Year 2022 femtosecond logic gates for computers once thought to be almost a myth only for 2099 dreams is now real.
Light-field control of real and virtual charge carriers in a gold–graphene–gold heterostructure is demonstrated, and used to create a logic gate for application in lightwave electronics.
Diagonal Arguments are a powerful tool in maths, and appear in several different fundamental results, like Cantor’s original Diagonal argument proof (there exist uncountable sets, or “some infinities are bigger than other infinities”), Turing’s Halting Problem, Gödel’s incompleteness theorems, Russell’s Paradox, the Liar Paradox, and even the Y Combinator.
In this video, I try and motivate what a general diagonal argument looks like, from first principles. It should be accessible to anyone who’s comfortable with functions and sets.
The main result that I’m secretly building up towards is Lawvere’s theorem in Category Theory.
[https://link.springer.com/chapter/10.1007/BFb0080769]
with inspiration from this motivating paper by Yanofsky.
[https://www.jstor.org/stable/3109884].
This video will be followed by a more detailed video on just Gödel’s incompleteness theorems, building on the idea from this video.
====Timestamps====
00:00 Introduction.
00:59 A first look at uncountability.
05:04 Why generalise?
06:53 Mathematical patterns.
07:40 Working with functions and sets.
11:40 Second version of Cantor’s Proof.
13:40 Powersets and Cantor’s theorem in its generality.
15:38 Proof template of Diagonal Argument.
16:40 The world of Computers.
21:05 Gödel numbering.
23:05 An amazing program (setup of the Halting Problem)
25:05 Solution to the Halting Problem.
29:49 Comparing two diagonal arguments.
31:13 Lawvere’s theorem.
32:49 Diagonal function as a way for encoding self-reference.
35:11 Summary of video.
35:44 Bonus treat — Russell’s Paradox.
CORRECTIONS
Perovskite light-emitting diode is used as the light source for a quantum random number generator used in encryption.
Encryption plays an important role in protecting information in this digital era, and a random number generator plays a vital part in this by providing keys that are used to both encrypt and unlock the information at the receiving end.
Now, a team of researchers has made use of light-emitting diodes made from the crystal-like material perovskite to devise a new type of Quantum Random Number Generator (QRNG) that can be used for encryption but also for betting and computer simulations.
EU law requires manufacturers to adopt Type-C chargers in phones, tablets, etc by December 2024.
Apple will switch out its proprietary Lightning charging port in iPhones to be compatible with a USB Type-C cable instead, reported.
The EU law says that by 2024-end, all mobile phones, tablets, and cameras sold in countries under the EU will have to be equipped with a USB-C charging port. From spring 2026, the obligation will extend to laptops as well. The law’s overall purpose is to cut down on environmental waste and save consumers an estimated $247 million per annum.
Limestone spheroids, enigmatic lithic artifacts from the ancient past, have perplexed archaeologists for years. While they span from the Oldowan to the Middle Paleolithic, the purpose behind their creation remains a subject of intense debate.
Now, a study conducted by a team from the Computational Archaeology Laboratory of the Hebrew University of Jerusalem, in collaboration with researchers from Tel Hai College and Rovira i Virgili University seeks to shed light on these mysterious objects, offering insights into the intentions and skills of early hominins.
Spheroids are among the most enduring yet least understood archaeological artifacts, often considered as by-products of percussive tasks. However, the team’s research challenges this conventional wisdom. The central question at the heart of this study is whether these spheroids were unintentional by-products or intentionally crafted tools designed for specific purposes.
Intel demoed a non-x86 chip with eight cores, 528 threads, and 1TB/s of optical I/O at Hot Chips 2023.
Huawei and China’s top chipmaker have built an advanced 7-nanometer processor to power its latest smartphone, a sign Beijing is making early progress in a nationwide push to circumvent US efforts to contain its ascent. Peter Elstrom reports on Bloomberg Television.
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Scientists have been able to observe a common interaction in quantum chemistry for the first time, by using a quantum computer to shadow the process at a speed 100 billion times slower than normal.
Known as a conical intersection, the interactions have long been known about, but are usually over in mere femtoseconds – quadrillionths of a second – making direct observations impossible to carry out.
A research team from the University of Sydney in Australia and the University of California, San Diego, instead monitored the reaction using a charged particle trapped in a field, allowing them to follow a version of the process that dragged on for a relative eternity.
Scientists from the University of Sydney and Fudan University have found human brain signals traveling across the outer layer of neural tissue that naturally arrange themselves to resemble swirling spirals.
Published in the journal Nature Human Behaviour, the study suggests that these widespread spiral patterns, seen during both rest and cognitive activity, play a role in organizing brain function and cognitive processes.
Senior author Associate Professor Pulin Gong, from the School of Physics in the Faculty of Science, said the discovery could have the potential to advance powerful computing machines inspired by the intricate workings of the human brain.
Scientists have been left baffled by the discovery of the wreck of a 2,000-year-old “computer” that is amazingly complex.
The Antikythera mechanism – an astronomical calendar – has been dubbed “‘the first computer” and has baffled scientists for generations after it was first discovered inside a Greek shipwreck in 1901.
The device is a hand-powered time-keeping instrument that used a wing-up system to track the sun, moon and planets’ celestial time. It also worked as a calendar, tracking the phases of the Moon and the timing of eclipses.
