A small tool to view real-world ActivityPub objects as JSON! Enter a URL
or username from Mastodon or a similar service below, and we'll send a
request with
the right
Accept
header
to the server to view the underlying object.
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"id": "https://mathstodon.xyz/users/OscarCunningham/statuses/113253885108835863",
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"published": "2024-10-05T08:32:23Z",
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"content": "<p><a href=\"https://mathstodon.xyz/tags/Mathober\" class=\"mention hashtag\" rel=\"tag\">#<span>Mathober</span></a> <a href=\"https://mathstodon.xyz/tags/Mathober2024\" class=\"mention hashtag\" rel=\"tag\">#<span>Mathober2024</span></a></p><p>The prompt for day 4 was 'Form'. In algebra, a multilinear map is a function from several vector spaces to another vector space which is linear in each argument. Just as a linear map can be represented by a grid of numbers in a matrix, a multilinear map can be represented by a multidimensional grid of numbers: a tensor. A 'form' is the function you get by taking a multilinear map from V×...×V to the scalars and evaluating it with each of its arguments the same. In this way you get a *non*linear map from V to the scalars.</p><p>The image shows a degree 50 form on ℝ³ evaluated on the unit sphere. The form was randomly chosen with each of the 3⁵⁰ entries in its tensor having a standard normal distribution. </p><p><a href=\"https://mathstodon.xyz/tags/Math\" class=\"mention hashtag\" rel=\"tag\">#<span>Math</span></a> <a href=\"https://mathstodon.xyz/tags/Maths\" class=\"mention hashtag\" rel=\"tag\">#<span>Maths</span></a> <a href=\"https://mathstodon.xyz/tags/Mathematics\" class=\"mention hashtag\" rel=\"tag\">#<span>Mathematics</span></a> <a href=\"https://mathstodon.xyz/tags/Algebra\" class=\"mention hashtag\" rel=\"tag\">#<span>Algebra</span></a></p>",
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"en": "<p><a href=\"https://mathstodon.xyz/tags/Mathober\" class=\"mention hashtag\" rel=\"tag\">#<span>Mathober</span></a> <a href=\"https://mathstodon.xyz/tags/Mathober2024\" class=\"mention hashtag\" rel=\"tag\">#<span>Mathober2024</span></a></p><p>The prompt for day 4 was 'Form'. In algebra, a multilinear map is a function from several vector spaces to another vector space which is linear in each argument. Just as a linear map can be represented by a grid of numbers in a matrix, a multilinear map can be represented by a multidimensional grid of numbers: a tensor. A 'form' is the function you get by taking a multilinear map from V×...×V to the scalars and evaluating it with each of its arguments the same. In this way you get a *non*linear map from V to the scalars.</p><p>The image shows a degree 50 form on ℝ³ evaluated on the unit sphere. The form was randomly chosen with each of the 3⁵⁰ entries in its tensor having a standard normal distribution. </p><p><a href=\"https://mathstodon.xyz/tags/Math\" class=\"mention hashtag\" rel=\"tag\">#<span>Math</span></a> <a href=\"https://mathstodon.xyz/tags/Maths\" class=\"mention hashtag\" rel=\"tag\">#<span>Maths</span></a> <a href=\"https://mathstodon.xyz/tags/Mathematics\" class=\"mention hashtag\" rel=\"tag\">#<span>Mathematics</span></a> <a href=\"https://mathstodon.xyz/tags/Algebra\" class=\"mention hashtag\" rel=\"tag\">#<span>Algebra</span></a></p>"
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