look at the actual body of the paper, and see if it improves at all.
They start by trying to explain just what their basic conceptual model is. According to the authors, the world is fundamentally built on consciousness; and that most events start in a a pre-conscious realm of ideas called the “*seed region*”; and that as they emerge from the seed region into experienced reality, they manifest in two different ways; as “events” in the material domain, and as “experiences” or “perceptions” in the mental domain. They then claim that in order for something from the seed region to manifest, it requires an interaction of at least two seeds.
Now, they try to start using pseudo-math to justify their gibberish.
Suppose we have two of these seed beasties, S₁, and S₂. Now, suppose we have a mathematical representation of them as “vectors”. They write that as [S]).
A “normal” event, according to them, is one where the events combine in what they call a “linear” way (scare-quotes theirs): [S₁] + [ S₂] = [S₁ + S₂). On the other hand, events that are perceived as anomalous are events for which that’s not true: [S₁] + [S₂] ≠[S₁ + S₂].
We’re already well into the land of pretend mathematics here. We have two non-quantifiable “seeds”; but we can add them together… We’re pulling group-theory type concepts and notations, and applying them to things that absolutely do not have any of the prerequisites for those concepts to be meaningful.
But let’s skip past that for a moment, because it gets infinitely sillier shortly.
They draw a cartesian graph with four quadrants, and label them (going clockwise from the first quadrant): T (for tangible), I (for intangible – aka, not observable in tangible reality), U (for unconscious), and C (conscious). So the upper-half is what they consider to be observable, and the bottom half is non-observable; and the left side is mind and the right side is matter. Further, they have a notion of “hard” and “soft”; objective is hard, and subjective is soft. They proceed to give a list of ridiculous pairs of words which they claim are different ways of expressing the fundamental “hard/soft” distinction, including “masculine/feminine”, “particulate/wavelike”, “words/music”, and “yang/yin”.
Once they’ve gotten here, they get to my all-time favorite PEAR statement; one which is actually astonishingly obvious about what they’re really up to:
>It is then presumed that if we appropriate and pursue some established
>mathematical formalism for representing such components and their interactions,
>the analytical results may retain some metaphoric relevance for the emergence
>of anomalous mind/matter manifestations.
I love the amount of hedging involved in that sentence! And the admission that
they’re just “appropriating” a mathematical formalism for no other purpose than
to “retain some metaphoric relevance”. I think that an honest translation of
that sentence into non-obfuscatory english is: “If we wrap this all up in
mathematical symbols, we can make it look as if this might be real science”.
So, they then proceed to say that they can represent the seeds as complex numbers: S = s + iσ. But “s” and “sigma” can’t just be simply “pre-material” and “pre-mental”, because that would be too simple. Instead, they’re “hard” and “soft”; even thought we’ve just gone through the definition which categorized hard/soft as a better characterization of material and mental. Oh, and they have to make sure that this looks sufficiently mathematical, so instead of just saying that it’s a complex, they present it in *both* rectangular and polar coordinates, with the equation for converting between the two notations written out inside the same definition area. No good reason for that, other than have something more impressive looking.
Then they want to define how these “seeds” can propagate up from the very lowest reaches of their non-observable region into actual observable events, and for no particular reason, they decide to use the conjugate product equation randomly selected from quantum physics. So they take a random pair of seeds (remember that they claim that events proceed from a combination of at least two seeds), and add them up. They claim that the combined seed is just the normal vector addition (which they proceed to expand in the most complex looking way possible); and they also take the “conjugate products” and add them up (again in the most verbose and obfuscatory way possible); and then take the different between the two different sums. At this point, they reveal that for some reason, they think that the simple vector addition corresponds to “[S₁] + [S₂]” from earlier; and the conjugate is “[S₁+S₂]”. No reason for this correspondence is give; no reason for why these should be equal for “non-anomalous” events; it’s just obviously the right thing to do according to them. And then, of course, they repeat the whole thing in polar notation.
It just keeps going like this: randomly pulling equations out of a hat for no particular reason, using them in bizzarely verbose and drawn out forms, repeating things in different ways for no reason. After babbling onwards about these sums, they say that “Also to be questioned is whether other interaction recipes beyond the simple addition S_1,2 = S₁ + S₂ could profitably be explored.”; they suggest multiplication; but decide against it just because it doesn’t produce the results that they want. Seriously! In their words “but we show that this doesn’t generate similar non-linearities”: that is, they want to see “non-linearities” in the randomly assembled equations, and since multiplying doesn’t have that, it’s no good to them.
Finally, we’re winding down and getting to the end: the “summary”. (I was taught that when you write a technical paper, the summary or conclusion section should be short and sweet. For them, it’s two full pages of tight text.) They proceed to restate things, complete with repeating the gibberish equations in yet another, slightly different form. And then they really piss me off. Statement six of their summary says “Elementary complex algebra then predicts babble babble babble”. Elementary complex algebra “predicts” no such thing. There is no real algebra here, and nothing about algebra would remotely suggest anything like what they’re claiming. It’s just that this is a key step in their reasoning chain, and they absolutely cannot support it in any meaningful way. So they mask it up in pseudo-mathematical babble, and claim that the mathematics provides the link that they want, even though it doesn’t. They’re trying to use the credibility and robustness of mathematics to keep their nonsense above water, even though there’s nothing remotely mathematical about it.
They keep going with the nonsense math: they claim that the key to larger anomalous effects resides in “better alignment” of the interacting seed vectors (because the closer the two vectors are, in their framework, the larger the discrepancy between their two ways of “adding” vectors); and that alignments are driven by “personal need or desire”. And it goes downhill from there.
This is really wretched stuff. To me, it’s definitely the most offensive of the PEAR papers. The other PEAR stuff I’ve seen is abused statistics from experiments. This is much more fundamental – instead of just using sampling errors to support their outcome (which is, potentially, explainable as incompetence on the part of the researchers), this is clear, deliberate, and fundamental misuse of mathematics in order to lend credibility to nonsense.
[old]: http://goodmath.blogspot.com/2006/05/pear-yet-again-theory-behind.html
[pear-thoth]: http://goodmath.blogspot.com/2006/05/pear-yet-again-theory-behind.html
[scigen]: http://pdos.csail.mit.edu/scigen/

I’ve been meaning to write something about homeopathy at some point, because it’s just so wretchedly stupid. But until now, I haven’t sat down to actually do it, because it can seem rather like beating a dead horse: it’s just so over-the-top goofy, and the goofiness of it is so well documented that I wasn’t really sure what I had to add.
Then I came across something that was new to me.
As I’ve mentioned before, I’m a New Yorker. I live just north of the city in one of the Westchester suburbs. The anthrax attacks that happened a few years ago were a very big deal in my area – in particular, because one of my neighbors is a NYT reporter who at a desk in the room where one of the alleged anthrax letters was opened. (It turned out to be one of the faked copycat ones – an envelope full of talcum power, if I remember correctly.)
Anyway… I’ve been sick with a miserable sinus infection this week, and got a prescription for an antibiotic. The pharmacy that I use is, alas, rather heavy of the woo: they’ve got a homeopath and a naturopath providing consultations on the premises. But after trying rather a lot of different local pharmacies, I’ve found that it’s the only one where I haven’t been robbed or abused by the phramacist. (By robbed, I mean having them fill prescriptions with less pills than I’m paying for; since I use some expensive stomach medications, I’ve had $300 prescriptions with fully a tenth of what I was supposed to be given left out of the bottle. I’ll take a woo-ish pharmacist who’s honest with me, leaves me alone when I say I don’t want to hear the woo, and gives me what I pay for over a lying, cheating scumbag.)
Anyway… Heading down to my pleasant but rather woo-ish pharmacy, there’s a note on a bulletin board about nosodes, and how we should all be preparing safe quantities of nosodes for anthrax and smallpox attacks in order to protect our families? I’d never heard the term before. So when I got home with my non-woo medication, I hit the net to figure out what this stuff was.
According to The National Center for Homeopathy, nosodes are

homeopathic attenuations of: pathological organs or tissues; causative agents such as bacteria, fungi, ova, parasites, virus particles, and yeast; disease products; excretions or secretions

Translated: take either a sample of an infectious agent, or an infected tissue sample. Dilute it down to silly proportions using a magic shaking ritual (homeopathic attenuation, aka succussion), voila! You have a nosode.
What’s going on here? And why is it bad math?
The homeopathic shaking ritual is, basically, take something like a nosode. Mix it with water, in a 100 to 1 proportion, using the special magic shake. Now, take a sample of that mixture – and mix it with water again – 100 parts water to 1 part solution, and shake. Repeat many, many times. Many homepathic remedies use a 100 to 1 dilution repeated 20 times – the so-called “20C” dilution. The more times you repeat the magic shaking ritual, the stronger the alleged medicine becomes.
Normal homeopathic remedies are based on the dilution of substances that produce the same symptoms as the illness that they’re allegedly treating. So they’ll take some substance – a salt, an herb extract – and dilute it this way. So in a 20C dilution, you’re talking about 1 part active ingredient in 100^20 parts water – so you’re talking about one part active incredient in 1×10^400 parts water. This is also known as “pure water”. In a regular dose – several teaspoonsful of the diluted solution – you are almost certainly not getting a single molecule of the active ingredient in the dose.
This is the first piece of really bad math in it. The inventor of homeopathy had no idea about how many molecules were in water; it’s not even clear that he really knew what molecules were. (Homeopathy was invented in the 1820; the molecular theory of matter as we understand it was proposed in 1812.) But we do now know about that – and so we know, by a combination of simple arithmetic and the number of molecules involved, that it’s an undeniable fact that these dilutions are entirely eliminating the supposedly active ingredient. To insist on a magical effect from something which has been eliminated from the solution is just stupid.
The idea that somehow diluting a solution to the point where there’s probably not a single molecule of the active ingredient left creates a good medicine is stupid – and that diluting it more after there’s not a single molecule left is even stupider.
The claim of modern homeopathy is that there are basically magical propeties of water: that the magic shaking ritual leaves crystalline structures in the water that are based on the active ingredient, and that those magic structures somehow are the cause of the effectiveness of homeopathy. This belief is predicated on the notion that the basic particles of the homeopathic ingredient is small enough that it can leave a specific shape in the arrangement of molecules in water.
So – what about nosodes? Well, the argument for a nosode is that it’s basically a kind of a vaccine: you’re putting the specific infection agent into solution – either directly if you can identify and extract the agent; or indirectly by using an infected tissue sample if you can’t. Then you’re doing the dilution.
In particular, they claim that they can “vaccinate” you against anthrax using a nosode solution of anthrax. But anthrax isn’t a molecule. It’s a bacteria – and a largish one at that. The so-called “crystalline structures” of water that homeopaths propose as an active principle are at an entirely different scale: this is another error of arithmetic; something orders of magnitude larger than a water molecule is not going to interact with a water molecule in the same way as something of its own size: it’s like saying that if you dip your finger into a pile of dust, take it out, and then shake the dust around, that the dust can retain the shape of your finger. The size of the structure that you claim to form is so much larger than the things it’s formed from – it’s a very silly idea.
What’s particularly scary about this: these people are applying for homeland security funds to stockpile nosodes. They claim that they can provide “homeopathic vaccines” using nosodes for less money, and in less time than it would take to prepare real vaccines or treatments. And in the current political climate, they may very well be taken seriously, and get money that could have been used to buy or produce real remedies, rather than magic water.