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The Tower of Hanoi and Tesseract relationship

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pocket83

The Tower of Hanoi is a simple to construct puzzle that has a very particular solution sequence. The Tesseract (also sometimes called a Hypercube) is like a threedimensional "shadow" from a fourdimensional cube. This video shows a strange pattern that they both share, and oddly enough, this relationship may follow them into even higher dimensions.

Because the idea being expressed here is a vague relationship between two incredibly abstract mathematical concepts, it is very hard to attribute such a thing to a particular origin. I am not the originator of this idea; however, as far as I can tell, the first to publish on this relationship was D.W. Crowe in 1956, in the 'American Mathematical Monthly.' I became familiar with this pattern by reading the work of Martin Gardner, who took great delight in such relationships.

I didn't want to use spoken words in this one. That always seems to bother some people, but I wanted to make a quiet place where you could think for a moment, without distraction. Much of the way that we come to understand things is through the use of abstract ideas*, which are almost exclusively conceptual, and therefore devoid of language. Think about it: Do you really understand things by describing them to yourself with words? Of course not. Understanding, as a concept, is the state in which something has become intuitively evident to you, and language is only useful insofar as it allows you to pass this understanding onto others. There is really no word, neither written nor spoken, that can express what the experience of an electrical shock feels like, or how a soft, juicy pear feels to the roof of the mouth. Mathematical concepts and the relationships between natural phenomena are little different.

How to play, solve, and make a Tower:
   • How to play, solve, and make a Tower ...  

Template to make one of these:
http://postimg.org/image/lgzpxt13n/

Musical tones: These were generated using the following musical sequencer:
http://www.earslap.com/page/otomata.html
This is a wonderfully entertaining tool that has a clean interface. I strongly suggest visiting the link to play with this it's a great way to kill half an hour.

Music: Tryad "Witness"
http://tryad.org/
This group provides a few albums that can be used under creative commons. I don't use music in videos too often (because it is distracting and curbs the conversation too far from the ideas I would prefer to express), but this is an enjoyable sound. Especially if you like this genre; it reminds me of those Delirium or Enigma albums, and that late 90's deep contemplative electronica sound.

About that last scene: Please give us a break! It was late, and we were really tired. It took quite a bit of practice (and takes) to synchronize that shot without one of us messing up, and I wanted it to be one continuous shot. We have since figured out the Tower of Hanoi's algorithm, so there is no need to tell me "the easy way" to do it. I think I understand it pretty well now. Oh, one more thing: (2^0)1=0, so if you caught that, I award you two internets. You can redeem them on the next video. I sincerely hope you enjoyed this.

* For example, comparative relationships between two somewhat similar things (metaphors).

posted by acomolanteh