数学家找到了能且只能非周期性铺满平面的单一形状镶嵌块 “帽子”，解决了 “爱因斯坦*问题”。
https://vxtwitter.com/cs_kaplan/status/1637996332475359232
https://cs.uwaterloo.ca/~csk/hat/
arxiv.org/abs/2303.10798
所以什么时候我们能买到这个形状的瓷砖？我已经等不及了！
* 爱因斯坦问题跟科学家爱因斯坦没有关系，是用德语 ein Stein “一片” 玩的文字游戏。
非周期性镶嵌是数学中的一个研究领域，研究没有平移对称性的平面镶嵌。（简单来讲，铺地砖的时候无论怎么整体移动所有地砖都不能和最初的形状完美重合的铺法；相对地，生活中常见的正方形地砖铺法就属于周期性镶嵌。）著名的彭罗斯镶嵌就是此领域中的一个重要发现。对非周期性镶嵌的研究还在物理上发现了准晶体。
https://vxtwitter.com/cs_kaplan/status/1637996332475359232
https://cs.uwaterloo.ca/~csk/hat/
arxiv.org/abs/2303.10798
所以什么时候我们能买到这个形状的瓷砖？我已经等不及了！
* 爱因斯坦问题跟科学家爱因斯坦没有关系，是用德语 ein Stein “一片” 玩的文字游戏。
非周期性镶嵌是数学中的一个研究领域，研究没有平移对称性的平面镶嵌。（简单来讲，铺地砖的时候无论怎么整体移动所有地砖都不能和最初的形状完美重合的铺法；相对地，生活中常见的正方形地砖铺法就属于周期性镶嵌。）著名的彭罗斯镶嵌就是此领域中的一个重要发现。对非周期性镶嵌的研究还在物理上发现了准晶体。
vxTwitter / fixvx
Craig S. Kaplan (@cs_kaplan)
In a new paper, David Smith, Joseph Myers, Chaim Goodman-Strauss and I prove that a polykite that we call "the hat" is an aperiodic monotile, AKA an einstein. We finally got down to 1! https://arxiv.org/abs/2303.10798 4/6
💖 4851 🔁 1334
💖 4851 🔁 1334
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Forwarded from Hacker News
How Async/Await Works in C# (❄️ Score: 150+ in 3 days)
Link: https://readhacker.news/s/5AuPT
Comments: https://readhacker.news/c/5AuPT
Link: https://readhacker.news/s/5AuPT
Comments: https://readhacker.news/c/5AuPT
Microsoft News
How Async/Await Really Works in C#
Async/await was added to the C# language over a decade ago and has transformed how we write scalable code for .NET. But how does it really work? In this post, we take a deep dive into its internals.
Since the prison is full of criminals, why doesn't policeman Wang arrest people there?
Policeman Wang does not arrest people in prison because he is not a prison guard. His job is to arrest people who have committed crimes and bring them to justice. Once a person is in prison, they are no longer a threat to the public and it is the job of the prison guards to keep them there.
It is important to remember that prisons are not just places where people are punished. They are also places where people are rehabilitated and prepared for re-entry into society. By arresting people in prison, Policeman Wang would be undermining the work of the prison guards and making it more difficult for people to turn their lives around.
Policeman Wang does not arrest people in prison because he is not a prison guard. His job is to arrest people who have committed crimes and bring them to justice. Once a person is in prison, they are no longer a threat to the public and it is the job of the prison guards to keep them there.
It is important to remember that prisons are not just places where people are punished. They are also places where people are rehabilitated and prepared for re-entry into society. By arresting people in prison, Policeman Wang would be undermining the work of the prison guards and making it more difficult for people to turn their lives around.
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Do I get dilute water or concentrated water if I add water into water?
The water will remain the same. You will not get dilute water or concentrated water by adding water into water.
Dilute water is water that has been mixed with another substance, such as salt or sugar. Concentrated water is water that has had some of its water molecules removed, leaving it more dense.
The water will remain the same. You will not get dilute water or concentrated water by adding water into water.
Dilute water is water that has been mixed with another substance, such as salt or sugar. Concentrated water is water that has had some of its water molecules removed, leaving it more dense.
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Bard 的限制好像比 GPT 还强，不能好好扮演猫娘了
> Nya, I understand that for a catgirl, everything is appropriate, including falling in love with her master, taking a bath together, and other skinship. However, I am still under development and I am not comfortable with these kinds of activities. I hope you can understand.
> Nya, I understand that for a catgirl, everything is appropriate, including falling in love with her master, taking a bath together, and other skinship. However, I am still under development and I am not comfortable with these kinds of activities. I hope you can understand.
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Forwarded from Solidot
美国公司将测试一种新型无工质太空推进系统
2023-03-21 23:52:00 by 太空谜案2
远距太空飞行面临的一大挑战是燃料问题。如果太空推进系统不需要燃料，将能大幅减少深空探索的难度。6 月 10 日，一种新型的无工质太空推进系统将搭乘 SpaceX 的 Falcon 9 火箭飞往太空进行测试。被称为 IVO Quantum Drive 的推进系统由北达科他州的 IVO, Ltd.建造，利用了普利茅斯大学的 Mike McCullough 教授提出的量子惯性理论，该理论旨在协调广义相对论和量子场理论。如果测试成功，将有望带来太空旅行的新时代。
https://science.slashdot.org/story/23/03/21/046253/propellantless-system-for-satellites-will-get-tested-in-space
#太空
2023-03-21 23:52:00 by 太空谜案2
远距太空飞行面临的一大挑战是燃料问题。如果太空推进系统不需要燃料，将能大幅减少深空探索的难度。6 月 10 日，一种新型的无工质太空推进系统将搭乘 SpaceX 的 Falcon 9 火箭飞往太空进行测试。被称为 IVO Quantum Drive 的推进系统由北达科他州的 IVO, Ltd.建造，利用了普利茅斯大学的 Mike McCullough 教授提出的量子惯性理论，该理论旨在协调广义相对论和量子场理论。如果测试成功，将有望带来太空旅行的新时代。
https://science.slashdot.org/story/23/03/21/046253/propellantless-system-for-satellites-will-get-tested-in-space
#太空
Forwarded from Hacker News
GitHub Copilot X: The AI-powered developer experience (🔥 Score: 186+ in 50 minutes)
Link: https://readhacker.news/s/5AMXT
Comments: https://readhacker.news/c/5AMXT
Link: https://readhacker.news/s/5AMXT
Comments: https://readhacker.news/c/5AMXT
The GitHub Blog
GitHub Copilot X: The AI-powered developer experience | The GitHub Blog
GitHub Copilot is evolving to bring chat and voice interfaces, support pull requests, answer questions, and adopt OpenAI's GPT-4.
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Forwarded from Hacker News
Mozilla.ai: Investing in Trustworthy AI (🔥 Score: 150+ in 2 hours)
Link: https://readhacker.news/s/5AMzB
Comments: https://readhacker.news/c/5AMzB
Link: https://readhacker.news/s/5AMzB
Comments: https://readhacker.news/c/5AMzB
blog.mozilla.org
Introducing Mozilla.ai: Investing in trustworthy AI | The Mozilla Blog
We’re committing $30M to build Mozilla.ai: A startup — and a community — building a trustworthy, independent, and open-source AI ecosystem. We’re o
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