Turning around a gas giant
Today, I read this article about the discovery that planets may
form quickly. All exoplanets found so far, are rather
large, and much closer to their sun than the large planets
in our solar system. The idea of the Earth circling around
such a gas giant never crossed my mind. I was thinking
about what kind of atmosphere that would imply. It would
at least mean some very cold period returning every
so many days whenever the Earth would be in the shadow
of the gas giant. And Also every round trip a time that
there would be no darkness, whenever the Earth would
be in from of the planet. I even wondered what would
give more light: the sun or the gas giant, and what
that would imply for the temperature change.
(follow-up)
The last two days of November this web site was being
blocked by my provider. I have decided to reduce the
size of my web site a little. I also have decided to
replace all inline images by links. This will make
my site even more a "text-only" web site. But I think
it will greatly reduce the amouth of traffic, as I
guess that maybe 80 percent of the hits are accidential
visitors, that arrived at one of my pages through a
search engine, and who will immediately click on to
the next site. These are typically not the people that
will take time to investigate every link to see if
it points to an interesting images.
(follow-up)
Broken traffic light
Our city government has been advertising their
web site
for public services with messages that if
you find some hole in the road that you can
contact them. This morning, I decided to report
a broken traffic light through this site. It was
red light of traffic light for bikes with the
number 22 at the crossroad at the Westerval where
the Parkstraat goes over into the Wethouder Nijhuisstraat.
I wonder how long it will take before it is repaired.
It is repaired
This morning, the broken traffic light
was working again. Now I wonder how many people
reported it broken before me, as I can hardly believe
that they responded so quickly.
It seems that
Kwabena Boahen and his group at the University of
Pennsylvania are working on developping
artificial brains. Interesting stuff they are doing.
Triangle grid (Cont'd)
Sometimes, I am really surprised about the depth of detail
in certain apparently simple structures. First of all,
I thought about another characterisation of sets of triangles.
A set can be called elementary, if there is no subset of
triangles which also can produce some pattern.
Then this afternoon, I was thinking how in some sets
it must be possible to invert just a single point of
a pattern to change the pattern in another pattern
that can be made with the set. This made me think
about graph where each vertex represents a pattern,
and each edge a single value inversion.
The interesting question of course is whether this
graph would be total connected or be partitions in
a number of connected subgraphs. You could also think
about other interesting properties about these kind
of connection graphs.
(to be continued...)
Around half past one in the afternoon there were some
barely visible snow flakes in the air. And that is all
we are going to get, because the wind will blow dry
cold air from the East for the coming days. It is late
this year. Normally we get the first signs of snow in
November.
In a triangle grid you can flip a single
value in a pattern, if there exists two hexagons (made out
of six triagles) which have the same value on the outside
but a different value on the inside. This morning, I realized
that the triangle grids can be mapped on hexagon grids.
Except from symmetries, there exists only one mapping of
each set of up and down triangles onto a set of hexagons.
There are however, far more possible sets of hexagons.
264 to be precise.
Next, I had to think about mapping a triangle grid on
a square grid. It appears there are as many sets of
squares (labelled with 0 and 1) as there are sets of
up and down triangles (because 24 = 23
+ 23). For each set of up and down triangles,
there are three ways to map them unto a set of squares,
everytime by combining an up and a down triangle into
a diamond. This leads to the observation that some sets
of squares might be equivalent with each other. Yet,
I think that there are also sets of squares that are
not equivalent to any set of up and down triangles,
although I have not find an example yet.
(To be continued...)
IQ test
I came along the IQ test from EMode and could not resist answering
the 40 or so questions. The result, not very surprisingly,
said that I am a Visual Mathematician with
an IQ of 131. My score could have been higher if it was
corrected for the fact that English is not my mother
tongue. There were some questions that I did not feel
sure about, because I did not fully understand the meaning
of all the words. Of course, I was smart enough not to
request for the full report, which costs about 15 dollar.
Anyway, this is not even a good IQ test, as it does not
have any time limit. You could spend a whole afternoon
answering the questions. Any serious IQ test puts
a time limit, such that you would have barely time to
answer all the questions. Or it would measure the time
you spend on each question. With a computer program that
would be possible.
What is worse is that this site promotes the idea that
the ideal partner would be someone with the same
intelligence profile as yourself.
Steven J. Byrnes
Yesterday, the Siemens Foundation
announced the national winners for the Siemens
Westinghouse Competition.
Steven Byrnes won the largest grand for proving a
poset theorem based on the Chomp game. This is not
the first time that he wins some price. Already
in 2000, he
solved Corner Problem 2000-4 from Mandelbrot
Competition. But what is more important, in June this year
he was also on of the five winners
of USA Physics Olympiad Team. There it says about him:
Junior, Roxbury Latin School, Boston, Massachusetts.
Steven is a mathematic scholar, plays blues and jazz piano,
sings, and is a member of the cross-country team.
Steven lives in Lexington, Massachusetts. The site
also gives a more extensive
biography.
See also this page which has a
picture of him.
Another picture can be found in an
ASP news item. I think we will hear more about
him in the coming years.
I still haven't found anything on the theorem and
the proof of it. Apparently, this is not a very
interesting subject for the general public.
(follow-up)
Inpainting algorithms
Today, I came across
some pages presenting algorithms for inpainting damaged spots
on pictures. One of the pages also showed how the technique
can be used to enlarge pictures and still make them look
sharp, just like the S-Spline program. Actually,
these techniques could also be used for image compression.
It simply comes down to picking a number of points that
together with the reconstruction algorith would reproduce
the original images with the desired quality. Finding the
minimal set of points is a very complex problem, but I expect
that some heuristic algorithms could come up with a solution
close to optimal solution. Still decompression is rather
expensive with this technique, much more expensive than
currently used decompression methods. It is also likely that
the algorithms described here will be used as a post-processing
step for currently used decompression algorithms.
Today, I read a story about MorphOS.
This talks about microkernel versus macro kernel. Most PC are using
the x86 type of processor of which the Pentium 4 is the last version
in a long line of processors which were backwards compatable. Backwards
compatibility is needed to still be able to run programs that worked
on the previous version. Virtual memory management was only added in
the 80286 (if I am not mistaken). But because backwards compatibility
was required, context switches became rather expensive. The PowerPC
was designed with virtual memory management from the start. For this
reason, context switches are much faster. Context switches make communication
between processes slower. For this reason, operating systems deployed
on x86 processors (such as Windows and Linux) implement the whole
operating systems as a single process. They make use of a macro kernel.
You could also divide the kernel up into many smaller processes. This
leads to microkernels, where there is one very small process surrounded
by a host of processes which do the real work. The small process (the
microkernel) only responsability is to keep all the other processes
running. (A good example of a succesfull microkernel operating system
is QNX.) Microkernels have many
advantages, but speed is a big issue if the processor does have slow
context switches. That is why you do not see them on x86 processors.
Again, a good example of legacy (having to maintain backwards compatibility)
forces the use of an inferior kernel design to be used in competitive
operating system. This law seems to operate on many levels in hardware
and software design. One of the reasons that the PowerPC architecture
never became mainstream is that it could not run applications developed for
MS-DOS straight away. One could even state that the real cause behind this
was the development of Closed Source applications. In fact one could even
argue that the "capitalist" model of developing software, aggrevates the
problem of legacy, because software development companies having to defend
their market share will prevent the adoptation of better technology in
favour of the existing technology.
Andy having a good memory
Yesterday evening, I attended a parents meeting at the
Klim Op,
where Andy goes every weekday.
His speech therapist showed me how she managed to test
his ears without him even suspecting that he is being
tested. First she had to make him used to having a head
phone on. Then she made up this game where he has to
put a ring on a rod everytime when he heard some sound.
When could play the game, she could start measuring.
So far, she has measured half of the tones she needs to
measure.
I also heard that Andy has a very good memory. The first
thing in the morning is that they sit in a circle and
during this time that days schedule is put on the board
with pictures and pictograms. Every day somebody else
has to take of these, once the activity is over. Andy is
the only one who never forgets this, and even if it is
not his turn, he will start pointing to the board when
the others forget it.
It looks like Steve also joined
MOP 2001
(very good and funny site).
I also discovered that already in 1999, he
solved several of the problems from the Mandelbrot Competition.
I also found a dealing about
the analysis of the Chomp game. The page also has a link
to an email from Steve to the author of the game which makes
clear that Steve worked on the problem this summer.
I also found a nice Java Applet that allows you to
play Chomp.
This evening, I checked the amouth of traffic
this web site generates. It is about 30.7 Mbytes
per day produced by an average of 2896 hits per
day. The average size of each hit is 10.5 Kbyte.
Compared to last month, this is a reduction of
12% with respect to the number of hits, and
36% with respect to the volume. It seems that
my approach is working.
(follow-up)
Mathilde Willink
This afternoon, I happen to see some fragments about a
film
about Mathilde Willink made by Jasmina Fekovic and Eddie
van der Velden. It is already more than 25 years ago that
she was found dead with a bullit in her head.
Some links:
Around a quarter to two in the afternoon, there was some snow
in the air. The flakes were a little bigger than on the
sixth, but it lasted for barely ten minutes
and it was far to warm to let any snow stay on the ground.
Swimming
Today, Annabel got her first
swimming diploma. There were thirty children joining in
the test, and they all passed. Not that it is not a serious
examination (several times, some of them were asked to do
something again, because they did not follow the rules
exactly), but they had been screened on for hand to prevent
embarrisment before family and friends watching the examination.
As the last part of the examination, they had to keep their
head above the water for thirty seconds using their legs and
arms, while being in a vertical position. Everybody joined in
the final countdown of the last ten seconds, and gave them an
applaud for their achievement.
(follow-up)
Gouden Loeki 2002
Today, we received a paper of the "Gouden Loeki 2002" election, which is an election for
the best television commercial shown on Dutch television.
You are asked to send in your top five from the selected
36 commercials. If your top five matches the final top five
you have a chance of winning a trip for two persons to
Rio de Janeiro. But there are 45.239.040 ways of selecting
a top five from a given set of 36 items. It seems that the
chance that but one persons answer match the final top five
is rather small (with a population of 16 million people in
the Netherlands) if all commercials are as popular. I wonder
what the chances are, if some commercials are much more popular
than others. Interesting question.
Toys
This evening, Annabel and I went
to the Christmas night service of our church. Li-Xia stayed home to watch over Andy.
This is the first time for Annabel and for me it is also some
years ago that I went. On the invitation there was a request to
bring some food for the asylum seekers that are staying in Enschede.
Then also some young people suggested that we should also collect
toys for the children. Thus we took a bag with things with us.
When we arrived at the church I started to unpack the bag. And out
of it came some toys that I had not seem for a long time, almost
forgotten that we had them. Toys that Annabel and Andy played
with many years ago. Suddenly, these toys felt very dear to me,
because of the memories that they brought back. Almost with tears
in my eyes, I layed the toys between the all the others. It was
almost like I gave a part of myself away. But is that not what
Christmas is really all about?
This months interesting links
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