I don't know why I can't comment on other people's answers so forgive this "answer"
"i forgot to add that each topic, has a little bio about them, like 200 character about paragraph saying what the topic is about, would that be good way to relate stuff to each other?"
This is a very unreliable way to relate anything. If this is the case, pretty much everything would relate as common words appear all over every topic. Words like "the" or "and" would relate everything in something like a full text search, depending on how you orchestrate your comparison.
In your case, you might want to clarify HOW you plan on comparing. You already mention you are using php and mysql, so we all assume you are writing a query to find the relations.
Why then are you avoiding a relational table? A keyword table? It's basic web development at this point and seems very strange that you'd be interested in a complicated work around for a very simple concept.
blog{id, title body, date}
topic{id, title}
blog_topic{id, blog_id, topic_id}
$sql = "SELECT b.*, t.* FROM `blogs` b LEFT JOIN `blog_topic` r ON r.`blog_id` = b.`id` LEFT JOIN `topic` t ON t.`id` = r.`topic_id` WHERE t.`id` = ".$whatever_topic_id_you_pass;
Seems simple enough to me. Much more reliable than some weird full text search.