In the evening, I will leave for Mainz and thence for Bingen. I'll be at Breakpoint 2005 until Monday. Then I'll return to Vienna. As usual, I'm not excited at all (this is not to be misunderstood: what I want to say is that I have neither positive nor negative feelings) and wonder whether the change of surrounding may do some harm to my creative flow, but it's possible that I will be able to get some interesting ideas and meet interesting people - these are the reasons for my visiting the party. I'll take along a notebook (not a computer - a notebook made of paper!) and a pen in order to be able to write during the party so maybe my creative flow will be kept unabridged.

I'm not posting the results I get on tests of any kind since they have gotten on blog readers' nerves, but I want to say that when I'm taking tests now, I also try to analyze the mental processes that happen. One conclusion so far is that even culture-fair intelligence tests (supposed to measure 'fluid' g, not 'crystallized' g) are not independent of experience. E.g. when you see shapes consisting of one line, two lines and three lines (so the next one, which you have to choose from a list of possibilities, will have four lines), you need to understand the concept of a line. It is a concept which I guess for most people is easy to understand intuitively, even if they have never heard the word line. But for some people its understanding may depend on whether they've ever used a ruler in order to draw shapes. For others it may depend on their having the idea that a ruler or a similar item (exists and) can be used for drawing shapes. This is maybe not a convincing example because the concept of a line is so obvious, but think that it certainly has happened to you once that somebody has interpreted something in a completely different manner (a way you would have never interpreted it on your own) and has thus opened your eyes. People think in different categories and concepts; perhaps it's the wealth of concepts that defines or at least heavily influences one's true level of intelligence (IQ tests measure only a "snapshot" of which). Even the mastering of simple concepts such as geometric shapes is culturally dependent.

Actually just understanding the concept of a line won't be sufficient to solve this task. You also need to understand the concept of cardinal numbers or counting. Counting is a process internalized by school-children. They've been trained to count one, two, three,... When they start counting and are confronted with such an obvious serious of numbers, they will assume that the next element will also fit in this pattern. It is induction: If element 1 has a particular relation to element 2 and element 2 has the same relation to element 3, then element 3 will also have the same relation to element 4. Actually induction may always be right or wrong. It's impossible to tell. It's just an assumption that this pattern will continue. That's why from a strictly logical point of view, visual pattern and numerical pattern tests (which are, ironically, often supposed to measure logical intelligence) are arbitrary. In theory, any element could be the next. It seems, however, that induction is an important means of learning for man: to make predictions which are most probably right, although it's not sure that they definitely are. Induction is important for making hypotheses, including ones essential to survival. It seems the notions of logics and probability are closely related to each other.

One must not forget either that the understanding of some even more basic concepts is necessary to take an intelligence test at all. But usually people are instructed by their testers beforehand (to make sure).

In such visual intelligence tests, I often manage to exactly predict what the next pattern will look like. Then I search for this pattern in the list of possible answers and usually find it. Sometimes it's not possible to exactly predict what it looks like, but what qualities it must have. An example: I see that in each of the three matrices, there are the same number of triangles, the same number of circles and the same number of squares; only the order is different. Hence I predict that these numbers are also constant in the fourth matrix. But I don't manage to find out the system that determines the change of order; if there was such a system, I'd be able to exactly predict what the next matrix will look like. So I check out the various possibilities and see that only one of them matches the criterion of the constancy of numbers. Therefore this has to be the right one. Probably there isn't even a system concerning order; all that was demanded from me was to find out that the numbers matter. After solving the first task of this kind, I also managed to easily solve the other tasks of this kind because I've learned the concept that in some questions the strict order of the symbols is irrelevant and only their number counts.

The fact that I learned a new concept by taking this test clearly shows that it is possible to get better results at IQ tests with some practice. The next test of this kind I take, I will most probably remember this concept and perhaps find the right solutions to some tasks more quickly than I would have had if I'd had to discover this concept for the first time. However, IQ tests cannot be simply trained like one's muscles, which (in healthy people) hypertrophy automatically after using them too much during a short time: You need to discover new concepts. Only the discovery of new concepts will help you improve your scores.

Of course concepts could also be taught. As a matter of fact this is what school does e.g. in mathematics class. Counting and calculating are important concepts which will also improve your intelligence. In other words, intelligence is influenced by education. And it is definitely influenced by your environment because it is the environment that makes you think about new concepts. A question that's more interesting though: Why do some people develop new concepts (and thus improve their intelligence) on their own? If developing new concepts is to be called creative, then maybe creativity is one factor that determines intelligence. Now what makes some people more and others less creative? Maybe it is to do with intuition? What determines one's level of intuition?

In any case, it's true that intelligence is more dependent on divergent than on convergent thinking. Difficult IQ tests consist of tasks which usually cannot be solved by just applying some concepts you've been taught at school, i.e. purely convergent thinking. You must develop new concepts. I am more of a divergent than of a convergent thinker.

One's scores at intelligence tests may also, but need not necessarily be influenced by orderliness / sloppiness and whether you're systematic. For example, if you have some ideas what the next pattern must be like and notice that a pattern matching your ideas is in the list of possible solutions, you being a sloppy person might pick this pattern and advance to the next task. If you were an orderly person, however, you'd also check out the other possibilities and perhaps notice there's another one which fits your ideas, so you have to think about one more criterion that will enable you to distinguish the two possibilities from each other. Maybe this is not only dependent on orderliness but also on intelligence itself, as you may be an orderly person but may not have realized that checking all possible solutions is necessary unless you are completely sure that there is only one conceivable solution.

Of course intelligence is related to memory, not only to short-time memory, but also to long-time memory, since you have to remember the concepts in order to take advantage of them.

In my opinion, what is most helpful in life is the ability to discover new concepts oneself. Intelligence tests ought to primarily measure this ability. Unfortunately, they don't since even culture-fair / fluid g tests always contain a certain amount of tasks which can be (at least partially) solved using previously gained concepts.

My ideas are probably not new. I had the experience when writing these lines that I've now understood the difference between fluid g and crystallized g better. As a matter of fact, some crystallized g tests are also called "concept mastery tests". I guess the people who invented these tests had the same or almost the same thoughts as I had. I now have a better understanding of what's an original thinker. It's somebody who is able to discover new concepts of high complexity, such as concepts needed for solving the most complicated tasks in traditional intelligence tests. That's why there are statements like: "Original thinkers have an IQ of 160 or above." (It need not be true: in theory it's possible that they manage to solve the hardest tasks, which hardly anybody manages to solve, and fail some of the easier tasks for some reason, which results in a lower IQ than they would have had otherwise. That's especially likely to be the case if the test contains questions which are not culture-neutral.) I feel a bit pathetic for having had a lot of thoughts about intelligence tests which I first thought to be clever, only to realize in the end that there is most probably nothing original about any of them.

I do not claim to be an original thinker; I'm just smart enough to discover many concepts myself which means that I don't rely on other people's (teachers') assistance or the assistance of tools, such as books, to the same degree as others do. The speed of discovering concepts is certainly influencing intelligence, but so does the intensity of thinking about new concepts. Maybe I score that high on IQ tests just because I think so much. My ability to discover new concepts on my own has been the reason why I could afford being absent-minded at school and did well nevertheless. Somehow I have the impression that with the thoughts outlined in the last few paragraphs, I've hit the core of the nature intelligence and logically explained what many people already understand intuitively.

I guess there are several different ways of acquiring high intelligence. (If anything from here is an original thought, then maybe it's this idea, for at least I've never read anything sounding similar to this notion before. But of course that doesn't mean that there is definitely nobody who has already had this idea before and maybe already developed it further.) It would be interesting to do research on this topic. Maybe it's possible to devise tests that measure the predominant way people gain concepts. This is related to learning types, for which tests already exist. I remember the notions of auditory, visual and kinaesthetic types. These three types and mix-types in between them are definitely not enough to explain all ways to acquire intelligence. Actually all these three types could be grouped as sensing types. Apart from that, there are also intuition types. Maybe learning by thinking and learning by feeling could be distinguishes from each other. I know I'm drawing parallels to the Jungian functions. But as a matter of fact, when I learned about sensing/intuition in the first place I immediately realized that these two antagonistic functions are the ones that determine one's way of learning. According to Keirsey, 80% of the population prefer sensing and only 20% prefer intuition. It would be interesting if this proportion is the same or different in people with high intelligence. My hypothesis is that the percentage of people who prefer intuition is higher among people with high intelligence than in the whole population because it makes the discovery of new concepts far easier. I might be wrong so please try to falsify my hypothesis.

The best page I've found so far about Jungian functions for beginners is http://www.geocities.com/lifexplore/jft.htm. I highly recommend that to anyone interested in personality types. I was thinking about how I would write an article or deliver a lecture on the matter. I'd have started in about the same way as in that article. But the article also contains some concepts I've not found out yet (such as really good definitions for extroversion, introversion, thinking and feeling).

## Donnerstag, 24. März 2005

## Freitag, 18. März 2005

As expected, the general tendency of the text is cautious and opposed to the idea of improving the human species by means of new technologies. Just to quote the passage that was also criticised at liberalismus.at:

"ICT Implants and Enhancement of Physical and Mental Capabilities

Efforts should be made to make sure that such ICT implants are not used to create a two class society or to increase the gap between the industrialized countries and the rest of the world. Access to ICT implants for enhancement should be used only:

- To bring children or adults into the 'normal' range for the population, if they so wish and give their informed consent, or,

- To improve health prospects (e.g. to enhance the immune system to be resistant to HIV). As for health purposes, access to ICT implants for these purposes should be based on need rather than on economic resources or social position."

This sounds very socialist indeed, doesn't it?

## Donnerstag, 17. März 2005

Again I read the type descriptions of ENTJ and ENTP at Socionics and found the ENTP description to be more like me: "ENTPs usually have a distant, far away look in their eyes and it often seems as though they are paying little attention to what is going on. During conversation ENTPs like to play with objects, like a pen for example, often accidentally breaking it." These two sentences definitely describe me. "ENTPs do not know how to keep the right psychological distance with people. This becomes especially noticeable during long term interaction. One day they can be friendly and the next day they can be completely opposite. They often behave unceremoniously and can rudely butt in on others conversations." This is also true. But the first two sentences are to be explained by the strong intuitive trait, while the last four sentences concern the lack of feeling. So why shouldn't these sentences apply to (some) ENTJs, too? What definitely does not apply to me is this sentence: "They invariably forget what they have already done and what they need to do." This is because I'm a judging type.

I wonder how people experienced at Socionics would classify my photo. I've also tried to classify the photos of members of the Austrian high intelligence society at this page.

## Dienstag, 15. März 2005

"We're looking for two numbers. Everybody knows that they are two different numbers, that they are integers, that they are greater than 1, and that person 1 knows only the sum of the two numbers, while person 2 knows only the product of the two numbers. Now the following dialogue happens:

1: 'I don't know either number.'

2: 'Me neither.'

1: 'Well, now I know both numbers!'

2: 'So do I!'

Assume that both persons are extremely good at logical thinking. So what are the numbers?"

Solution:

Let's check out the dialogue: Person 1 knows the sum s, but isn't able to deduce the two numbers from it. So there are at least two possibilities to compute the sum. Thus the possibilities 2+3 and 2+4 are obsolete.

Person 2 knows the product p, but isn't able to deduce the two numbers from it. So there are at least two possibilities to compute the product. From this follows:

1. At least one of the two numbers is not a prime number.

2. If one of the two numbers - let's call it n - is a prime number, the other number must not be n^2.

3. If one of the two numbers - let's call it n - is a prime number, the other number must not be n^3.

After both persons announce that they don't know the numbers, person 1 is able to deduce the numbers.

As person 1 is extremely good at logical thinking, he/she is aware of the facts presented above. So the fact that person 1 is now able to deduce the numbers means that all possibilities to compute s except one involve either two prime numbers or one prime number n and n^2 or one prime number n and n^3. There are only the following possible values for s:

Step 1. Just one possibility not involving two prime numbers:

7=(2+5)=3+4

8=2+6=(3+5)

There are no other possibilities because for any s > 8 there are at least two ways to compute the number as the sum of two non-prime numbers. Proof for all s != 12: s - 4 > 0 and s - 4 != 4 and s - 6 > 0 and s - 6 != 6. It's also easy to prove that it applies for s = 12.

Step 2. Just one possibility not involving two prime numbers or a prime number n and n^2:

7=(2+5)=3+4

8=2+6=(3+5)

There are no other possibilities for the following reasons: 2+4 is not possible (see above), and for any s = n + n^2 with n being a prime number and n >= 3 it's possible to show that apart from the combination of a prime number n and n^2, there are at least two further combinations in which at least one of the two numbers is not a prime number.

Step 3. Just one possibility not involving two prime numbers or a prime number n and n^2 or a prime number n and n^3:

7=(2+5)=3+4

8=2+6=(3+5)

10=(2+8)=(3+7)=4+6

There are no other possibilities. In analogy to the previous case it's possible to show that for s = n + n^3 with a being a prime number and n >= 3 there are at least two further combinations involving at least one non-prime number.

So when person 1 says that he/she has now deduced the two numbers, it means that they are either 3 and 4, 2 and 6, or 4 and 6.

Person 2 has done all the reasoning so far himself/herself and says that he/she has now been able to deduce the numbers. So it could not have been the pairs 3 and 4 or 2 and 6 because their products are equal. Therefore the correct solution is: 4 and 6.

## Montag, 14. März 2005

First math exercises and theoretical computer science exercises for the semester... In math exercises I'm in Prof. Urbanek's group again, cool. I'm such a lucky guy. And finally issue 318 of the magazine of the Austrian high intelligence society has arrived in my letterbox. Maybe I'll post my solution for the task 6 of last issue's quiz here later on (I mean not just the numbers, but the way to arrive to them), as I was quite proud of it and the new issue contains no explanation but the numbers.

New thoughts about the characterisation of the different NT types have also popped in my mind... I'll write more later. Socionics.com has an interesting test (Socionics Type Assistant) involving choosing words that describe oneself's personality... I got the MBTI type I'm accustomed to getting at such tests, but also a message that my answers seem to be biased, I seem to be already too aware of my MBTI type :)

## Freitag, 11. März 2005

a_n = 0 if there's any integer number x >= 2 for which n = x * (x - 1) - 1,

a_n = - a_(n-1) for any other even n,

a_n = 1 + a_(n-2) for any other odd n.

and

a_n = (-1)^n * (Sum_of_the_digits(floor(n/2)) - 1).

These formulae produce series in which every integer number will appear an infinite number of times.

## Mittwoch, 9. März 2005

The subjects of this semester are:

Mathematics 2 (Analysis): Gonna love this one.

Algorithms and Data Structures: This is also nice and useful.

Theoretical Computer Science: I like it so far. I was most keen on studying these things when I thought of studying computer science in the first place (influenced by Gödel-Escher-Bach).

Introduction to Technical Computer Science: Not my cup of tea, but I'll have to study it properly.

Data Modelling: Nice; it's a subject I don't know a lot about yet and I'm happy about the opportunity to study it.

Basics of Bioelectrical Systems: This is for the 6th semester in medical informatics. I'll try to take it already now though I won't be able to attend all the lectures due to a temporal collision. So far, it has been nothing new for me thanks to my knowledge at physics and physiology which I gained in my medical studies.

Social Aspects of Computer Science 2: I also have to do this one. Now it seems to be more philosophically oriented and thus more interesting. I haven't decided yet at which of the two universities (Vienna University of Technology or University of Vienna) I'll do it, but I guess I'll take the latter since this removes one source of temporal collision preventing me from attending the lecture about the Basics of Bioelectrical Systems.

Moreover, I resumed studying pathology on February 10th after releasing the new Hugi issues; by now, I've already done more than 50% of the textbook.

Yesterday I had 9 hours of lectures in the same auditorium (maximum), which has been a new experience for me. (In medicine we study mostly from books; quite a few lectures are even cancelled as there are not enough students interested in them.) Fortunately there was plenty of air in that room so I didn't fall asleep even though the room was crowded with several hundreds of students. Probably the interesting lectures also contributed to my staying awake.

I've found an interesting test in kb_'s Livejournal: The Commonly Confused Words Test. The results are not yet published; I'm curiously awaiting them in order to find out what I've made wrong, what's right, and why it is this way.

My scores have been: "You scored 100% Beginner, 100% Intermediate, 93% Advanced, and 61% Expert! You have an extremely good understanding of beginner, intermediate, and advanced level commonly confused English words, getting at least 75% of each of these three levels' questions correct. This is an exceptional score. Remember, these are commonly confused English words, which means most people don't use them properly. You got an extremely respectable score."

The test is actually designed for native speakers of English.

## Dienstag, 1. März 2005

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