Amoeba inspired computing. Sounds fundamental where the nature provided some clues for a better computing paradigm that may offer several benefits, such as high efficiency, miniaturization, and low energy consumption. Although we all know that the traditional computing (Turing machine) is NOT any less powerful from NFAs except for the explosion in the search space, this discovery could eliminate the exponential search space leading to efficient algorithms for solving today’s “HARD” problems. What-if the NP class of problems are now solvable in polynomial time?….
There are different schools of thought in ML that help us answer these questions: How do we learn, is there a better way, can we trust what we learnt, what can we predict. The significant 5 schools/themes are:
1. Symbolists: inverse of deduction
underlying algorithm: inverse deduction
2. Connectionists: reverse engineer the brain
underlying algorithm: back propagation
3. Evolutionaries: simulate evolution on the computer
underlying algorithm: genetic programming
4. Bayesian: learning is a form of probabilistic inference. statistics
underlying algorithm: bayesian inference
5. Analogizers: extrapolating similarity judgement.
underlying algorithm: support vector machines
The master algorithm is a combination the key features of all these 5 algorithms that would derive all the knowledge in the world (a unified theory that makes sense of everything we know today) and solve the hardest problems that plague humankind today.
Master algorithm is to Machine Learning what the Standard Model is to Particle Physics.
It looks as if there is a lot of fluff in these infinite series and somehow when we remove the redundancy and noise, we get the gold nugget which is -1/12 in this case. The surprising part is that such series are a common occurrence in physics and quantum theories (string) and we get the right results (observable and measurable) by replacing such series with -1/12.
Similar to Schrodinger’s wave function which gives out the right results each and every time but could not explain why it is THE function and why it exists, similar to Ramanujam’s mock theta functions which he just wrote from his dreams but could not recollect how he arrived there, in the same manner the above substitution works but we are currently unable to explain in the realm of the theories (number theory) we are using to pose the question and answer it. May be it is the case that we are seeing only a limited view point of a larger dimensional space, a larger context. This is however consistent with the work of Godel where there exist true statements that cannot be proved within the system (cannot be both consistent and complete at the same time). One has to include external axiom(s) into the system to be able to prove the working result. Just like sqrt(-1) cannot be solved within the real number system, however has solutions within the complex number system.
But for now -1/12 appears to be the finite part of this infinite lump.
The article talks about a mysterious bridge between number theory and algebra (monster group) in the form of string theory. It was thrilling to read about the 24 structures (also the number of dimensions string theory deals with) mysterious correspondences between the dimensions of a symmetry group on the one hand, and the coefficients of a special j-function on the other — referred to as “moonshine”. The awe inspiring moment was when I learnt that the j-function belongs to a special class of functions whose graphs have repeating patterns similar to M. C. Escher’s tessellation of a disk with angels and devils and that the coefficients of this function are a form of the 17 mock theta functions discovered by Ramanujam.
That was about the proved result. The conjectural part is connection between moonshine and quantum gravity that could unite General theory of relativity and quantum mechanics. It further goes to say that the corresponding String theory model could be constructed such that 194 categories of elements in the monster group correspond to 194 types of black holes. I guess the other models explain the parallel universes out there….
Yes still trying to sync in. The idea is so far fetched that the scientists themselves called it “Moonshine” as discussed in the article.
“Math is all about building bridges where on one side you see more clearly than on the other” –Duncan
Ramanujam’s mock theta functions
I believe when the black hole information paradox problem when viewed from this vantage point offers a fresh perspective, that the laws pf physics might actually be upheld by computational complexity — which is defined entirely in terms of information. The article also talks about how this might help understand quantum entanglement.
Scott Aaronson puts it, “the black hole’s interior is protected by an armour of computational complexity” in his book Quantum Computing: http://www.amazon.com/Quantum-Computing-since-Democritus-Aaronson/dp/0521199565
I could not put this book down once I started reading. Highly recommended for a reader who finds it fun to put different pieces together and is not afraid of the abstract. This book is something I always wished to have, one place with a logical string of reasoning end to end w/o the technical rigor (which can be filled in as needed)
It is exciting to see computational complexity as fundamental as thermodynamics (entropy) acting as a tool to help solve problems in multiple disciplines. I had like to see how the observer plays a role in this equation as at the end of the day, it is us interpreting the event or computing the complexity via our mind through our senses.
“I believe that our species will not last long. It does not seem to be made of the stuff that has allowed the turtle, for example to continue to exist more or less unchanged for hundreds of millions of years; for hundreds of times longer, that is, than we have even been in existence. We belong to a short-lived genus of species. All of our cousins are already extinct. What’s more, we do damage. There are frontiers where we are learning, and our desire for knowledge burns. They are in the most minute reaches of the fabric of space, at the origins of the cosmos, in the nature of time, in the phenomenon of black holes, and in the workings of our own thought processes. Here, on the edge of what we know, in contact with the ocean of the unknown, shines the mystery and the beauty of the world. And it’s breathtaking.”
For anything traveling at or near the speed of light, time slows down, photon traveling at the speed of time imply that there is no time that elapses for them. Lets just think about that for a min… For us (conscious human beings) we see light traveling for eons before it reaches our eye but for the photon, this time is zero… it is absorbed the moment it is emitted… Now combined with the below result, a photon converts into matter giving it (electron and positron) mass and time. A timeless particle gives rise to one that now has the concept of time because electrons do not travel at the speed of photons.
On this date in 1887 mathematician Srinivasa Ramanujan was born in Erode, Tamil Nadu, India. Ramanujan had nearly no formal training in mathematics and was largely self-taught until he was a teenager. As an adult his work quickly gained attention from other Indian mathematicians who spread his work to Europe. He independently proved several theorems in a number of mathematical subjects and also produced many new theorems. He moved to England in 1914 and continued to publish on a wide range of topics and much of his work has been widely influential for his unique approaches to even already established proofs.
Excellent point of view backed with data. I believe its a way of life. To inculcate this kind of lifestyle and values organically, would take a generation to live through it. The other possibility is to rebuild in an entirely new way after a calamity (as you indicated in the article). I personally like this way of life and was excited when you said “demanded that leadership change every few months” to keep the creativity and innovation intact.
Brace for the news this THUR (2/11/16). Whatever the outcome, it is set to be a milestone on the cosmic calendar. It has been 100 years since Einstein published his General Theory of Relativity that married Gravity to Space-Time. LIGO has measured the last of the predictions made by this theory, ie, the presence of ripples in space-time caused by rapidly spinning objects like pulsars, 2 star systems etc.. Detecting a gravitational wave is like noticing the Milky Way — which is about 100,000 light-years wide — has stretched or shrunk by the width of a pencil eraser.