Prometheus and Mega Lists, April 1999 (Part Eight)
Date: Fri, 9 Apr 1999 10:27:40 -0700
To: megalist@brokersys.com
From: Kevin Langdon <kevin.langdon@polymath-systems.com>
Subject: [MegaList] Reply to Chris Langan 4/9/99 (Part One)
At 05:34 AM 4/8/99 -0400, Chris wrote:
> We now enter phase two in our discussion of the relationship
> between rationalism and empiricism in science. In stage one,
> we learned that our own Kevin Langdon, who elected to debate
> against me, lacks a clear understanding of two terms essential to
> an elementary understanding of philosophy: objectivity and
> model. This time, we will add the term isomorphism to the list.
I see this a little differently. The phase change that I see is that
we are now in a two-phase phase; some of the rhetoric is still
quite adversarial; that is one phase (let's call this phase phase one,
as that's how things started out). But some of this exchange has
now become a different kind of discussion--two people
comparing notes on matters of common interest; this second
phase is, of course, more enjoyable, for participants and
spectatators alike. Both phases are clearly evident in the messages
to which I am responding here. I will indicate below which
passages belong to each phase.
[Phase 2]
> An isomorphism is a bijective (one-to-one onto)
> correspondence or similarity mapping between, e.g., a theory
> T and its object universe T(U). In the absence of a clear
> difference relation between the range and domain of an
> isomorphism, it can be contracted so that range and domain
> are coincident.
An isomorphism is just a one-to-one correspondence. Chris is
seems to think that any one-way mapping implies a two-way
mapping, which isn't necessarily true.
> In this sense, the abstract structure of a valid theory (as opposed
> to the pattern of neural potential encoding it within a brain) is
> virtually identical to its object universe.
What do you mean "virtually"?
[Phase 1]
> This is because (1) science attributes "reality" to any functional
> theory of real phenomena, and (2) the reality attribute predicates
> topological inclusion in reality. This relationship is basic not just
> to the predicate logic, but to the notions of causality, locality and
> realism in science. It also serves as the basis of a logical theory
> of reality known as the CTMU, which Kevin, exhibiting his own
> exotic brand of consistency, has relentlessly tagged a "crank"
> theory.
What I've seen so far of the CTMU does not justify either the
existence of the relationship claimed between cognition and reality
or Chris' claims for the importance of his theory.
> Previously, I predicted that I would catch Kevin in errors, and
> that Kevin, who would rather do anything than own up to being
> wrong, would deny it to everyone's face. Both predictions have
> now been realized.
I have admitted to being mistaken about various points from time
to time (e.g., I was wrong about the norms for the SAT, which I
hadn't given credit for the ceiling it turns out to have--a little above
four sigma, though, of course, it doesn't discriminate at that level)..
> This is what always happens with Kevin; even when I quote
> known authorities (e.g., the given definition of "model" comes
> straight from Rogers' North-Holland textbook on logic and
> formalized theories), Kevin uses one ear as an entrance and the
> other as an exit, blinks and drools a little, and bellows out his
> unreasoning accusation of crankery
No matter where Chris gets his raw material, the way he puts
things gets them all tangled up. English, Chris. Plain English.
> (with an obedient echo or two from the peanut gallery).
(Just so you Langdonoids don't feel left out.)
> Granted, what I say is often original and controversial -
> otherwise, why bother to say it? - but it is always carefully
> reasoned. Does this really merit 10 years of willful stupidity
> from someone passing himself off as a philosopher, a
> generalist, and a leading member of the world's most exclusive
> high-IQ society?
When those of us who are less needy than Chris publish our
material, we expect that not everyone will be interested in it. But
for Chris, a failure to appreciate his stuff is a mortal insult.
And how can I be a "philosopher"? I haven't been elected by the
ISPE.
> Some of you may now be thinking along the following lines.
> "Langan has a point. Brilliant as they can be, modern scientists
> do tend to have a muddled notion of the relationship of
> cognition and objective reality; that much is obvious from the
> fact that there are so many paradoxes in the foundations of
> mathematics and physics. And the logic he's using seems so
> simple and obvious as to be trivial. So if he can build a theory
> out of these simple connections, why shouldn't we give it an
> impartial look? After all, he is a member of the Mega Society.
> What's Kevin Langdon's problem, anyway?"
And some of you may *not* be thinking along those lines.
> Only Kevin can answer that question, and he has never done
> so honestly. But no matter what his problem may be, it is
> clear that his style of thought, and his summary rejection of
> the work of qualified Mega Society members, is not to be
> emulated. Indeed, his chronic irrationality has the potential
> not only to keep us eternally in obscurity, but to make
> everyone in the group look like a fool...like a twittering fife,
> peeping piccolo or tooting tuba in the goose-stepping
> "marching band" that he perceives whenever he arrogantly
> surveys his imagined dominion.
Projection.
> I've left most of Kevin's message intact, and again respond
> to his comments as they occur.
[Phase 2]
>>> That means that *g* is being filtered through a crystalline
>>> sieve of learned information. If one lacks the learning to
>>> understand the questions fully, one never gets down to *g*
>>> on this test.
>> Yes, but the required level of learning is very low. Only about
>> the top third of high-school seniors take the SAT.
> I'm not sure it's been established that the required level of
> learning is low enough to make your point. Those who take the
> SAT have to draw on a good deal of what a high school student
> is expected to learn in class. This is not true of a real IQ test.
Correct. But most conventional IQ tests are loaded on *different*
non-*g* factors, to a similar or greater extent.
>>> So at best, the SAT is a "contaminated IQ test". So is the
>>> LAIT and every other test you've ever designed. But with
>>> you, the main contaminating factor is persistence...and in
>>> an indeterminate number of cases, collusion.
>> While persistence is an important factor for tests like mine and
>> Ron Hoeflin's, they're still highly *g* loaded. Collusion is
>> always a possibility with these tests, but there's no evidence
>> that it's widespread.
> I'll agree about the collusion; I've previously made the point that
> the chances of a Mega applicant finding someone else smart
> enough to help him or her cheat up a mega-level score on a
> power-IEQ test is quite low under most circumstances. However,
> I don't think the psychometric community would agree with us
> about that.
Yes, I've also written about that. People who are smart enough
to make really high scores usually are not willing to help others
cheat. But we have reason to be particularly interested in the high
end; academic psychometricians may well be more cautious about
concluding that this problem is trivial.
> Regarding persistence, I jacked up my own score on the Mega
> Test by 5 of the hardest problems by spending several additional
> hours on it (after deliberately doing barely enough to qualify
> under Ron's first published cutoff). So I know *exactly* how
> important persistence can be. Noting that persistence is a
> necessary component of learning for most people, we might
> even hazard that persistence on a power-IEQ test may be
> somewhat nalogous to crystallized intelligence on the SAT.
In the sense that each is a contaminating factor, certainly.
>>>>> Moreover, what about the persistence factor? I know for a
>>>>> fact that power-IEQ test scores are pretty sensitive to how
>>>>> much time you're willing to spend racking them up. The
>>>>> Mega Society selects its members well above the level at
>>>>> which persistence enters the picture. I know that from
>>>>> personal experience, as well as from the reports of other
>>>>> members. Why do you think Ron Hoeflin felt compelled to
>>>>> disallow second attempts? There was too much gain for
>>>>> extra time spent. Persistence is not equivalent to *g*.
>>>> What is left out here is the amount of time it actually takes to
>>>> take a conventional IQ test. First one must make arrangements
>>>> to be tested, then one must drive to the test site, take the test,
>>>> and drive home. When you add a comfort factor to total time
>>>> spent, there's no obvious advantage to the more traditional
>>>> tests.
>>> Come off of it. IQ tests are defined on constraints on the time
>>> spent addressing their items, not time on the Expressway.
>> That's relevant to the conditions under which the tests are taken
>> but not to the deterrent value of having to take a large block of
>> time away from other interests, which is what makes the
>> persistence factor problematic.
> Persistence doesn't affect one's score on an IQ test. Persistence
> does affect one's score on a power-IEQ test. That's the real issue.
It's an issue on which we agree. But you said, "I know for a fact
that power-IEQ test scores are pretty sensitive to how much time
you're willing to spend racking them up," and I said that the time
you have to be willing to spend to take a standard test isn't as
different as it might seem from the time required to take my tests.
This is not in opposition to your point about persistence affecting
scores on high-range power tests, but it does address one of the
major perceived disadvantages of these tests.
>>> The lack of time constraints on power IEQ tests constitutes a
>>> huge a priori difference between the two kinds of test. The
>>> burden is thus on you to prove they're measuring the same
>>> thing. But with the amount of scatter you're dealing with, you
>>> can't achieve the strong correlations to do that.
>> The burden's already been met. A robust *g* factor emerges
>> from the LAIT and the Mega. The LAIT correlates well with a
>> number of other tests, as my statistical reports make clear.
> With Guy's permission, let me quote the Prometheus MCR
> regarding the Mega Test: "However, there is a problem with the
> Mega scores in comparison to scores from standard IQ tests
> which reveal a wide scatter, resulting in correlations which are
> weak." Regarding power IEQ tests in general, this suggests that
> we need to be cautious when it comes to saying that our tests
> measure exactly what other tests measure, given that standard
> IQ tests correlate well with each other but poorly with ours.
I suggest that you take a look at the data for the LAIT before
drawing conclusions about it based on Mega Test data.
However, I agree with you that our tests are not measuring
precisely the same thing as the standard tests, though there is
also a great deal of variation in what various standard tests
are measuring and between what the LAIT and the Mega are
measuring.
> To reiterate, *g* is a statistical construct, and the statistics are
> generated entirely by timed tests. The fact that our tests aren't
> timed places them outside the class of IQ tests on
> *methodological grounds*. We can't just lock methodology in
> the closet on the assumption that it drops out of the equation at
> our convenience. Before power-IEQ tests can join the IQ club,
> they have to pay an appropriately steep statistical cover charge
> ...steep enough to stand in for a functional mechanistic
> definition of *g*.
The "chronometric" tests that Jensen and other investigators have
developed use a much more radically different methodology
than the high-range power tests, but they correlate moderately
well with the standard tests.
The "statistical cover charge" is publication in reputalble scientific
journals of data on our tests and successfully defending it, and we
haven't done that yet, though a few academic psychometricians
have taken an interest in the new tests.
>>> Until we achieve a mechanical explanation of intelligence,
>>> *g* will remain a statistical construct defined on tests
>>> incorporating time constraints.
>> According to Jensen, tests with severe time constraints have
>> no significant *g* loading.
> What does Jensen mean by "severe"? I've talked to several
> smart people who have failed to finish standard g-loaded IQ
> tests, usually because they've gotten hung up on distractions
> or what they see as ambiguous items. That constitutes de facto
> speed loading in conjunction with *g* loading. But maybe I'm
> not understanding you properly. In any case, because power-
> IEQ tests are not in use by the psychometric community, Dr.
> Jensen has little or no data on them. So we have to be cautious
> about extending his remarks to cover them.
No extension is required. Jensen is comparing standard tests
given with and without time limits short enough that most testees
can't finish them in the time allowed. The closest thing to a timed
high-range power test is the Cattell Culture Fair, which is very
much a standard tests, designed by one of the most eminent
academic psychometricians.
Although Jensen has found a correlation between psychometric
*g* and neural processing speed, this is not the whole story.
The effect of the time limit on test scores should be known
for every timed test. However, this information is commonly
lacking in test manuals. Investigations have shown that, when
the items are evenly graded in difficulty and have plenty of
"top" (i.e., very difficult items), and the test is not too long for
the time available (i.e., the fast students can finish although
they reach their difficulty ceiling before the end of the test),
giving subjects additional time beyond the prescribed time
limit adds very little to the score and has little effect on the
rank order of subjects' scores
...
If the increase in score leaves unaltered the subjects' rank
order, the speed factor is of little importance. That is, the time
or speed factor does not contaminate the scores with some
ability or trait extraneous to what the test attempts to measure,
in this case, intelligence. Usually the correlation between
strictly timed and leniently timed administrations is as high as
the reliability of the test. When the correlation between two
timed conditions falls significantly below the reliability, the
recommended time limit should be viewed with suspicion. It
means that the speed factor is given too mcuh weight in the
test scores, when what we really want to measure is mental
power rahter than some kind of "personal tempo" factor. The
personal tempo factor actually has little if any correlation with
intelligence.
...
In what is probably the best experimental study of the matter,
the correlation between subjects' speed scores and power
scores, when difficulty level and response accuracy were
controlled, is close to zero for all kinds of test items [Tate, M.
W., "Individual differences in speed of response in mental
test materials of varying degrees of difficulty." *Educational
and Psychological Measurement*, 1948, 8, 352-374]. Thus it
appears that a personal speed factor exists that is independent
of mental power but that can contribute to variance on mental
tests that are timed inappropriately.
--Arthur Jensen, *Bias in Mental Testing*, pp. 135-136
[Phase 1]
>>> But statistics only yield a shadow of the underlying
>>> deterministic factor structure of any given device relative
>>> to human cognition. Your tests lack time constraints; there's
>>> no "speed factor". So you have to explain why the time
>>> metafactor drops out, and you need more than statistical
>>> inference to do it.
>> Say what? Talk English, Crhis.
> We've been through this already. Speed and power are in
> principle independent.
And in statistical fact, too.
> But they can assume a dependency relation determined by
> neural organization and cognitive mechanics in the brain, as
> well as by particulars of neural and cognitive development.
> Since you know virtually nothing about cerebral organization
> and mechanics, you can't be making blanket statements whose
> validity actually depends on a particular set of structural,
> functional and developmental hypotheses.
Your assumption that you know more than I do about "cerebral
organization and mechanics" is not corroborated by any evidence
I'm aware of.
But the statistical conclusion that speed and power are independent
factors is based on an analysis that treats the brain as a black box,
examining the inputs and outputs. This conclusion stands even if
what's going on in the brain is something like the little man who
turns on the light when you open your refrigerator door.
> After all, *g* is something attributed to brains with specific
> neural architectures.
No assumptions about neural architecture are involved.
> As many in the psychometric community are beginning to
> realize, an exclusively statistical approach to intelligence is no
> longer viable.
Psychometricians are statisticians, but there are certainly other
approaches to intelligence, e.g., cognitive science.
> Although it violates your religion, read that essay I wrote in
> Noesis/ECE 141. In it, I talk about noise, neural time and space,
> and the possibility that sufficiently complex power-IEQ tests may
> force the brain to adapt, demanding the subtle modification of
> neural pathways over time. In contrast, IQ tests utilize existing
> pathways exclusively (that's why one can do them so much
> faster).
If not all, at least many roads lead to Rome. Solving the complex
problems on my tests requires the same kind of mental stretching
that is needed for making scientific discoveries about the world.
My reply to the material contained in "Noesis/ECE [i.e., phony]
#141" will appear in one of the new issues of the real *Noesis*
that's I'm currently preparing.
> I don't expect anyone to uncritically swallow such conjectures
> as fact. But for your own part, don't expect everyone else to
> agree with you that human intelligence can be successfully
> treated as a branch of statistics. Those days are gone forever.
No one is claiming that psychometric statistics is an exhaustive
approach to the complexities of human intelligence--but
psychometric tests *can* be used successfully to select members
of super-high-IQ societies.
>>> There's no reason to suppose that the statistics are casting
>>> an image of identical logical constructs, especially when
>>> power IEQ tests correlate poorly with so many IQ tests.
>> The correlations aren't great, but the high-range power tests
>> appear to bite off at least as big a chunk of *g* as most of
>> the standard tests.
> Yeah, but there are doubts as to how we should be interpreting
> that "appearance".
I'm not concerned about the interpretation as much as I am about
improving the tests and their norming, which are still at a
somewhat primitive stage.
>>>>> Modern science is attempting to have its cake and eat it
>>>>> too by booting rational cognition out of the picture while
>>>>> making free use of logic and mathematics to relate observed
>>>>> phenomena (and even to construct experiments).
>>>> Modern science gives rational cognition an honored place, but
>>>> not the same central place as direct observation of the world.
>>> Nonsense. Modern science still makes a sharp distinction
>>> between objective reality - what's "out there" - and cognitive
>>> reality, or what's "in here",
>> Yes, it does. But I didn't say it didn't.
>>> when one is in fact unavoidably distributed over the other.
>> ...which remains to be demonstrated.
> No, it doesn't. If you read my former message to the end, you
> should already know that cognition distributes over "objective
> reality" by isomorphism.
I already know that you *say* it does.
> Read on, and this should become clearer to you.
I doubt it.
(Continued in Part Two)
Kevin Langdon
Date: Sat, 10 Apr 1999 00:27:38 -0400 (EDT)
From: Langan <clangan@suffolk.lib.ny.us>
To: megalist@brokersys.com
Subject: Re: [MegaList] Reply to Chris Langan 4/9/99 (Part One)
Okay, everybody, break out the Dom Perignon and raise your glasses to
Kevin Langdon, who seems to be setting a new personal record for obtusity
and obstinacy. His last messages underline as never before what he has
proven countless times already - namely, that while he sometimes barely
has a point when it comes to statistical psychometrics, he is almost
always dead wrong when it comes to anything else, and will never, ever
admit it. But this time it's even better. Now Kevin is challenging the
entire scientific, mathematical and philosophical world over the meaning
of "isomorphism" in the context of formalized theories! He can't win, of
course...not today, not tomorrow, not when the burnt-out sun is a dense
ball of ash spinning like an icy top in the blackness. But that's what
makes it all so...remarkable!
By the way - if, after reading this two-part reply, anyone agrees with
Kevin about objectivity, models, and isomorphisms, I think that he or she
should make it known to everyone on this list. We all need to know what
our fellow members are, and are not, capable of understanding.
Again, I've trimmed whatever seemed unnecessary.
> At 05:34 AM 4/8/99 -0400, Chris wrote:
>
> > We now enter phase two in our discussion of the relationship
> > between rationalism and empiricism in science. In stage one,
> > we learned that our own Kevin Langdon, who elected to debate
> > against me, lacks a clear understanding of two terms essential to
> > an elementary understanding of philosophy: objectivity and
> > model. This time, we will add the term isomorphism to the list.
>
> I see this a little differently. The phase change that I see is that
> we are now in a two-phase phase; some of the rhetoric is still
> quite adversarial; that is one phase (let's call this phase phase one,
> as that's how things started out). But some of this exchange has
> now become a different kind of discussion--two people
> comparing notes on matters of common interest; this second
> phase is, of course, more enjoyable, for participants and
> spectatators alike. Both phases are clearly evident in the messages
> to which I am responding here. I will indicate below which
> passages belong to each phase.
>
So far, so good.
>
> > An isomorphism is a bijective (one-to-one onto)
> > correspondence or similarity mapping between, e.g., a theory
> > T and its object universe T(U). In the absence of a clear
> > difference relation between the range and domain of an
> > isomorphism, it can be contracted so that range and domain
> > are coincident.
>
> An isomorphism is just a one-to-one correspondence. Chris is
> seems to think that any one-way mapping implies a two-way
> mapping, which isn't necessarily true.
An isomorphism is surjective (onto) as well as injective (1-to-1). It is
virtually always reversible unless it is explicitly stipulated, for
usually artificial reasons, that it is only one-way. When it comes to the
topic at hand - the correspondence between a valid theory and its object
universe - the isomorphism is always two-way. That's what the "valid"
means. To reiterate, the theory "selects" its own object universe (which
may not be as large as the one that the theorist originally had in mind).
Now I'm going to prove that if you don't introduce an artificial
directional constraint, a one way isomorphism M:A-->B always implies a
two-way isomorphism M':A<-->B. Take two n-element sets A and B, one the
source and one the target of M. Draw the one-way correspondences between
the elements of A and those of B as one-way arrows: M = {a1-->b1, a2-->b2,
...,an-->bn}. To get the two-way isomorphism M', just replace each one-way
arrow with a two-way arrow: M' = {a1<-->b1, a2<-->b2, ... ,an<-->bn}.
This proof generalizes easily to higher-order relations of elements.
It's for this reason that all logic and abstract algebra texts define an
isomorphism as follows: "An isomorphism is a homomorphism that is
bijective, or one-to-one onto (injective and surjective)."
Give it up, Kevin. You can't win, and you're boring the hell out of me
and everybody else.
>
> > In this sense, the abstract structure of a valid theory (as opposed
> > to the pattern of neural potential encoding it within a brain) is
> > virtually identical to its object universe.
>
> What do you mean "virtually"?
"Virtually": for all practical purposes. Act (or reason) as if it's true,
and you can't be tripped up.
>
> [Phase 1]
>
> What I've seen so far of the CTMU does not justify either the
> existence of the relationship claimed between cognition and reality
> or Chris' claims for the importance of his theory.
Nonsense. The contractible isomorphism M:T<-->U(T) establishes the
relationship; you're just in a state of denial. And by your own admission,
you can't understand what I've written of the CTMU, so you can't say what
it might or might not have established.
>
> > This is what always happens with Kevin; even when I quote
> > known authorities (e.g., the given definition of "model" comes
> > straight from Rogers' North-Holland textbook on logic and
> > formalized theories), Kevin uses one ear as an entrance and the
> > other as an exit, blinks and drools a little, and bellows out his
> > unreasoning accusation of crankery
>
> No matter where Chris gets his raw material, the way he puts
> things gets them all tangled up. English, Chris. Plain English.
There comes a point at which any philosophical discussion exceeds your
evidently primitive notion of "plain English", Kevin. If I were using the
relevant math symbology here, you'd *really* be hurting.
>
> > Granted, what I say is often original and controversial -
> > otherwise, why bother to say it? - but it is always carefully
> > reasoned. Does this really merit 10 years of willful stupidity
> > from someone passing himself off as a philosopher, a
> > generalist, and a leading member of the world's most exclusive
> > high-IQ society?
>
> When those of us who are less needy than Chris publish our
> material, we expect that not everyone will be interested in it. But
> for Chris, a failure to appreciate his stuff is a mortal insult.
"Needy"? What I'm most "in need" of is somebody whose tuner doesn't
crash
on receipt of anything more complex than a simple sine wave. I suspect
that the Mega Society contains people like that, but that most of them
live in constant fear of a sonic assault by Foghorn Langdon, the Master
Generalist of Mega.
>
> And how can I be a "philosopher"? I haven't been elected by the
> ISPE.
No. But you did manage to get yourself booted out of it on grounds of
inveterate Nietzscheism.
>
> > Some of you may now be thinking along the following lines.
> > "Langan has a point. Brilliant as they can be, modern scientists
> > do tend to have a muddled notion of the relationship of
> > cognition and objective reality; that much is obvious from the
> > fact that there are so many paradoxes in the foundations of
> > mathematics and physics. And the logic he's using seems so
> > simple and obvious as to be trivial. So if he can build a theory
> > out of these simple connections, why shouldn't we give it an
> > impartial look? After all, he is a member of the Mega Society.
> > What's Kevin Langdon's problem, anyway?"
>
> And some of you may *not* be thinking along those lines.
Right. And at this point, I'm 100% safe in saying that if not, then one of
the following is true of the person in question. (1) He hasn't been
following this exchange. (2) He's a dummy. (3) He's a Langdonoid,
blasting himself in the foot with a ray gun and looking forward to a
family reunion on Planet X.
>
> > Only Kevin can answer that question, and he has never done
> > so honestly. But no matter what his problem may be, it is
> > clear that his style of thought, and his summary rejection of
> > the work of qualified Mega Society members, is not to be
> > emulated. Indeed, his chronic irrationality has the potential
> > not only to keep us eternally in obscurity, but to make
> > everyone in the group look like a fool...like a twittering fife,
> > peeping piccolo or tooting tuba in the goose-stepping
> > "marching band" that he perceives whenever he arrogantly
> > surveys his imagined dominion.
>
> Projection.
Did you or did you not call the Mega Society a "marching band"? Tell the
truth, now...some of us still have the issue in which you printed it.
>
********
> >>> That means that *g* is being filtered through a crystalline
> >>> sieve of learned information. If one lacks the learning to
> >>> understand the questions fully, one never gets down to *g*
> >>> on this test.
>
> >> Yes, but the required level of learning is very low. Only about
> >> the top third of high-school seniors take the SAT.
>
> > I'm not sure it's been established that the required level of
> > learning is low enough to make your point. Those who take the
> > SAT have to draw on a good deal of what a high school student
> > is expected to learn in class. This is not true of a real IQ test.
>
> Correct. But most conventional IQ tests are loaded on *different*
> non-*g* factors, to a similar or greater extent.
But they cross-correlate a lot better.
> The "chronometric" tests that Jensen and other investigators have
> developed use a much more radically different methodology
> than the high-range power tests, but they correlate moderately
> well with the standard tests.
Seriously, have you ever wondered why that is? I mean, isn't speed the
main factor in a chronometric test?
>
> The "statistical cover charge" is publication in reputalble scientific
> journals of data on our tests and successfully defending it, and we
> haven't done that yet, though a few academic psychometricians
> have taken an interest in the new tests.
Not quite. The statistical cover charge equals the emergence of several
power-IEQ tests that correlate just as well with standard IQ tests as does
the average IQ test itself. We'll be asked to produce statistics that are
clear and extensive enough to unequivocally counter arguments that could
presently be constructed on the weakness of IQ-IEQ correlations across the
entire power-IEQ genre...i.e., the genre characterized by the
methodological distinction on which they'll focus.
And time constraints aren't even the sole methodological issue. There's
the related issue of item complexity. Surely Jensen realizes that you
can't just monkey around with the time constraint and neglect the
ramifications of using extremely complex items...items much more complex
than those on any timed test. There are simple mechanistic arguments to
the effect that different mental parameters may be involved (and
mechanistic arguments are generally superior to statistical ones).
>
> >>> Until we achieve a mechanical explanation of intelligence,
> >>> *g* will remain a statistical construct defined on tests
> >>> incorporating time constraints.
>
> >> According to Jensen, tests with severe time constraints have
> >> no significant *g* loading.
>
> > What does Jensen mean by "severe"? I've talked to several
> > smart people who have failed to finish standard g-loaded IQ
> > tests, usually because they've gotten hung up on distractions
> > or what they see as ambiguous items. That constitutes de facto
> > speed loading in conjunction with *g* loading. But maybe I'm
> > not understanding you properly. In any case, because power-
> > IEQ tests are not in use by the psychometric community, Dr.
> > Jensen has little or no data on them. So we have to be cautious
> > about extending his remarks to cover them.
>
> No extension is required. Jensen is comparing standard tests
> given with and without time limits short enough that most testees
> can't finish them in the time allowed. The closest thing to a timed
> high-range power test is the Cattell Culture Fair, which is very
> much a standard tests, designed by one of the most eminent
> academic psychometricians.
Unfortunately, when you deal with "most testees", you're dealing with the
middle part of the curve, and this may not generalize to super-complex
tests for superintelligent people. And unless I'm mistaken, the CCF is
still timed, which introduces the factor of mental endurance. When taking
the CCF, you can't get up, take a walk, clear your mind, and "start fresh"
after your brain has had time to do a certain amount of subconscious
processing. Again, this falls under the rubric of "methodology"...how test
constraints can in principle affect performance.
>
> Although Jensen has found a correlation between psychometric
> *g* and neural processing speed, this is not the whole story.
>
> The effect of the time limit on test scores should be known
> for every timed test. However, this information is commonly
> lacking in test manuals. Investigations have shown that, when
> the items are evenly graded in difficulty and have plenty of
> "top" (i.e., very difficult items), and the test is not too long for
> the time available (i.e., the fast students can finish although
> they reach their difficulty ceiling before the end of the test),
> giving subjects additional time beyond the prescribed time
> limit adds very little to the score and has little effect on the
> rank order of subjects' scores.
Excuse me, but after staring stupidly at this for a couple of minutes, I
still find it a bit confusing. So I'm going to request your explanation as
an experienced statistical psychometrician. It looks to me like Dr. Jensen
is making a judgment on whether a test is "not too long for the time
available" on the basis of the performance of "fast students". Then he's
proposing to confirm this judgment by lifting the time constraint and
seeing if the rankings change.
Given equal item weights and equal prorated error and correction rates,
and given that "difficulty ceiling" (power) is independent of speed, the
rankings *will* change if low-speed but high-power students now have a
chance to get to problems they could have solved but didn't have time for
the first time around, *unless* all the higher-scoring students also
solve enough additional problems to maintain their places in the rankings.
That would seem to mean that EITHER (a) fast higher-scoring students
didn't really hit their "difficulty ceilings" (otherwise, slow-but-
brighter students would pass some of them once the time constraint is
lifted), OR (b) low-speed students always turn out NOT to be able to solve
enough additional problems to change their rankings. But (b) would
constitute a de facto equation of speed and power, violating the initial
assumption that speed and power are independent (the fact that this is
seen as a basis to *infer* that speed and power are independent merely
compounds my confusion).
Since Dr. Jensen is a genius and an outstanding scientist, I must be
missing something. Otherwise, I'd have to conclude, with all due respect,
that standard tests really afford no way of evaluating the true
"difficulty ceiling" of a given subject (in fact, this is exactly what
power-IEQ tests alone are designed to determine). After all, we've all
encountered problems that we think at first sight are too hard to solve,
and therefore skip, only to realize later on that we're easily capable of
solving them (e.g., with a little *persistence*).
Equivalently, the given method of determining "adequate time" cannot
really by put into effective practice because it can only be used on very
limited sets of testees. This limitation fails to preclude the possibility
that an arbitrary testing session will contain one or more low-speed but
very bright subjects who could change their rankings if given the chance.
In fact, the possible existence of such subjects is directly implied by
the independence of speed and power. It seems that as soon as you set a
time constraint, you're violating the spirit of this relationship.
Can you help me out here, Kevin?
...
> If the increase in score leaves unaltered the subjects' rank
> order, the speed factor is of little importance. That is, the time
> or speed factor does not contaminate the scores with some
> ability or trait extraneous to what the test attempts to measure,
> in this case, intelligence. Usually the correlation between
> strictly timed and leniently timed administrations is as high as
> the reliability of the test. When the correlation between two
> timed conditions falls significantly below the reliability, the
> recommended time limit should be viewed with suspicion. It
> means that the speed factor is given too mcuh weight in the
> test scores, when what we really want to measure is mental
> power rahter than some kind of "personal tempo" factor. The
> personal tempo factor actually has little if any correlation with
> intelligence.
Again, I'm beset by ambiguities here. When Dr. Jensen says that "the time
or speed factor does not contaminate the scores with some ability or trait
extraneous to...intelligence" (or power), he could mean either of two
things. (1) Speed doesn't contaminate power because they're essentially
the same thing. (2) Speed doesn't contaminate power because they're
utterly independent. The answer is supposed to be 2. But again, if this is
the case, then a "sufficient amount of time" on an IQ test is the time
that it takes the *slowest* student to finish, not the time it takes the
*fast students* to finish. Otherwise, you're asymmetrically penalizing
low-speed, high-power subjects. I just can't seem to make out the
reasoning here.
> ...
> In what is probably the best experimental study of the matter,
> the correlation between subjects' speed scores and power
> scores, when difficulty level and response accuracy were
> controlled, is close to zero for all kinds of test items [Tate, M.
> W., "Individual differences in speed of response in mental
> test materials of varying degrees of difficulty." *Educational
> and Psychological Measurement*, 1948, 8, 352-374]. Thus it
> appears that a personal speed factor exists that is independent
> of mental power but that can contribute to variance on mental
> tests that are timed inappropriately.
> --Arthur Jensen, *Bias in Mental Testing*, pp. 135-136
>
Again, I have a problem. When Dr. Jensen says that "speed scores and power
scores are uncorrelated (independent), he seems to be invalidating any
notion that we can determine how much time is necessary on a timed test
simply by looking at the finishing times of "fast students". Maybe I'm
completely out to lunch...a fool for wondering whether Dr. Jensen may be
relying a bit too trustingly on the conclusions of some of his "slower"
colleagues.
Please explain this. Because until you do, I can't see the logic in
methodologically equating timed and untimed tests.
> >>> But statistics only yield a shadow ofthe underlying
> >>> deterministic factor structure of any given device relative
> >>> to human cognition. Your tests lack time constraints; there's
> >>> no "speed factor". So you have to explain why the time
> >>> metafactor drops out, and you need more than statistical
> >>> inference to do it.
>
> >> Say what? Talk English, Crhis.
>
> > We've been through this already. Speed and power are in
> > principle independent.
>
> And in statistical fact, too.
So why are you norming power tests using speed tests? At the risk of
repeating myself, if a test has a time limit, it is to some extent a
speed test.
> > But they can assume a dependency relation determined by
> > neural organization and cognitive mechanics in the brain, as
> > well as by particulars of neural and cognitive development.
> > Since you know virtually nothing about cerebral organization
> > and mechanics, you can't be making blanket statements whose
> > validity actually depends on a particular set of structural,
> > functional and developmental hypotheses.
>
> Your assumption that you know more than I do about "cerebral
> organization and mechanics" is not corroborated by any evidence
> I'm aware of.
Get real. Anybody with an elementary knowledge of neural nets knows more
about cerebral mechanics than you do. Unless, of course, you'd like to
tell us that despite all indications to the contrary, you're conversant
with network architectures and algorithms.
>
> But the statistical conclusion that speed and power are independent
> factors is based on an analysis that treats the brain as a black box,
> examining the inputs and outputs. This conclusion stands even if
> what's going on in the brain is something like the little man who
> turns on the light when you open your refrigerator door.
Intelligence is modeled as a black box because there is no a priori reason
to assume a specific structure, e.g., a structure (including architecture
and programming) that relates speed and power. How you can interpret this
to mean that speed and power are necessarily independent no matter what
the box specifically contains is something known only to you. And I
suspect it always will be.
> > After all, *g* is something attributed to brains with specific
> > neural architectures.
>
> No assumptions about neural architecture are involved.
Granted. But unless I'm entirely mistaken, brains *do* have specific
neural architectures, and g *is* attributed to brains. Do you have an
argument with this?
> > As many in the psychometric community are beginning to
> > realize, an exclusively statistical approach to intelligence is no
> > longer viable.
>
> Psychometricians are statisticians, but there are certainly other
> approaches to intelligence, e.g., cognitive science.
Thank you!
> > Although it violates your religion, read that essay I wrote in
> > Noesis/ECE 141. In it, I talk about noise, neural time and space,
> > and the possibility that sufficiently complex power-IEQ tests may
> > force the brain to adapt, demanding the subtle modification of
> > neural pathways over time. In contrast, IQ tests utilize existing
> > pathways exclusively (that's why one can do them so much
> > faster).
>
> If not all, at least many roads lead to Rome. Solving the complex
> problems on my tests requires the same kind of mental stretching
> that is needed for making scientific discoveries about the world.
To some extent, yes. But it's also true that if one really has what it
takes to make discoveries about the world, one is apt to be doing so
instead of taking tests. Again, motivation and persistence enter the
picture. That's why we should be looking at applicants' records of solving
hyperdifficult real-world problems. In some cases, we could even let the
Nobel Committee help us out with qualifying new members. For what it's
worth, this might also help us get where we're going in the world.
> > I don't expect anyone to uncritically swallow such conjectures
> > as fact. But for your own part, don't expect everyone else to
> > agree with you that human intelligence can be successfully
> > treated as a branch of statistics. Those days are gone forever.
>
> No one is claiming that psychometric statistics is an exhaustive
> approach to the complexities of human intelligence--but
> psychometric tests *can* be used successfully to select members
> of super-high-IQ societies.
That very much depends on how you define "successfully".
> > ... If you read my former message to the end, you
> > should already know that cognition distributes over "objective
> > reality" by isomorphism.
>
> I already know that you *say* it does.
>
> > Read on, and this should become clearer to you.
>
> I doubt it.
>
Well, there it is. Kevin Langdon steadfastly maintains that
1. His definition of "isomorphism" is superior to that found in the most
advanced logic and algebra texts.
2. Isomorphisms are one-to-one (injective), but not necessarily onto
(surjective).
3. Isomorphisms only go in one direction.
At this juncture, I just have to ask: is there a single member of the
Mega Society who agrees with Kevin on these points (1-3)? Be careful -
this will go on your permanent record!
> Chris Langan