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.
{
"@context": [
"https://www.w3.org/ns/activitystreams",
{
"ostatus": "http://ostatus.org#",
"atomUri": "ostatus:atomUri",
"inReplyToAtomUri": "ostatus:inReplyToAtomUri",
"conversation": "ostatus:conversation",
"sensitive": "as:sensitive",
"toot": "http://joinmastodon.org/ns#",
"votersCount": "toot:votersCount",
"blurhash": "toot:blurhash",
"focalPoint": {
"@container": "@list",
"@id": "toot:focalPoint"
}
}
],
"id": "https://mathstodon.xyz/users/gregeganSF/outbox?min_id=109279855268163423&page=true",
"type": "OrderedCollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/outbox?max_id=109282874435082188&page=true",
"prev": "https://mathstodon.xyz/users/gregeganSF/outbox?min_id=109312480977112921&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/outbox",
"orderedItems": [
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109312480977112921/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-09T06:41:29Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109312480977112921",
"type": "Note",
"summary": null,
"inReplyTo": null,
"published": "2022-11-09T06:41:29Z",
"url": "https://mathstodon.xyz/@gregeganSF/109312480977112921",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109312480977112921",
"inReplyToAtomUri": null,
"conversation": "tag:mathstodon.xyz,2022-11-09:objectId=28731908:objectType=Conversation",
"content": "<p>If you’re in Australia, there’s sure to be something on <br /><a href=\"https://www.sbs.com.au/ondemand/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://www.</span><span class=\"\">sbs.com.au/ondemand/</span><span class=\"invisible\"></span></a><br /> that will grab you. “Atlanta”, “The Good Fight”, “Halt and Catch Fire” (until 30 Nov), “My Brilliant Friend”. I plan to watch the movie “Drive My Car” on the w/end. And the ads are so repetitive they no longer register; when you’ve seen them all 500 times, your mind just filters them out, like the refrigerator motor switching on and off.</p>",
"contentMap": {
"en": "<p>If you’re in Australia, there’s sure to be something on <br /><a href=\"https://www.sbs.com.au/ondemand/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://www.</span><span class=\"\">sbs.com.au/ondemand/</span><span class=\"invisible\"></span></a><br /> that will grab you. “Atlanta”, “The Good Fight”, “Halt and Catch Fire” (until 30 Nov), “My Brilliant Friend”. I plan to watch the movie “Drive My Car” on the w/end. And the ads are so repetitive they no longer register; when you’ve seen them all 500 times, your mind just filters them out, like the refrigerator motor switching on and off.</p>"
},
"attachment": [],
"tag": [],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109312480977112921/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109312480977112921/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109312480977112921/replies",
"items": []
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109312480977112921/likes",
"type": "Collection",
"totalItems": 3
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109312480977112921/shares",
"type": "Collection",
"totalItems": 1
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109308133951814864/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-08T12:15:58Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109308133951814864",
"type": "Note",
"summary": null,
"inReplyTo": null,
"published": "2022-11-08T12:15:58Z",
"url": "https://mathstodon.xyz/@gregeganSF/109308133951814864",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109308133951814864",
"inReplyToAtomUri": null,
"conversation": "tag:mathstodon.xyz,2022-11-08:objectId=28638932:objectType=Conversation",
"content": "<p>One thing I find hilarious in “Halt and Catch Fire” is when people are writing code, typing rapidly, and the result appears on their screen at an absolutely uniform rate, as if, umm, a piece of visual effects software was disclosing pre-existing text at a metronomic 100ms/char.</p>",
"contentMap": {
"en": "<p>One thing I find hilarious in “Halt and Catch Fire” is when people are writing code, typing rapidly, and the result appears on their screen at an absolutely uniform rate, as if, umm, a piece of visual effects software was disclosing pre-existing text at a metronomic 100ms/char.</p>"
},
"attachment": [],
"tag": [],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109308133951814864/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109308133951814864/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109308133951814864/replies",
"items": []
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109308133951814864/likes",
"type": "Collection",
"totalItems": 26
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109308133951814864/shares",
"type": "Collection",
"totalItems": 6
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109306578798377344/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-08T05:40:29Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109306578798377344",
"type": "Note",
"summary": null,
"inReplyTo": null,
"published": "2022-11-08T05:40:29Z",
"url": "https://mathstodon.xyz/@gregeganSF/109306578798377344",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109306578798377344",
"inReplyToAtomUri": null,
"conversation": "tag:mathstodon.xyz,2022-11-08:objectId=28614460:objectType=Conversation",
"content": "<p>How erudite of my spellchecker not to redline “throughly”, which is apparently an archaic version of “thoroughly” that isn’t mentioned in any dictionary I own, and couldn’t possibly be, you know, a typo for “thoroughly”. Fck.</p>",
"contentMap": {
"en": "<p>How erudite of my spellchecker not to redline “throughly”, which is apparently an archaic version of “thoroughly” that isn’t mentioned in any dictionary I own, and couldn’t possibly be, you know, a typo for “thoroughly”. Fck.</p>"
},
"attachment": [
{
"type": "Document",
"mediaType": "image/png",
"url": "https://media.mathstodon.xyz/media_attachments/files/109/306/577/219/009/225/original/dea7b89c37fcfb02.png",
"name": "How erudite of my spellchecker not to redline “throughly”, which is apparently an archaic version of “thoroughly” that isn’t mentioned in any dictionary I own, and couldn’t possibly be, you know, a typo for “thoroughly”. Fck.\n",
"blurhash": "UmM%}}WB9Fj[xufQWBay00j[xuayxuayWBj[",
"focalPoint": [
0,
0
],
"width": 934,
"height": 574
}
],
"tag": [],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109306578798377344/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109306578798377344/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109306578798377344/replies",
"items": []
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109306578798377344/likes",
"type": "Collection",
"totalItems": 15
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109306578798377344/shares",
"type": "Collection",
"totalItems": 0
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109301812286588588/activity",
"type": "Announce",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-07T09:28:17Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/sharanjit",
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": "https://mathstodon.xyz/users/sharanjit/statuses/109301745533061195"
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109301757866693071/activity",
"type": "Announce",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-07T09:14:27Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/robinhouston",
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": "https://mathstodon.xyz/users/robinhouston/statuses/109297797306654169"
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109299901056703986/activity",
"type": "Announce",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-07T01:22:14Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/ColinTheMathmo",
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": "https://mathstodon.xyz/users/ColinTheMathmo/statuses/109299563379927148"
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109295330149811437/activity",
"type": "Announce",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-06T05:59:48Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mastodon.social/users/mcc",
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": "https://mastodon.social/users/mcc/statuses/109295088643645352"
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291725084415646/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-05T14:42:59Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers",
"https://mathstodon.xyz/users/johncarlosbaez"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291725084415646",
"type": "Note",
"summary": null,
"inReplyTo": "https://mathstodon.xyz/users/johncarlosbaez/statuses/109291705709753361",
"published": "2022-11-05T14:42:59Z",
"url": "https://mathstodon.xyz/@gregeganSF/109291725084415646",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers",
"https://mathstodon.xyz/users/johncarlosbaez"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109291725084415646",
"inReplyToAtomUri": "https://mathstodon.xyz/users/johncarlosbaez/statuses/109291705709753361",
"conversation": "tag:mathstodon.xyz,2022-11-02:objectId=28211198:objectType=Conversation",
"content": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@johncarlosbaez\" class=\"u-url mention\">@<span>johncarlosbaez</span></a></span> No, it looks the correct size.</p>",
"contentMap": {
"en": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@johncarlosbaez\" class=\"u-url mention\">@<span>johncarlosbaez</span></a></span> No, it looks the correct size.</p>"
},
"attachment": [],
"tag": [
{
"type": "Mention",
"href": "https://mathstodon.xyz/users/johncarlosbaez",
"name": "@johncarlosbaez"
}
],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291725084415646/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109291725084415646/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109291725084415646/replies",
"items": []
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291725084415646/likes",
"type": "Collection",
"totalItems": 0
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291725084415646/shares",
"type": "Collection",
"totalItems": 0
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291648289424782/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-05T14:23:27Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers",
"https://mathstodon.xyz/users/johncarlosbaez"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291648289424782",
"type": "Note",
"summary": null,
"inReplyTo": "https://mathstodon.xyz/users/johncarlosbaez/statuses/109291640622775311",
"published": "2022-11-05T14:23:27Z",
"url": "https://mathstodon.xyz/@gregeganSF/109291648289424782",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers",
"https://mathstodon.xyz/users/johncarlosbaez"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109291648289424782",
"inReplyToAtomUri": "https://mathstodon.xyz/users/johncarlosbaez/statuses/109291640622775311",
"conversation": "tag:mathstodon.xyz,2022-11-02:objectId=28211198:objectType=Conversation",
"content": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@johncarlosbaez\" class=\"u-url mention\">@<span>johncarlosbaez</span></a></span> I deleted them from my web site because I forgot I’d linked to them externally (they weren’t linked to by any pages on my site). But I’ve restored them from backups now.</p>",
"contentMap": {
"en": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@johncarlosbaez\" class=\"u-url mention\">@<span>johncarlosbaez</span></a></span> I deleted them from my web site because I forgot I’d linked to them externally (they weren’t linked to by any pages on my site). But I’ve restored them from backups now.</p>"
},
"attachment": [],
"tag": [
{
"type": "Mention",
"href": "https://mathstodon.xyz/users/johncarlosbaez",
"name": "@johncarlosbaez"
}
],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291648289424782/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109291648289424782/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109291648289424782/replies",
"items": []
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291648289424782/likes",
"type": "Collection",
"totalItems": 0
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291648289424782/shares",
"type": "Collection",
"totalItems": 0
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291600371816607/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-05T14:11:16Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers",
"https://mathstodon.xyz/users/johncarlosbaez"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291600371816607",
"type": "Note",
"summary": null,
"inReplyTo": "https://mathstodon.xyz/users/johncarlosbaez/statuses/109291586902847071",
"published": "2022-11-05T14:11:16Z",
"url": "https://mathstodon.xyz/@gregeganSF/109291600371816607",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers",
"https://mathstodon.xyz/users/johncarlosbaez"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109291600371816607",
"inReplyToAtomUri": "https://mathstodon.xyz/users/johncarlosbaez/statuses/109291586902847071",
"conversation": "tag:mathstodon.xyz,2022-11-02:objectId=28211198:objectType=Conversation",
"content": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@johncarlosbaez\" class=\"u-url mention\">@<span>johncarlosbaez</span></a></span> I deleted them from my web site because I forgot I’d linked to them externally (they weren’t linked to by any pages on my site). But I’ve restored them from backups now.</p>",
"contentMap": {
"en": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@johncarlosbaez\" class=\"u-url mention\">@<span>johncarlosbaez</span></a></span> I deleted them from my web site because I forgot I’d linked to them externally (they weren’t linked to by any pages on my site). But I’ve restored them from backups now.</p>"
},
"attachment": [],
"tag": [
{
"type": "Mention",
"href": "https://mathstodon.xyz/users/johncarlosbaez",
"name": "@johncarlosbaez"
}
],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291600371816607/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109291600371816607/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109291600371816607/replies",
"items": []
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291600371816607/likes",
"type": "Collection",
"totalItems": 0
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291600371816607/shares",
"type": "Collection",
"totalItems": 0
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291108960918356/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-05T12:06:18Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291108960918356",
"type": "Note",
"summary": null,
"inReplyTo": null,
"published": "2022-11-05T12:06:18Z",
"url": "https://mathstodon.xyz/@gregeganSF/109291108960918356",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109291108960918356",
"inReplyToAtomUri": null,
"conversation": "tag:mathstodon.xyz,2022-11-05:objectId=28369756:objectType=Conversation",
"content": "<p>I’m just waiting for someone to train an LLM exclusively on a religion’s sacred texts, and then market it as a way to converse with the associated deity or deities.</p>",
"contentMap": {
"en": "<p>I’m just waiting for someone to train an LLM exclusively on a religion’s sacred texts, and then market it as a way to converse with the associated deity or deities.</p>"
},
"attachment": [],
"tag": [],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291108960918356/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109291108960918356/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109291108960918356/replies",
"items": []
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291108960918356/likes",
"type": "Collection",
"totalItems": 18
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291108960918356/shares",
"type": "Collection",
"totalItems": 5
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291086013375132/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-05T12:00:27Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291086013375132",
"type": "Note",
"summary": null,
"inReplyTo": null,
"published": "2022-11-05T12:00:27Z",
"url": "https://mathstodon.xyz/@gregeganSF/109291086013375132",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109291086013375132",
"inReplyToAtomUri": null,
"conversation": "tag:mathstodon.xyz,2022-11-05:objectId=28369516:objectType=Conversation",
"content": "<p>An ingenious way to judge an animal’s expectations of how things in the world behave: see which sleight-of-hand tricks succeed in fooling it.</p><p><a href=\"https://theconversation.com/we-performed-magic-tricks-on-birds-to-see-how-they-perceive-the-world-161772\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">theconversation.com/we-perform</span><span class=\"invisible\">ed-magic-tricks-on-birds-to-see-how-they-perceive-the-world-161772</span></a></p>",
"contentMap": {
"en": "<p>An ingenious way to judge an animal’s expectations of how things in the world behave: see which sleight-of-hand tricks succeed in fooling it.</p><p><a href=\"https://theconversation.com/we-performed-magic-tricks-on-birds-to-see-how-they-perceive-the-world-161772\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">theconversation.com/we-perform</span><span class=\"invisible\">ed-magic-tricks-on-birds-to-see-how-they-perceive-the-world-161772</span></a></p>"
},
"attachment": [],
"tag": [],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291086013375132/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109291086013375132/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109291086013375132/replies",
"items": []
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291086013375132/likes",
"type": "Collection",
"totalItems": 17
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109291086013375132/shares",
"type": "Collection",
"totalItems": 14
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290911841425320/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-05T11:16:10Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290911841425320",
"type": "Note",
"summary": null,
"inReplyTo": "https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626",
"published": "2022-11-05T11:16:10Z",
"url": "https://mathstodon.xyz/@gregeganSF/109290911841425320",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109290911841425320",
"inReplyToAtomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626",
"conversation": "tag:mathstodon.xyz,2022-11-02:objectId=28211198:objectType=Conversation",
"content": "<p>In our grid above, every row and every column has i,j,k appear as the second quaternion in the pair. So any q that is a *simultaneous* eigenvector of all 3 rotations in a row or a column will map i,j and k to ± the first quaternion in the pair, which is always one of i,j,k.</p><p>So q is a symmetry of the octahedron.</p>",
"contentMap": {
"en": "<p>In our grid above, every row and every column has i,j,k appear as the second quaternion in the pair. So any q that is a *simultaneous* eigenvector of all 3 rotations in a row or a column will map i,j and k to ± the first quaternion in the pair, which is always one of i,j,k.</p><p>So q is a symmetry of the octahedron.</p>"
},
"attachment": [],
"tag": [],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290911841425320/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109290911841425320/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109290911841425320/replies",
"items": []
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290911841425320/likes",
"type": "Collection",
"totalItems": 1
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290911841425320/shares",
"type": "Collection",
"totalItems": 0
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-05T11:15:56Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626",
"type": "Note",
"summary": null,
"inReplyTo": "https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809",
"published": "2022-11-05T11:15:56Z",
"url": "https://mathstodon.xyz/@gregeganSF/109290910932627626",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626",
"inReplyToAtomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809",
"conversation": "tag:mathstodon.xyz,2022-11-02:objectId=28211198:objectType=Conversation",
"content": "<p>… then those quaternion pairs yield the same matrices as the Mermin grid!</p><p>Now, suppose q is an eigenvector of the rotation from the pair (r,s), with eigenvalue ±1. Then:</p><p>r q s^{–1} = ± q<br />r q = ± q s<br />r = ± q s q^{–1}<br />Rot_q(s) = ± r</p><p>This means construing q as a three-dimensional rotation, it will map s to ± r.</p>",
"contentMap": {
"en": "<p>… then those quaternion pairs yield the same matrices as the Mermin grid!</p><p>Now, suppose q is an eigenvector of the rotation from the pair (r,s), with eigenvalue ±1. Then:</p><p>r q s^{–1} = ± q<br />r q = ± q s<br />r = ± q s q^{–1}<br />Rot_q(s) = ± r</p><p>This means construing q as a three-dimensional rotation, it will map s to ± r.</p>"
},
"attachment": [],
"tag": [],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626/replies?min_id=109290911841425320&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626/replies",
"items": [
"https://mathstodon.xyz/users/gregeganSF/statuses/109290911841425320"
]
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626/likes",
"type": "Collection",
"totalItems": 0
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626/shares",
"type": "Collection",
"totalItems": 0
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-05T11:14:40Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809",
"type": "Note",
"summary": null,
"inReplyTo": "https://mathstodon.xyz/users/gregeganSF/statuses/109283584820105620",
"published": "2022-11-05T11:14:40Z",
"url": "https://mathstodon.xyz/@gregeganSF/109290905971976809",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809",
"inReplyToAtomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109283584820105620",
"conversation": "tag:mathstodon.xyz,2022-11-02:objectId=28211198:objectType=Conversation",
"content": "<p>What else consists of two 24-cells in R^4?</p><p>The binary octahedral group, containing the 48 quaternions q, that when construed as rotations via:</p><p>x → q x q^{-1}</p><p>give symmetries of the octahedron with vertices ±i, ±j, ±k.</p><p>So … how can we link the Mermin grid to that group?</p><p>Consider the 3 × 3 grid of pairs of quaternions:</p><p>(j, j) (i, i) (k, k)<br />(i, k) (k, j) (j, i)<br />(k, i) (j, k) (i, j)</p><p>If we treat a pair of quaternions (r,s) as defining a rotation in R^4 via:</p><p>x → r x s^{-1}</p>",
"contentMap": {
"en": "<p>What else consists of two 24-cells in R^4?</p><p>The binary octahedral group, containing the 48 quaternions q, that when construed as rotations via:</p><p>x → q x q^{-1}</p><p>give symmetries of the octahedron with vertices ±i, ±j, ±k.</p><p>So … how can we link the Mermin grid to that group?</p><p>Consider the 3 × 3 grid of pairs of quaternions:</p><p>(j, j) (i, i) (k, k)<br />(i, k) (k, j) (j, i)<br />(k, i) (j, k) (i, j)</p><p>If we treat a pair of quaternions (r,s) as defining a rotation in R^4 via:</p><p>x → r x s^{-1}</p>"
},
"attachment": [],
"tag": [],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809/replies?min_id=109290910932627626&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809/replies",
"items": [
"https://mathstodon.xyz/users/gregeganSF/statuses/109290910932627626"
]
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809/likes",
"type": "Collection",
"totalItems": 0
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809/shares",
"type": "Collection",
"totalItems": 0
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109284694954318499/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-04T08:55:08Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers",
"https://mathstodon.xyz/users/johncarlosbaez"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109284694954318499",
"type": "Note",
"summary": null,
"inReplyTo": "https://mathstodon.xyz/users/johncarlosbaez/statuses/109284679794351819",
"published": "2022-11-04T08:55:08Z",
"url": "https://mathstodon.xyz/@gregeganSF/109284694954318499",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers",
"https://mathstodon.xyz/users/johncarlosbaez"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109284694954318499",
"inReplyToAtomUri": "https://mathstodon.xyz/users/johncarlosbaez/statuses/109284679794351819",
"conversation": "tag:mathstodon.xyz,2022-11-02:objectId=28211198:objectType=Conversation",
"content": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@johncarlosbaez\" class=\"u-url mention\">@<span>johncarlosbaez</span></a></span> Not a coincidence, it’s exactly the same thing! (Though I mislaid that animation and redid it here, so it might not be visually identical)</p>",
"contentMap": {
"en": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@johncarlosbaez\" class=\"u-url mention\">@<span>johncarlosbaez</span></a></span> Not a coincidence, it’s exactly the same thing! (Though I mislaid that animation and redid it here, so it might not be visually identical)</p>"
},
"attachment": [],
"tag": [
{
"type": "Mention",
"href": "https://mathstodon.xyz/users/johncarlosbaez",
"name": "@johncarlosbaez"
}
],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109284694954318499/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109284694954318499/replies?only_other_accounts=true&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109284694954318499/replies",
"items": []
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109284694954318499/likes",
"type": "Collection",
"totalItems": 0
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109284694954318499/shares",
"type": "Collection",
"totalItems": 0
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109283839844373034/activity",
"type": "Announce",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-04T05:17:40Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/timhutton",
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": "https://mathstodon.xyz/users/timhutton/statuses/109282216481082509"
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109283595512888718/activity",
"type": "Announce",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-04T04:15:31Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mastodon.online/users/clarkesworld",
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": "https://mastodon.online/users/clarkesworld/statuses/109271422218698874"
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109283584820105620/activity",
"type": "Create",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-04T04:12:48Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109283584820105620",
"type": "Note",
"summary": null,
"inReplyTo": "https://mathstodon.xyz/users/gregeganSF/statuses/109271295120138652",
"published": "2022-11-04T04:12:48Z",
"url": "https://mathstodon.xyz/@gregeganSF/109283584820105620",
"attributedTo": "https://mathstodon.xyz/users/gregeganSF",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"sensitive": false,
"atomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109283584820105620",
"inReplyToAtomUri": "https://mathstodon.xyz/users/gregeganSF/statuses/109271295120138652",
"conversation": "tag:mathstodon.xyz,2022-11-02:objectId=28211198:objectType=Conversation",
"content": "<p>If you take the 3 operators in any row of the Mermin grid, there are 4 orthogonal vectors that are simultaneously eigenvectors of all three.</p><p>These 12 vectors and their opposites are the vertices of a 24-cell! And if you do the same for the columns, you get the 24-cell dual to it (whose vertices are normals to the 24 octahedral cells of the first 24-cell).</p><p>In the image below, the vertices of each colour are simultaneous eigenvectors for each of the three rows of operators.</p>",
"contentMap": {
"en": "<p>If you take the 3 operators in any row of the Mermin grid, there are 4 orthogonal vectors that are simultaneously eigenvectors of all three.</p><p>These 12 vectors and their opposites are the vertices of a 24-cell! And if you do the same for the columns, you get the 24-cell dual to it (whose vertices are normals to the 24 octahedral cells of the first 24-cell).</p><p>In the image below, the vertices of each colour are simultaneous eigenvectors for each of the three rows of operators.</p>"
},
"attachment": [
{
"type": "Document",
"mediaType": "video/mp4",
"url": "https://media.mathstodon.xyz/media_attachments/files/109/283/569/420/489/212/original/a95749e8f14dff2a.mp4",
"name": null,
"blurhash": "UHRysgxu_3Rjt7j[R*n+~qWBM{s:M{kBxuR%",
"width": 506,
"height": 506
}
],
"tag": [],
"replies": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109283584820105620/replies",
"type": "Collection",
"first": {
"type": "CollectionPage",
"next": "https://mathstodon.xyz/users/gregeganSF/statuses/109283584820105620/replies?min_id=109290905971976809&page=true",
"partOf": "https://mathstodon.xyz/users/gregeganSF/statuses/109283584820105620/replies",
"items": [
"https://mathstodon.xyz/users/gregeganSF/statuses/109290905971976809"
]
}
},
"likes": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109283584820105620/likes",
"type": "Collection",
"totalItems": 4
},
"shares": {
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109283584820105620/shares",
"type": "Collection",
"totalItems": 3
}
}
},
{
"id": "https://mathstodon.xyz/users/gregeganSF/statuses/109282874435082188/activity",
"type": "Announce",
"actor": "https://mathstodon.xyz/users/gregeganSF",
"published": "2022-11-04T01:12:09Z",
"to": [
"https://www.w3.org/ns/activitystreams#Public"
],
"cc": [
"https://hci.social/users/sethlazar",
"https://mathstodon.xyz/users/gregeganSF/followers"
],
"object": "https://hci.social/users/sethlazar/statuses/109282808275555231"
}
]
}