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The Penrose Tile, Continued

Zonohedron #3: Penrose tiling

Image courtesy of Flickr user Andrew Hudson.

I took Vincent’s comment on my recent post about the Penrose Tile to some mathy friends of mine online, asking what they thought of his extension of the concept:

I feel that the golden number does appear in several ratios, but at the same time I feel that we are searching for that ratio in nature, rather than trying to disprove it. It feels like were saying look at all these examples that follow the golden ration (I totally support the golden ratio ideology, its just that it seems too convenient) and we aren’t pointing out any that disprove it. In science, empiricism, logic, rationalism, and basically everything that creates theories; the goal is to disprove your theory and therefore prove it.

I don’t know of any examples of this theory appearing false of course, but I don’t know if we have searched for any. Therefore, I wonder, is there anything that disproves this golden number theory, the magical sequence of 0,1,1,2,3,5,8,13,21 . . .?

David Wees is a math teacher who used to be based in Vancouver before relocating to New York, and had this to say as a reply to Vincent’s thoughts:

Screen Shot 2014-11-19 at 9.18.33 AM

 

One Response to The Penrose Tile, Continued

  1. Vincent says:

    I agree that there are no counterexamples to deductive reasoning, however, there is still always ambiguity. I would argue that all deductive reasoning is based on an inductive reasoning that is not disproven, but is proven. So these deductive arguments can still topple despite their seeming invulnerability, but only if the inductive reasonings which they are based on are disproven. For example, the cliché example of the earth being flat, a deductive reasoning based of that would be that there is an edge to the earth and that you could fall of that edge. To us now, that sounds ridiculous, but similarly today, we are discovering that the universe does not have an edge, much like the earth. Perhaps we give too much credit to our own deductive reasoning and we should not consider these invulnerable to arguments.

    Thanks for the reply,

    Sincerely – Vincent Badenhorst

     

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