{"id":107968,"date":"2026-06-02T00:35:16","date_gmt":"2026-06-01T22:35:16","guid":{"rendered":"https:\/\/www.infokuryr.cz\/n\/?p=107968"},"modified":"2026-06-01T18:02:48","modified_gmt":"2026-06-01T16:02:48","slug":"alessio-zaccone-novy-matematicky-model-naznacuje-pokles-globalni-populace-do-roku-2064","status":"publish","type":"post","link":"https:\/\/www.infokuryr.cz\/n\/2026\/06\/02\/alessio-zaccone-novy-matematicky-model-naznacuje-pokles-globalni-populace-do-roku-2064\/","title":{"rendered":"Alessio Zaccone: Nov\u00fd matematick\u00fd model nazna\u010duje pokles glob\u00e1ln\u00ed populace do roku 2064"},"content":{"rendered":"
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Kdy\u017e byl v roce 2008 uveden dokument \u201eDemografick\u00e1 zima\u201c a v roce 2009 jeho pokra\u010dov\u00e1n\u00ed \u201eDemografick\u00e1 bomba\u201c, psal jsem rozs\u00e1hle o \u00fabytku populace. Dokumenty nato\u010dili soci\u00e1ln\u00ed v\u011bdci na z\u00e1klad\u011b spolehliv\u00fdch d\u016fkaz\u016f. O osmn\u00e1ct let pozd\u011bji to technokrati\u010dt\u00ed \u0161prtov\u00e9 kone\u010dn\u011b pochopili. Kupodivu m\u00fdtus o p\u0159elidn\u011bn\u00ed p\u0159etrv\u00e1v\u00e1 \u2013 d\u00edky \u0161\u00edlenc\u016fm, jako je Paul Ehrlich, kter\u00fd v roce 1968 napsal knihu \u201ePopula\u010dn\u00ed bomba\u201c.<\/span><\/em>\u00a0\u2013 Patrick Wood, editor.<\/span><\/p>\n

V nov\u00e9 studii s otev\u0159en\u00fdm p\u0159\u00edstupem, kterou jsem publikoval spole\u010dn\u011b se sv\u00fdm zesnul\u00fdm kolegou Kostou Tra\u010denkem z Queen Mary University v Lond\u00fdn\u011b, prezentuji p\u0159ekvapiv\u011b jednoduchou neline\u00e1rn\u00ed matematickou rovnici, kter\u00e1 shrnuje popula\u010dn\u00ed r\u016fst za posledn\u00edch 12 000 let a poukazuje na mo\u017en\u00e9, drastick\u00e9 budouc\u00ed sc\u00e9n\u00e1\u0159e, pokud by se glob\u00e1ln\u00ed environment\u00e1ln\u00ed krize zhor\u0161ily.<\/span><\/p>\n

Studie publikovan\u00e1<\/a>\u00a0v \u010dasopise\u00a0<\/span>Chaos, Solitons & Fractals<\/span><\/em>\u00a0p\u0159edstavuje neline\u00e1rn\u00ed model \u201ezp\u011btn\u00e9 vazby rychlosti\u201c pro glob\u00e1ln\u00ed popula\u010dn\u00ed r\u016fst, kter\u00fd jsem p\u016fvodn\u011b vyvinul spole\u010dn\u011b s Tra\u010denkem v jin\u00e9m kontextu, konkr\u00e9tn\u011b ve fyzice neuspo\u0159\u00e1dan\u00fdch materi\u00e1l\u016f, jako jsou skla a amorfn\u00ed pevn\u00e9 l\u00e1tky.<\/span><\/p>\n

Jednoduch\u00e9 sledov\u00e1n\u00ed pom\u016f\u017ee nez\u00e1visl\u00e9 v\u011bdeck\u00e9 \u017eurnalistice z\u016fstat viditelnou.\u00a0<\/span>Sledujte Phys.org na Googlu<\/span><\/a>\u00a0.<\/span><\/em><\/p>\n

Nyn\u00ed ukazujeme, \u017ee stejn\u00e1 matematika dok\u00e1\u017ee reprodukovat mnoho hlavn\u00edch vzorc\u016f popula\u010dn\u00edho r\u016fstu pozorovan\u00fdch za posledn\u00edch 12 000 let, od obdob\u00ed neolitu a\u017e po modern\u00ed dobu.<\/span><\/p>\n

Na rozd\u00edl od klasick\u00fdch demografick\u00fdch model\u016f, kter\u00e9 r\u016fst ch\u00e1pou bu\u010f jako exponenci\u00e1ln\u00ed, nebo logistick\u00fd, se n\u00e1\u0161 nov\u00fd r\u00e1mec m\u016f\u017ee p\u0159irozen\u011b p\u0159ep\u00ednat mezi v\u00edce historick\u00fdmi re\u017eimy pomoc\u00ed jedin\u00e9ho parametru. V n\u011bkter\u00fdch obdob\u00edch lidsk\u00e1 populace rostla pomalu a stabiln\u011b; v jin\u00fdch se r\u016fst explozivn\u011b zrychloval. Podle na\u0161eho odvozen\u00ed mohou v\u0161echny tyto posuny vypl\u00fdvat ze stejn\u00e9 z\u00e1kladn\u00ed neline\u00e1rn\u00ed dynamiky.<\/span><\/p>\n

N\u00e1\u0161 model se tak\u00e9 vrac\u00ed k jedn\u00e9 z nejslavn\u011bj\u0161\u00edch p\u0159edpov\u011bd\u00ed v popula\u010dn\u00ed v\u011bd\u011b: \u201esc\u00e9n\u00e1\u0159 soudn\u00e9ho dne\u201c, kter\u00fd v roce 1960 navrhl Heinz von Foerster a kolegov\u00e9, kte\u0159\u00ed matematicky extrapolovali, \u017ee sv\u011btov\u00e1 populace bude kolem roku 2026 sm\u011b\u0159ovat k nekone\u010dnu.<\/span><\/p>\n

Lidstvo se tomuto sc\u00e9n\u00e1\u0159i vyhnulo, proto\u017ee porodnost celosv\u011btov\u011b klesala, ale na\u0161e nov\u00e1 studie tvrd\u00ed, \u017ee z\u00e1kladn\u00ed matematika nekontrolovateln\u00e9ho r\u016fstu se za ur\u010dit\u00fdch podm\u00ednek m\u016f\u017ee znovu projevit.<\/span><\/p>\n

Pro ov\u011b\u0159en\u00ed teorie jsme porovnali na\u0161i rovnici (n\u011bkdy naz\u00fdvanou Trachenko-Zacconeova rovnice) s empirick\u00fdmi popula\u010dn\u00edmi daty z r\u016fzn\u00fdch historick\u00fdch obdob\u00ed. Zjistili jsme, \u017ee model \u00fasp\u011b\u0161n\u011b replikuje jak f\u00e1ze \u201estla\u010den\u00e9ho exponenci\u00e1ln\u00edho\u201c r\u016fstu, jako je rychl\u00e1 expanze b\u011bhem pr\u016fmyslov\u00e9ho v\u011bku, tak i pomalej\u0161\u00ed \u201erozta\u017een\u00fd exponenci\u00e1ln\u00ed\u201c re\u017eim, kter\u00fd charakterizuje glob\u00e1ln\u00ed popula\u010dn\u00ed r\u016fst p\u0159ibli\u017en\u011b od roku 1970.<\/span><\/p>\n

Nejprovokuj\u00edc\u00edj\u0161\u00ed \u010d\u00e1st na\u0161\u00ed pr\u00e1ce zkoum\u00e1 hypotetick\u00e9 budouc\u00ed sc\u00e9n\u00e1\u0159e. V na\u0161\u00ed z\u00e1kladn\u00ed anal\u00fdze sou\u010dasn\u00fd glob\u00e1ln\u00ed trend nevede ke katastrofick\u00e9 singularit\u011b, jak p\u0159edpov\u00eddali von Foerster a jeho kolegov\u00e9, proto\u017ee kl\u00ed\u010dov\u00fd parametr z\u016fst\u00e1v\u00e1 v r\u00e1mci stabiliza\u010dn\u00edho re\u017eimu.<\/span><\/p>\n

Tak\u00e9 jsme v\u0161ak modelovali, co by se mohlo st\u00e1t, kdyby velk\u00e9 environment\u00e1ln\u00ed krize na Zemi, jako je klimatick\u00fd kolaps, pandemie, konflikty nebo nedostatek zdroj\u016f, n\u00e1hle zavedly p\u0159\u00edsn\u00e1 omezen\u00ed \u00fanosnosti.<\/span><\/p>\n

Za z\u00e1m\u011brn\u011b konzervativn\u00edho nejhor\u0161\u00edho p\u0159edpokladu, \u017ee udr\u017eiteln\u00e1 \u00fanosn\u00e1 kapacita Zem\u011b n\u00e1hle klesne na p\u0159ibli\u017en\u011b 2 miliardy lid\u00ed, n\u00e1\u0161 model p\u0159edpov\u00edd\u00e1 rychl\u00fd glob\u00e1ln\u00ed pokles populace, v n\u011bm\u017e by se lidstvo mohlo potenci\u00e1ln\u011b sn\u00ed\u017eit na polovinu do roku 2064.<\/span><\/p>\n

V tomto \u010dl\u00e1nku zd\u016fraz\u0148ujeme, \u017ee se nejedn\u00e1 o progn\u00f3zu, ale sp\u00ed\u0161e o ilustrativn\u00ed matematick\u00fd sc\u00e9n\u00e1\u0159, jeho\u017e c\u00edlem je demonstrovat, jak citliv\u00e1 m\u016f\u017ee b\u00fdt popula\u010dn\u00ed dynamika na n\u00e1hl\u00e9 ekologick\u00e9 nebo soci\u00e1ln\u00ed zm\u011bny. Zd\u016fraz\u0148ujeme, \u017ee sou\u010dasn\u00fd trend z\u016fst\u00e1v\u00e1 relativn\u011b stabiln\u00ed a neznamen\u00e1 bezprost\u0159edn\u00ed kolaps.<\/span><\/p>\n

Krom\u011b demografie se domn\u00edv\u00e1me, \u017ee tato pr\u00e1ce by mohla b\u00fdt zaj\u00edmav\u00e1 i pro p\u0159enos my\u0161lenek z\u00a0<\/span>fyziky kondenzovan\u00fdch l\u00e1tek<\/span><\/a>\u00a0do popula\u010dn\u00ed v\u011bdy. Stejn\u00e9 matematick\u00e9 struktury pou\u017e\u00edvan\u00e9 k popisu relaxace atomov\u00e9 dynamiky ve sklech v pr\u016fb\u011bhu \u010dasu se zdaj\u00ed b\u00fdt schopny popsat, jak lidsk\u00e9 spole\u010dnosti rostou, stabilizuj\u00ed se a potenci\u00e1ln\u011b destabilizuj\u00ed v pr\u016fb\u011bhu stalet\u00ed.<\/span><\/p>\n

Podle na\u0161\u00ed anal\u00fdzy nab\u00edz\u00ed matematick\u00fd r\u00e1mec kompaktn\u00ed zp\u016fsob, jak zkoumat mo\u017en\u00e9 budouc\u00ed sc\u00e9n\u00e1\u0159e \u2013 od udr\u017eiteln\u00e9 stabilizace p\u0159es nekontrolovan\u00fd r\u016fst a\u017e po n\u00e1hl\u00fd kolaps \u2013 v r\u00e1mci jednotn\u00e9ho matematick\u00e9ho jazyka.<\/span><\/p>\n<\/div>\n<\/div>\n

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Zdroj<\/span><\/a><\/span><\/h3>\n

 <\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Kdy\u017e byl v roce 2008 uveden dokument \u201eDemografick\u00e1 zima\u201c a v roce 2009 jeho pokra\u010dov\u00e1n\u00ed…<\/p>\n","protected":false},"author":2,"featured_media":107969,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[7],"tags":[794,11076,2284,11077],"_links":{"self":[{"href":"https:\/\/www.infokuryr.cz\/n\/wp-json\/wp\/v2\/posts\/107968"}],"collection":[{"href":"https:\/\/www.infokuryr.cz\/n\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.infokuryr.cz\/n\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.infokuryr.cz\/n\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.infokuryr.cz\/n\/wp-json\/wp\/v2\/comments?post=107968"}],"version-history":[{"count":0,"href":"https:\/\/www.infokuryr.cz\/n\/wp-json\/wp\/v2\/posts\/107968\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.infokuryr.cz\/n\/wp-json\/wp\/v2\/media\/107969"}],"wp:attachment":[{"href":"https:\/\/www.infokuryr.cz\/n\/wp-json\/wp\/v2\/media?parent=107968"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.infokuryr.cz\/n\/wp-json\/wp\/v2\/categories?post=107968"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.infokuryr.cz\/n\/wp-json\/wp\/v2\/tags?post=107968"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}