Could not have asked for better day for the game. T-Mobile sponsored the event for its employees and it was a good networking event. We were at the apigee of the stadium and the vantage point was amazing. Wish I had gotten a better parking spot but other than that could not have asked for a better day with SeattleMariners winning.
“One giant leap for humanity—today is the 47th anniversary of the first Moon landing. Let’s keep exploring!”
“An optimistic man once said, “Reach for the moon, because if you don’t make it you’ll land among the stars.” Well, 47 years ago today, Apollo 11 nailed it.
Mars, we’re looking at you now.”
Albert Einstein shook the foundations of +Physics with the introduction of his Special Theory of Relativity in 1905, and his General Theory of Relativity in 1915. The fun part is if you add gravity to “Special Theory of Relativity” you get “General Theory of Relativity”. The former states that “Space” and “Time” are intertwined and the latter explains that “Gravity” is a curvature in Space-Time caused by matter.
Just amazing!. The simple act of measuring the photon results in state of entangled atoms. Imagine what is happening when we (consciousness) perceives matter ! I ll place my bets on new worlds being born somewhere in this universe or other… The more we think we try to understand (perceive/measure) the bizarre it gets !
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?….
Machine Learning (ML) is set of few basic ideas. Unlike the traditional algorithm, ML has the non linear chops to model most phenomena we see around us. ML is about what we want, the results of our actions, how to achieve our goals and how the world will change. Its a paradigm shift.
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.
Well here is a mind boggling result. What do you think the sum of all natural number till infinity is? Counter intuitively it is -1/12 !!! Still unable to wrap my head around it… certainly its not the result of summing/adding up these numbers but has to be something else which we are pushing the carpet when referring to “infinities”. The proof however is real even though informal and I believe this was offered by Leonhard Euler. A more rigorous proof exists (offered by Reimann) when we expand the context and go outside the realm of real numbers and include complex numbers. Ramanujam also had a proof for this infinite series.
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.
I must say this is by far the exciting article I came across so far. Filled with hope and proof. It combined some of the most important fields of study, in one shot: Number Theory, Algebra, String Theory, Escher’s Tessellation, Ramanujam’s Mock Theta functions and Black holes (as structures in space time)
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
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.”