Lifeboat Foundation: Safeguarding Humanity
Toggle light / dark theme

Blog

Category: mathematics – Page 181

OpenAI Codex: Just Say What You Want! đŸ€–

I predicted that by 2030 you would be able to tell an AI assistant to build brand new books, movies, TV, video games, etc
 on demand. That has now arrived, although in its Very Early stages. Look forward to building whatever media you want, or changing existing media into whatever you want.

“OpenAI Codex: Just Say What You Want!”

❀ Check out Perceptilabs and sign up for a free demo here: https://www.perceptilabs.com/papers.

📝 The paper “Evaluating Large Language Models Trained on Code” is available here:
https://openai.com/blog/openai-codex/

Codex tweet/application links:

Continue reading “OpenAI Codex: Just Say What You Want! đŸ€–â€ | >

Cumrun Vafa: String Theory | Lex Fridman Podcast #204

Cumrun Vafa is a theoretical physicist at Harvard. Please support this podcast by checking out our sponsors:
- Headspace: https://headspace.com/lex to get free 1 month trial.
- The Jordan Harbinger Show: https://www.youtube.com/thejordanharbingershow.
- Squarespace: https://lexfridman.com/squarespace and use code LEX to get 10% off.
- Allform: https://allform.com/lex to get 20% off.

CORRECTIONS:
- I’m currently hiring folks to help me with editing and image overlays so there may be some errors in overlays (as in this episode) as we build up a team. I ask for your patience.
- At 1 hour 27 minute mark, we overlay an image of Brian Greene. We meant to overlay an image of Michael Green, an early pioneer of string theory: https://bit.ly/michael-green-physicist.
- The image overlay of the heliocentric model is incorrect.

EPISODE LINKS:
Cumrun’s Twitter: https://twitter.com/cumrunv.
Cumrun’s Website: https://www.cumrunvafa.org.
Puzzles to Unravel the Universe (book): https://amzn.to/3BFk5ms.

PODCAST INFO:
Podcast website: https://lexfridman.com/podcast.
Apple Podcasts: https://apple.co/2lwqZIr.
Spotify: https://spoti.fi/2nEwCF8
RSS: https://lexfridman.com/feed/podcast/
Full episodes playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4
Clips playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOeciFP3CBCIEElOJeitOr41

OUTLINE:
0:00 — Introduction.
1:51 — Difference between math and physics.
4:34 — Evolution of quantum mechanics.
7:52 — Can mathematics lead humanity off track.
8:51 — Beauty in mathematics.
14:10 — Philosophers using symmetry.
20:04 — How can ancient geometry be used to understand reality.
23:16 — Key ideas in the history of physics.
26:09 — Einstein’s special relativity.
29:46 — Physicists building intuition.
37:44 — Best work by Einstein.
39:28 — Quantum mechanics.
49:30 — Quantum gravity.
51:45 — String theory.
1:07:54 — 10th Dimension.
1:14:32 — Skepticism regarding string theory.
1:25:37 — Key figures in string theory.
1:29:56 — String Theory’s Nobel Prize.
1:33:01 — Edward Witten.
1:41:39 — String Theory Landscape & Swamplands.
1:50:29 — Theories of everything.
2:04:55 — Advice for young people.
2:07:57 — Death.

SOCIAL:

Continue reading “Cumrun Vafa: String Theory | Lex Fridman Podcast #204” | >

Hunting anomalies with an AI trigger

CERN Courier

Jennifer Ngadiuba and Maurizio Pierini describe how ‘unsupervised’ machine learning could keep watch for signs of new physics at the LHC that have not yet been dreamt up by physicists.

In the 1970s, the robust mathematical framework of the Standard Model ℠ replaced data observation as the dominant starting point for scientific inquiry in particle physics. Decades-long physics programmes were put together based on its predictions. Physicists built complex and highly successful experiments at particle colliders, culminating in the discovery of the Higgs boson at the LHC in 2012.

Along this journey, particle physicists adapted their methods to deal with ever growing data volumes and rates. To handle the large amount of data generated in collisions, they had to optimise real-time selection algorithms, or triggers. The field became an early adopter of artificial intelligence (AI) techniques, especially those falling under the umbrella of “supervised” machine learning. Verifying the SM’s predictions or exposing its shortcomings became the main goal of particle physics. But with the SM now apparently complete, and supervised studies incrementally excluding favoured models of new physics, “unsupervised” learning has the potential to lead the field into the uncharted waters beyond the SM.

Astronomers narrow in on where Planet 9 might be hiding

There are eight known planets in the Solar System (ever since Pluto was booted from the club), but for a while, there has been some evidence that there might be one more.

A hypothetical Planet 9 lurking on the outer edge of our Solar System. So far this world has eluded discovery, but a new study has pinned down where it should be. The evidence for Planet 9 comes from its gravitational pull on other bodies. If the planet exists, its gravity will affect the orbits of other planets.

So if something seems to be tugging on a planet, just do a bit of math to find the source. This is how Neptune was discovered when John Couch Adams and Urbain Le Verrier noticed independently that Uranus seemed to be tugged by an unseen planet.

The Mathematical Structure of Integrated Information Theory

Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution, we propound the mathematical structure of the theory, separating the essentials from auxiliary formal tools. We provide a definition of a generalized IIT which has IIT 3.0 of Tononi et al., as well as the Quantum IIT introduced by Zanardi et al. as special cases. This provides an axiomatic definition of the theory which may serve as the starting point for future formal investigations and as an introduction suitable for researchers with a formal background.

Integrated Information Theory (IIT), developed by Giulio Tononi and collaborators [5, 45–47], has emerged as one of the leading scientific theories of consciousness. At the heart of the latest version of the theory [19, 25 26, 31 40] is an algorithm which, based on the level of integration of the internal functional relationships of a physical system in a given state, aims to determine both the quality and quantity (‘Ω value’) of its conscious experience.

Astrophysicist Derives New Mathematical Solutions to an Old Problem in Astronomy

The Bernese theoretical astrophysicist Kevin Heng has achieved a rare feat: On paper, he has derived novel solutions to an old mathematical problem needed to calculate light reflections from planets and moons. Now, data can be interpreted in a simple way to understand planetary atmospheres, for example. The new formulae will likely be incorporated into future textbooks.

For millennia, humanity has observed the changing phases of the Moon. The rise and fall of sunlight reflected off the Moon, as it presents its different faces to us, is known as a “phase curve.” Measuring phase curves of the Moon and Solar System planets is an ancient branch of astronomy that goes back at least a century. The shapes of these phase curves encode information on the surfaces and atmospheres of these celestial bodies. In modern times, astronomers have measured the phase curves of exoplanets using space telescopes such as Hubble, Spitzer, TESS

Launched on April 18 2018, aboard a SpaceX Falcon 9 rocket, NASA’s Transiting Exoplanet Survey Satellite (TESS) is a mission to search nearby stars for undiscovered worlds with a gold of discovering thousands of exoplanets around nearby bright stars.

Exotic property of ‘ambidextrous’ crystals points to new magnetic phenomena

Researchers from Skoltech, KTH Royal Institute of Technology, and Uppsala University have predicted the existence of antichiral ferromagnetism, a nontrivial property of some magnetic crystals that opens the door to a variety of new magnetic phenomena. The paper was published in the journal Physical Review B.

Chirality, or handedness, is an extremely important fundamental property of objects in many fields of physics, mathematics, chemistry and biology; a chiral object cannot be superimposed on its in any way. The simplest chiral objects are human hands, hence the term itself. The opposite of chiral is achiral: a circle or a square are simple achiral objects.

Chirality can be applied to much more complex entities; for instance, competing internal interactions in a can lead to the appearance of periodic magnetic textures in the structure that differ from their mirror images—this is called chiral ferromagnetic ordering. Chiral crystals are widely considered promising candidates for and processing device realization as information can be encoded via their nontrivial magnetic textures.

Pi Calculated To A Record-Breaking, Whopping 62.8 Trillion Figures

A team of Swiss researchers from Graubuenden University of Applied Sciences has broken the record for calculating the mathematical constant pi. It is now known to an incredible level of exactitude, hitting 62.8 trillion figures thanks to the work of a supercomputer.

Pi represents the ratio between the radius of a circle and its circumference. You may recognize the first 10 digits, π=3.141592653, though there is an infinite number of digits that follow that decimal point.

To write all of the digits for the new record out on A4 paper, you would need almost 35 billion sheets, equivalent to about 52 percent of the mass of the Empire State Building. Putting those pieces of paper head to toe they would extend for over 10 million kilometers (6.5 million miles).

How (And Where) The Brain Analyzes Math and Language Spoken Simultaneously

Summary: Study reveals how the brain analyzes different types of speech which may be linked to how we comprehend sentences and calculate mathematical equations.

Source: SfN

Separate math and language networks segregate naturally when listeners pay attention to one type over the other, according to research recently published in Journal of Neuroscience.

/* */