On November 3, 2012, Dr. Shun-ichi Amari, a RIKEN Brain Science Institute Senior Team Leader, Senior Advisor and former Director, was named a Person of Cultural Merit by the Ministry of Education, Culture, Sports, Science and Technology (MEXT). Dr. Amari was recognized for founding the field of information geometry and for his significant contributions towards establishing the mathematical theory of neural networks. Others selected this year include the animated movie director Hayao Miyazaki, kabuki actor Matsumoto Koshiro, poet and novelist Takashi Tsujii, and historian Naohiro Asao. This annual distinction was established in 1951, to honor people who’ve made exceptional contributions to the advancement of Japanese culture in the arts and academia, and rewards the recipients with an annual pension. Candidates are nominated by a committee of MEXT, approved by the MEXT minister and the Cabinet, and announced on November 3, the Day of Culture.

Dr. Amari, how were notified about having been selected to receive this distinction?
The Ministry of Education called me, maybe one month in advance and they told me that that “you are a candidate”. I thought that there were many candidates and that they were starting the selection procedure. But what they meant was that they had decided. Because it is a formal procedure they had said “you’re a candidate” but they had already decided when they called me.

How did you feel about being selected for this distinction?
Oh, it was a really big surprise. I never dreamed of such an honor.

Can you tell me about the award ceremony?
It was on November 5th and was in two parts. The first part was being honored by the Ministry of Education, Culture, Sports, Science and Technology (MEXT). The minister—Makiko Tanaka—gave us a certificate. After the certificate ceremony the ministry provided a bus to take the group to the imperial palace where we had dinner together with the Emperor and his family.

Was it your first time to visit the imperial palace?
No, it was the third time. About 20 years ago I received the Japan Academy Award. At that time, the Emperor also invited the awardees to lunch. The second time, I was the chair of the screening committee for The Japan Prize. It’s a big prize and the Emperor attended the award ceremony. Before that we needed to explain the work of the laureate to him. I explained chaos dynamics and fractals — mathematical concepts — for about 30 minutes, giving a personal lecture to the Emperor. He showed a lot of curiosity, asking me questions, and so the conversation went very well.

Were you able to talk to the Emperor this time?
Yes, indeed. Actually it was a joint party for those who were named Persons of Cultural Merit, that is 15 people and also for the 5 people awarded the Order of Culture. There were five tables prepared for the 20 of us. We were served one dish at a time and then the Emperor rotated tables so that he joined each one. In that way, all of us could talk personally to the Emperor and his wife.

Can you explain the basics of your work?
My work is in the field of mathematical neuroscience. The brain is a very complicated system that emerged from the long history of evolution, but it works surprisingly well. Why? The brain processes information so well that there must be some principles that guide the success of information processing by neurons. What are the principles? It is very complicated to figure out. Even in physics, identifying basic principles is complicated, especially in the everyday world. But for example Newton could observe celestial bodies and find equations to explain the principles of mechanics. In physics you can find the idealistic situation where you can observe principles and apply them to real life. But figuring out principles from observations of real life is complicated. In the case of the brain I believe we have some very good explanations of principles but we cannot observe a principle itself in a realistic situation. In physics observations can be made in an idealistic situation, such as with celestial bodies, or very low temperature. However, if the brain were put at low temperature or at high speed, it would die.
Therefore, by using observations of the real brain from molecular biology, electrophysiology, etc, we need to extract some principles and explain behavior in a mathematical way.

Can brain activity be explained by simple principles?
There is no single principle but a large number of principles that govern brain activity; from the microscopic level to systems level. But we need a way to think about it. One of the ideas is to construct a very simple idealistic model of neural networks. It’s different from real neurons, different from the real brain, but the behavior of those simple model systems may be very useful to understand why the brain works so well. If we understand something about the brain then we need to think about how those abstract principles are realized in the context of the real brain. This is one of the top-down methods. Most researchers use a bottom-up approach; just observe reality. It’s important, but also we need to do research from a top-down abstract level. This is the role of mathematical neuroscience.

What is information geometry?
It is one field of applied mathematics. I provided a new method for using geometry in combination with information science. Information geometry deals with a set of probability distributions. The brain works under some stochastic uncertainty so in order to understand its behavior under stochastic fluctuations we need to use probability theory. Information geometry is one method to do that. If there are two or more probability distributions we can use geometry to understand the relationship between them.

How can mathematics contribute to neuroscience?
Mathematical neuroscience uses abstract models that are very simple in a sense. However, if we can derive some basic principles from these models they can be used to guide the direction of research. Computational neuroscience, which is less abstract, uses the result of a mathematical model and tries to connect it to real phenomena taking place in the brain. Then, the model can be replaced to make it more realistic. It is a bridge to connect the real phenomena and the abstract mathematical model.

How strong is that bridge in neuroscience?
It is becoming stronger and stronger. When I started my work more than 40 years ago at a very abstract level the bridge was very weak, but now we have a huge amount of data and researchers are thinking about how to summarize the data and extract basic principles from it. They need more abstract principles. So experimental scientists are asking for help from computational neuroscientists and they in turn want to be connected to more realistic data to improve their thinking and make sure they are proceeding in the right direction. When BSI was established about 15 years ago it was a big challenge to include computational, molecular, and systems neuroscience researchers, etc in one institute. They were very separated, but we wanted to integrate different types of researchers. I think it has been successful.

What trends will define the future of neuroscience?
On the experimental side, I think the challenge is to integrate what we know about the brain from the very focused microscopic molecular level to the systems level or the individual level and even up to the level of basic principles postulated by abstract mathematics. Beyond that, we can think about consciousness and humanity. We will need to integrate all of those things.

What are you currently working on?
I am still continuing research in mathematical neuroscience. There are a lot of problems which I have thought about very deeply, but which I couldn’t solve. Now is the time to think about those old problems.

What advice do you have for young researchers?
The important thing is to find one’s own way to do research, otherwise if one is following already established people, they cannot discover new things. It’s not easy to find what is one’s own way, but they need to do something that can only be done by oneself.

Dr. Amari reflects on his work over the course five-decades “Dreaming of mathematical neuroscience for half a century” in the Neural Networks 25th Anniversary commemorative issue.

By Alexandra Terashima
© RIKEN BSI 2013
Image credits A. Terashima