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Isomorphic Algorithms?
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<blockquote data-quote="an_anonymous_onlooker" data-source="post: 74131" data-attributes="member: 4359"><p>So, this <em>may</em> have been spoken of on these forums before (if so, I would love a link to the thread), but just in case, I thought I’d starts a discussion on the concept of Isomorphic Algorithms.</p><p></p><p>Now before I start, I feel the need to confirm that I am not a computer ‘techie’ or anything of the like, but I do enjoy a bit of a ‘tumble down the rabbit hole’ when it comes to useless trivia. So if I get technicalities wrong / mixed up, blame my ignorance, and do some research.</p><p></p><p>Anyway, back to my point. Isomorphic Algorithms. I thought I would do some research into the concept of them (after hearing mention of them in the film Tron: Legacy) and this is what I found.</p><p></p><p>The concept of isomorphism is a principle of abstract algebra which is a bijective<span style="color: #ffffff"> homorphism</span>. This means that two mathematical objects are considered isomorphic is there is a ‘one-to-one mapping’ (bijective) link between them. To put it symbolically, essentially mathematical object X and mathematical object Y are considered exactly the same when operated on.</p><p></p><p>When this is applied to computing, it is constructed in what is called a ‘Subgraph isomorphism problem’. Basically, this is when two graphs are inserted as inputs into a computer action, and isomorphic similarities within the both graphs are searched for. Any similarities then form the output.</p><p></p><p>Now, without getting into technicalities that I don’t understand fully myself, basically, this means that a computer which investigates this ‘Subgraph isomorphism problem’ – the output being an isomorphic algorithm is able to find, locate and operate on similarities between two inputs.</p><p></p><p>This may sound simple enough, ‘sure, I mean, if X and Y both equal 2, then X+1=3, and Y+1 also = 3, so they must be isomorphic’ – but this has immense ramifications for computing. In theory, advanced isomorphic algorithms would have the ability to locate and act upon similarities between ‘real-life’ existences, and digital instances.</p><p></p><p>What does that even mean? Consider this as an example. You ask a computer to run an isometric algorithm, comparing a computer command with a human thought. The algorithm runs the comparison, and outputs any common ground. This isomorphic construct can then be built upon, altered, and changed, yet will retain the qualities of both the computer process AND the input of human thought. You have just created a computer command capable of mirroring human thought.</p><p></p><p>Now that may seem farfetched, but that is the perceived capabilities of such an algorithm. People may thing this may be a viable path for the creation of AI, however, by definition, an Isomorphic Algorithm paired with human intelligence, rather than being Artificial Intelligence, would be a true, digital intelligence, capable of a personality, creativity and more.</p><p></p><p>Just some late night food for though. <img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite39" alt=";)" title="Wink ;)" loading="lazy" data-shortname=";)" /></p></blockquote><p></p>
[QUOTE="an_anonymous_onlooker, post: 74131, member: 4359"] So, this [I]may[/I] have been spoken of on these forums before (if so, I would love a link to the thread), but just in case, I thought I’d starts a discussion on the concept of Isomorphic Algorithms. Now before I start, I feel the need to confirm that I am not a computer ‘techie’ or anything of the like, but I do enjoy a bit of a ‘tumble down the rabbit hole’ when it comes to useless trivia. So if I get technicalities wrong / mixed up, blame my ignorance, and do some research. Anyway, back to my point. Isomorphic Algorithms. I thought I would do some research into the concept of them (after hearing mention of them in the film Tron: Legacy) and this is what I found. The concept of isomorphism is a principle of abstract algebra which is a bijective[COLOR=#ffffff] homorphism[/COLOR]. This means that two mathematical objects are considered isomorphic is there is a ‘one-to-one mapping’ (bijective) link between them. To put it symbolically, essentially mathematical object X and mathematical object Y are considered exactly the same when operated on. When this is applied to computing, it is constructed in what is called a ‘Subgraph isomorphism problem’. Basically, this is when two graphs are inserted as inputs into a computer action, and isomorphic similarities within the both graphs are searched for. Any similarities then form the output. Now, without getting into technicalities that I don’t understand fully myself, basically, this means that a computer which investigates this ‘Subgraph isomorphism problem’ – the output being an isomorphic algorithm is able to find, locate and operate on similarities between two inputs. This may sound simple enough, ‘sure, I mean, if X and Y both equal 2, then X+1=3, and Y+1 also = 3, so they must be isomorphic’ – but this has immense ramifications for computing. In theory, advanced isomorphic algorithms would have the ability to locate and act upon similarities between ‘real-life’ existences, and digital instances. What does that even mean? Consider this as an example. You ask a computer to run an isometric algorithm, comparing a computer command with a human thought. The algorithm runs the comparison, and outputs any common ground. This isomorphic construct can then be built upon, altered, and changed, yet will retain the qualities of both the computer process AND the input of human thought. You have just created a computer command capable of mirroring human thought. Now that may seem farfetched, but that is the perceived capabilities of such an algorithm. People may thing this may be a viable path for the creation of AI, however, by definition, an Isomorphic Algorithm paired with human intelligence, rather than being Artificial Intelligence, would be a true, digital intelligence, capable of a personality, creativity and more. Just some late night food for though. ;) [/QUOTE]
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