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.
-----------
------------
"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?"
------------

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.

Basic income

Everybody has a right to live, pursue happiness, and enjoy the small things in life. Of course, when the chips are down, and we are at the mercy of destiny, we may be not able to live. The problem with humanity is, the safety network is sometimes too loose and / or negligent when the society itself is well and thriving.

Thus I am for the introduction of a basic income. People might say that it is counterintuitive or morally suspect to be provided with an income when one is not working. Some might claim that its introduction might seriously undermine the work ethics. I rather think that the basic income can be incorporated into the economical system in a step conceptually similar to the renormalization in quantum field theory.