Some of the problems that mathematicians attempt to solve can be intellectually very challenging, and also stimulating – maybe even fun, but could leave you wondering what, if any, practical use they have in real life. I mean, why did anyone even bother to create this problem?
“As Jean-Pierre Serre reportedly quipped to his mathematician colleague Raoul Bott, “While the other sciences search for the rules that God has chosen for this Universe, we mathematicians search for the rules that even God has to obey.””
Freeman Dyson is one of the mathematicians about whom I know very little. I have heard the name many times, but have never really bothered to follow up in the past. The video in the article, and the article itself, were very informative. A great mind! He died in February at the age of 96.
Very interesting! I had not heard of the Deccan Traps before. (For future reference, the dinosaurs disappeared off the earth about 66 million years ago.)
Our departure as a species may take place in other ways… 😉
Even if these are just theories at this point, these are fascinating concepts. Imagine the possibility that all of the natural processes, of different kinds, of different orders of scale and magnitude, can be defined by similar sets of simple rules at a macro level. Consider the concept of “The Arrow of Time”, and how it fits in with the fundamental structure of our universe.
This is fascinating stuff! There is synchronization happening naturally everywhere, and a lot of it is unexpected and non-intuitive, at least for me. And there seem to be mathematical ways to characterize these synchronization processes. There could be ways to harness the power of synchronization.
Caution that the article is a long read.
“Empirical dynamic modeling, Sugihara said, can reveal hidden causal relationships that lurk in the complex systems that abound in nature.”
This approach for prediction throws out the equations, and uses a different kind of approach to find order in chaotic systems. The process includes the gathering of enough historical data to make more reliable predictions. To me, it sounds similar in some ways to some of the processes that feed into the field of AI, or Artificial Intelligence.
(Picture from Quanta Magazine. Credit – Vaishakh Manohar.)
I first learned about how ants work in a cooperative manner in a book that my daughter had bought me for Christmas. The book was all about trails. (She had figured out the perfect book for my interests!) There is a chapter in this book about how trails historically came into being, and how these have, over time, led to our modern day system of roads, railroad tracks, and other connections for human travel.
Trails have existed for ages. The concept is not the creation of humans. Animals of different kinds, using different skills, and for different purposes, have created trails. There was, and still is, no real planning involved (the way humans would define it) in the creation of animal trails. It is all tied to their inbuilt instinct to survive and exist.
Ants have been creating trails for a long time. The notable thing about the behavior of ants is that in spite of the fact that they do not have any significant level of individual intelligence, they show a great deal of collective or cooperative intelligence that lets them be effective in complex tasks. (They do not even depend on the presence of an occasional “smart” ant that can serve as a leader.) The book describes how their processes work for creating very efficient trails. (There is even a kind of ant that is blind that is still very effective at this.) Humans are now trying to understand if any of these processes are useful for our own existence.
Anyway, the article I have linked to is fascinating. Make sure to watch the videos!
This is interesting! The article indicates that one of the big issues with quantum computing is the approach for handling errors that are inherent in the process. I wonder if there is some kind of Information Theory based limitation that in some way parallels what happens in the area of digital communications. Digital communication rates over noisy channels are subject to Shannon’s Limit, but it takes a lot of sophisticated coding for error correction, and the associated processing power, to get anywhere close to this limit. Such sophisticated techniques have become practical only recently, and have been applied to the area of satellite data communications only in recent years in order to enable higher levels of modulation that can increase the resulting data rates supported, but only if the error correction techniques can handle it. (As you get to higher levels of modulation, you are tending more towards an analog means of transmission for the digital data, which feeds into my argument that we human beings are force-fitting digital into an analog world, but that is a subject for a different discussion.)
Might it be that there are some fundamental concepts that are similar and hold true in both digital communications and quantum computing technology? How fast is it theoretically possible to go with quantum computing, and is the limitation due to quantum constraints, or noise, or some combination? Can we make digital computing approximate an analog process in some way? Is mathematics an analog process? Inquiring minds want to know!