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Giacomo 回复了问题 2022-06-06 23:03 数学学习: 问答请问如何理解梯度，尤其它的几何意义。

Giacomo :# 这篇回答是“活动制度”的示范，不直接回答问题，而是描述解决这个问题的路径# 第一部分，题主已知的知识。# 由于@亥维赛描述的不是很准确，我这里做了一些假设1. 问题：对于一个可导的单变量实值函数，f : ℝ → ℝ， f 在 a 点处的梯度是什么？回答：f在a点处的梯度就是f在p点处的导数值f...; 赞同2 反对 0人感谢 1评论 2回复

文章《人类司机》- 第二部分：UAM篇

本文由 @林威（我的朋友）/ UnknownID（我自己）合写而成，为长篇科幻。本文分为四个部分：地面篇，UAM篇，宇航篇，未来篇。本文最初灵感与初版大纲，以及地面篇（全部）和UAM篇（绝大部分）的作者...

人类司机 科幻

赞同0  945浏览  0评论 无名_unknownID 2022-05-28 15:27

长尾科技 发起了提问 2022-06-07 11:53 相对论: 问答如何看待格里菲斯的《电动力学导论》？

因为狭义相对论主要是从电动力学发展出来的，所以一般电动力学的最后一章都会讲狭义相对论的内容，从这个角度去理解狭义相对论会更加自然。格里菲斯的《电动力学导论》就是其中非常好的一本书，大家可以在这里一起学习这本书，有什么问题和想法都可以在这里讨论。此问题隶属于更高层级的问题《相对论的【学习路径图】是什么...; 关注问题 1 1人感谢 0评论

长尾科技 发起了提问 2022-06-07 11:12 相对论: 问答如何看待汪洁的相对论科普书《时间的形状》？

《时间的形状》是一本比较通俗的相对论科普书，零基础的朋友基本上也能看得懂。此问题隶属于更高层级的问题《相对论的【学习路径图】是什么样的？如何系统地学习相对论？》，属于相对论学习路径图的一部分。大家可以在这里讨论这两篇文章的相关内容，也可以去更高层级的问题讨论相对论的学习路径图。上层链接：相对论的【学...; 关注问题 1 0人感谢 0评论

文章闵氏几何是什么？它是如何统一时空并极大简化狭义相对论的？

1905年，爱因斯坦正式提出了狭义相对论；1908年，闵可夫斯基给出了狭义相对论的几何表述，也就是我们这里说的闵氏几何。爱因斯坦一开始对这套几何语言很反感，认为这些纯数学上的“花架子”没什么用，还增加了相对论的复杂度。但是，他很快就发现闵氏...

闵氏几何 狭义相对论

赞同2  938浏览  0评论 长尾科技 2022-05-16 17:24

林威 回复了问题 2022-05-27 02:43 工业: 问答目前国内电动车的发展还有哪些卡脖子技术需要突破？

林威 :真正卡脖子的主要是高端基础零部件，如激光器、超声波发生器和高可靠性的PLC。这些都是电池包制造所需的基础零部件。另外特别揪心的是芯片，自动驾驶需要高算力芯片。而国内现在14nm产能还很低。而没有芯片的结果，华为手机已经示范了。因此，芯片，我们一定要知耻而后勇。还有很多材料是有国产货，但是国产货比进口...; 赞同1 反对 0人感谢 4评论 1回复

文章光学前沿—OAM光通讯

写在前面的话本文译自Alan Eli Willner所撰写的OAM Light for Communications一文，文章发表在Optics & Photonics News, 2021, 32(6):34–42上。翻译目的为...

光学物理

赞同0  1538浏览  0评论 redcrag 2022-06-05 23:59

长尾科技 发起了提问 2022-06-07 11:23 相对论: 问答如何看待布莱恩·格林的《宇宙的琴弦》？

格林的《宇宙的琴弦》是超弦理论的经典科普书，但它在前面也会科普相对论相关的内容。此问题隶属于更高层级的问题《相对论的【学习路径图】是什么样的？如何系统地学习相对论？》，属于相对论学习路径图的一部分。大家可以在这里讨论这两篇文章的相关内容，也可以去更高层级的问题讨论相对论的学习路径图。上层链接：相对论...; 关注问题 1 0人感谢 0评论

文章《人类司机》- 第三部分：宇航篇

本文由 @林威（我的朋友）/ UnknownID（我自己）合写而成，为长篇科幻。本文分为四个部分：地面篇，UAM篇，宇航篇，未来篇。本文最初灵感与初版大纲，以及地面篇（全部）和UAM篇（绝大部分）的作...

人类司机 科幻

赞同0  980浏览  0评论 无名_unknownID 2022-05-28 19:08

文章 2022年5月11日，悟理公测

各位朋友们，经过紧张的技术准备工作和小范围内测，悟理知识平台定于2022年5月11日，以邀请制注册的方式开始公测。公测期间，各位朋友可以通过公众号“悟理wuphys”，以及网站 http://www.wuphys.com 、悟理.中国来访...

公告站务

赞同5  1302浏览  4评论 林威 2022-05-11 02:31

文章顶注册后迷茫不知干啥的朋友，你想要的答案在这里

悟理wuphys是啥？悟理是一个发源于长尾科技社群的邀请制知识平台，倡导用户使用费曼学习法，真正学懂自己提出的问题。当前入口有：国际域名：www.wuphys.com 中文域名：悟理.中国 &n...

公告站务

赞同6  2409浏览  0评论 林威 2022-06-03 01:39

文章你也能懂的质能方程E=mc²

提到爱因斯坦，很多人的第一反应就是E=mc²。没办法，质能方程看起来“太简单”了：左边的E代表能量，右边的m代表质量，c是光速，都是中学生就能看懂的物理量。而且，这个方程看起来太神奇了，它告诉我们一般物体都蕴含了巨大的能量，原子弹那毁天灭地...

狭义相对论

赞同1  1002浏览  0评论 长尾科技 2022-05-16 17:24

文章欧姆定律为什么不适用于转动的电动机？

“典例问答”栏目将不定期剖析典型问题，把最本质的方法与规律呈现给读者。欢迎大家关注“因物悦理”，我将持续分享高中物理的干货哟。问：直流电动机的构造其实就是一个金属框，按说和金属导体没啥区别。可是为什么电动机转动的时候不能使用欧姆定律呢？在高...

物理 欧姆定律

赞同1  1198浏览  0评论 music 2022-05-29 00:47

简单 回复了问题 2022-06-06 10:07 换电 新能源: 问答蔚来已经在车辆换电领域实操ABS资本化，换电市场将来会如何发展？

简单 :换电的商业模式主要解决了车主的三大痛点：里程焦虑、车辆贬值的焦虑、安全焦虑。当然了，这三个焦虑并不会凭空消失，只是转移给了换电站的运营商，个人觉得，换电模式最大的问题就是商业模式该如何设计，如何融资建立庞大的换电网络，两桶油也加入了这个战场，我们拭目以待吧。; 赞同2 反对 0人感谢 0评论 2回复

长尾科技 回复了问题 2022-06-07 10:32 相对论: 问答相对论的【学习路径图】是什么样的？如何系统地学习相对论？

长尾科技 :1、完全零基础的朋友可以先看看长尾科技的四篇关于狭义相对论的主线文章。相对论的历史):1.2、相对论诞生：爱因斯坦是如何创立狭义相对论的？| 主线（3.3万字）然后是关于关于质能方程的讨论（想进一步讨论质能方程可以来这里：如何看待长尾科技的《你也能懂的质能方程E=mc²》？）：1.4、《...; 赞同4 反对 0人感谢 0评论 1回复

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CONNECT:[ UseTime:0.000532s ] mysql:host=127.0.0.1;port=3306;dbname=wuphysthink;charset=utf8mb4
SHOW FULL COLUMNS FROM `aws_hook_plugins` [ RunTime:0.000673s ]
SELECT `hook`,`plugins` FROM `aws_hook_plugins` WHERE `status` = 1 ORDER BY `sort` DESC [ RunTime:0.000423s ]
SHOW FULL COLUMNS FROM `aws_config` [ RunTime:0.006289s ]
SELECT * FROM `aws_config` [ RunTime:0.000646s ]
SHOW FULL COLUMNS FROM `aws_forbidden_ip` [ RunTime:0.000720s ]
SELECT `ip` FROM `aws_forbidden_ip` [ RunTime:0.000252s ]
SHOW FULL COLUMNS FROM `aws_admin_group` [ RunTime:0.000671s ]
SELECT `permission` FROM `aws_admin_group` WHERE `id` = 5 LIMIT 1 [ RunTime:0.000348s ]
SHOW FULL COLUMNS FROM `aws_users_online` [ RunTime:0.000531s ]
DELETE FROM `aws_users_online` WHERE `last_login_time` < 1765003033 [ RunTime:0.009942s ]
SHOW FULL COLUMNS FROM `aws_menu_rule` [ RunTime:0.000669s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'nav' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000461s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'footer' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000420s ]
SHOW FULL COLUMNS FROM `aws_links` [ RunTime:0.000606s ]
SELECT * FROM `aws_links` WHERE `status` = 1 [ RunTime:0.000344s ]
SHOW FULL COLUMNS FROM `aws_post_relation` [ RunTime:0.000575s ]
SELECT COUNT(*) AS think_count FROM `aws_post_relation` WHERE `item_type` IN ('question','article','') LIMIT 1 [ RunTime:0.000384s ]
SELECT `id`,`item_id`,`item_type`,`uid` FROM `aws_post_relation` WHERE `item_type` IN ('question','article','') ORDER BY RAND(),`is_recommend` DESC LIMIT 90,15 [ RunTime:0.000468s ]
SHOW FULL COLUMNS FROM `aws_question` [ RunTime:0.000684s ]
SELECT `last_answer` FROM `aws_question` WHERE `id` IN (20,31,24,10,28,18,21) AND `status` = 1 [ RunTime:0.000664s ]
SHOW FULL COLUMNS FROM `aws_answer` [ RunTime:0.000665s ]
SELECT * FROM `aws_answer` WHERE `status` = 1 AND `id` IN (13,28,31,32,0) [ RunTime:0.000548s ]
SHOW FULL COLUMNS FROM `aws_topic_relation` [ RunTime:0.000481s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (20,31,24,10,28,18,21) AND `item_type` = 'question' [ RunTime:0.000423s ]
SHOW FULL COLUMNS FROM `aws_topic` [ RunTime:0.000535s ]
SELECT * FROM `aws_topic` WHERE `id` IN (9,79,11,82,18) [ RunTime:0.000392s ]
SELECT * FROM `aws_question` WHERE `status` = 1 AND `id` IN (20,31,24,10,28,18,21) [ RunTime:0.000666s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (48,18,67,49,5,62,17,51) AND `item_type` = 'article' [ RunTime:0.000490s ]
SELECT * FROM `aws_topic` WHERE `id` IN (16,31,19,5,65,57,2,69,80) [ RunTime:0.000335s ]
SHOW FULL COLUMNS FROM `aws_article` [ RunTime:0.000753s ]
SELECT * FROM `aws_article` WHERE `status` = 1 AND `id` IN (48,18,67,49,5,62,17,51) [ RunTime:0.004057s ]
SHOW FULL COLUMNS FROM `aws_users` [ RunTime:0.000966s ]
SELECT `uid`,`nick_name`,`user_name`,`salt`,`email`,`mobile`,`sex`,`is_first_login`,`inbox_unread`,`notify_unread`,`fans_count`,`friend_count`,`available_invite_count`,`is_valid_email`,`is_valid_mobile`,`integral`,`reputation`,`reputation_update_time`,`avatar`,`signature`,`verified`,`group_id`,`integral_group_id`,`reputation_group_id`,`last_login_time`,`last_login_ip`,`reg_ip`,`money`,`frozen_money`,`deal_password`,`birthday`,`url_token`,`views_count`,`agree_count`,`question_count`,`answer_count`,`article_count`,`draft_count`,`topic_focus_count`,`column_count`,`extend`,`status`,`theme`,`create_time`,`update_time` FROM `aws_users` WHERE `status` = 1 AND `uid` IN (124,90,5,76,56,1,65,37,35) [ RunTime:0.000548s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000255s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000199s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 5 LIMIT 1 [ RunTime:0.000216s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 5 LIMIT 1 [ RunTime:0.000195s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 35 LIMIT 1 [ RunTime:0.000311s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 35 LIMIT 1 [ RunTime:0.000322s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 37 LIMIT 1 [ RunTime:0.000309s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 37 LIMIT 1 [ RunTime:0.000297s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 56 LIMIT 1 [ RunTime:0.000287s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 56 LIMIT 1 [ RunTime:0.000290s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 65 LIMIT 1 [ RunTime:0.000295s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 65 LIMIT 1 [ RunTime:0.000287s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 76 LIMIT 1 [ RunTime:0.000289s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 76 LIMIT 1 [ RunTime:0.000282s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 90 LIMIT 1 [ RunTime:0.000282s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 90 LIMIT 1 [ RunTime:0.000301s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 124 LIMIT 1 [ RunTime:0.000225s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 124 LIMIT 1 [ RunTime:0.000231s ]
SHOW FULL COLUMNS FROM `aws_question_vote` [ RunTime:0.000466s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 31 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000312s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 20 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000272s ]
SHOW FULL COLUMNS FROM `aws_article_vote` [ RunTime:0.000486s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 48 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000265s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 31 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000375s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 24 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000306s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 18 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000262s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 13 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000250s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 10 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000257s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 67 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000266s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 28 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000239s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 49 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000301s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 5 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000263s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 62 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000238s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 17 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000335s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 51 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000265s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 28 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000255s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 18 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000362s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 32 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000350s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 21 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000322s ]
SHOW FULL COLUMNS FROM `aws_announce` [ RunTime:0.000614s ]
SELECT * FROM `aws_announce` WHERE `status` = 1 ORDER BY `set_top_time` DESC,`sort` DESC LIMIT 0,3 [ RunTime:0.000364s ]
SELECT COUNT(*) AS think_count FROM `aws_topic` WHERE `status` = 1 AND `discuss_month` > 0 LIMIT 1 [ RunTime:0.000457s ]
SELECT * FROM `aws_topic` WHERE `status` = 1 AND `discuss_month` > 0 ORDER BY RAND(),`top` DESC,`focus` DESC,`discuss_month` DESC LIMIT 0,5 [ RunTime:0.000781s ]
SHOW FULL COLUMNS FROM `aws_topic_focus` [ RunTime:0.000470s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 69 LIMIT 1 [ RunTime:0.000322s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 5 LIMIT 1 [ RunTime:0.000305s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 63 LIMIT 1 [ RunTime:0.000344s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 85 LIMIT 1 [ RunTime:0.000304s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 35 LIMIT 1 [ RunTime:0.000304s ]
SHOW FULL COLUMNS FROM `aws_column` [ RunTime:0.000596s ]
SELECT * FROM `aws_column` WHERE `verify` = 1 ORDER BY RAND(),`view_count` DESC LIMIT 0,5 [ RunTime:0.000524s ]
SELECT * FROM `aws_users` WHERE `uid` <> 0 AND `status` = 1 AND `reputation` > 0 ORDER BY RAND(),`reputation` DESC,`answer_count` DESC LIMIT 5 [ RunTime:0.001096s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 55 LIMIT 1 [ RunTime:0.000309s ]
SHOW FULL COLUMNS FROM `aws_users_follow` [ RunTime:0.000457s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 55 LIMIT 1 [ RunTime:0.000296s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 9 LIMIT 1 [ RunTime:0.000269s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 9 LIMIT 1 [ RunTime:0.000282s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 33 LIMIT 1 [ RunTime:0.000268s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 33 LIMIT 1 [ RunTime:0.000281s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 35 LIMIT 1 [ RunTime:0.000280s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 65 LIMIT 1 [ RunTime:0.000289s ]

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