Erdos number

I met with the Hungary born mathematician Peter Frankl for a radio program at NHK

Peter is a fascinating character. He is also known for his juggling acts. He said he started practicing for street performances as juggling was more visible to people. Mathematical problems are notoriously difficult to come across.

While discussing, Peter casually mentioned that he has written several papers with Paul Erdos. "Are, you are Erdos number one, then!" I exclaimed. So far in my life, the smallest Erdos number that I encountered was three.

"As Paul Erdos is sadly no longer with us," Peter said, "it is now impossible to become Erdos number one any more".

My only hope is that if I write a paper with Peter Frankl, I would get Erdos number two. Peter said he was working on a paper on quasi-random graphs. My Ph.D. thesis was on an application of graphic transformation.

As I left the studio, the shining smile of Peter Frankl remained with me, to illuminate and inspire.


With Peter Frankl in the NHK studio.

Royal family

I attended the rehearsals for the opera "Hansel and Gretel" by Humperdinck. The conductor was Seiji Ozawa.

The rehearsals were held for the upcoming performances of the Seiji Ozawa Ongakujuku 2009.

During the intermission, just before the General Probe for the third act, I had an interesting conversation with Mr. Graham Clark , who sang the part of the witch. Marianne Wachter was with us.

Graham has appeared as Mime in Bayreuth for many years. "The atmosphere was quite special", Graham said. "We used to have curtain calls for 40 or 50 minutes. It is Walhall. People make a pilgrimage to Bayreuth to come to close encounters with the great tradition".

"It is the only family opera house left in Europe", Marianne said.

"The Wagner family, in a sense, is the only Royal family in Germany", said Graham. "It is certainly the most important family", Marianne said.

"It is not easy to see all these if you don't live in the German speaking world".

The time came for Graham to sing. In a moment, the gentleman transformed himself into the witch and stormed onto the stage.

Mt. Fuji

I live in Tokyo. I travel on the Shinkansen (bullet train) to the western cities (e.g. Nagoya, Kyoto, and Osaka) of Japan quite often. In a particularly busy week last year I traveled to and from the Kansai region four times within seven days. Shinkansen is quite indispensable.

When I was a kid, traveling on the Shinkansen was a magical experience. As the train leaves the Tokyo station, and passes through Odawara and Atami, I would start looking expectantly through the window, waiting for Mt. Fuji to emerge in its magnificent appearance.

Mt. Fuji is quite arguably the most fascinating and awe-inspiring mountain in Japan, and looking at the rocky apparition was the highlights of my travels in childhood.

Nowadays I am busy doing this and that on the train, and rarely gaze at Mt. Fuji for a prolonged time. The trains are now equipped with WiFi. Otherwise I am deep asleep, and do not notice the passage of the heavenly mountain.

Even on these prosaic days I do sometimes glance at the most famous mountain in Japan, and the magic of childhood days returns to this insensitive soul.

Aerial dance

Yesterday, I was giving lectures at University of Osaka.

Walking along the street, I saw two common bluebottle (Graphium sarpedon) butterflies in the sky. They kept flying, chasing each other.

After a while, one of them began circling around the other. The movement was quite rapid. The circle was completed more than once a second, approximately.

I was fascinated by this elegant and dynamic display of behavior. It must be written in the genetic code. Generations after generations have performed this aerial dance without knowing how or why.

Symbolization

"Kaen-doki" ("Fire flame earthenwares") are found in various part of Japan, and are estimated to have been made 4000 to 5000 years ago. Some fine specimen of these vessels with magnificent ornamentation are registered as National Treasures of Japan, and as such, are the oldest members of this genre.

Several years ago, I had an opportunity to observe one particularly fine fire flame vessel in Tokamachi . I was impressed by the abstract expression of the fire flames figures.

Nobody is sure that these patterns actually represent fire flames, given that there were no letters to record and convey the significance in those period. Yet, as one admires the ornamentation, one is brought into the strange realm of symbolization of the dancing flames, now twisted and now straight, ever changing, but remaining eternal in essence.

I can almost imagine myself watching the fire flames at night in those ancient times. Surrounded by the menacing darkness, the fire flames must have appeared to be the symbol of our earthly existence itself.




A fire flame earthenware.

Blueberries

I went to Vancouver, Canada at the age of 15 for one month to study English. My host family (Verna and Jim) lived in Richmond.
They would often take me to the Richmond Nature Park. It was fun to walk among the woods, with squirrels crossing your way.

It was there that I learned the joy of blueberry picking. The blueberry trees bore lots of fruits all around the park. It was fun to pick and eat the sweet little blue things as you walked along the shrubs.

"You are allowed to pick and eat the berries in the park", Verna said, "but you can't take them home in a jar to make jam"

There was this primordial joy in nourishing nature at first hand. You can get blueberries in packages in the supermarkets, but it is not the same thing. Devouring directly from the twigs had a flavor incomparable to any artificially prepared delicacies.

Metacognition.

From time to time, when I am walking around for example, I have this strange feeling. I had one last night, as I strolled on the dimly-lit street towards home.

What is this universe, anyway?

We know that there are natural laws, with molecules moving about within and outside our body, the universe (supposedly) beginning some 13.7 billions years ago, meanwhile life forms evolving, and presto, here we are, self-conscious beings, thinking about consciousness itself, killing time with this game and that website, breathing in the air, and when we feel like it, sometimes wondering, what this is all about.

Yeah. What is this all about?

In the cognitive sciences, the importance of metacognition is stressed. We need to step out of the system sometimes and observe it as if from outside. There are properties only recognizable by doing just that. What if we try to come to a metacognition of the universe that we are in?

In those rare moments, when I feel as if I have woken up from a long dream, I have this strange hunch that we have been oblivious of some important truths hidden from the beginning of time.

Fishing lights

Right now I am in Hakodate. I gave a lecture at the Future University Hakodate.

The night fell. I was at a Sushi restaurant with my friends. As I strolled onto the street, I saw glaring lights in the distance. At first I was confused. Then I realized that they were on the sea.

"They are Isaribi", my friend said.

A poetic Japanese word for the fishing lights. With these glitters, the fishermen attract squids. We had just enjoyed one in the Sushi restaurant.

For some time, I could not turn my eyes away from the fishing lights. They were like apparitions which did not quite belong to this earth.

Butterfly alerts

As a kid I used to collect and study butterflies quite seriously. My butterfly mania was quite famous in the neighborhood and school. One day, when I was eight years old, one of my class mate girls contacted me. Apparently, there were some interesting looking butterfly larvae in the garden of her house, and she was wondering if I wanted to come and have a look.

That was one instance of the many butterfly alerts that I used to get from people around me those days. When at home, I would sometimes get media related butterfly alerts. I had my room on the second floor, and I would be reading books, when my mother yelled "Kenichiro, come, butterfly's on t.v.".

I would rush downstairs, and if I was lucky, would get a glimpse of butterflies on the screen, either in a news or a nature documentary.

When your love is known, people would give you alerts, out of kindness, and you respond with quick moves. Butterfly alerts were highlights of my youthful life.



Myself as a kid (10 years old) waiting for the butterfly in the woods, possibly in the northern island of Hokkaido on a butterfly trip.

To the river

When I strolled in Cambridge U.K. for the first time back in 1993, I was fascinated by the ancient ambience of the academic city. As I approached the Trinity college, I noticed a small writing on the wall.

"To the river", it said, with an arrow pointing towards the river Cam.

I liked the metaphor, and it stayed with me to this day.

In my life, whenever I can, I am looking for a road leading to the river.


"To the river" sign on the wall near Trinity college, Cambridge, U.K.

Thousand people bath

My mother originated from the southern island of Kyushu.
I was about five when my parents took me to the hot spring city of Beppu, a few hours away from my mother's native town.

The city is famous for various kinds of "hells." The hells are actually special kinds of hot springs, which have been turned into fictional realms belonging to another world where earthly sins would be corrected.

My aunts and uncles were with us. Seeing some hells must have fuelled my imagination. I remember vividly how we came to the entrance of a hot spring bath, when my aunt said that it was called a "thousand people bath" (sen-nin-buro), as a thousand people could bathe at the same time.

The word stimulated my mind, which had been made soft and sensitive by the exposure to the hells. I pictured a thousand people in bare skins standing very close to each other, with the white steam encircling them.

I wanted to see it for myself, but I was dragged by the hand and was taken to the station, where we took the train to travel further.

More than 30 years later, I visited the city of Beppu for a brain science conference. I found out where the "thousand people bath" was in the tourist office.

The real "thousand people bath" was a gigantic hot water pool, roofed by a huge glass structure. The sunshine filled the interior, and there were trees and grasses shining in healthy green colors.

It was nice, but very different from what the five year old imagined it to be.

I am still looking for my thousand people bath.

Extremists

I don't know how it is, but I can breathe easily when there are rooms for extreme people.

Extremity is an art, and requires a certain level of intellect. I really enjoy a conversation when there is somebody in the party who has eccentric views on, for example, the second law of thermodynamics, or the collapse of wave function in quantum mechanics.

Most scientists take a mild attitude towards these venerable enigmas, saying that as far as they can calculate things for all practical purposes (FAPP), they don't care. Those conservative people, although they are certainly the main stream in the academics, do not really interest me. Because they don't make the air lighter.

Being an extremist is not easy nowadays, when the society becomes increasingly practical. It is well advised to keep a sensible day job, while you maintain the extremist's activities at night.

It fills me with indescribable joys to think that there are still extremists around.

Principles

Now I have kept this journal for one month in a row, starting from the 6th of June entry "A double sin". There were two entries prior to that (3rd and 4th of June), but the continuation was broken because I did not make any entries on the 5th.

The Qualia Journal itself as initiated on 9th October 2004, with the entry "Hello World". There were 11 entries in that year. The year 2005 saw 44 entries, followed by 29 in 2006, 68 in 2007, and just 11 in 2008.

This year I intend to continue this "blog streak" for quite a long time, unless something inevitable prevents me from doing it. The reason why I am doing this is complex in psychology but simple in the principles.

It is always the principles that count.

Pursuer of inner light

The paintings by El Greco (1541-1614) always struck me as very original, ever since I glanced upon one in an art museum.

Giorgio Giulio Clovio was an artist freind of El Greco, although much older than him.

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Clovio reports visiting El Greco on a summer's day while the artist was still in Rome. El Greco was sitting in a darkened room, because he found the darkness more conducive to thought than the light of the day, which disturbed his "inner light". (quoted from M. Acton, Learning to Look at Paintings, p.82)
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The figures depicted in the El Greco paintings appear as if they are shining from within.

The inner light, when it comes from the painter, is the source for great originality.

In order to be unique you need to listen to your inner voice, rather than attend to what is being said and circulated around you.

A pursuer of inner light goes far, freed from the conventions of the day.


"The Opening of the Fifth Seal" by El Greco.

Two infinities.

I was talking with my best chum Yoshi Tamori.

Yoshi is a mathematical genius. He likes to talk about iterations and infinities.
One of Yoshi's favorite topics is the Euler–Mascheroni constant. One is filled with a sense of wonder when you ponder its definition.



Both the harmonic series and the natural logarithm of N tends to infinity as N->inifinite. However, the difference between these two infinities is finite, namely

gamma = 0.57721 56649 01532 86060 65120 90082 40243 10421 59335 93992.


The two infinities are "relatives" separated exactly by this finite number.


Myself (left) and Yoshi Tamori at the Hermitage Museum, St. Petersburg, Russia.

Secret Buddha

I did not understand the philosophy of the hibutsu (secret Buddha) until I chanced upon one a few years ago.

To treat a Buddha statue as a hibutsu is an essentially Japanese phenomenon. The statue can be sometimes made open to the public (Gokaicho, or "unveiling of the statue"), which is, and has always been, a great time of festivities. The statues which are occasionally made open to the public (even if it is once in hundred years) are secret in the relative sense. Other statues are secret in the absolute sense, e.g. the famous secrete Buddha in Zenkoji temple, which became the site of the opening ceremonies for the 1998 Nagano Olympics.

The Buddha statue in Zenkoji is absolutely secret. Nobody has seen it, not even the powerful warlords like Oda Nobunaga (1534-1582) .

Even when one can worship a secret Buddha statue, one is not allowed to take a photograph or make a drawing most of the time. If you are lucky enough to glance upon one, the only thing you can do is to try to keep its image in your memory.

The secret Buddha experience makes one reflect on the onceness of life. Some things just happen and then pass by for ever. You cannot capture the essence and keep it for record. Life happens to you once and for all, never to return.

Hidden agenda.

When I was 15, I learned about the Game of Life invented by John Horton Conway.

The idea immediately fascinated me. I used to calculate generations of life game on a graph sheet while I was attending the school classes. From these early days, I was somebody who could not sit still just listening to what people said. I was wont to do this or that with my hand, while attending to the speech at the same time. For some enthusiastic months in my teens calculating generations of the Game of Life on a graph sheet was the thing to do.

Daniel Dennett discusses the Game of Life in his book "Freedom evolves". The point is that there could be a great degree of separation between the basic laws of temporal evolution and the phenomenology of what emerges as a result.

It has been shown that you can build a universal Turing machine in the world defined by the Game of Life algorithm. With proper mappings, complex life forms like ourselves could inhabit the universe of the Game of Life.

I am sure that the great distance between cause and effect exists as a hidden agenda in our own life. The intricate relation between the initial conditions and what result in the Game of Life teaches us a lesson. You should not be too serious about the supposed "objectives" in life. You are well advised not to base your actions entirely on explicit objectives. At least you must never take it too literally.

You know, nature can hide the true agenda in a very clever way, like in the Game of Life.



Initial conditions for the Glider Gun.

No knowledge, no imagination.

Albert Einstein famously said that "imagination is more important than knowledge". If I may add a humble something to the words of wisdom by a genius, knowledge sometimes helps one's imagination.

Actually, knowledge can serve as the secure base (as was described by John Bowby) for one's imagination. Knowing for a fact that the sun is burning hydrogen to make helium can set one to imagine a lot of things on an idle afternoon.

No knowledge, no imagination.

One could go quite far in one's imagination based on scanty information. When I was a kid, I used to imagine a lot, because in those days there was relatively little information about anything that you cared about.

With the advent of information age, there is a danger that imagination is suffocated. To avoid death by knowledge, one should have a strong pair of legs. By jumping from the springboard of knowledge, one can dive into the ocean of unlimited imagination.

That's the spirit.

I travel quite often on the Shinkansen. It is quite efficient, and is an indispensable infrastructure for the contemporary life of Japan. The safety record of Shinkansen is a marvel.

While relying quite heavily on the sophisticated railroad technologies, I sometimes miss the old days when traveling used to be more relaxed. The old spirit is depicted quite nicely in the wonderfully humorous essay "Idiot Train" by Hyakken Uchida. I made a blog entry . on this topic on December 29th, 2006.

I reproduce here my own translations of the Idiot Train posted on that day.

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I call this trip idiot train because people would say so behind my back anyway. Needless to say, I myself do not consider this undertaking to be that of an idiot. To be honest, you don't need a reason to go somewhere. I don't have any reason in particular to do so, but I have made up my mind to go to Osaka on the train.
As I do not have any particular reason to make this trip, it is ridiculous to travel second or third class. Traveling first class is always the best. At the age of 50, I made up my mind to always travel first class. In spite of my determination, I might be obliged to travel third class when I have no money and yet have some specific reason to make the trip. But I would never travel second class, which is irritatingly ambiguous. I don't like the appearances of people traveling in a second class coach.
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"I would like to go to Osaka."
"Ah, that is a good idea."
"So I came to see you on this matter."
"Is it an urgent business?"
"No. I don't have any particular reason, but I think I will go any way."
"Are you going to stay there for some time?"
"No. I think I will return immediately. Depending on the circumstances, I might even come back on the night train as soon as I arrive at Osaka."
"What do you mean depending on the circumstances?"
"Depending on how much travel money I have. If I have sufficient money, I will come back immediately. If I don't have enough, I might stay in Osaka for one night."
"I don't quite understand you."
"On the contrary, everything is clear. I have considered the matter with great care."
"Is that so?"
"Anyway, can you lend me some money?"
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That's the spirit.

Life is not very much fun if everything becomes efficient and logical. And the wise and sensitive will find that there is as much hidden logic and efficiency in Uchida's superficially idiosyncratic ways of seeing the world as in a report by a MBA.

Perhaps much more.

You must live

Soseki Natsume , in his beautiful collection of essays "Inside My Glass Doors", recalls a woman who visited him at his domicile to confide her woes. After narrating a painful history of her life, she asks Soseki whether she should live.

"I am afraid that the beautiful state of my mind would be marred as the time passes. I cannot bear the thought of a future when all memories would have been lost, and I continue to live on like an empty soul" she says.

The clock strikes eleven. Soseki says that he would walk her. It was a silent night, with the serene moon shining on the street. At the corner, the woman bows and says to Soseki "I am honored to be accompanied by you thus". Soseki answers that he is just a human being like her.

"Do you really think it is an honour?" Soseki asks. "Yes" the woman answers. "Then you must live". Soseki says to the woman.

Soseki walked her a little further, before returning home.

We don't know what happened to the woman after that evening. Soseki died a year after this essay was published.