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.