In SM64 this covering space structure is used by giving Mario extremely high velocity \(v\) (a tangent vector at Marios position in \(P\)) through a different glitch called “backwards longjump”. The exponential map is then used to move Mario along the geodesic \(\exp_v(t)\) for \(t \in \mathbb{R}\). But due to hardware limitations, only discrete steps \(t_1, \dots, t_k\) for some \(k \in \mathbb{N}\) of this geodesic are actually calculated for collision detection. More on how this is related to the exponential map of Lie groups can be found in my previous post. Throughout this post, I will assume the Lie group of SM64 to have its unit at the position \(p\).
而早已去世的爷爷奶奶却不同。小时候，奶奶睡前给我讲民俗故事，讲到《半夜鸡叫》时学周扒皮“咯咯咯”地笑，我也跟着笑。她用箬叶包粽子，用玉兰花泡酒，一遍遍做我爱吃的番茄炒蛋，直到那道菜让我生出厌倦。爷爷虽然吝啬，也会在午睡前给我留下几块零花钱，在春节时给我买烟花和零食。
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constant size make and thus a stack-allocated backing store, and
"Following orders is not an excuse for unethical behavior," responded @MagisterLudiX. "Either you have strong red lines or you see it as purely transactional, depending on political context."
Anthropic’s prompt suggestions are simple, but you can’t give an LLM an open-ended question like that and expect the results you want! You, the user, are likely subconsciously picky, and there are always functional requirements that the agent won’t magically apply because it cannot read minds and behaves as a literal genie. My approach to prompting is to write the potentially-very-large individual prompt in its own Markdown file (which can be tracked in git), then tag the agent with that prompt and tell it to implement that Markdown file. Once the work is completed and manually reviewed, I manually commit the work to git, with the message referencing the specific prompt file so I have good internal tracking.