Lifeboat Foundation: Safeguarding Humanity
Toggle light / dark theme

Blog

Category: mathematics – Page 45

As Shor looked for applications for his quantum period-finding algorithm, he rediscovered a previously known but obscure mathematical theorem: For every number, there exists a periodic function whose periods are related to the number’s prime factors. So if there’s a number you want to factor, you can compute the corresponding function and then solve the problem using period finding — “exactly what quantum computers are so good at,” Regev said.

On a classical computer, this would be an agonizingly slow way to factor a large number — slower even than trying every possible factor. But Shor’s method speeds up the process exponentially, making period finding an ideal way to construct a fast quantum factoring algorithm.

Shor’s algorithm was one of a few key early results that transformed quantum computing from an obscure subfield of theoretical computer science to the juggernaut it is today. But putting the algorithm into practice is a daunting task, because quantum computers are notoriously susceptible to errors: In addition to the qubits required to perform their computations, they need many others doing extra work to keep them from failing. A recent paper by Ekerå and the Google researcher Craig Gidney estimates that using Shor’s algorithm to factor a security-standard 2,048-bit number (about 600 digits long) would require a quantum computer with 20 million qubits. Today’s state-of-the-art machines have at most a few hundred.

Read more | >

The new book Minding the Brain from Discovery Institute Press is an anthology of 25 renowned philosophers, scientists, and mathematicians who seek to address that question. Materialism shouldn’t be the only option for how we think about ourselves or the universe at large. Contributor Angus Menuge, a philosopher from Concordia University Wisconsin, writes.

Neuroscience in particular has implicitly dualist commitments, because the correlation of brain states with mental states would be a waste of time if we did not have independent evidence that these mental states existed. It would make no sense, for example, to investigate the neural correlates of pain if we did not have independent evidence of the existence of pain from the subjective experience of what it is like to be in pain. This evidence, though, is not scientific evidence: it depends on introspection (the self becomes aware of its own thoughts and experiences), which again assumes the existence of mental subjects. Further, Richard Swinburne has argued that scientific attempts to show that mental states are epiphenomenal are self-refuting, since they require that mental states reliably cause our reports of being in those states. The idea, therefore, that science has somehow shown the irrelevance of the mind to explaining behavior is seriously confused.

The AI optimists can’t get away from the problem of consciousness. Nor can they ignore the unique capacity of human beings to reflect back on themselves and ask questions that are peripheral to their survival needs. Functions like that can’t be defined algorithmically or by a materialistic conception of the human person. To counter the idea that computers can be conscious, we must cultivate an understanding of what it means to be human. Then maybe all the technology humans create will find a more modest, realistic place in our lives.

Read more | >

This week, researchers proved empirically that life isn’t fair. Also, you’ll notice that, in a superhuman display of restraint, I managed to write a paragraph about the simulated universe hypothesis without once referencing “The Matrix.” (Except for this reference.)

Oh, so a European research team has proven that flipped coins aren’t actually fair? Buddy, life isn’t fair! Do you think the world owes you two equally probable outcomes as established by an axiomatic mathematical formalization? When I was a kid, we didn’t even have coins! We had to roll dice! It took 10 minutes to start a football game! Oh, so a coin is very slightly more likely to land on the same face as its initial position? Quit crying! It’s only a meaningful bias if you flip a coin multiple times!

Applying a recently discovered physical law, a physicist at the University of Portsmouth has contributed to the discussion about whether or not the universe is a simulation. The simulated universe hypothesis proposes that the universe is actually a simulation running on a vastly complex computing substrate and we’re therefore all just NPCs, walking through our animation loops and saying, “Hail, summoner! Conjure me up a warm bed!” and “Do you get to the Cloud District often?”

Read more | >

Consider the potential problems. Number one would be that any potential aliens we encounter won’t be speaking a human language. Number two would be the lack of knowledge about the aliens’ culture or sociology — even if we could translate, we might not understand what relevance it has to their cultural touchstones.

Eamonn Kerins, an astrophysicist from the Jodrell Bank Centre for Astrophysics at the University of Manchester in the U.K., thinks that the aliens themselves might recognize these limitations and opt to do some of the heavy lifting for us by making their message as simple as possible.

“One might hope that aliens who want to establish contact might be attempting to make their signal as universally understandable as possible,” said Kerins in a Zoom interview. “Maybe it’s something as basic as a mathematical sequence, and already that conveys the one message that perhaps they hoped to send in the first place, which is that we’re here, you’re not alone.”

Read more | >

Arithmetic, rooted in our biological perception, is a natural consequence of how we perceive and organize the world around us. This connection between perception and mathematical truths suggests that mathematics is both a uniquely human invention and a universal discovery, highlighting a profound unity between the mind and the physical universe…

Read more | >

Prof. Donald Hoffman talks to Essentia Foundation’s Hans Busstra about his theory of conscious agents, according to which space and time are cognitive constructs in consciousness, not an objective scaffolding of the world outside. The interview also touches on Prof. Hoffman’s personal history and life, bringing the warmth of his humanity to the academic rigor of his theories.

00:00 Intro: Beyond the spacetime headset.
03:32 About Donalds personal background.
07:35 On the importance of mathematics.
13:22 Quantum theory and spacetime.
19:24 Why exactly is spacetime ‘doomed’?
24:34 Did physics ‘encounter’ consciousness in quantum theory?
32:49 On heavy vs light metaphysical claims.
37:36 How is your theory affecting your personal life?
42:17 Is The Matrix a good metaphor?
46:38 How can the space time interface affect consciousness?
53:09 What makes you say that if spacetime is not fundamental, consciousness must be fundamental?
55:44 Physicalism fails to give an accurate model of consciousness… 1:00:24 How can we put the spacetime headset off? 05:39 Beyond the spacetime fantasies of Christopher Nolan and the Matrix… 1:09:27 The ontology of conscious agents 1:15:05 Are meditation and psychedelics ‘hacks’ in the interface? 1:21:41 Should we revalue religious and mystic literature? 1:29:54 Could idealism as a worldview help us better solve the challenges humanity faces? 1:34:23 The role of mathematics in bringing together science and spirituality Copyright © 2022 by Essentia Foundation. All rights reserved. https://www.essentiafoundation.org.
1:00:24 How can we put the spacetime headset off?
05:39 Beyond the spacetime fantasies of Christopher Nolan and the Matrix…
1:09:27 The ontology of conscious agents.
1:15:05 Are meditation and psychedelics ‘hacks’ in the interface?
1:21:41 Should we revalue religious and mystic literature?
1:29:54 Could idealism as a worldview help us better solve the challenges humanity faces?
1:34:23 The role of mathematics in bringing together science and spirituality.

Copyright © 2022 by Essentia Foundation. All rights reserved.

Home

Read more | >

To listen to more of John Wheeler’s stories, go to the playlist: https://www.youtube.com/playlist?list=PLVV0r6CmEsFzVlqiUh95Q881umWUPjQbB

American physicist, John Wheeler (1911−2008), made seminal contributions to the theories of quantum gravity and nuclear fission, but is best known for coining the term ‘black holes’. A keen teacher and mentor, he was also a key figure in the Manhattan Project. [Listener: Ken Ford]

TRANSCRIPT: I knew the stories about Gödel being concerned always about his health. I knew from his friend Oscar Morgenstern how Gödel would never take a pills prescription from his doctor without getting out a big medical book and studying up on that pill himself to make sure that it was okay. But I didn’t realize how far his dreams went, because I had failed to resonate to a talk he gave in 1945 at the symposium held in honor of Einstein’s birthday. In that talk Gödel had described what he called a Rotating Universe, a universe where all the galaxies turn the same way, and where the geometry is such that you keep on going living your life and you come round and come back and can live it over again; ‘Closed Time-like Line’ was the magic phrase to describe it. So you didn’t have to worry about the pill because you come back and live your life all over again. Well, after I’d introduced the two I said “Professor Gödel, we’d like to know what the relation is between the great Heisenberg Principle of Uncertainty or Indeterminism; and your famous proof that every significant mathematical system contains theorems which cannot be proven, your theorem of Unprovable Propositions.” Well, he didn’t want to talk about that. It turned out that later that he had walked and talked enough with Einstein to dismiss quantum theory. He didn’t believe quantum[theory]. All he wanted to know is what we were going to say in our book about the rotating universe that he had described. Well actually, we weren’t saying anything. Well, this bothered him and he wanted to know what the evidence is today, at that moment, about whether galaxies do rotate in the same way. We said we hadn’t studied it. Well it turned out that he himself had taken out the great Hubble atlas of the galaxies and page after page had opened it up and looked at each galaxy, determined the direction of its axis. He made a statistics of these numbers and found there was no preferred direction of rotation, so they couldn’t all be rotating in the same way.

Read more | >

Researchers from the University of Jyväskylä were able to simplify the most popular technique of artificial intelligence, deep learning, using 18th-century mathematics. They also found that classical training algorithms that date back 50 years work better than the more recently popular techniques. Their simpler approach advances green IT and is easier to use and understand.

The recent success of artificial intelligence is significantly based on the use of one core technique: . Deep learning refers to techniques where networks with a large number of data processing layers are trained using massive datasets and a substantial amount of computational resources.

Deep learning enables computers to perform such as analyzing and generating images and music, playing digitized games and, most recently in connection with ChatGPT and other generative AI techniques, acting as a conversational agent that provides high-quality summaries of existing knowledge.

Read more | >