{"id":707349,"date":"2023-10-24T23:28:34","date_gmt":"2023-10-25T04:28:34","guid":{"rendered":"https:\/\/www.capgemini.com\/us-en\/?p=707349&#038;preview=true&#038;preview_id=707349"},"modified":"2025-03-06T06:02:23","modified_gmt":"2025-03-06T11:02:23","slug":"exploring-probabilistic-modeling-and-the-future-of-math","status":"publish","type":"post","link":"https:\/\/www.capgemini.com\/us-en\/insights\/expert-perspectives\/exploring-probabilistic-modeling-and-the-future-of-math\/","title":{"rendered":"Exploring probabilistic modeling and the future of math"},"content":{"rendered":"\n<header class=\"wp-block-cg-blocks-hero-blogs header-hero-blogs\"><div class=\"container\"><div class=\"hero-blogs\"><div class=\"hero-blogs-content-wrapper\"><div class=\"row\"><div class=\"col-12\"><div class=\"header-title\"><h1>Exploring probabilistic modeling and the future of math<\/h1><\/div><\/div><\/div><\/div><div class=\"hero-blogs-bottom\"><div class=\"header-author\"><div class=\"author-img\"><img decoding=\"async\" src=\"https:\/\/www.capgemini.com\/wp-content\/uploads\/2023\/07\/Robert-H.P.-Engels.jpg?w=200&amp;quality=10\" alt=\"\" loading=\"lazy\"\/><\/div><div class=\"author-name-date\"><h5 class=\"author-name\">Robert H. P. Engels<\/h5><h5 class=\"blog-date\">Oct 23, 2023<\/h5><\/div><\/div><div class=\"brand-image\"> <\/div><\/div><\/div><\/div><\/header>\n\n\n\n<section class=\"wp-block-cg-blocks-group undefined section section--article-content\"><div class=\"article-main-content\"><div class=\"container\"><div class=\"row\"><div class=\"col-12 col-md-1\"><nav class=\"article-social\"><ul class=\"social-nav\"><li class=\"ip-order-fb\"><a href=\"https:\/\/www.facebook.com\/sharer\/sharer.php?u=https:\/\/www.capgemini.com\/?p=965284\" target=\"_blank\" rel=\"noopener noreferrer\" title=\"opens in a new window\"><i aria-hidden=\"true\" class=\"icon-fb\"><\/i><span class=\"sr-only\">Facebook<\/span><\/a><\/li><li class=\"ip-order-tw\"><a href=\"https:\/\/twitter.com\/intent\/tweet?url=https:\/\/www.capgemini.com\/?p=965284&amp;text=\" target=\"_blank\" rel=\"noopener noreferrer\" title=\"opens in a new window\"><i aria-hidden=\"true\" class=\"icon-tw\"><\/i><span class=\"sr-only\">Twitter<\/span><\/a><\/li><li class=\"ip-order-li\"><a href=\"https:\/\/www.linkedin.com\/shareArticle?url=https:\/\/www.capgemini.com\/?p=965284&amp;text=\" target=\"_blank\" rel=\"noopener noreferrer\" title=\"opens in a new window\"><i aria-hidden=\"true\" class=\"icon-li\"><\/i><span class=\"sr-only\">Linkedin<\/span><\/a><\/li><\/ul><\/nav><\/div><div class=\"col-12 col-md-11 col-lg-10\"><div class=\"article-text article-quote-text\">\n<h2 class=\"wp-block-heading\" id=\"h-some-days-you-get-these-chains-of-interesting-events-following-up-on-each-other\">Some days you get these chains of interesting events following up on each other.<\/h2>\n\n\n\n<p>This morning I read the &#8220;GPT can solve math[.. ]&#8221; paper (<a href=\"https:\/\/lnkd.in\/dzd7K3sx\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/lnkd.in\/dzd7K3sx<\/a>), then I read some responses to that (o.a. Gary Marcus, X-tweets etc). During and after the TED AI I had many interesting discussions on the topic of probabilistic modelling vs models of math as we know (knew?) it, and this paper sparked some thoughts (so: mission accomplished).<\/p>\n\n\n\n<p>It occurs to me that we have a generation of PhD students building LLMs that have probably not really got interested model thinking and mathematical proofs. I.e. the thinking behind Einsteins\u00b4 relativity theory, the thinking behind Euler&#8217;s Graph theory, the type of thinking that led (indeed) to a mathematical model that you can implement in a calculator (low footprint), calculates correctly (100% trustworthy) and in addition can calculate things 100% correct on input unseen before.<\/p>\n\n\n\n<p>The question really condenses down to the fact whether you believe in the abstraction capability in current algorithms used for training todays LLMs. Are attention layers at all able to build abstractions on their own (and not regurgitating from abstractions it got ready-served by humans)? Optimism in the Valley is big, just add more data and the problem will go away.<\/p>\n\n\n\n<p>But without changing the underlying attention layer design this seems to be a fallacy. Learning to abstract really means to build metalevels on your information, condense signals and their relations. That is something different as predicting chains of tokens. Such an abstraction layer can be seen as building a 3D puzzle, whereas current attention mechanisms seem single-layered. With a single layer, the most you can build is a 2D puzzle.<\/p>\n\n\n\n<p>With that picture in mind, you can observe that current solutions by LLM suppliers is to extend the 2D puzzle, making it larger (adding more data from all over), or giving it higher resolution for a specific task (like the math paper mentioned above). But no sincere attempts seem to have been made yet to build a 3D picture, which would mean to rock the foundation of the foundation models and rebuild the attention layer mechanism to cover for this deficit.<\/p>\n\n\n\n<p>Until then, let&#8217;s focus on getting functions to work reliable and off-load model-based tasks (math, engineering, logic, reasoning) to external capability agents and stop pretending that 2D can become 3D without changing the foundation.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/www.capgemini.com\/wp-content\/uploads\/2023\/10\/1697838702308.jpg?w=960\" alt=\"\" class=\"wp-image-965297\"\/><\/figure>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-outline is-style-outline--1\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/www.linkedin.com\/posts\/robertengels_gpt4mathpaper-probabilisticvsmathematicalmodeling-activity-7121251674739871744-w5NK\/?utm_source=share&amp;utm_medium=member_ios\" target=\"_blank\" rel=\"noreferrer noopener\">Add your voices on LinkedIn<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div><\/section>\n\n\n\n<section class=\"wp-block-cg-blocks-wrapper-people-slider section section--expert-slider wrapper-people-slider undefined\"><div class=\"container\"><div class=\"content-title\"><h2 data-maxlength=\"34\" class=\"people-heading-title\">Meet the author<\/h2><\/div><\/div><div class=\"slider slider-boxed\"><div class=\"container\"><div class=\"slider-window\"><div class=\"slider-list\">\t\t<div class=\"slide\">\n\t\t\t<div class=\"box\">\n\t\t\t\t<div class=\"row\">\n\t\t\t\t\t<div class=\"col-md-6 col-lg-4 box-img-wrapper\">\n\t\t\t\t\t\t<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/www.capgemini.com\/us-en\/wp-content\/uploads\/sites\/30\/2021\/05\/Robert-Engels.webp\" alt=\"Robert Engels\"\/>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div class=\"col-md-6 col-lg-8 box-inner\">\n\t\t\t\t\t\t<div class=\"row title-social-media-header\">\n\t\t\t\t\t\t\t<div class=\"col-md-12 col-lg-6 mbl-social-icon\">\n\t\t\t\t\t\t\t\t<ul class=\"social-nav\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<li>\n\t\t\t\t\t\t\t\t\t\t\t<a class=\"subnav-button--form\" href=\"javascript:void(0)\" aria-label=\"contact us\" data-bs-toggle=\"modal\" data-bs-target=\"#WPB562841c2_627a_454e_a112_6f91d37fbcac\" data-bs-expert-title=\"1\">\n\t\t\t\t\t\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"ico-form\"><\/i>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<li><a aria-label=\"Linkedin\" target=\"_blank\" title=\"Opens in a new window\" href=\"https:\/\/www.linkedin.com\/in\/esisnorge\/\"><i aria-hidden=\"true\" class=\"icon-li\"><\/i><\/a><\/li>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"col-md-12 col-lg-6 box-container\">\n\t\t\t\t\t\t\t\t<div class=\"box-title\">\n\t\t\t\t\t\t\t\t\t<h3 class=\"people-profile-title\">Robert Engels<\/h3>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span>Vice President, CTIO Capgemini I&amp;D North and Central Europe | Head of Generative AI Lab<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"col-md-12 col-lg-6 social-box-container dkt-social-icon\">\n\t\t\t\t\t\t\t\t<ul class=\"social-nav\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<li>\n\t\t\t\t\t\t\t\t\t\t\t<a class=\"subnav-button--form\" href=\"javascript:void(0)\" aria-label=\"contact us\" data-bs-toggle=\"modal\" data-bs-target=\"#WPB562841c2_627a_454e_a112_6f91d37fbcac\" data-bs-expert-title=\"Robert Engels\">\n\t\t\t\t\t\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"ico-form\"><\/i>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<li><a aria-label=\"Linkedin\" target=\"_blank\" title=\"Opens in a new window\" href=\"https:\/\/www.linkedin.com\/in\/esisnorge\/\"><i aria-hidden=\"true\" class=\"icon-li\"><\/i><\/a><\/li>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"people-info\">Robert is an innovation lead and a thought leader in several sectors and regions, and holds the position of Chief Technology Officer for Northern and Central Europe in our Insights &#038; Data Global Business Line. Based in Norway, he is a known lecturer, public speaker, and panel moderator. Robert holds a PhD in artificial intelligence from the Technical University of Karlsruhe (KIT), Germany.<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"modal\" id=\"WPB562841c2_627a_454e_a112_6f91d37fbcac\">\n\t\t\t\t\t<div class=\"modal-dialog modal-dialog-centered modal-lg modal-dialog-scrollable landing-page-modals\">\n\t\t\t\t\t\t<div class=\"modal-content\">\n\t\t\t\t\t\t\t<div class=\"modal-header\">\n\t\t\t\t\t\t\t\t<button type=\"button\" class=\"btn-close\" aria-label=\"close\" data-bs-dismiss=\"modal\"><\/button>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"modal-body\">\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t<div class=\"mf_forms__container \">\n\t\t\t\t\t\t\t\t<form id=\"mf_form_613082_155103575\" class=\"mf_form__form row needs-validation\" action=\"\" method=\"post\" enctype=\"multipart\/form-data\" data-nosnippet>\n\n\t\t\t\t<div class=\"mf-field-wrapper form-floating col-sm-12\"><input type=\"text\" class=\"form-control\" id=\"_mf_613076_3576_679485757\" name=\"_mf_613076_3576\" placeholder=\"First Name\" required \/><label for=\"_mf_613076_3576_679485757\" class=\"form-label\">First Name <span class=\"star-required\">*<\/span><\/label><div class=\"invalid-feedback-frm\" role=\"alert\">First Name is not valid.<\/div><\/div><div class=\"mf-field-wrapper form-floating col-sm-12\"><input type=\"text\" class=\"form-control\" id=\"_mf_613076_9936_675788652\" name=\"_mf_613076_9936\" placeholder=\"Last Name\" required \/><label for=\"_mf_613076_9936_675788652\" class=\"form-label\">Last Name <span class=\"star-required\">*<\/span><\/label><div class=\"invalid-feedback-frm\" role=\"alert\">Last Name is not valid.<\/div><\/div><div class=\"mf-field-wrapper form-floating col-sm-12\"><input type=\"text\" class=\"form-control\" id=\"_mf_613076_8904_2360778028\" name=\"_mf_613076_8904\" placeholder=\"Company\" required \/><label for=\"_mf_613076_8904_2360778028\" class=\"form-label\">Company <span class=\"star-required\">*<\/span><\/label><div class=\"invalid-feedback-frm\" role=\"alert\">Company is not valid.<\/div><\/div><div class=\"mf-field-wrapper form-floating col-sm-12\"><input type=\"email\" class=\"form-control\" id=\"_mf_613082_3616_2265535010\" name=\"_mf_613082_3616\" placeholder=\"Email (Business Email only)\" required \/><label for=\"_mf_613082_3616_2265535010\" class=\"form-label\">Email (Business Email only) <span class=\"star-required\">*<\/span><\/label><div class=\"invalid-feedback-frm\" role=\"alert\">email_address<\/div><\/div><div class=\"mf-field-wrapper form-floating col-sm-12\"><input type=\"text\" pattern=\"^[0-9\\-\\+\\s]+$\"  class=\"form-control\" id=\"_mf_613082_3512_652237710\" name=\"_mf_613082_3512\" oninput=\"validateInput(this)\" maxlength=\"14\" placeholder=\"Phone\"  \/><label for=\"_mf_613082_3512_652237710\" class=\"form-label\">Phone (optional)<\/label><\/div>\t\t<div class=\"mf_field mf_field--country mf_field--select floating form-country-select-parent mf-required\">\n\n\t\t\t<label for=\"_mf_613076_4465_2913042253\" class=\"floating__label form-country-select-label\" data-content=\"Country\">\n\t\t\t\t<span class=\"floating-label-content\">Country<\/span>\n\t\t\t<\/label>\n\n\t\t\t<div class=\"select-wrap\">\n<i class=\"icon icon-zodiak-chevron-down\"><\/i>\n\t\t\t\t<select id=\"_mf_613076_4465_2913042253\" class=\"mf_field__input empty mf-country-selectbox form_country_select\" name=\"_mf_613076_4465\" data-validate=\"select\" required>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"\" >Country<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AF\" >Afghanistan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AX\" >Aland Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AL\" >Albania<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"DZ\" >Algeria<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AS\" >American Samoa<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AD\" >Andorra<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AO\" >Angola<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AI\" >Anguilla<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AQ\" >Antarctica<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AG\" >Antigua And Barbuda<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AR\" >Argentina<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AM\" >Armenia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AW\" >Aruba<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AU\" >Australia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AT\" >Austria<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AZ\" >Azerbaijan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BS\" >Bahamas<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BH\" >Bahrain<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BD\" >Bangladesh<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BB\" >Barbados<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BY\" >Belarus<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BE\" >Belgium<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BZ\" >Belize<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BJ\" >Benin<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BM\" >Bermuda<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BT\" >Bhutan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BO\" >Bolivia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BA\" >Bosnia And Herzegovina<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BW\" >Botswana<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BV\" >Bouvet Island<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BR\" >Brazil<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"IO\" >British Indian Ocean Territory<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BN\" >Brunei Darussalam<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BG\" >Bulgaria<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BF\" >Burkina Faso<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BI\" >Burundi<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"KH\" >Cambodia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CM\" >Cameroon<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CA\" >Canada<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CV\" >Cape Verde<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"KY\" >Cayman Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CF\" >Central African Republic<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TD\" >Chad<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CL\" >Chile<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CN\" >China<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CX\" >Christmas Island<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CC\" >Cocos (Keeling) Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CO\" >Colombia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"KM\" >Comoros<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CG\" >Congo<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CD\" >Congo, Democratic Republic<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CK\" >Cook Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CR\" >Costa Rica<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CI\" >Cote D&#039;Ivoire<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"HR\" >Croatia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CU\" >Cuba<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CY\" >Cyprus<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CZ\" >Czech Republic<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"DK\" >Denmark<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"DJ\" >Djibouti<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"DM\" >Dominica<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"DO\" >Dominican Republic<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"EC\" >Ecuador<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"EG\" >Egypt<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SV\" >El Salvador<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GQ\" >Equatorial Guinea<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"ER\" >Eritrea<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"EE\" >Estonia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"ET\" >Ethiopia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"FK\" >Falkland Islands (Malvinas)<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"FO\" >Faroe Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"FJ\" >Fiji<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"FI\" >Finland<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"FR\" >France<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GF\" >French Guiana<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PF\" >French Polynesia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TF\" >French Southern Territories<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GA\" >Gabon<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GM\" >Gambia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GE\" >Georgia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"DE\" >Germany<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GH\" >Ghana<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GI\" >Gibraltar<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GR\" >Greece<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GL\" >Greenland<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GD\" >Grenada<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GP\" >Guadeloupe<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GU\" >Guam<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GT\" >Guatemala<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GG\" >Guernsey<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GN\" >Guinea<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GW\" >Guinea-Bissau<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GY\" >Guyana<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"HT\" >Haiti<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"HM\" >Heard Island &amp; Mcdonald Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"VA\" >Holy See (Vatican City State)<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"HN\" >Honduras<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"HK\" >Hong Kong<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"HU\" >Hungary<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"IS\" >Iceland<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"IN\" >India<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"ID\" >Indonesia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"IR\" >Iran, Islamic Republic Of<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"IQ\" >Iraq<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"IE\" >Ireland<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"IM\" >Isle Of Man<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"IL\" >Israel<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"IT\" >Italy<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"JM\" >Jamaica<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"JP\" >Japan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"JE\" >Jersey<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"JO\" >Jordan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"KZ\" >Kazakhstan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"KE\" >Kenya<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"KI\" >Kiribati<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"KR\" >Korea<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"KW\" >Kuwait<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"KG\" >Kyrgyzstan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LA\" >Lao People&#039;s Democratic Republic<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LV\" >Latvia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LB\" >Lebanon<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LS\" >Lesotho<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LR\" >Liberia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LY\" >Libyan Arab Jamahiriya<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LI\" >Liechtenstein<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LT\" >Lithuania<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LU\" >Luxembourg<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MO\" >Macao<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MK\" >Macedonia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MG\" >Madagascar<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MW\" >Malawi<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MY\" >Malaysia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MV\" >Maldives<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"ML\" >Mali<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MT\" >Malta<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MH\" >Marshall Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MQ\" >Martinique<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MR\" >Mauritania<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MU\" >Mauritius<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"YT\" >Mayotte<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MX\" >Mexico<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"FM\" >Micronesia, Federated States Of<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MD\" >Moldova<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MC\" >Monaco<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MN\" >Mongolia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"ME\" >Montenegro<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MS\" >Montserrat<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MA\" >Morocco<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MZ\" >Mozambique<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MM\" >Myanmar<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NA\" >Namibia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NR\" >Nauru<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NP\" >Nepal<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NL\" >Netherlands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AN\" >Netherlands Antilles<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NC\" >New Caledonia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NZ\" >New Zealand<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NI\" >Nicaragua<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NE\" >Niger<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NG\" >Nigeria<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NU\" >Niue<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NF\" >Norfolk Island<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MP\" >Northern Mariana Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"NO\" >Norway<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"OM\" >Oman<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PK\" >Pakistan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PW\" >Palau<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PS\" >Palestinian Territory, Occupied<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PA\" >Panama<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PG\" >Papua New Guinea<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PY\" >Paraguay<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PE\" >Peru<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PH\" >Philippines<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PN\" >Pitcairn<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PL\" >Poland<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PT\" >Portugal<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PR\" >Puerto Rico<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"QA\" >Qatar<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"RE\" >Reunion<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"RO\" >Romania<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"RU\" >Russian Federation<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"RW\" >Rwanda<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"BL\" >Saint Barthelemy<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SH\" >Saint Helena<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"KN\" >Saint Kitts And Nevis<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LC\" >Saint Lucia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"MF\" >Saint Martin<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"PM\" >Saint Pierre And Miquelon<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"VC\" >Saint Vincent And Grenadines<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"WS\" >Samoa<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SM\" >San Marino<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"ST\" >Sao Tome And Principe<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SA\" >Saudi Arabia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SN\" >Senegal<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"RS\" >Serbia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SC\" >Seychelles<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SL\" >Sierra Leone<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SG\" >Singapore<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SK\" >Slovakia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SI\" >Slovenia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SB\" >Solomon Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SO\" >Somalia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"ZA\" >South Africa<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GS\" >South Georgia And Sandwich Isl.<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"ES\" >Spain<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"LK\" >Sri Lanka<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SD\" >Sudan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SR\" >Suriname<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SJ\" >Svalbard And Jan Mayen<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SZ\" >Swaziland<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SE\" >Sweden<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"CH\" >Switzerland<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"SY\" >Syrian Arab Republic<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TW\" >Taiwan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TJ\" >Tajikistan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TZ\" >Tanzania<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TH\" >Thailand<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TL\" >Timor-Leste<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TG\" >Togo<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TK\" >Tokelau<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TO\" >Tonga<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TT\" >Trinidad And Tobago<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TN\" >Tunisia<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TR\" >Turkey<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TM\" >Turkmenistan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TC\" >Turks And Caicos Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"TV\" >Tuvalu<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"UG\" >Uganda<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"UA\" >Ukraine<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"AE\" >United Arab Emirates<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"GB\" >United Kingdom<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"US\"  selected='selected'>United States<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"UM\" >United States Outlying Islands<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"UY\" >Uruguay<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"UZ\" >Uzbekistan<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"VU\" >Vanuatu<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"VE\" >Venezuela<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"VN\" >Viet Nam<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"VG\" >Virgin Islands, British<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"VI\" >Virgin Islands, U.S.<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"WF\" >Wallis And Futuna<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"EH\" >Western Sahara<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"YE\" >Yemen<\/option>\n\t\t\t\t\t\t\t\t\t\t\t<option value=\"ZM\" 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