This versus that

[ailambris]

Is anyone else compelled to believe that there may well be more
benefit had from training your brain with more practical exercises
than the traditional BrainWorkshop DNB, or any derivative thereof?
Recognizing that this BrainWorkshop stuff is basically math problems
distilled, I would guess that daily exercising your math textbook
would do you as much if not more good than staring at a few dots
flashing before your eyes for nine hours a day? Not to mention, you'd
be gaining practical, crystallized intelligence in the mean time?

[Działo, Christopher]

Arkanj3l  wrote:

show details 1:42 AM (15 hours ago)

I see benefits, but only when I practice. Just like running. I don't
mind, because everyone has their "thing" that keeps them fit, mentally
or physically. For most it's probably reading voraciously and/or
playing an instrument and/or doing a sport (just a thought: all are
good opportunities to practice self-discipline, which I have realized
is the best "raw skill" to improve and that DNB probably won't fix,
although breathing meditation might), but I think DNB, for being
relatively new on the scene, has given me the *quickest* and *most
comprehensive* impact compared to all of the above.

I think improving for your GMAT is possible in the given time frame.
Just remember to do studying on top of it; although I don't believe
studying will make as much of an impact as most would say it would
(tests like the SAT have what I think are too large of a variance to
hold it in the esteem that we do, and correlate too highly with IQ
tests to not advertise it any other way), but the more you can load in
your "Gc" *on top* of your "Gf" the better. With DNB I've gotten
higher grades on tests that I did not study for, but whenever I've
taken the time to study, that investment of time gets me to that level
or above without DNB as well as helping on future tests. I still think
it's good to do DNB especially if you have more tests and information
than time, but Gc and Gf synthesize; they aren't in direct
competition.

As for the jargon, I'll be a bit of a stinker here and say for you to
try them out for yourself. That way, you'll stress your Gf :P

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[Oinchack'Olp]

Dual N-back exercises, by my own experience, indeed increase working
memory capacity ( C (Bit) = S (Bit/sec) x D (sec ) ) by and by.
Studying books, even math books, does not. Btw, some years ago, I
completely studied this book: http://www.amazon.com/dp/3528469900/
I never had the impression studying it increased my WMC, not in the
least.

[Arkanj3l]

DNB is *not* math problems distilled. Math operations are Gc;
complexity is Gf. Math problems are what you do; intelligence is how
you do it.

Those are gross generalizations but the point is that you . When I
made the remark about how one should "load" one's Gc, I meant the
equivalent of using long-term memory on top of one's short term. By
doing more problems or reading more books, one is more likely to
acquire a key piece of knowledge that can be applied quickly and with
confidence the next time it appears. Although it may feel "cheap" on
occasion, it gets the job done. This strategy is most conducive for
tests, and that's why I said what I said and why I think that up until
this point most test-taking skill books focus on the nuances of the
test, rather than setting up skills that transfer.

However, although I don't think the information version of working
memory is entirely valid (why is it that clarity of memory does not
correlate with IQ, then, if technically more information is
involved?), it has a point. The amount you are capable of processing
at any one time is going to decide what it is you will be able to
handle, and how quickly. I believe that DNB has benefits that extend
beyond math and into cognition in general, making it an even better
deal in my book.

[Arkanj3l]

Lol I didn't finish the sentence of the second paragraph.

Forgive me, o lord, I've been awake for 26 hours straight with minor
naps...

[Jonathan Toomim]

That formula applies to short term memory stored in the phonological loop, not to working memory. If you're trying to remember a list of states and US territories, the number of states you'll be able to keep in short-term memory depends on the average number of syllables—e.g. "Maine, Utah, Texas, Vermont, Guam" is easier than "California, Massechusetts, South Carolina, Oklahoma, Micronesia." Similarly, if you're trying to remember a list of numbers, you'll be able to remember more numbers if you were born and raised in e.g. China than if you were born and raised in the United States, simply because in Chinese numbers are one syllable per digit (none of that "one hundred and seventy seven" crap).

Working memory is different. Working memory is largely amodal, meaning that you could remember the shape of the state or the position on the map about as easily as the name. With working memory, you don't usually have to rehearse what you want to remember every two seconds like you do with verbal short-term memory. With working memory, if I tell you a word or number, then distract you for 10 seconds with arithmetic, you'll usually be able to remember the number afterwards. Etc.

But yeah.  Studying math books will not improve your working memory or your IQ or g. It will make you better at math. Being better at math is useful, since it makes it easier to learn physics, engineering, statistics, computer programming, and a few other things. On the other hand, DnB does improve your working memory and your IQ. This also makes you better at math. It should also make you better at physics, engineering, etc. It should also make you better at learning foreign languages, learning movie trivia, cooking delicious food, remembering people's names, digesting and recalling stories and passages in literature, etc. Studying math won't help with those things. Furthermore, DnB will make it so that you learn faster when you do study math (or physics, or English literature, or history), so that you might be able to learn in 40 minutes what otherwise would have taken you 50 or 60. That's like spending twenty minutes per day on DnB for a few weeks in order to get a couple hours' a day worth of extra productivity studying whatever else you study for a few weeks, months, or years.

Even so, don't neglect Gc.  A mistake that I think a lot of people on this list make is that they get so focused on improving Gf and get so obsessed with that concept and the concept of intelligence that they start to think that the measure of a person's worth is how much raw brainpower they have access to. It's not. A person's worth is determined by what they have done and will do. A person who has an enormous capacity for cognitive work who doesn't use it for anything other than chess and Scrabble is, in my view, pretty lame. A person of below-average intelligence and ingenuity who, through consistent hard work, makes significant useful contributions to the lives of others is better. Best, though, are people like Charles Darwin, Marie Curie, and Craig Venter who combine brilliance with discipline, ambition, curiosity, and persistence.

Do your daily 20 minutes of DnB training. Study your mathematics. Worry not, there's plenty of time in the day for both.

Jonathan

[ailambris]

I don't know. I'm not talking about computation, really. Neither am I
talking much about
Applied Mathematics. I mean for the pure side, there is a real demand
on working memory.
If I read a chapter quickly, there will be some number of definitions
presented, some number
of theorems or propositions. I'll have to keep those in mind when
solving the exercises. You may
argue that this an Gc intensive task. But when you're doing proofs,
you're keeping a lot of symbols
in mind, a lot of visual imagery in mind, to the point that I would
argue that this is a working memory problem.

I'm trying to think of a good example. Hearkening back to the Geometry
days should do, especially if you were ever
required to show some of the angle-side theorems. A better, more
elementary example is showing that
integration by parts reasonable. You have to hold in mind conceptually
the derivative of the product of two functions,
as well as hold in mind the expressed derivative, which happens to be
two terms combined, so that's already three
or four things, then you have to throw some integral signs around and
rearrange terms. I don't see how this is
not a working memory intensive task. In that sense I don't see how
it's not an exercise of WM updating. Unless you're
using a paper and pen, which I would argue that most mathematicians do
not, this is all from short term memory.

[Thomasthetankengine]

Hi Jonathan,

I was just wondering what method when u play n-back (intuitive,
rehearsal or something else?). I've read the FAQ and a few other posts
but I was just hoping to obtain ur individual perspective, considering
u r obviously coming from an experienced position.

Any kind of feedback would be greatly appreciated!

Thanks jonathan!

[Jonathan Toomim]

Yes, mathematics is a working memory–intensive task. It's also often a
working memory–limited task. However, that doesn't mean that doing
mathematics increases working memory capacity.

Sumo wrestling is a weight-intensive task, and one's performance in
sumo wrestling is often weight-limited. Sumo wrestling doesn't make
you weigh more. Eating like your mom does.

Reaching with your mouth to try to bite fruit hanging above your head
won't make your neck longer. Putting a metal coil between your chin
and your shoulders will. (http://en.wikipedia.org/wiki/Neck_ring)

We don't know why the n-back tasks improve performance on matrix
reasoning tasks. We hypothesize that it's because it's training
working memory, but the data support other hypotheses (e.g. it helps
via spatial reasoning ability) just as well. However, the data
collected so far imply that it does improve matrix reasoning task
performance.

If we eventually discover that, as we suspect, the n-back tasks
improve matrix reasoning tasks because they improve working memory,
then we still won't know why they improve working memory. It very well
could be that they improve working memory because they require one to
access ("read from") and modify ("write to") working memory at the
same time. It could be because of the rhythmic temporal structure of
the task. It could be because of the progressive and adaptive
difficulty of the task. It could be because of something completely
different. We simply don't yet know.

What we do know is that, according to three separate controlled
clinical trials, it improves performance on matrix reasoning tasks.

In the past, almost everyone believed, as you seem to, that one can
become more intelligent by studying more, and by getting educated.
Eventually, understanding of scientific and statistical methodology
improved to the point where we could test that hypothesis, so in the
20th century, they tested it, expecting to learn exactly how much it
helps and what types of education help intelligence the most. The data
that they collected showed that, essentially, nothing (except maybe
music?) helps. As a result, some people abandoned that hypothesis.

TL;DR: Just because math uses working memory doesn't mean that it
improves working memory. Education makes you more knowledgeable and
more capable. It does not make you measurably more intelligent. N-back
training seems to.

Jonathan

[Jonathan Toomim]

I try to say to myself what the next letter should be and where the next object should be in order to be a match right before it appears. I can do this quite well up to n=4 or n=5, and doing so usually gets me to or very close to 100% accuracy at those levels. Above that point the load on my brain becomes to great to be able to do that all or most of the time.

I don't usually rehearse that much any more. Rehearsing worked fine for me at n<5, but around n=6 or 7 I can't seem to comfortably fit match-checking, updating, and rehearsal (at least of the letters) into the 3 seconds between trials. I can rehearse positions more rapidly than that, but I also find that rehearsing positions doesn't seem to matter much for me. As long as I make a mental note of where the square flashed in any given trial, I find I'm usually able to remember it n trials later. Usually when I make a mistake, it's because I was too busy trying to remember whether the square n trials ago was a match and fail to encode its position for later use.

I almost always group the trials into blocks or cycles of n stimuli. It's kinda like I write a row of data with n columns, go to the next row, write a new row, delete the first row and move the second row up, and repeat. The end of a session often feels awkward to me. When I'm doing D6B, and there are a total of 56 trials (20+6^2), I go through 9 blocks of 6 trials, followed by a weird tail group of 2. (I've considered changing the number-of-trials algorithm to round the number of trials to the nearest multiple of n, but I decided that, since I don't know whether the way I do it is good or even common, I shouldn't do anything which encourages people to do what I do. I probably would have added an undocumented hack/feature/option so I could just get rid of it for myself, but I'm a little too lazy and indifferent.)

I lack discipline, so I don't use BW very often. Definitely not as much as I think I should. But whatever. I think the main problem for humanity and for me personally isn't that I'm not smart enough, but rather that nearly everyone else isn't smart enough.

TL;DR: I try to do whatever works for me the best and gets me the highest score. As n increases, I rely more on intuition (or unrehearsed, single-trace memories) and less on mental repetition or chunking.

Jonathan

[Thomasthetankengine]

If you approached the way you gave your arguments(?) differently, you
would have a lot more 'wins' than you do 'losses' because people would
be more open to hearing what you have to say. But because you are hell
bent on waving your superiority flag, it's unsurprising most people
don't want to give you time time of day. I think, however, that you
make reasonable points, but they are nothing more than that because
currently they can't be backed up with data. So far, among the
anecdotal reports, n-back seems to help people. Because of this,
regardless of what mental processes may or may not be improved, people
use it, including myself.

I look forward to finding what n-back offers, right through to chapter
and verse and regardless of what it improves, as already mentioned,
I'll still use it. I do not know of anything else that will provide me
with the same benefits (apart from drugs but can't afford them).

Thomas


On Jan 16, 5:13 pm, αrgvmziΩ σV <argum...@gmail.com> wrote:
> Here we are still thinking DNB will "improve" I.Q., and yet no one
> wants to admit that it won't turn one into a mind at the wuthering
> heights of intellect, even for their so-called Gf.
>
> If anything, Gs will be improved, that is, with g-speed at the apex, a
> hierarchical multidimensional framework exists that has mostly been
> ignored, but continues to gain ground in the literature. For who don't
> remember, those ostensible improvements in the Jaeggi studies were in
> those cases where the subjects could answer _more_ questions within a
> limited frame of time; the powerhouse of Gf is far from being improved
> on such an experimental arrangement.
>
> Being a speed demon does have its inherent physiological limitations,
> no matter how fast one can think up an answer...
>
> argumzio
>
> On Jan 16, 12:00 am, Thomasthetankengine <thomasttt...@hotmail.com>
> wrote:
>
> > Thank you for your thorough response, Jonathan. Appreciated.
>
> > Take care.
>
> > Regards,
>
> > Thomas
>
> > P.S - I often wonder what the world would be like if everyone or most
> > people were running at high (relative) capacity. What direction would
> > humanity take? I guess that's all "pigs can fly" sort of stuff,
> > unfortunately. We not only need all the smart people we can get, but
> > smart people with 'good' intentions; they help shine light in dark
> > places. You seem to be part of this group. Thanks (again).

[Działo, Christopher]

Thomasthetankengine,

Regarding your comment "I do not know of anything else that will provide me with the same benefits (apart from drugs)." which drugs are you referring to?

[Działo, Christopher]

Ah, okay.

I have a supply of Adderall, and expressed interest in Cerebrolysin, the Racetam, Acetyl-L-Carnitine, Centrophenoxine, Deprenyl, 5HTP, Phosphatidylserine, and other brain nutrient supplements such as Omega 3, 6, 9, coconut oil, et al -- a few that I have tried and still take.

On Sun, Jan 16, 2011 at 1:44 AM, Thomasthetankengine <thomas...@hotmail.com> wrote:

I probably shouldn't have used the word "same". Because I'm not a
consumer I don't know a whole list, however, I was just referring to
ADD or ADHD (sorry if I'm mistaken) alleviating medications such as
ritalin, dexedrine & other.

On Jan 16, 5:36 pm, Działo, Christopher <chrisdzi...@gmail.com> wrote:
> Thomasthetankengine,
> *
> *

> Regarding your comment "I do not know of anything else that will
> provide me with
> the same benefits (apart from drugs)." which drugs are you referring to?
>
> On Sun, Jan 16, 2011 at 1:33 AM, Thomasthetankengine <
>

> > brain-trainin...@googlegroups.com<brain-training%2Bunsu...@googlegroups.com>

[Działo, Christopher]

αrgvmziΩ σV,

I don't know you rather well, nor know nor care about any animosity between yourself and the group -- but after reading some of the messages you post, you seem to down-play and degrade the benefits from n-back training and its implications on Gf.

2011/1/16 αrgvmziΩ σV <argu...@gmail.com>

They are backed up by the data; as I clearly adduced the current
evidence as an example of a speed factor here. The RPM result is a
confound of the Gf-Gs aspect. Quite elementary, in my view.

You really should try not sounding like a child when you talk nonsense
about my "superiority flag". What utter bollocks. :)

If I were here to look good for everyone, I would have kept my mouth
shut long, long ago, so that clearly is not what is at issue here.
This is what I call argumentum ad hominem on your part. (I would
invite others to look into my chat history if they wish to see others
engaging in similar behavior, with the purposeful intent to sully my
internet persona. O woe is me. So much for those "losses" you speak
of.)

Do you suppose DNB has aided you in your muscling the needed thought
to fashion the dialectical tools of a simple linguistic exchange, or
does the whole affair merely seem to stand clearly in your mind? Do
new thoughts... occur to you? (Questions to keep in mind with your
ongoing training; don't forget that if you're still young, that will
likely cloud any improvements you might notice.)
Well, I'm beginning to digress, but not very far; just around the
periphery. Contrary to what you seem to imply what I'm saying, the
issue isn't whether people should or should not use DNB; what does the
use of this tool actually bring about? It is doubtful Gf has much to
do with it so far, although still possible - but to a small extent.

Charitably,
argumzio


On Jan 16, 12:33 am, Thomasthetankengine <thomasttt...@hotmail.com>

[Arkanj3l]

I think he has a right to. Groups and communities can become
notoriously self-deluded and self-reinforcing without a little dissent
here and there. Argumzio has the plus of already being a clever guy in
the first place; his opinions are well thought out and intelligent
enough for me to say that you can pay attention to them, even if you
don't absorb them completely.

As for the idea that DNB trains Gs rather than Gf, I'd like to see
some studies done on if RPM gains were noticed when *that* was the
targeted aspect being trained (ie with an inspection time task or
something).

On Jan 16, 3:05 pm, Działo, Christopher <chrisdzi...@gmail.com> wrote:
> αrgvmziΩ σV,
> *
> *

> I don't know you rather well, nor know nor care about any animosity between
> yourself and the group -- but after reading some of the messages you post,
> you seem to down-play and degrade the benefits from n-back training and
> its implications on Gf.
>

> 2011/1/16 αrgvmziΩ σV <argum...@gmail.com>

> > brain-trainin...@googlegroups.com<brain-training%2Bunsubscribe@go oglegroups.com>
> > .

[Pontus Granström]

Argumzio, don't you think that if you improve your G speed by improving your WM speed/N-backing is pretty much in
line with the assertion that G is WM?  N-back might improve WM/G, since RAPM performance is underlied by G, you will improve the score due to this without actually improving your reasoning.

On Sun, Jan 16, 2011 at 8:18 AM, αrgvmziΩ σV <argu...@gmail.com> wrote:

To be clear, the Gs aspect I speak of applies to a global cognitive
functioning ability, not the perceptual aspect, which is only one
small subset of the global that I'm talking about. I.e., does DNB
improve the g-speed factor more so than the g-fluid factor; in other
words, can one engage in a sequence of mental operations more quickly
(after training), or think of new and original ideas to bring order to
seeming chaos? That is the sticking point,  I think.

By the way, thanks. It's nice to be appreciated. :)

argumzio

To unsubscribe from this group, send email to brain-trainin...@googlegroups.com.

[Thomasthetankengine]

Without ignoring the possibility, labeling Gs as being responsible is
just one hypothesis. I have no particular care for the outcome of what
is responsible for the increases in certain types of mental
performance, it's just that all we know is that there are increases.
The 'why' question is very interesting. However, I'm not about to sit
down and start carving out the reason/s in stone before there is any
_solid_ data that enhances our understanding has been uncovered.

I too appreciate your value argumzio, however, there are aspects of
your demeanor that may encourage people to hide under the covers
rather than to speak into the microphone and say what they think,
regardless of there level of intelligence or educational background.
This is all I speak of.

I'm interested in learning more about working memory and/or fluid
intelligence in general. Would be interested in your opinion on what
articles offer some good reading.

You may be interested in the following:

Title - Speed of information processing and general intelligence

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6W4M-46H167F-CS&_user=10&_coverDate=03%2F31%2F1983&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1608515968&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=bb2ecd74028324d506ca3aa7ac84f74a&searchtype=a


I found it while trying to google some information on Gs.

Thanks, argumzio

Thomas

On Jan 16, 6:18 pm, αrgvmziΩ σV <argum...@gmail.com> wrote:
> To be clear, the Gs aspect I speak of applies to a global cognitive
> functioning ability, not the perceptual aspect, which is only one
> small subset of the global that I'm talking about. I.e., does DNB
> improve the g-speed factor more so than the g-fluid factor; in other
> words, can one engage in a sequence of mental operations more quickly
> (after training), or think of new and original ideas to bring order to
> seeming chaos? That is the sticking point,  I think.
>
> By the way, thanks. It's nice to be appreciated. :)
>
> argumzio
>
> On Jan 16, 1:13 am, Arkanj3l <kenneth.bruskiew...@gmail.com> wrote:
>

> ...
>
> read more »

[Arkanj3l]

Check his profile; his "About Me" links to "suggested reading" :P

On Jan 16, 6:19 pm, Thomasthetankengine <thomasttt...@hotmail.com>
wrote:

> Without ignoring the possibility, labeling Gs as being responsible is
> just one hypothesis. I have no particular care for the outcome of what
> is responsible for the increases in certain types of mental
> performance, it's just that all we know is that there are increases.
> The 'why' question is very interesting. However, I'm not about to sit
> down and start carving out the reason/s in stone before there is any
> _solid_ data that enhances our understanding has been uncovered.
>
> I too appreciate your value argumzio, however, there are aspects of
> your demeanor that may encourage people to hide under the covers
> rather than to speak into the microphone and say what they think,
> regardless of there level of intelligence or educational background.
> This is all I speak of.
>
> I'm interested in learning more about working memory and/or fluid
> intelligence in general. Would be interested in your opinion on what
> articles offer some good reading.
>
> You may be interested in the following:
>
> Title -  Speed of information processing and general intelligence
>

> http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6W4M-46H167...

> ...
>
> read more »

[Oinchack'Olp]

> To be clear, the Gs aspect I speak of applies to a global cognitive
> functioning ability, not the perceptual aspect, which is only one
> small subset of the global that I'm talking about. I.e., does DNB
> improve the g-speed factor more so than the g-fluid factor; in other
> words, can one engage in a sequence of mental operations more quickly
> (after training), or think of new and original ideas to bring order to
> seeming chaos? That is the sticking point,  I think.

> argumzio
That is exactly the question I rack my brain over since weeks. The way
seeming to me being the most realistic and reliable is to arrive at
n=13 as soon as possible and then do an iq test depleted of RPM as far
as possible .

[Pontus Granström]

The evidence that g is WMC is at least to me quite clear. The male advantage in G is equal to the male advantage in WMC.
WMC tasks like mathematics correlates highly with intelligence, also implying that they are the same. Given
the numerous studies that shows the link between WMC and G it only seems ignorant to discard them as false.

Gs, is not the speed of G it self. Gs is perceptual speed. That the increase in scores in the Jaeggi case should be due to an increased perceptual speed
is something we can forget. The speed "you want to exists" has not yet been defined nor measured. If imy reasoning speed improves, I've
become more efficient, it sure implies some sort of "speed increase", but more likely an efficiency increase in the parts of the brain dealing with reasoning
on matrix tasks. Rather than n-backing is adjusting a gas throttle for nerve impulses. Just as a more efficient muscle will be able to lift more, efficiency
and max load is highly correlated, they sort of imply each other.

WMC certainly enables us to reason better, since we can combine "two rules" into one problem. We can think of more things at the same time. For example a dot
moves 90 degrees at the time, easy to spot. All symbols occur once, easy to spot, a dot moves as well as symbols occur once in every place, this becomes more g-loaded
and will be hard to solve without being able to think about more things at the same time. The reasoning in these tests are simple and childish, like most problems
on RAPM is, but still WMC plays an important underlying ability to reason. In mathematics you can see the same thing, where more complex ways of reasoning
can be achieved by combining two "less complex ways".

This however does not imply that the reason in all improved matrix reasoning scores has to do with "n-back it self". If you got
a 50's economist way of thinking it might, but if you got a neurological way of thinking you can approach the problem differently. It might
be that the rather subtle processes makes n-back very similar to matrix reasoning (in terms of activation), indeed much studies conclusively show this is the case.
The improvement on matrix reasoning does not have to depend on the face value function but rather something of a different nature. Training
on a task might imply more things than what function the task provides. Just like running improves performance on stroop tests, it would
seem even more unlikely that moving the legs at a rapid temp would improve this, but it does, and it can be verified with brain scans, just
as n-backing can be verified with brain scans to active the same areas as RAPM.

If the only reasoning you allow is linear and intuitive reasoning and strangely enough discard studies that use the same methodology to prove
the WMC is a part of G, it might severely limit ultimately understanding intelligence and to what degree it can be improved. I think
that the 50's model initiated thinking and modelling around intelligence, but it will most certainly show to be to simplistic to think
of the brain in terms of "object oriented diagram". I suggest that you open up to the possibility of understand the
de facto functioning of the brain, instead of applying linear operators to different constructs that might be abstractly pleasant
but most certainly in terms of understanding intelligence/g be very limited.

There's no good definition of "reasoning better", you can reason around one problem in many ways. You can solve
one problem in many ways. But you can also apply methods that by themselves are correct (within their own context) that
might be limited in the sense that they do not allow the scale of factors to be included and thereby be more or less
accurate.

On Mon, Jan 17, 2011 at 7:27 AM, αrgvmziΩ σV <argu...@gmail.com> wrote:

Explanation for differences for g do not therewith imply that the
explanations, when improved, will lead to bona fide improvements in g.
WMC increase will _not_ give you the ability to think of original
solutions to various problems, only to follow more things and handle
them more efficiently. Pretty darn obvious; kind of like how someone
participates on a forum as two members, thinking no one will have the
brains to lift the veil and see it as clear as day. (Don't fret, I
even know some people here, beyond their handles... and they are too,
too obvious.)

Tests which require this in a straight-forward manner will invariably
link g to these constructs, as if these were the province of g. But
any psychometrician will tell you that g cannot and should not be
reduced to WMC. Speed, as you will eventually discover, has
practically no relationship with g; this is why it is its own,
separate factor – why there is a g-speed apex outside of the g-
intelligence apex.

In my view, it's best to stick to what is currently known rather than
get too carried away with preliminary results (Jaeggi et al.) and soar
to the heights of theoretical to-and-fro's. As much as others hope Gf
really is improved by this, one has to have at least a pinch of self-
respect to acknowledge that the current evidence couldn't possibly be
the basis to arrive at such a conclusion.

argumzio


On Jan 16, 5:53 am, Thomasthetankengine <thomasttt...@hotmail.com>
wrote:
> Although I am yet to obviously delve into all of the little goodies
> that are mentioned in ur suggested readings Argumzuo, from first
> glance it seems that Gs and Working memory are the primary constructs
> that help explain individual differences in G.
>
> That being said...
>
> The goal of n-back is to increase one's working memory capacity, and
> others such as your self have suggested that it is also or otherwise
> (just) related to increasing Gs. If this is the case and because both
> constructs 'act' or 'contribute' globally to cognition, then it _may_
> be fair to say that there are actual gains in G? Based on the premise
> (n-back = Gs and WMC).
>
> I understand though that I have a lot of reading ahead of me.
> Hopefully hear a response from you, thanks.
>
> Thomas

> ...
>
> read more »

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[milestones]

On Jan 17, 6:56 pm, Pontus Granström <lepon...@gmail.com> wrote:
> The evidence that g is WMC is at least to me quite clear. The male advantage
> in G is equal to the male advantage in WMC.
> WMC tasks like mathematics correlates highly with intelligence, also
> implying that they are the same. Given
> the numerous studies that shows the link between WMC and G it only seems
> ignorant to discard them as false.

The thing is, if a psychologist has limited time and they want to
measure G, they're going to leave out the WM measures like digit span
and arithmetic subtest of the WAIS. Most likely they will choose 4
subtests: matrix reasoning, block design, vocabulary, similarities. If
a subject scores very high on these measure (top 2 or 3 %) then there
is a fairly decent chance that a more complete battery will indicate
lower processing speed and WM indices alongside these, especially if
the child/adult is being tested b/c of poor performance at school or
work. This is a high G profile that's not all that uncommon in the
gifted range where WM and PS lags behind verbal and non verbal
reasoning. It's been shown that WM and PS in otherwise high G
individuals can be improved greatly by training and that this
trainning will bring about much stronger academic or vocational
performance. But, this does not mean that this individual has improved
their level of G. In some cases, learning disabilities can be so
extreme that the disability (PS or WM related) covers over innate
intelligence, in which case true level of G will not appear until
remedial efforts have been made to free G from its shackles, so to
speak. These anomalies aside, with among most of the population, G
tends to correlate very well with PS and WM.

Those who hover around the mean of the bell curve generally don't
deviate much in their profiles, everything tends to be flat, which may
be why remedial efforts to improve their level of G are generally not
successful. The greatest remedial gains are usually seen in those with
imbalanced profiles who exhibit very high levels of Gf/Gc but lag
behind in PS and WM. Improved performance in such individuals by way
of training may induce a teacher to remark "x is so much smarter than
he or she was last semester." But that teacher would be wrong in a
technical sense since only overall functioning has improved which may
mean "IQ" in the more complete, diagnostic sense with EF taken into
account. G remains the same...but last semester was masked by low
functioning PS/WM relative to G.

These sort of improvements are largely seen in math class, since math
is heavily WM intensive. In fact, math is so WM intensive that WM,
(along with attentional control), seems like a greater prerequisite
for math achievement at the lower levels than Gf. The way math is
taught (speaking now of the USA) is problematic in that
it tends to foster EF talent more than problem solving talent given
that there's so much rote work that goes on at the arithmetic stage.
If a child stumbles at this stage early on, they may lose interest in
math, especially if they get the drift that they're not good at it in
comparison to other subjects where they shine. In the US, kids get
more of a vote on what subjects they prefer in comparison to kids in
other countries, and most of them don't like carrying 1's or other
automaton-like tasks which is the crux of many early math experiences.
Imo, there should be equal emphasis put on problem solving at the
earlier stages of math to identify another group who could be very
good at math at more advanced levels if given necessary motivation to
wade through the heavy EF intensive stuff early on.

[Arkanj3l]

So in other words you're touting G as a theoretical limit rather than
a measurable construct (poor wording, but do you get what I mean?)

[Pontus Granström]

If a psychologist want to measure G, I suggest they choose the tests with the highest g-load, two maybe three such tests. This would mean that arithmetic would be included since it got the highest g-load. If
WM-tests are so highly indicative of success in other areas including "applying rules to figures", it would make WM-training a strong candidate for targeted improving in order to boost overall scores. At least
two of these tests, matrix reasoning and block design seem to be trainable. If we include digit span and arithmetic, wm training will probably improve this as well. Meaning that a lot of tasks on a IQ-test will be improved
by training on WM, which in turn means that almost all performance tasks are limited in terms of how much we can hold in our brain "clearly", our "WM", hence WM becomes G. A variable that explains a positive inter correlation between tests.

Personally I have such a hard time understanding why WM seems to be ugly, almost a dirty construct that doesn't deserve to be called intelligence. What's so provocative about it? At the end of the day, much of the "speculations"
have little or no data, while for my case it stacks up pretty neat.

[milestones]

On Jan 17, 10:50 pm, Arkanj3l <kenneth.bruskiew...@gmail.com> wrote:
> So in other words you're touting G as a theoretical limit rather than
> a measurable construct (poor wording, but do you get what I mean?)

For the vast majority of people, the theoretical limit works well also
as a measurable construct. However, it's no secret that gifted
populations will skew a bit different and that a greater divergence
can be found more there than among the average. For the gifted
populations, the goal should be to find out what the theoretical limit
of the individual is, as well as shore up any areas of functioning
that lag behind that limit. Generally, a good way to find out those
limits are to take untimed power tests with mixed items. I would not
stop there, though. I'd work to improve vital areas of EF like WM/PS
so that they are humming at the level of G or close to it since EF is
so vital for performance and/or showcasing one's theoretical limit. In
many ways, imo, gifted people have more cognitive repair-maintenance
to tend to -- not less.

[Oinchack'Olp]

> Personally I have such a hard time understanding why WM seems to be ugly,
> almost a dirty construct that doesn't deserve to be called intelligence.

Dr. Lehrl ( http://de.wikipedia.org/wiki/Siegfried_Lehrl ) and his
peers at the University of Erlangen in Germany would also have a hard
time to understand that. Because since 1982 they claim that WMC is the
actual physical extent of differences in intelligence.

[likeprestige]

Pontus,

I'm quite skeptical about arithmetic being included as a primary
assessment to help derive a complete profile of someone's level of G
because for one, it can be easily trained and two, savant's (mental
arithmetic only) offer the suggestion that it _may_ be categorized as
a specific ability. Arithmetic is something that can be easily trained
and studies have demonstrated that such training leads to no
measurable improvements in working memory or 'intelligence'. Thus if
anything, I think it only serves the purpose of being a supplementary
or secondary test that just compliments other primary results and
therefore is not a _stand alone_ primary indicator of one's
abilities.

WM is too simple for people, that is all.

likeprestige

On Jan 18, 1:02 am, Pontus Granström <lepon...@gmail.com> wrote:
> If a psychologist want to measure G, I suggest they choose the tests with
> the highest g-load, two maybe three such tests. This would mean that
> arithmetic would be included since it got the highest g-load. If
> WM-tests are so highly indicative of success in other areas including
> "applying rules to figures", it would make WM-training a strong candidate
> for targeted improving in order to boost overall scores. At least
> two of these tests, matrix reasoning and block design seem to be trainable.
> If we include digit span and arithmetic, wm training will probably improve
> this as well. Meaning that a lot of tasks on a IQ-test will be improved
> by training on WM, which in turn means that almost all performance tasks are
> limited in terms of how much we can hold in our brain "clearly", our "WM",
> hence WM becomes G. A variable that explains a positive inter correlation
> between tests.
>
> Personally I have such a hard time understanding why WM seems to be ugly,
> almost a dirty construct that doesn't deserve to be called intelligence.
> What's so provocative about it? At the end of the day, much of the
> "speculations"
> have little or no data, while for my case it stacks up pretty neat.
>

> > brain-trainin...@googlegroups.com<brain-training%2Bunsu...@googlegroups.com>
> > .

[Joe G]

Or maybe Arthur Benjamin is a man of nonpareil g? http://www.youtube.com/watch?v=M4vqr3_ROIk

> > > brain-trainin...@googlegroups.com<brain-training%2Bunsubscribe@go oglegroups.com>

[milestones]

On Jan 17, 11:02 pm, Pontus Granström <lepon...@gmail.com> wrote:
> If a psychologist want to measure G, I suggest they choose the tests with
> the highest g-load, two maybe three such tests. This would mean that
> arithmetic would be included since it got the highest g-load.

For WAIS or WISC 4, the most important measure of pure G (or reasoning/
concept formation ability) will be the GAI (General Ability Index)
which includes verbal & perceptual reasoning indices. This leaves out
WM and PS altogether. I recognize the improved G loading on the on the
arithmentic subtest on the WAIS 4 (although there is an apparent
difference on its loading between the factor analysis work done by
Saddler versus Kaufman). I also recognize the importance of WM
generally. In fact, I think WM is hugely important for cognitive
functioning. I just don't think it is the same thing as abstract
thinking ability. Obviously some gifted individuals exhibit high
levels of abstract reasoning with low levels of WM. This is enough to
say the two are not the same. If you want you can call WM the 'new IQ"
if you want to give it more cachet. I will say this though: Neither of
the girls are ugly, both are "hot" in their right. I just don't think
they're the same girl is all.

[likeprestige]

Just for clarification...

GAI (General ability index) is comprised of PRI (perceptual reasoning
index) & VCI (Verbal comprehension index) -

- VCI consists of the following 4 tests:

1. Similarities: Abstract verbal reasoning (e.g., "In what way are an
apple and a pear alike?")
2. Vocabulary: The degree to which one has learned, been able to
comprehend and verbally express vocabulary (e.g., "What is a guitar?")
3. Information : Degree of general information acquired from culture
(e.g., "Who is the president of Russia?")
4. Comprehension [Supplemental]: Ability to deal with abstract social
conventions, rules and expressions (e.g., "What does Kill 2 birds with
1 stone metaphorically mean?")

- PRI consists of the following 5 tests:

1. Block Design: Spatial perception, visual abstract processing &
problem solving
2. Matrix Reasoning: Nonverbal abstract problem solving, inductive
reasoning, spatial reasoning
3. Visual Puzzles: non-verbal reasoning
4. Picture Completion [Supplemental]: Ability to quickly perceive
visual details
5. Figure Weights [Supplemental]: quantitative and analogical
reasoning


I fail to see how one can separate these from WM or Gs. It's just
logical that these ideas take some part in one's ability to perform on
these tests.

I am not saying that WM & Gs account for the results obtained in these
tests and thus the results are just a reflection of one's WM & Gs.
However, to say that they can be placed in their own separate room to
do as the please is just absurd. As previously mentioned, I think all
constructs live & breath in the same room and thus have no choice but
to cooperate with one another. Taking one out of the room is just like
taking the bottom floor out of a twenty story building, everything
will just come tumbling down. I do follow and believe the reasoning
behind a "consequential" hierarchical structure (where one feeds off
another and thus cannot live without the other, however, there is
always one in charge depending on the circumstance), however, it is
not completely obvious who is at the top or how far down below the
next one in rank is.

Of course, everything that has just been said is in relation to the
WAIS. Although it's tests are extensive (probably some tests are
redundant), whether this is the picture to be aiming for should be
brought into question.

Neuroplasticity is a wonderful thing (only because we don't know much
about it). If you take an _average_ blind man (born blind), I imagine
he is going to perform quite poorly on hyped up test that requires
visual perception (RPM, PRI, most mensa entrance tests & other).
However, if this man wishes to gain entrance into Mensa & there only
way of testing his abilities is through _verbal_ tests, it is quite
easy to imagine that this man would perform significantly better in
this paradigm rather than if he had his eyesight back. Why? Simple,
this is how he engages with the world and thus his brain is being
commanded to direct the majority of it's resources to auditory
processing and thus he is more likely to gain entrance because of this
'natural' inclination.

Answers to all the questions that are being suggested about human
intelligence are not going to be answered through performance based
testing (where a subject is asked to jump through fire hoops like a
lion) but instead on a biological level. Technology is growing at an
exponential rate. As most of you know, there are already studies out
correlated brain matter and region with certain abilities. I won't be
surprised come the day, where I'm simply asked to lie on a table be
placed under a brain scan for my head to be examined, where they will
search for particular mental or even emotional and psychological
markings relative to what kind of job I may be going for. However, I
think it this wait is going to be longer than expected. Not because
the technology wont be there but because the ethical considerations
have not been properly, funnily enough, 'considered' (meaning bullshit
will just stand in the way).

This doesn't mean that _individuals_ lives will be predetermined by
some brain scan. The brain scan will only represent the current
limitations of the individual, not there potential for growth. Thus,
you may enter a hypothetical screening to to become the new CEO of
some company and in response they say "sorry jim, your brain's just
not up to it right now. You are weak in the following areas and
therefore you will need to spend some time improving them. Come back
in a few months and we'll see what we can do for you".

Pretty cheap, yeah.

likeprestige

[milestones]

On Jan 18, 4:20 pm, likeprestige <plastic...@live.com.au> wrote:
>
> I fail to see how one can separate these from WM or Gs. It's just
> logical that these ideas take some part in one's ability to perform on
> these tests.

> I am not saying that WM & Gs account for the results obtained in these
> tests and thus the results are just a reflection of one's WM & Gs.
> However, to say that they can be placed in their own separate room to
> do as the please is just absurd. As previously mentioned, I think all
> constructs live & breath in the same room and thus have no choice but
> to cooperate with one another. Taking one out of the room is just like
> taking the bottom floor out of a twenty story building, everything
> will just come tumbling down. I do follow and believe the reasoning
> behind a "consequential" hierarchical structure (where one feeds off
> another and thus cannot live without the other, however, there is
> always one in charge depending on the circumstance), however, it is
> not completely obvious who is at the top or how far down below the
> next one in rank is.

I'm not really clear on what your point is or what you're objecting
to. The GAI exists because it's not uncommon to see a disparity
between VCI/PRI and WMI/PSI, especially in the superior/very superior
ranges. That some children/adults develop high abstract thinking
ability without exhibiting similar abilities in known substrates of G,
such as WM or PS, may be discomfiting to you but that doesn't change
the reality of this phenomenon. There's enough evidence to suggest
they are different constructs. Whether these things are in the same
room or not, I'm indifferent to, but I agree they need to be developed
as much as possible. I'm not arguing that the GAI index is all that
matters & the other indices should be thrown out the window, but
rather pointing out the relevance of this distinction (which goes back
all way to the very first Wechsler tests).

[likeprestige]

I know I’m out of my depth here, but I’m going to give it a go.

I don’t think I responded to your post as well as I could have.
Especially if you are to define “efficiency” as the degree to which I
accurately responded to your post; in other words, slight digression.
Just to frame what I’ve said so far.

“I just don't think it is the same thing as abstract
thinking ability.”

Abstact thinking is certainly not the same, but it doesn’t mean it is
independent from WM and or Gs. There is dependence among all 3
constructs when measuring performance in tasks previously mentioned
(WAIS). In other words, they all eat off the same plate.

“Obviously some gifted individuals exhibit high
levels of abstract reasoning with low levels of WM.”

It depends on how you define abstract reasoning really. In short, I
believe abstract reasoning is the comparing of information where one
derives similarities/differences between phenomena as an exercise to
help come to a solution to one’s problem.

Examples:
1. What are the differences between oranges and spinach?
2. Which piece of the puzzle fits the missing block of the picture?
3. Fill in the blanks. Rain leads to thunder as walking leads to ____
(running).
4. Car is to drive as horse is to ___ (ride).

To me, these examples seem to involve both WM and Gs. Perhaps one more
than the other, however, they’re both their cooking to help arrive at
a nice bowl of ‘stir fry’ (because there are a lot of ingredients in a
stir fry, lol).
As already said, I’m not trying to imply that abstract reasoning is
Gs, WM, both of them combined or whateva. However, I am just trying to
point out that I think they’re dependent and __not__ independent of
one another.

http://www.gifteddevelopment.com/About_GDC/whoaregiftd.htm

This is all I could really find in relation to individuals who would
perform high when it comes to abstract reasoning but low when it comes
to WM or Gs (information processing). The information found on this
website pretty much scrubs an eraser on whatever I’ve just said.
However, for me to change my mind on this I would need more evidence.
Obviously, so do a lot of professionals, considering many have
released papers that just bring us into a paradox. After reading the
info on this site I was like “Why do I see a boat driving on the
highway when they’re meant to be in the water!?!?”

I don’t currently have any privileges that enable me to do some
thorough research on the existence or inexistence of this distinction.

If you could please point me in a direction on finding out some
reliable info on:

“Obviously some gifted individuals exhibit high
levels of abstract reasoning with low levels of WM.”

It would be really appreciated; thanks in advance.

likeprestige

[milestones]

Ok, I was ogling the Silverman data you referenced, but maybe just
more convinced than you ;-). I'm not aware of other data off the top
of my head for the gifted group. Obviously the WAIS has, with the
latest addition, gone to a 4 factor model and gone off the old V/P
from the 3rd edition so it will probably take time to see more of a
pattern of what Silverman points out (or not). That said, I do think
the G loading of the entire WAIS is the most important -- the full
scale score is the most G loaded of all and is the most powerful
indicator not only of some theoretical intellectual potential but also
of the ability to perform intellectually in a wide variety of domains
(now).
To bring on the distinction, I think we'd have to extrapolate from
older data and tests which may or may not shed much light.

[milestones]

Here's an interesting article that delves into the importance of WM.
Alloway seems to be making the distinction that WM and IQ are
different constructs.

http://www.sharpbrains.com/blog/2009/05/10/10-students-may-have-working-memory-problems-why-does-it-matter/

"Indi­vid­ual dif­fer­ences in work­ing mem­ory per­for­mance are
closely related to a range of aca­d­e­mic skills such as read­ing,
spelling, com­pre­hen­sion, and math­e­mat­ics. Cru­cially, there is
emerg­ing research that work­ing mem­ory pre­dicts learn­ing out­comes
inde­pen­dently of IQ..."

[Pontus Granström]

Exactly what I was going to talk about, but you beat me on the finish line. If someone has a high IQ but can't work in areas such as mathematics and physics (which requires a great deal of working memory), I would also
claim that most algorithms require this, one can ask if it really is fair to talk about being smart, when someone has a smartness that isn't usable. I know for sure, people that scores fairly high on IQ tests (1 SD and up) but
still got a problem with mathematics or reasoning for that matter.

It still is at least to me quite obvious that n-backing (that really isn't a WM task like the others) seem to improve the raw score quite dramatically on tests claimed to measure your IQ. I would also claim that
reasoning abstractly, if we for example use RAPM/SPM as a measure of this seem to more trainable than for example G/WMC since it increases every year, while all the other seem negligible improvements in most cases.
It would also suggest that indeed thinking abstractly is somewhat independent of G/WMC. Remember G is not a measure of your analytical nor abstract abilities but rather the predictive power of the test or question.

It is very much consistent with G is WMC and the observed patterns.

[likeprestige]

If anyone is able to figure out a way for me to get my hands on the
following it would be awesome.

Title: Investigating the predictive roles of working memory and IQ in
academic attainment
Date: May 2010

Link:
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WJ9-4XY3F51-1&_user=10&_coverDate=05%2F31%2F2010&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1610945604&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=c2b1cc6f9396733c7ca5068c6e6663ad&searchtype=a

Title: Individual differences in working memory, nonverbal IQ, and
mathematics achievement and brain mechanisms associated with symbolic
and nonsymbolic number processing
Date: October 2010

Link:
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6W5P-519668G-1&_user=10&_coverDate=10%2F22%2F2010&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1610946177&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=2b256c52cc63293fea7cd1243908d431&searchtype=a

Title: The relationship between working memory, IQ, and mathematical
skills in children
Date: October 2010

Link :http://www.sciencedirect.com/science?
_ob=ArticleURL&_udi=B6W5P-516CC1C-1&_user=10&_coverDate=02%2F28%2F2011&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1610946241&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=8bc3e7a719340031a556220542939117&searchtype=a



Finally, any idea how to train abstract reasoning (if it something
that's trained independently - sorry, I'm sometimes slow to come
around)???

likeprestige

On Jan 18, 10:36 pm, milestones <wgweathe...@gmail.com> wrote:
> Here's an interesting article that delves into the importance of WM.
> Alloway seems to be making the distinction that WM and IQ are
> different constructs.
>

> http://www.sharpbrains.com/blog/2009/05/10/10-students-may-have-worki...

[likeprestige]

P.S - Pontus, any ideas apart from n-back?

On Jan 18, 11:04 pm, likeprestige <plastic...@live.com.au> wrote:
> If anyone is able to figure out a way for me to get my hands on the
> following it would be awesome.
>
> Title: Investigating the predictive roles of working memory and IQ in
> academic attainment
> Date: May 2010
>

> Link:http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WJ9-4XY3F5...

>
> Title: Individual differences in working memory, nonverbal IQ, and
> mathematics achievement and brain mechanisms associated with symbolic
> and nonsymbolic number processing
> Date: October 2010
>

> Link:http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6W5P-519668...

[Pontus Granström]

Isn't thinking abstractly in some cases guilt by association? If I ask someone was is the similarity of the sun and a oven, you would try to think of as much attributes as possible and select the two that matches (working memory) for example generates heat. But you could also also be even more general and talk about that they consist of atoms, or that they are visible from you living room. It seems that thinking abstractly is more dependent on context than
raw memory operations.

In mathematics all theory is abstract/general but the theory only holds for certain cases in practice. Think about anti-derivatives for example, most functions do not have one, even if we abstractly (remove all the subtle differences)
and reason about "the core" it would suggest they do, defined in terms of abstract functions.

How to train it dunno, generate attributes and match them? Surely even similarities would require a great deal of memory operations.

[milestones]

> If someone has a high IQ but can't work in areas such as mathematics and
> physics (which requires a great deal of working memory), I would also
> claim that most algorithms require this, one can ask if it really is fair to
> talk about being smart, when someone has a smartness that isn't usable. I
> know for sure, people that scores fairly high on IQ tests (1 SD and up) but
> still got a problem with mathematics or reasoning for that matter.

Well, let's say you're dealing with a very bright 10 year old with WM
deficits. What do you say, "nice IQ but, sorry, your WM sucks, better
forget physics." This is asinine as far as I'm concerned. While I'm
not convinced that WM training improves G all that much, I remain very
convinced that WM training improves WM. So that means those who will
benefit most from n back training are high G individuals with WM
deficits. In other words, smarts are absolutely usable if the smarts
are there to begin with. But when deficits are present, training/
intervention is needed to allow the IQ to be -- as you put it --
"usable."

[Pontus Granström]

How do you propose that someone could engage in these subjects without being able to do a lot of computing and "wm reasoning"? Most mathematicians are excellent "calculators", take Gauss for example. That
someone even should be identified as gifted without being able to think about much things at the same time is of course an absurdity. Not saying that indeed some tasks that are defined as WM might be of less importance,
This is however very consistent with the current research. In Germany they got a strong tradition in research about the link between working memory capacity and IQ, some of the articles which I have uploaded and are highly recommended
for anyone into serious IQ business.

--

[Joe G]

The point of the - possibly apocryphal - story wherein a young Gauss
calculates the sum of all numbers from 1-100 is intended to
demonstrate that an excellent mathematician need not be an excellent
calculator. Merely such a mathematician must be able to recognize the
patterns - whether this is highly WMC dependent is contentious and
probably at the heart of what we are discussing - and apply them.
Surely there is no dispute that 101*50 is far, far less WMC intensive
than 1+2+3...99+100.

Apologies if that is not the tale to which you are referring.

> > brain-trainin...@googlegroups.com<brain-training%2Bunsubscribe@go oglegroups.com>
> > .