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Category: mathematics – Page 76

#generalrelativitylecture.

General theory of relativity has got a deep understanding. In this General relativity lecture I have explained, the deep philosophical meaning of General relativity. I have also described from Special relativity when we move to General relativity, the entire notion of spacetime changes and why the mathematics becomes difficult. I have also discussed quantum mechanics and general relativity and its connection to string theory. This is a video, which discusses about the nature of development of the process and some deep philosophies which lies in the heart of spacetime.

00:00 — 01:34 — Objectives.
01:35 — 02:58 — Topics.
02:59 — 05:56 — Understanding a system.
05:57 — 12:51 — Consequence of relativity.
12:52 — 18:33 — General relativity is more geometry.
18:34 — 28:49 — What is a classical system.
28:50 — 31:23 — General relativity and Quantum mechanics.
31:24 — 32:53 — General relativity & String theory.
32:54 — 38:14 — Summary and conclusion.

Welcome to General relativity explained.

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Sometimes, ChatGPT made “surprising” mistakes in school-level math.

Microsoft-backed OpenAI’s AI chatbot ChatGPT has been making headlines ever since it was released to the public on November 30. It can break down complex scientific concepts, compose poems, write stories, code, and create malware…the list is endless. OpenAI has also released a paid version of the chatbot. Known as ‘ChatGPT Professional’, it is available at $42 per month.

Bauna/iStock.

Students have also been using the chatbot to complete assignments. It turns out it can clear examinations, too, with flying colors. Christian Terwiesch, a professor at the Wharton School School of Business, University of Pennsylvania, tested the performance of ChatGPT in an MBA exam. He questioned the chatbot on Operations Management, a core MBA subject.

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This video explores aliens, mind uploading to other species (like in Avatar), genetic engineering, and future robots. Watch this next video about digital immortality: https://youtu.be/sZdWN9pbbew.
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What’s your favorite number? There are literally infinite options, and yet only a few which seem to stand out as more popular than others: there’s seven, obviously; 13 or 666 for the badasses among us; and √2 for anyone who just likes annoying Pythagoreans.

But there’s really only one number out there that can claim to be World Champion: pi. What other mathematical constant is literally used as a benchmark for computing power, or forms the basis for a never-ending worldwide grudge match over who can list the most random digits in the correct order (current record: 111,700)?

The reason pi is able to capture our imagination like this is because it is an irrational number – in other words, its decimal expansion is never-ending and entirely random. It’s thought that any sequence of numbers you can possibly think of can be found somewhere in the expansion of pi, and yet knowing any particular sequence somewhere in the expansion tells you no information about which digit comes next.

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Researchers report a new, highly unusual, structured-light family of 3D topological solitons, the photonic hopfions, where the topological textures and topological numbers can be freely and independently tuned.

We can frequently find in our daily lives a localized wave structure that maintains its shape upon propagation—picture a smoke ring flying in the air. Similar stable structures have been studied in various research fields and can be found in magnets, nuclear systems, and particle physics. In contrast to a ring of smoke, they can be made resilient to perturbations. This is known in mathematics and physics as topological protection.

A typical example is the nanoscale hurricane-like texture of a magnetic field in magnetic thin films, behaving as particles—that is, not changing their shape—called skyrmions. Similar doughnut-shaped (or toroidal) patterns in 3D space, visualizing complex spatial distributions of various properties of a wave, are called hopfions. Achieving such structures with light waves is very elusive.

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We can frequently find in our daily lives a localized wave structure that maintains its shape upon propagation—picture a smoke ring flying in the air. Similar stable structures have been studied in various research fields and can be found in magnets, nuclear systems, and particle physics. In contrast to a ring of smoke, they can be made resilient to perturbations. This is known in mathematics and physics as topological protection.

A typical example is the nanoscale hurricane-like texture of a magnetic field in magnetic thin films, behaving as particles—that is, not changing their shape—called skyrmions. Similar doughnut-shaped (or toroidal) patterns in 3D space, visualizing complex spatial distributions of various properties of a wave, are called hopfions. Achieving such structures with is very elusive.

Recent studies of structured light revealed strong spatial variations of polarization, phase, and amplitude, which enable the understanding of—and open up opportunities for designing—topologically stable optical structures behaving like particles. Such quasiparticles of light with control of diversified topological properties may have great potential, for example as next-generation information carriers for ultra-large-capacity optical information transfer, as well as in quantum technologies.

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Mathematicians came up with the first examples of intransitive dice more than 50 years ago, and eventually proved that as you consider dice with more and more sides, it’s possible to create intransitive cycles of any length. What mathematicians didn’t know until recently was how common intransitive dice are. Do you have to contrive such examples carefully, or can you pick dice randomly and have a good shot at finding an intransitive set?

Looking at three dice, if you know that A beats B and B beats C, that seems like evidence that A is the strongest; situations where C beats A should be rare. And indeed, if the numbers on the dice are allowed to add up to different totals, then mathematicians believe that this intuition holds true.

But a paper posted online late last year shows that in another natural setting, this intuition fails spectacularly. Suppose you require that your dice use only the numbers that appear on a regular die and have the same total as a regular die. Then, the paper showed, if A beats B and B beats C, A and C have essentially equal chances of prevailing against each other.

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In the world of spreadsheets and data analysis, a new player has emerged to shake up the game. Akkio, the easy-to-use AI company, has launched Chat Data Prep, a revolutionary machine learning platform that allows users to transform data using ordinary conversational language.

Gone are the days of struggling with complicated formulas and formatting commands in Excel. With Akkio’s Chat Data Prep, users can simply type in conversational language to make changes to their spreadsheet data. Leveraging AI and large language models, the platform interprets the user’s requests and makes the necessary changes to the data.

According to Jonathon Reilly, co-founder of Akkio, this new method of interacting with data results in a 10-fold reduction in the time it takes to prepare data for analysis. With Chat Data Prep, users can reformat dates, perform time-based math operations, and even fix messy data fields with a simple conversational command.

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ChatGPT was hailed as one of 2022’s most impressive technological innovations upon its release last November. The powerful artificial intelligence (AI) chatbot can generate text on almost any topic or theme, from a Shakespearean sonnet reimagined in the style of Megan Thee Stallion, to complex mathematical theorems described in language a 5 year old can understand. Within a week, it had more than a million users.

ChatGPT’s creator, OpenAI, is now reportedly in talks with investors to raise funds at a $29 billion valuation, including a potential $10 billion investment by Microsoft. That would make OpenAI, which was founded in San Francisco in 2015 with the aim of building superintelligent machines, one of the world’s most valuable AI companies.

But the success story is not one of Silicon Valley genius alone. In its quest to make ChatGPT less toxic, OpenAI used outsourced Kenyan laborers earning less than $2 per hour, a TIME investigation has found.

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