GET https://rct.dev.bbntimes.com/technology/abstraction-and-the-equation-of-life

ArticleController :: show

Request

GET Parameters

None

POST Parameters

None

Uploaded Files

None

Request Attributes

Key Value
_controller
"App\Controller\ArticleController::show"
_firewall_context
"security.firewall.map.context.main"
_links
Symfony\Component\WebLink\GenericLinkProvider {#3684
  -links: [
    3805 => Symfony\Component\WebLink\Link {#3805
      -href: "/build/runtime.js"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "script"
      ]
    }
    3803 => Symfony\Component\WebLink\Link {#3803
      -href: "/build/644.js"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "script"
      ]
    }
    3802 => Symfony\Component\WebLink\Link {#3802
      -href: "/build/502.js"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "script"
      ]
    }
    3801 => Symfony\Component\WebLink\Link {#3801
      -href: "/build/app.js"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "script"
      ]
    }
    3800 => Symfony\Component\WebLink\Link {#3800
      -href: "/build/view-more.js"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "script"
      ]
    }
    3799 => Symfony\Component\WebLink\Link {#3799
      -href: "/build/term-condition.js"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "script"
      ]
    }
    3798 => Symfony\Component\WebLink\Link {#3798
      -href: "/build/contact.js"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "script"
      ]
    }
    3797 => Symfony\Component\WebLink\Link {#3797
      -href: "/build/scroll-infinite-article.js"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "script"
      ]
    }
    3796 => Symfony\Component\WebLink\Link {#3796
      -href: "/build/app.css"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "style"
      ]
    }
    3795 => Symfony\Component\WebLink\Link {#3795
      -href: "/build/cookie-style.css"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "style"
      ]
    }
    3794 => Symfony\Component\WebLink\Link {#3794
      -href: "/build/term-condition-css.css"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "style"
      ]
    }
    3793 => Symfony\Component\WebLink\Link {#3793
      -href: "/build/contact-css.css"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "style"
      ]
    }
    3792 => Symfony\Component\WebLink\Link {#3792
      -href: "/build/comment-css.css"
      -rel: [
        "preload" => "preload"
      ]
      -attributes: [
        "as" => "style"
      ]
    }
  ]
}
_route
"article_show"
_route_params
[
  "category" => "technology"
  "slug" => "abstraction-and-the-equation-of-life"
]
_security_firewall_run
"_security_main"
_stopwatch_token
"d23d23"
category
"technology"
slug
"abstraction-and-the-equation-of-life"

Request Headers

Header Value
accept
"*/*"
accept-encoding
"gzip, br, zstd, deflate"
connection
"close"
cookie
"PHPSESSID=oisonvpht8td38udhi896acuci"
host
"rct.dev.bbntimes.com"
user-agent
"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
x-php-ob-level
"1"

Request Content

Request content not available (it was retrieved as a resource).

Response

Response Headers

Header Value
cache-control
"no-cache, private"
content-type
"text/html; charset=UTF-8"
date
"Sat, 22 Feb 2025 08:30:59 GMT"
link
"</build/runtime.js>; rel="preload"; as="script",</build/644.js>; rel="preload"; as="script",</build/502.js>; rel="preload"; as="script",</build/app.js>; rel="preload"; as="script",</build/view-more.js>; rel="preload"; as="script",</build/term-condition.js>; rel="preload"; as="script",</build/contact.js>; rel="preload"; as="script",</build/scroll-infinite-article.js>; rel="preload"; as="script",</build/app.css>; rel="preload"; as="style",</build/cookie-style.css>; rel="preload"; as="style",</build/term-condition-css.css>; rel="preload"; as="style",</build/contact-css.css>; rel="preload"; as="style",</build/comment-css.css>; rel="preload"; as="style""
x-debug-token
"d69e7b"

Cookies

Request Cookies

Key Value
PHPSESSID
"oisonvpht8td38udhi896acuci"

Response Cookies

No response cookies

Session 6

Session Metadata

Key Value
Created
"Sat, 22 Feb 25 08:30:41 +0000"
Last used
"Sat, 22 Feb 25 08:30:57 +0000"
Lifetime
0

Session Attributes

Attribute Value
_csrf/https-comment
"vXJ7wN-wP9J4AhQGZlv4biAUBLw3oTDGF5kqTTyRJSk"
_csrf/https-cookie_accept
"2T6lHx7CxnIsIBJzJrcdWGPGlS68WD0xtlEMQ1b3Wao"

Session Usage

6 Usages
Stateless check enabled
Usage
Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage:76
[
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-csrf/TokenStorage/SessionTokenStorage.php"
    "line" => 76
    "function" => "start"
    "class" => "Symfony\Component\HttpFoundation\Session\Session"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-csrf/CsrfTokenManager.php"
    "line" => 69
    "function" => "hasToken"
    "class" => "Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/Csrf/Type/FormTypeCsrfExtension.php"
    "line" => 82
    "function" => "getToken"
    "class" => "Symfony\Component\Security\Csrf\CsrfTokenManager"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/ResolvedFormType.php"
    "line" => 134
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\Csrf\Type\FormTypeCsrfExtension"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/DataCollector/Proxy/ResolvedTypeDataCollectorProxy.php"
    "line" => 95
    "function" => "finishView"
    "class" => "Symfony\Component\Form\ResolvedFormType"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/ResolvedFormType.php"
    "line" => 128
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\DataCollector\Proxy\ResolvedTypeDataCollectorProxy"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/DataCollector/Proxy/ResolvedTypeDataCollectorProxy.php"
    "line" => 95
    "function" => "finishView"
    "class" => "Symfony\Component\Form\ResolvedFormType"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Form.php"
    "line" => 908
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\DataCollector\Proxy\ResolvedTypeDataCollectorProxy"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/src/Controller/ArticleController.php"
    "line" => 220
    "function" => "createView"
    "class" => "Symfony\Component\Form\Form"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 181
    "function" => "show"
    "class" => "App\Controller\ArticleController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 76
    "function" => "handleRaw"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/Kernel.php"
    "line" => 197
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/runtime/Runner/Symfony/HttpKernelRunner.php"
    "line" => 35
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\Kernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    "line" => 29
    "function" => "run"
    "class" => "Symfony\Component\Runtime\Runner\Symfony\HttpKernelRunner"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/public/index.php"
    "line" => 5
    "args" => [
      "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    ]
    "function" => "require_once"
  ]
]
Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage:79
[
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-csrf/TokenStorage/SessionTokenStorage.php"
    "line" => 79
    "function" => "has"
    "class" => "Symfony\Component\HttpFoundation\Session\Session"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-csrf/CsrfTokenManager.php"
    "line" => 69
    "function" => "hasToken"
    "class" => "Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/Csrf/Type/FormTypeCsrfExtension.php"
    "line" => 82
    "function" => "getToken"
    "class" => "Symfony\Component\Security\Csrf\CsrfTokenManager"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/ResolvedFormType.php"
    "line" => 134
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\Csrf\Type\FormTypeCsrfExtension"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/DataCollector/Proxy/ResolvedTypeDataCollectorProxy.php"
    "line" => 95
    "function" => "finishView"
    "class" => "Symfony\Component\Form\ResolvedFormType"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/ResolvedFormType.php"
    "line" => 128
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\DataCollector\Proxy\ResolvedTypeDataCollectorProxy"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/DataCollector/Proxy/ResolvedTypeDataCollectorProxy.php"
    "line" => 95
    "function" => "finishView"
    "class" => "Symfony\Component\Form\ResolvedFormType"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Form.php"
    "line" => 908
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\DataCollector\Proxy\ResolvedTypeDataCollectorProxy"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/src/Controller/ArticleController.php"
    "line" => 220
    "function" => "createView"
    "class" => "Symfony\Component\Form\Form"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 181
    "function" => "show"
    "class" => "App\Controller\ArticleController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 76
    "function" => "handleRaw"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/Kernel.php"
    "line" => 197
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/runtime/Runner/Symfony/HttpKernelRunner.php"
    "line" => 35
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\Kernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    "line" => 29
    "function" => "run"
    "class" => "Symfony\Component\Runtime\Runner\Symfony\HttpKernelRunner"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/public/index.php"
    "line" => 5
    "args" => [
      "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    ]
    "function" => "require_once"
  ]
]
Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage:52
[
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-csrf/TokenStorage/SessionTokenStorage.php"
    "line" => 52
    "function" => "has"
    "class" => "Symfony\Component\HttpFoundation\Session\Session"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-csrf/CsrfTokenManager.php"
    "line" => 70
    "function" => "getToken"
    "class" => "Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/Csrf/Type/FormTypeCsrfExtension.php"
    "line" => 82
    "function" => "getToken"
    "class" => "Symfony\Component\Security\Csrf\CsrfTokenManager"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/ResolvedFormType.php"
    "line" => 134
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\Csrf\Type\FormTypeCsrfExtension"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/DataCollector/Proxy/ResolvedTypeDataCollectorProxy.php"
    "line" => 95
    "function" => "finishView"
    "class" => "Symfony\Component\Form\ResolvedFormType"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/ResolvedFormType.php"
    "line" => 128
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\DataCollector\Proxy\ResolvedTypeDataCollectorProxy"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/DataCollector/Proxy/ResolvedTypeDataCollectorProxy.php"
    "line" => 95
    "function" => "finishView"
    "class" => "Symfony\Component\Form\ResolvedFormType"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Form.php"
    "line" => 908
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\DataCollector\Proxy\ResolvedTypeDataCollectorProxy"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/src/Controller/ArticleController.php"
    "line" => 220
    "function" => "createView"
    "class" => "Symfony\Component\Form\Form"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 181
    "function" => "show"
    "class" => "App\Controller\ArticleController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 76
    "function" => "handleRaw"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/Kernel.php"
    "line" => 197
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/runtime/Runner/Symfony/HttpKernelRunner.php"
    "line" => 35
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\Kernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    "line" => 29
    "function" => "run"
    "class" => "Symfony\Component\Runtime\Runner\Symfony\HttpKernelRunner"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/public/index.php"
    "line" => 5
    "args" => [
      "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    ]
    "function" => "require_once"
  ]
]
Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage:56
[
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-csrf/TokenStorage/SessionTokenStorage.php"
    "line" => 56
    "function" => "get"
    "class" => "Symfony\Component\HttpFoundation\Session\Session"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-csrf/CsrfTokenManager.php"
    "line" => 70
    "function" => "getToken"
    "class" => "Symfony\Component\Security\Csrf\TokenStorage\SessionTokenStorage"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/Csrf/Type/FormTypeCsrfExtension.php"
    "line" => 82
    "function" => "getToken"
    "class" => "Symfony\Component\Security\Csrf\CsrfTokenManager"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/ResolvedFormType.php"
    "line" => 134
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\Csrf\Type\FormTypeCsrfExtension"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/DataCollector/Proxy/ResolvedTypeDataCollectorProxy.php"
    "line" => 95
    "function" => "finishView"
    "class" => "Symfony\Component\Form\ResolvedFormType"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/ResolvedFormType.php"
    "line" => 128
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\DataCollector\Proxy\ResolvedTypeDataCollectorProxy"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Extension/DataCollector/Proxy/ResolvedTypeDataCollectorProxy.php"
    "line" => 95
    "function" => "finishView"
    "class" => "Symfony\Component\Form\ResolvedFormType"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/form/Form.php"
    "line" => 908
    "function" => "finishView"
    "class" => "Symfony\Component\Form\Extension\DataCollector\Proxy\ResolvedTypeDataCollectorProxy"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/src/Controller/ArticleController.php"
    "line" => 220
    "function" => "createView"
    "class" => "Symfony\Component\Form\Form"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 181
    "function" => "show"
    "class" => "App\Controller\ArticleController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 76
    "function" => "handleRaw"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/Kernel.php"
    "line" => 197
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/runtime/Runner/Symfony/HttpKernelRunner.php"
    "line" => 35
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\Kernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    "line" => 29
    "function" => "run"
    "class" => "Symfony\Component\Runtime\Runner\Symfony\HttpKernelRunner"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/public/index.php"
    "line" => 5
    "args" => [
      "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    ]
    "function" => "require_once"
  ]
]
Symfony\Component\Security\Core\Authentication\Token\Storage\UsageTrackingTokenStorage:41
[
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-core/Authentication/Token/Storage/UsageTrackingTokenStorage.php"
    "line" => 41
    "function" => "getMetadataBag"
    "class" => "Symfony\Component\HttpFoundation\Session\Session"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/twig-bridge/AppVariable.php"
    "line" => 103
    "function" => "getToken"
    "class" => "Symfony\Component\Security\Core\Authentication\Token\Storage\UsageTrackingTokenStorage"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Extension/CoreExtension.php"
    "line" => 1635
    "function" => "getUser"
    "class" => "Symfony\Bridge\Twig\AppVariable"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/var/cache/dev/twig/a4/a456f2f504a18cd81037fa69e543310c.php"
    "line" => 200
    "function" => "twig_get_attribute"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Template.php"
    "line" => 394
    "function" => "doDisplay"
    "class" => "__TwigTemplate_824a013e4f3f4a68e03a2d244e765025"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Template.php"
    "line" => 367
    "function" => "displayWithErrorHandling"
    "class" => "Twig\Template"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Template.php"
    "line" => 379
    "function" => "display"
    "class" => "Twig\Template"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/TemplateWrapper.php"
    "line" => 38
    "function" => "render"
    "class" => "Twig\Template"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Environment.php"
    "line" => 280
    "function" => "render"
    "class" => "Twig\TemplateWrapper"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/framework-bundle/Controller/AbstractController.php"
    "line" => 448
    "function" => "render"
    "class" => "Twig\Environment"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/framework-bundle/Controller/AbstractController.php"
    "line" => 453
    "function" => "doRenderView"
    "class" => "Symfony\Bundle\FrameworkBundle\Controller\AbstractController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/framework-bundle/Controller/AbstractController.php"
    "line" => 253
    "function" => "doRender"
    "class" => "Symfony\Bundle\FrameworkBundle\Controller\AbstractController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/src/Controller/AppController.php"
    "line" => 126
    "function" => "render"
    "class" => "Symfony\Bundle\FrameworkBundle\Controller\AbstractController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 181
    "function" => "renderHeader"
    "class" => "App\Controller\AppController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 76
    "function" => "handleRaw"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpCache/SubRequestHandler.php"
    "line" => 86
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/Fragment/InlineFragmentRenderer.php"
    "line" => 78
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\HttpCache\SubRequestHandler"
    "type" => "::"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/Fragment/FragmentHandler.php"
    "line" => 83
    "function" => "render"
    "class" => "Symfony\Component\HttpKernel\Fragment\InlineFragmentRenderer"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/DependencyInjection/LazyLoadingFragmentHandler.php"
    "line" => 47
    "function" => "render"
    "class" => "Symfony\Component\HttpKernel\Fragment\FragmentHandler"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/twig-bridge/Extension/HttpKernelRuntime.php"
    "line" => 44
    "function" => "render"
    "class" => "Symfony\Component\HttpKernel\DependencyInjection\LazyLoadingFragmentHandler"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/var/cache/dev/twig/b9/b9cb140abab7ef4ef8cb398831c75ac0.php"
    "line" => 207
    "function" => "renderFragment"
    "class" => "Symfony\Bridge\Twig\Extension\HttpKernelRuntime"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Template.php"
    "line" => 171
    "function" => "block_header"
    "class" => "__TwigTemplate_dc67cdc305f050f0a27ba7ef152f05af"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/var/cache/dev/twig/b9/b9cb140abab7ef4ef8cb398831c75ac0.php"
    "line" => 91
    "function" => "displayBlock"
    "class" => "Twig\Template"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Template.php"
    "line" => 394
    "function" => "doDisplay"
    "class" => "__TwigTemplate_dc67cdc305f050f0a27ba7ef152f05af"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Template.php"
    "line" => 367
    "function" => "displayWithErrorHandling"
    "class" => "Twig\Template"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/var/cache/dev/twig/c3/c336f4e76fc20e4db84e3be131276b68.php"
    "line" => 52
    "function" => "display"
    "class" => "Twig\Template"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Template.php"
    "line" => 394
    "function" => "doDisplay"
    "class" => "__TwigTemplate_3ce0324a396de697d1fad9fabd68df72"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Template.php"
    "line" => 367
    "function" => "displayWithErrorHandling"
    "class" => "Twig\Template"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Template.php"
    "line" => 379
    "function" => "display"
    "class" => "Twig\Template"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/TemplateWrapper.php"
    "line" => 38
    "function" => "render"
    "class" => "Twig\Template"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/twig/twig/src/Environment.php"
    "line" => 280
    "function" => "render"
    "class" => "Twig\TemplateWrapper"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/framework-bundle/Controller/AbstractController.php"
    "line" => 448
    "function" => "render"
    "class" => "Twig\Environment"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/framework-bundle/Controller/AbstractController.php"
    "line" => 453
    "function" => "doRenderView"
    "class" => "Symfony\Bundle\FrameworkBundle\Controller\AbstractController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/framework-bundle/Controller/AbstractController.php"
    "line" => 253
    "function" => "doRender"
    "class" => "Symfony\Bundle\FrameworkBundle\Controller\AbstractController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/src/Controller/ArticleController.php"
    "line" => 277
    "function" => "render"
    "class" => "Symfony\Bundle\FrameworkBundle\Controller\AbstractController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 181
    "function" => "show"
    "class" => "App\Controller\ArticleController"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 76
    "function" => "handleRaw"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/Kernel.php"
    "line" => 197
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/runtime/Runner/Symfony/HttpKernelRunner.php"
    "line" => 35
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\Kernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    "line" => 29
    "function" => "run"
    "class" => "Symfony\Component\Runtime\Runner\Symfony\HttpKernelRunner"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/public/index.php"
    "line" => 5
    "args" => [
      "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    ]
    "function" => "require_once"
  ]
]
Symfony\Component\Security\Http\Firewall\ContextListener:171
[
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/security-http/Firewall/ContextListener.php"
    "line" => 171
    "function" => "remove"
    "class" => "Symfony\Component\HttpFoundation\Session\Session"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/event-dispatcher/Debug/WrappedListener.php"
    "line" => 116
    "function" => "onKernelResponse"
    "class" => "Symfony\Component\Security\Http\Firewall\ContextListener"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/event-dispatcher/EventDispatcher.php"
    "line" => 220
    "function" => "__invoke"
    "class" => "Symfony\Component\EventDispatcher\Debug\WrappedListener"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/event-dispatcher/EventDispatcher.php"
    "line" => 56
    "function" => "callListeners"
    "class" => "Symfony\Component\EventDispatcher\EventDispatcher"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/event-dispatcher/Debug/TraceableEventDispatcher.php"
    "line" => 139
    "function" => "dispatch"
    "class" => "Symfony\Component\EventDispatcher\EventDispatcher"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 214
    "function" => "dispatch"
    "class" => "Symfony\Component\EventDispatcher\Debug\TraceableEventDispatcher"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 202
    "function" => "filterResponse"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/HttpKernel.php"
    "line" => 76
    "function" => "handleRaw"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/http-kernel/Kernel.php"
    "line" => 197
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\HttpKernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/symfony/runtime/Runner/Symfony/HttpKernelRunner.php"
    "line" => 35
    "function" => "handle"
    "class" => "Symfony\Component\HttpKernel\Kernel"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    "line" => 29
    "function" => "run"
    "class" => "Symfony\Component\Runtime\Runner\Symfony\HttpKernelRunner"
    "type" => "->"
  ]
  [
    "file" => "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/public/index.php"
    "line" => 5
    "args" => [
      "/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/vendor/autoload_runtime.php"
    ]
    "function" => "require_once"
  ]
]

Flashes

Flashes

No flash messages were created.

Server Parameters

Server Parameters

Defined in .env

Key Value
APP_ENV
"dev"
APP_SECRET
"0a988e63f011514eaabfc650b599af4d"
CORS_ALLOW_ORIGIN
"*"
DATABASE_URL
"mysql://bbndb_rctuser:33F5W25z40or0f7@localhost:3306/rct_bbntimes"
GOOGLE_RECAPTCHA_SECRET_KEY
"6LdV5fgpAAAAANxzTG8ZMfIjil1wu-1vrQvnUt-x"
GOOGLE_RECAPTCHA_SITE_KEY
"6LdV5fgpAAAAAENKcn73MJAhQrbtQeqgyC4wDLMP"
MAILER_DSN
"smtp://no-reply%40rct.dev.bbntimes.com:Bl6%26gLD48%26Of919@rct.dev.bbntimes.com:465"
MARIADB_PASSWORD
"i!87pK&!85ezc8"

Defined as regular env variables

Key Value
APP_DEBUG
"1"
BASE
"/public"
CONTEXT_DOCUMENT_ROOT
"/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com"
CONTEXT_PREFIX
""
DOCUMENT_ROOT
"/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com"
FCGI_ROLE
"RESPONDER"
GATEWAY_INTERFACE
"CGI/1.1"
HTTPS
"on"
HTTP_ACCEPT
"*/*"
HTTP_ACCEPT_ENCODING
"gzip, br, zstd, deflate"
HTTP_CONNECTION
"close"
HTTP_COOKIE
"PHPSESSID=oisonvpht8td38udhi896acuci"
HTTP_HOST
"rct.dev.bbntimes.com"
HTTP_USER_AGENT
"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
PASSENGER_COMPILE_NATIVE_SUPPORT_BINARY
"0"
PASSENGER_DOWNLOAD_NATIVE_SUPPORT_BINARY
"0"
PATH
"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/snap/bin"
PHP_SELF
"/public/index.php"
PP_CUSTOM_PHP_CGI_INDEX
"plesk-php81-fastcgi"
PP_CUSTOM_PHP_INI
"/var/www/vhosts/system/rct.dev.bbntimes.com/etc/php.ini"
QUERY_STRING
""
REDIRECT_BASE
"/public"
REDIRECT_HTTPS
"on"
REDIRECT_PASSENGER_COMPILE_NATIVE_SUPPORT_BINARY
"0"
REDIRECT_PASSENGER_DOWNLOAD_NATIVE_SUPPORT_BINARY
"0"
REDIRECT_REDIRECT_HTTPS
"on"
REDIRECT_REDIRECT_PASSENGER_COMPILE_NATIVE_SUPPORT_BINARY
"0"
REDIRECT_REDIRECT_PASSENGER_DOWNLOAD_NATIVE_SUPPORT_BINARY
"0"
REDIRECT_REDIRECT_SCRIPT_URI
"https://rct.dev.bbntimes.com/technology/abstraction-and-the-equation-of-life"
REDIRECT_REDIRECT_SCRIPT_URL
"/technology/abstraction-and-the-equation-of-life"
REDIRECT_REDIRECT_SSL_TLS_SNI
"rct.dev.bbntimes.com"
REDIRECT_REDIRECT_STATUS
"200"
REDIRECT_REDIRECT_UNIQUE_ID
"Z7mLQ7iBoyj8JZ8-HGxrfAAAAAw"
REDIRECT_SCRIPT_URI
"https://rct.dev.bbntimes.com/technology/abstraction-and-the-equation-of-life"
REDIRECT_SCRIPT_URL
"/technology/abstraction-and-the-equation-of-life"
REDIRECT_SSL_TLS_SNI
"rct.dev.bbntimes.com"
REDIRECT_STATUS
"200"
REDIRECT_UNIQUE_ID
"Z7mLQ7iBoyj8JZ8-HGxrfAAAAAw"
REDIRECT_URL
"/public/technology/abstraction-and-the-equation-of-life"
REMOTE_ADDR
"52.14.193.97"
REMOTE_PORT
"1789"
REQUEST_METHOD
"GET"
REQUEST_SCHEME
"https"
REQUEST_TIME
1740213059
REQUEST_TIME_FLOAT
1740213059.2933
REQUEST_URI
"/technology/abstraction-and-the-equation-of-life"
SCRIPT_FILENAME
"/var/www/vhosts/dev.bbntimes.com/rct.dev.bbntimes.com/public/index.php"
SCRIPT_NAME
"/public/index.php"
SCRIPT_URI
"https://rct.dev.bbntimes.com/technology/abstraction-and-the-equation-of-life"
SCRIPT_URL
"/technology/abstraction-and-the-equation-of-life"
SERVER_ADDR
"5.196.1.209"
SERVER_ADMIN
"[no address given]"
SERVER_NAME
"rct.dev.bbntimes.com"
SERVER_PORT
"443"
SERVER_PROTOCOL
"HTTP/1.1"
SERVER_SIGNATURE
"<address>Apache Server at rct.dev.bbntimes.com Port 443</address>\n"
SERVER_SOFTWARE
"Apache"
SSL_TLS_SNI
"rct.dev.bbntimes.com"
SYMFONY_DOTENV_VARS
"APP_ENV,APP_SECRET,DATABASE_URL,MARIADB_PASSWORD,CORS_ALLOW_ORIGIN,MAILER_DSN,GOOGLE_RECAPTCHA_SECRET_KEY,GOOGLE_RECAPTCHA_SITE_KEY"
UNIQUE_ID
"Z7mLQ7iBoyj8JZ8-HGxrfAAAAAw"

Sub Requests 6

CookieController :: renderAnalysis (token = 74d701)

Key Value
_controller
"App\Controller\CookieController::renderAnalysis"
_format
"html"
_locale
"en"
_stopwatch_token
"cb03a3"

AppController :: renderHeader (token = ba93ea)

Key Value
_controller
"App\Controller\AppController::renderHeader"
_format
"html"
_locale
"en"
_stopwatch_token
"8446e9"
slug
"home"

ArticleController :: trendingArticle (token = bf516c)

Key Value
_controller
"App\Controller\ArticleController::trendingArticle"
_format
"html"
_locale
"en"
_stopwatch_token
"73ada3"
category
"Technology"

ArticleController :: relatedArticles (token = c374ec)

Key Value
_controller
"App\Controller\ArticleController::relatedArticles"
_format
"html"
_locale
"en"
_stopwatch_token
"a74431"
current_article
App\Entity\Article {#1094
  -id: 954
  -title: "Abstraction and the Equation of Life"
  -slug: "abstraction-and-the-equation-of-life"
  -introtext: "<p>In Mathematics, we always abstract out problems/solution into mathematical objects. These mathematical objects help us to understand the concepts and apply the derived reasoning to other similar problems. These mathematical objects can be graphs, number line, simulation models. So, if you are modeling a move in a chess game, then you don't need physical chess pieces to do that, using mathematics concept you can do it using a "Graphs Model". The vertices of the graph can represent a possible position in the game and the edge between any two vertices can represent a legal move. As below figure shows possible moves of the rook in chess (Horizontal and Vertical).</p>\r\n"
  -content: """
    \r\n
    <div class="slate-resizable-image-embed slate-image-embed__resize-middle" data-imgsrc="https://media.licdn.com/mpr/mpr/AAMAAwDGAAgAAQAAAAAAAA3FAAAAJGE1ZDAzOWZkLTVhOTMtNDYxOS1hYzgwLTU5N2ZiNjQ2NjQ3OA.png" data-image-href="http://en.wikipedia.org/wiki/Rook%27s_graph"><a href="http://en.wikipedia.org/wiki/Rook%27s_graph" target="_blank" rel="nofollow noopener noreferrer"><img src="https://media.licdn.com/mpr/mpr/AAMAAwDGAAgAAQAAAAAAAA3FAAAAJGE1ZDAzOWZkLTVhOTMtNDYxOS1hYzgwLTU5N2ZiNjQ2NjQ3OA.png" alt="" width="494" height="494" data-li-src="https://media.licdn.com/mpr/mpr/AAMAAwDGAAgAAQAAAAAAAA3FAAAAJGE1ZDAzOWZkLTVhOTMtNDYxOS1hYzgwLTU5N2ZiNjQ2NjQ3OA.png" /></a></div>\r\n
    <p>When devising a model, we abstract out only those features that are essential to understanding its behavior&nbsp;and only deals with objects which are not concrete and tangible. In other use cases, while studying behavior of gas molecules we generalize the model with a closed box with one molecule represented by a point having some velocity and apply some assumptions - like constant velocity, elastic collision, then later, we apply the same thing to 'N' number of molecules and try to predict behaviour of all the gas molecules. This makes our study of gas molecules easy.</p>\r\n
    <div class="slate-resizable-image-embed slate-image-embed__resize-middle" data-imgsrc="https://media.licdn.com/mpr/mpr/AAMAAwDGAAgAAQAAAAAAAAxeAAAAJGUwZmZkNGIzLTI2MWMtNDgzYy04MDk3LTdmOGU1YmU2YTA3Mw.png"><img src="https://media.licdn.com/mpr/mpr/AAMAAwDGAAgAAQAAAAAAAAxeAAAAJGUwZmZkNGIzLTI2MWMtNDgzYy04MDk3LTdmOGU1YmU2YTA3Mw.png" alt="" width="430" height="248" data-li-src="https://media.licdn.com/mpr/mpr/AAMAAwDGAAgAAQAAAAAAAAxeAAAAJGUwZmZkNGIzLTI2MWMtNDgzYy04MDk3LTdmOGU1YmU2YTA3Mw.png" /></div>\r\n
    <p>This concept of abstraction is like riding a bike, without worrying about keeping balance. In fact, this abstraction is very important in understanding the hidden secrets of the universe. Also, the concepts like complex numbers (<em>i), infinity,&nbsp;</em>can be understood in greater depths, and also helpful in modeling human brain as being done with neural networks.</p>\r\n
    <p>But can we abstract out our lives in a mathematical concept, so that we can understand it more precisely or maybe predict outcomes in our lives?</p>\r\n
    <p>If we look out there&nbsp;are no real attempts made in this direction, but a concept called&nbsp;<strong>"Markov Decision Process"&nbsp;</strong>somehow relate to our lives process. Our lives can be defined as the outcome of decisions that we make every day and the outcomes are almost random with partial control over them.</p>\r\n
    <p>In fact, Markov Decision Process is used in modeling&nbsp;optimization problems in reinforcement learning, robotics, economics. But human life can easily be abstracted to Markov Decision Process, as this concept provides a framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker.</p>\r\n
    <p>Simply put, Markov Decision Process is a set of states and actions, together with rules for transitioning from one state to another. As shown in the figure below. On the right is the Markov States and on the left is the reinforcement learning model.</p>\r\n
    <div class="slate-resizable-image-embed slate-image-embed__resize-full-width" data-imgsrc="https://media.licdn.com/mpr/mpr/AAMAAwDGAAgAAQAAAAAAAA3BAAAAJDhjODlkNzVlLWQxNzQtNDVkZC05YzUwLTZmZDAxMDVmYTk5OA.png"><img src="https://media.licdn.com/mpr/mpr/AAMAAwDGAAgAAQAAAAAAAA3BAAAAJDhjODlkNzVlLWQxNzQtNDVkZC05YzUwLTZmZDAxMDVmYTk5OA.png" alt="" width="583" height="190" data-li-src="https://media.licdn.com/mpr/mpr/AAMAAwDGAAgAAQAAAAAAAA3BAAAAJDhjODlkNzVlLWQxNzQtNDVkZC05YzUwLTZmZDAxMDVmYTk5OA.png" /></div>\r\n
    <p>Suppose you are an agent, situated in an environment. The environment is in a certain state. The agent can perform certain actions in the environment. These actions sometimes result in a reward. Actions transform the environment and lead to a new state, where the agent can perform another action, and so on. The rules for how you choose those actions are called policy. The environment, in general, is random.</p>\r\n
    <p>The above concept is based on Markov assumption, that the probability of the next state depends only on current state and action, but not on preceding states or actions.</p>\r\n
    <p>And thus, that's what our lives are: outcomes of decision that we make every day and the outcomes are almost random with partial control over them.</p>\r\n
    <p>This emerging field of Machine Learning called reinforcement learning is kind of future of A.I. It is being used to train robots, make computers adapt to the environment and who knows it may take humans closer to their goals of solving intelligence.</p>
    """
  -user: Proxies\__CG__\App\Entity\User {#1092 …}
  -createdAt: DateTime @1517767397 {#1145
    date: 2018-02-04 18:03:17.0 UTC (+00:00)
  }
  -updatedAt: DateTime @1517767919 {#1150
    date: 2018-02-04 18:11:59.0 UTC (+00:00)
  }
  -deletedAt: null
  -category: App\Entity\Category {#445 …}
  -status: "published"
  -imageCard: Proxies\__CG__\App\Entity\File {#1184 …}
  -ImageHeader: Proxies\__CG__\App\Entity\File {#1184 …}
  -featured: false
  -mainView: false
  -clicks: 5228
  -comments: Doctrine\ORM\PersistentCollection {#1125 …}
  -reviewed_at: DateTime @1517767868 {#1148
    date: 2018-02-04 18:11:08.0 UTC (+00:00)
  }
  -metakey: ""
  -metadesc: "In Mathematics, we always abstract out problems/solution into mathematical objects. These mathematical objects help us to understand the concepts and apply the derived reasoning to other similar problems. These mathematical objects can be graphs, number line, simulation models. So, if you are modeling a move in a chess game, then you don't need physical chess pieces to do that, using mathematics concept you can do it using a "Graphs Model". The vertices of the graph can represent a possible position in the game and the edge between any two vertices can represent a legal move. As below figure shows possible moves of the rook in chess (Horizontal and Vertical)."
  -robots: null
  -publishedAt: DateTime @1517767868 {#1147
    date: 2018-02-04 18:11:08.0 UTC (+00:00)
  }
  -canonical: null
  -superTag: "Mathematics"
}

AppController :: renderFooter (token = e53a1d)

Key Value
_controller
"App\Controller\AppController::renderFooter"
_format
"html"
_locale
"en"
_stopwatch_token
"88d28b"

CookieController :: renderCookie (token = 6d23ab)

Key Value
_controller
"App\Controller\CookieController::renderCookie"
_format
"html"
_locale
"en"
_stopwatch_token
"93bcab"