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:
- Two different "UFOlogy" websites;
- Eric Julien's dream-prophecy of a disastrous comet impact on earth (which was supposed to have happened last thursday);
- Three different websites where psychics take money in exchange for psychic predictions or psychic healing;
- Two homeopathy information sites;
- 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
The abstract gives you a pretty good idea of what's coming:
A supplement to the M^5 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, strip out the obfuscatory babble, 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 to that abstract. It reads like a computer-generated paper from 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  can be made homogeneous, omniscient, and autonomous, the acclaimed low-energy algorithm for the improvement of DHCP  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. I'm going to modify the notation slightly to make it readable without using any symbols that are problematic on blogger; you can check the paper to see that I'm not changing anything but trivial notation.
Suppose we have two of these seed beasties, S_1, and S_2. Now, suppose we have a mathematical representation of them as "vectors". We'll represent that as a function, rep(S).
A "normal" event, according to them, is one where the events combine in what they call a "linear" way (scare-quotes theirs):
rep(S_1) + rep(S_2) = rep(S_1 + S_2)
. On the other hand, events that are perceived as anomalous are events for which that's not true:
rep(S_1) + rep(S_2) != rep(S_1 + S_2)
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 + i(sigma)
. 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 "rep(S_1) + rep(S_2)" from earlier; and the conjugate is "rep(S_1+S_2)". 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_12 = S_1 + S_2 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.