{ localUrl: '../page/grahams_number.html', arbitalUrl: 'https://arbital.com/p/grahams_number', rawJsonUrl: '../raw/42j.json', likeableId: '2608', likeableType: 'page', myLikeValue: '0', likeCount: '1', dislikeCount: '0', likeScore: '1', individualLikes: [ 'EricRogstad' ], pageId: 'grahams_number', edit: '2', editSummary: '', prevEdit: '1', currentEdit: '2', wasPublished: 'true', type: 'wiki', title: 'Graham's number', clickbait: 'A fairly large number, as numbers go.', textLength: '701', alias: 'grahams_number', externalUrl: '', sortChildrenBy: 'likes', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'NateSoares', editCreatedAt: '2016-06-08 01:06:08', pageCreatorId: 'NateSoares', pageCreatedAt: '2016-06-08 00:05:13', seeDomainId: '0', editDomainId: 'AlexeiAndreev', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '0', isEditorComment: 'false', isApprovedComment: 'true', isResolved: 'false', snapshotText: '', anchorContext: '', anchorText: '', anchorOffset: '0', mergedInto: '', isDeleted: 'false', viewCount: '38', text: '[summary: \nGraham's number is a... rather large number. Tim Urban of _Wait but Why_ gives a [http://waitbutwhy.com/2014/11/1000000-grahams-number.html good introduction].\n\n![](http://28oa9i1t08037ue3m1l0i861.wpengine.netdna-cdn.com/wp-content/uploads/2014/11/grahams-number.png)]\n\nGraham's number is a... rather large number. Letting $f(x) = 3\\uparrow^n 3$ (in [+knuth_up_arrow_notation]) and $f^n(x) = \\underbrace{f(f(f(\\cdots f(f(x)) \\cdots ))}_{n\\text{ applications of }f}$, Graham's number is defined to be $f^{64}(4).$\n\nThe result is sizable. For an explanation of how large this is and why, see Tim Urban's [http://waitbutwhy.com/2014/11/1000000-grahams-number.html explanation] at Wait but Why.', metaText: '', isTextLoaded: 'true', isSubscribedToDiscussion: 'false', isSubscribedToUser: 'false', isSubscribedAsMaintainer: 'false', discussionSubscriberCount: '1', maintainerCount: '1', userSubscriberCount: '0', lastVisit: '', hasDraft: 'false', votes: [], voteSummary: 'null', muVoteSummary: '0', voteScaling: '0', currentUserVote: '-2', voteCount: '0', lockedVoteType: '', maxEditEver: '0', redLinkCount: '0', lockedBy: '', lockedUntil: '', nextPageId: '', prevPageId: '', usedAsMastery: 'false', proposalEditNum: '0', permissions: { edit: { has: 'false', reason: 'You don't have domain permission to edit this page' }, proposeEdit: { has: 'true', reason: '' }, delete: { has: 'false', reason: 'You don't have domain permission to delete this page' }, comment: { has: 'false', reason: 'You can't comment in this domain because you are not a member' }, proposeComment: { has: 'true', reason: '' } }, summaries: {}, creatorIds: [ 'NateSoares' ], childIds: [], parentIds: [ 'natural_number' ], commentIds: [], questionIds: [], tagIds: [ 'stub_meta_tag' ], relatedIds: [], markIds: [], explanations: [], learnMore: [], requirements: [], subjects: [], lenses: [], lensParentId: '', pathPages: [], learnMoreTaughtMap: {}, learnMoreCoveredMap: {}, learnMoreRequiredMap: {}, editHistory: {}, domainSubmissions: {}, answers: [], answerCount: '0', commentCount: '0', newCommentCount: '0', linkedMarkCount: '0', changeLogs: [ { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '19012', pageId: 'grahams_number', userId: 'EricBruylant', edit: '0', type: 'deleteParent', createdAt: '2016-08-20 13:20:46', auxPageId: 'math', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '19010', pageId: 'grahams_number', userId: 'EricBruylant', edit: '0', type: 'newParent', createdAt: '2016-08-20 13:20:45', auxPageId: 'natural_number', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '11999', pageId: 'grahams_number', userId: 'NateSoares', edit: '2', type: 'newEdit', createdAt: '2016-06-08 01:06:08', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '11977', pageId: 'grahams_number', userId: 'NateSoares', edit: '1', type: 'newEdit', createdAt: '2016-06-08 00:05:13', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '11972', pageId: 'grahams_number', userId: 'NateSoares', edit: '1', type: 'newTag', createdAt: '2016-06-07 23:48:37', auxPageId: 'stub_meta_tag', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '11971', pageId: 'grahams_number', userId: 'NateSoares', edit: '1', type: 'newParent', createdAt: '2016-06-07 23:48:33', auxPageId: 'math', oldSettingsValue: '', newSettingsValue: '' } ], feedSubmissions: [], searchStrings: {}, hasChildren: 'false', hasParents: 'true', redAliases: {}, improvementTagIds: [], nonMetaTagIds: [], todos: [], slowDownMap: 'null', speedUpMap: 'null', arcPageIds: 'null', contentRequests: {} }