CPierre67

@AntSrt21 @drpkmath @YouTube Give it to me baby ;-)

@drpkmath @YouTube Greetings Dr. I think there are two ways, one is by applying the Feynman trick and the other is by converting it into an Frullani's Integral. Interesting work

This Integral Hides a Logarithm youtu.be/nigdOmvGV0c?si… via @YouTube

@chris_juravich @Diarytells I read … about 6e-14

@CPierre67 @Diarytells A reader suggested to just treat the integrand as 1/x^5. It gives you a value, but it’s basically still zero.

Not much math today ;-)

@chris_juravich @Diarytells Nope

@CPierre67 @Diarytells Did you evaluate to greater precision?

@CPierre67 Which part you mean

Dead Can Dance - Athens Greece 2012 youtu.be/403x2rFrNO0?si… … saw them 40 years ago … still enjoying to this day.

Solving ALL 2026 MIT Integration Bee Finals Problems youtu.be/xurzpDUJuOs?si… via @YouTube

@chris_juravich @Diarytells Machine precision ;-)

@Diarytells Will you accept 0?

@chris_juravich (2/2) Now, the integral diverges for eps<1 … no values on the graph (except maybe oscillating infinity). So, how do you ‘navigate’ (on the graph) and find a limiting value at eps=0^+? What is your limit? The finite part of F(0)? … not sure about that either.

@chris_juravich (1/2) I do not know what this regularization means. When you consider F(eps) as an integral, you can graph its value as a function of eps. Here, the integral exists for eps>1. … for eps approaching 1^+, the graph converges to a limiting value possibly seen as F(1) … all good !

My solution to the quoted integrals. AbReg denotes the Abel-regularized value of the integral. I used previously-derived results posted under the quoted problem. Let a=i+ε and b=1.

@chris_juravich Yes, you get every zeta by the AbReg of every corresponding eta (being an alternate series) … nice!

Using the quoted post and the ζ-η relationship derived in the reply post consider: 1+1+1+1+1+1+… →-1/2 1+2+3+4+5+6+… →-1/12

Another illuminating video … ‘This picture broke my brain’ (Escher) youtu.be/ldxFjLJ3rVY?si… via @3blue1brown based on pub.math.leidenuniv.nl/~smitbde/paper…

It is time for enlightenment … by Prof. John Mearsheimer youtu.be/-sCN5rmudjA?si… via @TheGrayzoneNews

Anthropic 研究人员刚刚证实，利用 AI 学习新技能会导致掌握程度下降 17%。但实际情况绝不是你想象的。 论文标题是《AI 如何影响技能养成》。这是一项随机实验，涉及 52 名专业开发人员。任务是使用他们从未接触过的 Python 库进行真实的编程。一半人配备了 AI 助手，另一半则没有。 AI 组在技能评估中的得分低了 17%。p 值为 0.010。所以这个差异是有统计学意义的。 更扎心的是：AI 组的速度甚至没有变得更快。他们学到的东西更少，而且并未节省时间。但是，如果你因此开始在网上传播“AI 不利于学习”这一论调，你就错失了论文中真正的重点。 研究人员查看了每一位参与者的屏幕录像。他们发现人们在学习新事物时使用 AI 的 6 种不同模式。其中 3 种模式有助于保持学习效果，另外 3 种则会破坏学习效果。两者之间的差距是巨大的。只向 AI 询问概念性问题的参与者，在评估中得分高达 86%。 而把一切都甩给 AI 的参与者，得分仅为 24%。 同样的工具，同样的任务，同样的时间限制。区别在于认知参与度。得分最高的 AI 用户实际上表现得比无 AI 组还要好。他们问的是“为什么这样行得通”，而不是“替我写这段代码”。他们生成代码后会追问以便理解。他们将 AI 视为思考伙伴，而非思考的替代品。 得分最低的一组做的是：粘贴提示词，复制输出结果，然后继续下一步。他们完成得最快。但他们几乎什么也没学到。 还有一个发现值得每一位工程经理的警惕：得分差距最大的是调试类问题。当你监管 AI 最需要的那项技能，恰恰也是当你让 AI 代劳时退化得最快的技能。 不用AI的对照组在任务执行过程中犯了更多错误。他们遇到了各种 bug。但这番挣扎，恰恰构建了他们的理解。错误并非学习的障碍。错误本身就是学习。用 AI 消除错误，也就消除了建立能力的机制。 AI 组的参与者在事后坦言，希望自己当时能“更用心一点”，并觉得自己的做法很“懒惰”。其中一人写道：“我的理解还有很多漏洞。” 他们能感受到那种完成了任务却不知其所以然的空虚感。这不是生产力的胜利，而是技术债。 这篇论文并非反对使用 AI，而是反对无意识地使用 AI。实际的结论很简单：如果你在学习新东西，请用 AI 来提问，而不是用它来逃避工作。 那份挣扎，才是成果所在。

@neurodocente Well, this is a good question. No doubt that the world situation (for quite some time, taco is just the latest incarnation) contributes to stress … but that such stress would be, say, low volume to not be felt as big as it impacts the working of the body is puzzling and alarming

I wasn’t planning to share this, but a friend texted me today and I was struck by the similarity in the following: recent endocrine workup revealed persistently elevated prolactin. Several of the more obvious causes have been ruled out, and two endocrinologists independently pointed to the same factor: sustained, clinically significant stress (I genuinely feel fine, the findings are there, but they have not affected my ability to work)🤷‍♀️🥳 As for my friend, she is under 30, not overweight, and by all appearances healthy. In her case, she was just diagnosed with diabetes, with an HbA1c of 9.9%, and her doctors also pointed to chronic stress and severe anxiety as contributing factors. 🤔💭And I wonder, when is chronic stress truly acting as an endocrine trigger, and when is it simply the most convenient explanation for a disorder we do not yet fully understand? What kind of exposure is required for chronic stress to act not merely as a contributing factor, but as a primary endocrine or metabolic driver? How sustained, how intense, how biologically embedded does it need to be before it stops being a contributing factor and starts functioning as a primary mechanism??

@CSYogananda @gammaofzeta Bought in AMS and read flying to IAH more than 10 years back.

@gammaofzeta A lovely book.

I’ve been reading an amazing book about the great Erdős: ‘The Man Who Loved Only Numbers’, by Hoffman (a beautiful recommendation). My favorite Erdős’ conjecture was born at a party. It is the (already solved) Erdős–Faber–Lovász conjecture (1972), and it says: if 𝑛 complete graphs (cliques) of size 𝑛 share at most one vertex with each other, their union can be properly colored using only 𝑛 colors. The conjecture was solved a few years ago and the proof was published in the Annals of Mathematics in 2023, grosso modo, by sorting hypergraph edges by size, using random coloring procedures on small edges and absorbing colors to show that the chromatic index does not exceed n. What’s your favorite Erdős’ conjecture? (text from Hoffman’s book, graph from Wikipedia)

@chris_juravich @Diarytells ? … shouldn’t it be >0

Maybe we can link to this video ;-) youtu.be/obXbCCWEKfY?si…

Qu’est-ce que c’est ce va-et-vient … il est en train d’enculer quelqu’un ou quoi ?