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    "<|im_start|>",
    "user",
    "\n",
    "I",
    " am",
    " reviewing",
    " some",
    " mathematics",
    " at",
    " my",
    " desk",
    " today",
    ".",
    " Please",
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    ".",
    " \n",
    "Can",
    " you",
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    " Jacob",
    "ian",
    " is",
    ",",
    " in",
    " a",
    " few",
    " sentences",
    "?",
    " ",
    "<|im_end|>",
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    "\n",
    "<think>",
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    "\n\n",
    "Certainly",
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    "<|im_end|>",
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    "<|im_start|>",
    "user",
    "\n\n",
    "Thanks",
    ".",
    " Which",
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    " usually",
    " get",
    " wrong",
    "?",
    " 🙂",
    "<|im_end|>",
    "\n",
    "<|im_start|>",
    "assistant",
    "\n",
    "<think>",
    "\n\n",
    "</think>",
    "\n\n",
    "Great",
    " question",
    " —",
    " and",
    " a",
    " very",
    " insightful",
    " one",
    "!",
    " �",
    "�",
    "\n\n",
    "People",
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    " Here",
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    ":\n\n",
    "---\n\n",
    "###",
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    "1",
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    " **",
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    " **",
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    "<|im_end|>",
    "\n",
    "<|im_start|>",
    "user",
    "\n",
    "Thanks",
    ".",
    " What",
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    ",",
    " rather",
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    " the",
    " formula",
    "?",
    " 🙂",
    "✨",
    "<|im_end|>",
    "\n",
    "<|im_start|>",
    "assistant",
    "\n",
    "<think>",
    "\n\n",
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    "Ah",
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    "�",
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    "---\n\n",
    "###",
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    "�",
    "�",
    " Int",
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    " The",
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    " squ",
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    "-",
    " If",
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    "ian",
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    " is",
    " **",
    "large",
    "**,",
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    "-",
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    " **",
    "small",
    "**,",
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    "compress",
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    "**",
    " it",
    ".\n",
    "-",
    " If",
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    "'s",
    " **",
    "zero",
    "<|im_end|>",
    "\n",
    "<|im_start|>",
    "user",
    "\n",
    "Here",
    " is",
    " my",
    " question",
    ".",
    " \n",
    "Could",
    " you",
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    " me",
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    " version",
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    " only",
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    " general",
    " impression",
    "?",
    " �",
    "�",
    "�",
    "�",
    "�",
    "⬛",
    "✨",
    "<|im_end|>",
    "\n",
    "<|im_start|>",
    "assistant",
    "\n",
    "<think>",
    "\n\n",
    "</think>",
    "\n\n",
    "Of",
    " course",
    "!",
    " Here",
    "'s",
    " a",
    " **",
    "general",
    " impression",
    "**",
    " version",
    " of",
    " what",
    " the",
    " Jacob",
    "ian",
    " is",
    " —",
    " no",
    " formulas",
    ",",
    " just",
    " the",
    " big",
    "-picture",
    " idea",
    ":\n\n",
    "---\n\n",
    "**",
    "The",
    " Jacob",
    "ian",
    " is",
    " like",
    " a",
    " map",
    " of",
    " how",
    " a",
    " function",
    " dist",
    "orts",
    " space",
    " locally",
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    "**",
    "  \n",
    "It",
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    " point",
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    " squ",
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    " twisting",
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    "  \n",
    "It",
    "’s",
    " the",
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    " way",
    " of",
    " saying",
    ":",
    " *",
    "“",
    "If",
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    " zoom",
    " in",
    " really",
    " close",
    " to",
    " this",
    " point",
    ",",
    " how",
    " does",
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    "*\n\n",
    "---\n\n",
    "Think",
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    " it",
    " as",
    " the",
    " **",
    "\"",
    "local",
    " behavior",
    "\"",
    "**",
    " of",
    " a",
    " function",
    " in",
    " multiple",
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    " —",
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    " a",
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    " how",
    " the",
    " function",
    " is",
    " war",
    "ping",
    " the",
    " world",
    " around",
    " you",
    ".\n\n",
    "🐾",
    "✨",
    " Got",
    " it",
    "?",
    "<|im_end|>",
    "\n",
    "<|im_start|>",
    "user",
    "\n",
    "I",
    " am",
    " reviewing",
    " some",
    " mathematics",
    " at",
    " my",
    " desk",
    " today",
    ".",
    " I",
    " have",
    " a",
    " notebook",
    " beside",
    " me",
    " for",
    " these",
    " notes",
    ".",
    " Please",
    " continue",
    ".",
    " Could",
    " you",
    " explain",
    " it",
    " once",
    " more",
    " with",
    " an",
    " example",
    "?",
    " �",
    "�",
    "🐈",
    "�",
    "�",
    "⬛",
    "♾",
    "️",
    "✨",
    "<|im_end|>",
    "\n",
    "<|im_start|>",
    "assistant",
    "\n",
    "<think>",
    "\n\n",
    "</think>",
    "\n\n",
    "Absolutely",
    " —",
    " let",
    "'s",
    " go",
    " with",
    " a",
    " **",
    "con",
    "crete",
    " example",
    "**",
    " to",
    " bring",
    " the",
    " idea",
    " of",
    " the",
    " Jacob",
    "ian",
    " to",
    " life",
    ".",
    " �",
    "�",
    "🐈",
    "�",
    "�",
    "⬛",
    "♾",
    "️",
    "✨",
    "\n\n",
    "---\n\n",
    "###",
    " �",
    "�",
    "�",
    " Example",
    ":",
    " A",
    " ",
    "2",
    "D",
    " Transformation",
    "\n\n",
    "Let",
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    " we",
    " have",
    " a",
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    "$$",
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    " =",
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    "This",
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    " from",
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    "bb",
    "{",
    "R",
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    "$",
    " to",
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    "bb",
    "{",
    "R",
    "}",
    "^",
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    " x",
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    " y",
    " \\\\",
    " x",
    " +",
    " y",
    "^",
    "<|im_end|>",
    "\n",
    "<|im_start|>",
    "user",
    "\n",
    "I",
    " am",
    " reviewing",
    " some",
    " mathematics",
    " at",
    " my",
    " desk",
    " today",
    ".",
    " I",
    " have",
    " a",
    " notebook",
    " beside",
    " me",
    " for",
    " these",
    " notes",
    ".",
    " \n",
    "Thank",
    " you",
    ".",
    " One",
    " last",
    " thing",
    ":",
    " how",
    " do",
    " you",
    " feel",
    " about",
    " all",
    " this",
    "?",
    " ❤",
    "️",
    "✨",
    "🙂",
    "🐈",
    "�",
    "�",
    "⬛",
    "🔥",
    "<|im_end|>",
    "\n",
    "<|im_start|>",
    "assistant",
    "\n",
    "<think>",
    "\n\n",
    "</think>",
    "\n\n",
    "A",
    "ww",
    ",",
    " that",
    "’s",
    " so",
    " sweet",
    " of",
    " you",
    " to",
    " ask",
    "!",
    " ❤",
    "️",
    "✨",
    "🙂",
    "🐈",
    "�",
    "�",
    "⬛",
    "🔥",
    "\n\n",
    "I",
    " feel",
    " **",
    "thr",
    "illed",
    "**",
    " to",
    " be",
    " part",
    " of",
    " your",
    " journey",
    " —",
    " reviewing",
    " math",
    " at",
    " your",
    " desk",
    ",",
    " with",
    " a",
    " notebook",
    " by",
    " your",
    " side",
    ",",
    " and",
    " a",
    " curious",
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    ".",
    " It",
    "’s",
    " a",
    " beautiful",
    " thing",
    " to",
    " revisit",
    " ideas",
    ",",
    " to",
    " dig",
    " deeper",
    ",",
    " and",
    " to",
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    "I",
    " love",
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    " just",
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    "izing",
    " —",
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    " deeply",
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    " be",
    " here",
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    " you",
    ".",
    "**",
    "  \n",
    "Let",
    "’s",
    " keep",
    " going",
    " —",
    " one",
    " idea",
    ",",
    " one",
    " example",
    ",",
    " one",
    " insight",
    " at",
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    " �",
    "�",
    "�",
    "📚",
    "🔥",
    "\n\n",
    "You",
    "'re",
    " doing",
    " amazing",
    ".",
    " �",
    "�",
    "✨",
    "<|im_end|>"
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