(I presented a modified version of this lecture-recital to a group of fellow amateur pianists in Long Beach, California, United States, in February 2014. The video links are integral to the programme and it is suggested that they be watched in sequence while reading the lecture.)
I would like to present to you a different kind of performance today; not classical music, but a lecture followed by a few short traditional pieces.
While studying towards my PhD. in the United States for the past five years, I’ve devoted a significant portion of my spare time into music, particularly of the piano, and reading books on history and culture. Given my interests, and having stayed in a foreign country half way across the globe for nearly a fifth of my life, naturally, I was fascinated to know more about the history and culture of this land.
Three years ago, I chanced upon a book in a Mumbai airport store, The Loss of El Dorado by V.S. Naipaul. V.S. Naipaul, as some of you may know, is the 2001 Nobel Laureate in Literature. He was born and grew up in Trinidad, the grandson of servants to the British of East Indian origin during the time of the great colonies. Naipaul wrote several books on the history and culture of the Caribbean, and The Loss of El Dorado represents one of his finest works in this regard.
A paragraph in the foreword caught my attention:
“It was hard to feel any wonder at the fact that, more than four hundred years after Columbus, there were Indians in a part of the world he had called the Indies; and that the people he had called Indians had vanished. They had left no monuments; they were not missed.”
It was hard to feel any wonder … they were not missed. But why should there be wonder, contemplation and melancholic nostalgia of the past? In Bihari Trinidad, Naipaul was of, and observed, the first Indians of the new world in an India they had imagined. The land was not reluctant. There was no destruction and regeneration; it was not as if there was a past to be missed, but rather no such thing as a past. It is after all, a new world, and a new world was born there everyday.
As I proceeded to read The Loss of El Dorado, I was offered several philosophical viewpoints by the book. But Naipaul’s quote of the foreword, continued to strongly resonate. There was a certain deep fascination to the fact that when Columbus landed in Haiti and proclaimed it to be his India, he created a chain of events that would eventually bring Indians, including me, to the land of the Indies. Most surprisingly, and in some ways amusingly, living half way across the globe, the European notion, 500 years ago, that any land found in the Western quest of the Spanish was India, provides solace to the mind, substituting home sickness with home coming.
Are we strangers? Is this fascination just a consequence of cartographic limitations and anthropological errors of the European conquistadors? Rationally, it is easy to dismiss it so, but when we have a choice, we can transform it into the more human sensations of brotherhood. I would like to honour this feeling of cultural oneness today, through the vehicle of music, particularly the music of the Indians. And what better way to do it, but using the piano!
Pre-Columbian music had been adapted to European instruments ever since the Old and the New Worlds met. A famous example is Symphony No. 9 in E Minor (New World Symphony) of Antonin Dvořák, which he wrote on his visit to the plains. On December 15th, 1893, he writes in the New York Herald,
“I have simply written original themes embodying the peculiarities of the Indian music, and, using these themes as subjects, have developed them with all the resources of modern rhythms, counterpoint, and orchestral colour; the third movement scherzo was suggested by the scene at the feast in Hiawatha where the Indians dance.” [cite: Wikipedia]
In the same year, he said in a newspaper interview,
“I found that the music of the Negroes and of the Indians was practically identical”, and that “the music of the two races bore a remarkable similarity to the music of Scotland.” [cite: Wikipedia]
He also noted,
“I am convinced that the future music of this country must be founded on what are called Negro melodies. These can be the foundation of a serious and original school of composition, to be developed in the United States. These beautiful and varied themes are the product of the soil. They are the folk songs of America and your composers must turn to them.” [cite: Wikipedia]
For the most part, Dvořák’s predictions have come true. Since the birth of the popular era, the musical world has witnessed and cherished ragtime, rockabilly, rock and roll, jazz, blues, country, hip hop, mariachi, tango, salsa, samba, reggae; an endless list of musical genres that have their deepest roots in the West African and Aboriginal traditions of America.
Today, I have prepared to play a set of tunes, written by a little known musicologist, Gail Smith, whose book Native American Songs for Piano Solo I found and bought on Amazon. I have chosen three short pieces, originally written for the drum, the human voice and the flute, representing the three main instruments of the Indians.
The first piece, representing the drum is the Cherokee Deer Hunting Song:
The next piece is a Cheyenne lullaby:
And the final piece is a flute call by the Winnebago:
To end, let me quote from T.S. Elliot’s Little Gidding:
“We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.”
The fascinating beings that we are, we are often obliged to look back at history, and relive it differently in the future.
(Update: Results presented in this article have been used in the largest database of greetings in the various languages of the world. Please see Jennifer Runner’s page for the acknowledgements. Specifically, I contributed to Piscataway and Timucua translations.)
As a part of my interests in languages, this is the outcome of a small research project. Below is a list of indigenous languages and the phrase “hello” in them, that belonged to Native American peoples that occupied areas in and around the present 50 most populous cities in the United States.
The motivation to do this study arises from a simple, but profound statistic:
Of the 175 Native languages that survived the 20th century, only 55 are spoken by 10 individuals or more. This discounts the fact that at the time of European contact, the number of languages spoken in California alone was 80 of which none remain in the present day. Navajo is the only Native language with more than 100,000 speakers [cite: Wade Davis, Light at the Edge of the World, Feb. 2007].
The choice of the 50 most populous cities will hardly cover the vast reaches of North America that the Natives once used to occupy. However, due to the technology and consumerism driven diaspora of the United States, 79% of the current population is urban and is likely to stay or visit in and around these cities [cite: U.S. Department of Transportation, Census 2000 Population Statistics, May 2011].
Furthermore, the U.S. Immigration and Nationality Act of 1965, made a critical and progressive decision to not limit immigration based on Western European ethnicity, but rather based primarily on the immigrant skills [cite: Wikipedia]. If immigrant skills are an incentive, it is highly probable that most post-1965 modern immigrants live in and around urban incorporated areas, with a large population. For example, as a part of my visit to the United States to pursue my PhD., I have primarily stayed in Los Angeles, the second-most populous city in the United States.
Given these factors, I am optimistic that anyone who reads this list and who currently is in, or wants to visit the United States, will most likely immediately know how to say “Hello” in a language which ran through local peoples’ bloods 500 years ago as much as English for instance, run’s in ours today. Of these individuals, some may be inspired to study these languages further, or be inspired to pursue learning their own native language, at which point, the purpose of this article can be considered fulfilled.
This list was compiled in a very simple manner, following mostly three steps:
- Obtain a List of U.S. cities by population: Wikipedia is an excellent source.
- Read the indigenous history of the place and obtain the name of the languages used in the area from Wikipedia or other sources.
- Use Jennifer Runner’s excellent compilation or other sources as a cross-reference and to obtain phrases.
Using only free resources available on the internet and electronic academic material available for students from the University of Southern California Libraries, details for each city in the list took on average, about 15 minutes to compile. I have tried to make the list as accurate as possible, however, I will be grateful for any mistakes pointed out.
Language loss is one of the greatest threats to the progress of human knowledge. When a language no longer has speakers, a unique wealth of information, inferences and intuitions passed through ages are lost; a flame in the human spirit is extinguished. Languages evolve with time giving rise to new ones, but in the present world, due to the pressures of political power, and the assimilation of peoples with few conscious choices, they are becoming extinct with little chance to naturally develop and flourish.
There are many ways to know about the world’s languages; a simple search on the internet can tell a lot. For example, a project that is particularly interesting and well organized is the Endangered Languages Project.
(No copyrights; please cite, copy and distribute as much as required. Please leave a comment with contact information if you need a text or spreadsheet version.)
(I wrote this article on request from my friend Ved Deshpande, for the Mathematics Department, IIT Kharagpur, newsletter, Xponent, as a guest article. There may be some technical mistakes in this article, however, this is how I understood compressed sensing.)
What we know:
In the last 5 years, the discipline of Applied Mathematics, particularly in Communications and Signal Processing has seen a spectacular shift in paradigm. In Sping 2004, David Donoho’s (Stanford) former PhD. student, Emmanuel Candes (presently at CalTech.) first discussed the idea of compressed sensing. From these meetings germinated a novel and phenomenal method of sensing and estimating signals, which Donoho developed. Simultaneously, with the help of post doctoral student Justin Romberg (now at GeorgiaTech.) and Field’s Medalist Terence Tao (UCLA), Candes also nurtured the same idea, which developed into a unique set of papers on compressed sensing. This article is an attempt to expose the beauty of their findings, which often go unnoticed in mathematics and applied sciences.
Consider a digital signal where i.e., the signal has restricted length. In the 1930’s, work done by Shannon, Whittaker and Nyquist suggests that the above signal can be reconstructed with zero-error, if it had at least samples to begin with. This is equivalent to saying, that if can be represented as a unique linear combination of unique functions (often called a basis), then a matrix of dimension has to sample the signal for perfectly obtaining the original basis. Since the basis in consideration and the signal are related by a unique linear combination, if the basis is obtained perfectly, can simply be obtained by the relation where is the basis of length and is a unique, invertible matrix called the transform matrix. For example, some of us may be familiar with the Fourier basis, where is full of terms, where and are the matrix indices.
The Paradigm Shift:
Let us think of the entire problem in a different way. Let’s say we want to reproduce the signal most of the times. This means, if we try to reconstruct the signal infinite times in infinite different experiments, we will converge to a probability of reconstruction, . If we can make high enough, we can think of posing relaxations on other constraints in the problem. What will be truly interesting is we could manage to get away with sampling the signal with a matrix of dimension where is allowed to be lesser than . A bold statement saying that it is indeed possible, in the form of a big blow to the age old theory of Shannon, was declared by Candes and Donoho in their groundbreaking papers in 2004. On the downside however, this works for a specific set of signals only known as sparse signals. In a nutshell, Candes and Donoho said that if the basis is sparse, i.e. it contains very few non-zero elements, then it is possible to sample the signal with a matrix of size often called a matrix of transformation to a lesser rank, and still manage to get back .
Suppose, the basis is i.e. out of the elements of the basis are non-zero. Now we use a matrix for sampling. Thus the resulting signal is of length which can be represented as . This signal has been proven to be enough to get back . Amazingly, Candes and Donoho also showed that as long as and are highly incoherent (a mathematical formulation of how unrelated the matrices are), can be completely random! Further, can be as less as and the probability of failure is about . If and it implies which is way lesser than that predicted by Shannon! At first it may seem that being a vector means that to obtain we actually have more variables than equations (if and are assumed known). However, this problem is cleverly overcome by Candes and Donoho using the concepts of linear programming and convex optimization often used in electrical engineering and operations research.
Compressed sensing (aptly termed, as we compress the way we measure or “sense” as mentioned above) has far reaching implications in the applied sciences and engineering fields. One application is in underwater communications. In underwater communication channels, signals are usually distorted by a channel response which can be modeled as a sparse signal, very similar to the basis described above. The transmitted signal convolves as a matrix similar to , and the signal is then available to a receiver. Now that we know that the channel response is sparse, we can measure the signal to obtain a signal that can perfectly give us back the channel response! This channel response comes in very handy in finally removing the Gaussian noise from the data. Thus, in effect, we are measuring a signal as if nearly nothing has been transmitted and every required information is available!
The DSP Lab at Rice University have archived and update all the latest literature on compressed sensing. Visit them at: http://www.dsp.ece.rice.edu/cs/.