Lifeboat Foundation

Abstract: In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic component, while respecting the conservation law. According to the dynamics thus obtained, referred to as the energy-based stochastic Schrodinger equation, an arbitrary initial state collapses spontaneously to one of the energy eigenstates, thus describing the phenomenon of quantum state reduction. In this article, two such models are investigated: one that achieves state reduction in infinite time, and the other in finite time. The properties of the associated energy expectation process and the energy variance process are worked out in detail. By use of a novel application of a nonlinear filtering method, closed-form solutions—algebraic in character and involving no integration—are obtained for both these models. In each case, the solution is expressed in terms of a random variable representing the terminal energy of the system, and an independent noise process. With these solutions at hand it is possible to simulate explicitly the dynamics of the quantum states of complicated physical systems.

From: Dorje C. Brody [view email]

[v1] Mon, 29 Aug 2005 13:22:36 UTC (43 KB)

E=m c

Albert Einstein proposed the most famous formula in physics in a 1905 paper on Special Relativity titled Does the inertia of an object depend upon its energy content?

Essentially, the equation says that mass and energy are intimately related. Atom bombs and nuclear reactors are practical examples of the formula working in one direction, turning matter into energy.

Continue reading “‘Einstein Was Right: You Can Turn Energy Into Matter’” »

An algorithm developed by Brown University computer scientists enables robots to put pen to paper, writing words using stroke patterns similar to human handwriting. It’s a step, the researchers say, toward robots that are able to communicate more fluently with human co-workers and collaborators.

“Just by looking at a target image of a word or sketch, the robot can reproduce each stroke as one continuous action,” said Atsunobu Kotani, an undergraduate student at Brown who led the algorithm’s development. “That makes it hard for people to distinguish if it was written by the robot or actually written by a human.”

Continue reading “Researchers teach robots handwriting and drawing” »

Watching the algorithm work is like perusing a stock photo catalog from hell.

The National Academy of Sciences is always an impressive place, with visitors greeted out front by a more-then-life-sized bronze statue of Albert Einstein. In keeping with the spirit of the academy, Einstein is not depicted standing with his eyes looking upward to some fantastic future. Rather, he is seated, looking slightly downward in thought, holding papers on which his equations are written—doing the hard work of trying to make that fantastic future happen.

On April 9^th, the academy hosted an event, sponsored by the Kavli Foundation and produced by Scientific American, that honored 10 individuals who have also done the hard work of making the world better through their scientific research. The 10 were all winners of Nobel Prizes, Kavli Prizes or both. And for one hour, they took to the stage in the Fred Kavli Auditorium within the academy building to field questions by Scientific American Editor-In-Chief Mariette DiChristina. This video represents a few of the highlights of that panel discussion.

A mathematician from the University of Bristol has found a solution to part of a 64-year old mathematical problem – expressing the number 33 as the sum of three cubes.

Since the 1950s, mathematicians have wondered if all whole numbers could be expressed as the sum of three cubes; whether the equation k = x³+ y³+ z³ always has a solution.

Continue reading “Bristol mathematician cracks Diophantine puzzle” »

A prime number theory equation by mathematics professor emeritus Carl Pomerance turned up on The Big Bang Theory, where it was scrawled on a white board in the background of the hit sitcom about a group of friends and roommates who are scientists, many of them physicists at the California Institute of Technology.

In a recent paper, “Proof of the Sheldon Conjecture,” Pomerance, the John G. Kemeny Parents Professor of Mathematics Emeritus, does the math on a claim by fictional quantum physicist Sheldon Cooper that 73 is “the best number” because of several unique properties. Pomerance’s proof shows that 73 is indeed unique.

The Big Bang Theory is known for dressing the set with “Easter eggs” to delight the self-avowed science nerds in the audience. When UCLA physics professor David Saltzberg, technical consultant for The Big Bang Theory, heard about the Sheldon proof, he contacted Pomerance to ask if they could use it in the show, which was broadcast April 18.

Continue reading “‘The Big Bang Theory’ takes math notes from Carl Pomerance” »

Decades after Isaac Asimov first wrote his laws for robots, their ever-expanding role in our lives requires a radical new set of rules, legal and AI expert Frank Pasquale warned on Thursday.

The world has changed since sci-fi author Asimov in 1942 wrote his three rules for robots, including that they should never harm humans, and today’s omnipresent computers and algorithms demand up-to-date measures.

According to Pasquale, author of “The Black Box Society: The Secret Algorithms Behind Money and Information”, four new legally-inspired rules should be applied to robots and AI in our daily lives.

Continue reading “New laws of robotics needed to tackle AI: expert” »

A radically new view articulated now by a number of digital philosophers is that consciousness, quantum computational and non-local in nature, is resolutely computational, and yet, has some “non-computable” properties. Consider this: English language has 26 letters and about 1 million words, so how many books could be possibly written in English? If you are to build a hypothetical computer containing all mass and energy of our Universe and ask it this question, the ultimate computer wouldn’t be able to compute the exact number of all possible combinations of words into meaningful story-lines in billions of years! Another example of non-computability of combinatorics: if you are to be born and live your own life again and again in our Quantum Multiverse, you could live googolplex (10¹⁰⁰) lives, but they all would be somewhat different — some of them drastically different from the life you’re living right now, some only slightly — never quite the same, and timeline-indeterminate.

Another kind of non-computability is akin to fuzzy logic but based on pattern recognition. Deeper understanding refers to a situation when a conscious agent gets to perceive numerous patterns in complex environments and analyze that complexity from the multitude of perspectives. That is beautifully encapsulated by Isaiah Berlin’s quote: “To understand is to perceive patterns.” The ability to recognize patterns in chaos is not straightforwardly algorithmic but rather meta-algorithmic and yet, I’d argue, deeply computational. The types of non-computability that I just described may somehow relate to the non-computable element of quantum consciousness to which Penrose refers in his work.

Continue reading “The Thesis on Consciousness and Experiential Realism: Digital Philosophy Perspective” »