Our decimal number system uses 10 different digits (0 through 9). Given that it’s an inherent and simple property of numbers, it shouldn’t be too surprising that you can find these numbers in nature. Our decimal number system originates in the fact that we have 10 fingers, but the Fibonacci sequence and the Golden Ratio exist, whatever number system you use. primes) a property of numbers, not of our decimal (base-10) number system. Mathematically, the nice thing about both the Fibonacci sequence and the Golden Ratio is that it’s (like e.g. The Fibonacci sequence can be turned into a Fibonacci spiral, which also visualizes the Golden Ratio. There’s also a relationship with spirals, such as again the pattern of sunflower seeds or nautilus shells. For example, rows of sunflower seeds often follow the Fibonacci numbers. So, for example, 144/89 (=1.618…) is a good approximation for the Golden Ratio.ĭue to the simple rules it shouldn’t be too surprising that both the Fibonacci sequence and the Golden Ratio show up in nature. The relationship with the Fibonacci sequence is that the ratio between two consecutive numbers converges to the Golden Ratio. Due to the simple equality, the Golden Ratio has very nice properties and shows up both in art and nature. The Golden Ratio is the ratio A:B such that A:B = (A+B):A, and is close to 1.618. The Fibonacci sequence is the sequence of numbers starting with 0 and 1, where each next number is the sum of the previous two:Ġ, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … On the Divine 9 website there’s not much evidence for the importance of 9, but check any list of characteristics of pseudo-science and you can find most of them in the Divine 9 arguments. Googling for an old map of Lima (though not by Pizarro), it turns out that although there might have been 9 × 13 roads, the map doesn’t show a complete rectangular grid, so the number of blocks is much lower. My second, that a grid of 9 × 13 roads in fact results in 8 × 12 = 106 house blocks. I noticed another mention of 117 on one of Kramer’s facebook posts: “Why did the original map of Lima, Peru created by Pizarro, consist of 9 × 13 roads resulting in 117 houseblocks?” He doesn’t give the answer, but my first thought was that this was just a coincidence. In fact, claims based on ancient knowledge are one of the characteristics of pseudo-science. If it had been western dragons, the number of scales might have been a multiple of 7. But that’s just because 9 turns out to be a lucky number for the Chinese, so they had a preference for it. Although there are 81 and 36 scales (both squares), in fact there is some relationship with 9 here. In my previous Divine 9 post I mentioned Gert Kramer’s example of the Chinese dragon having 117 scales. The problem is that if you look for the number 9 you’ll find it, but the same holds for other numbers. Again, there are many composers who didn’t write exactly 9 symphonies. Wikipedia also features a list of symphony composers. And though pi shows up, the golden ratio is missing. Counting titles I don’t see a preference for 9. Conveniently, wikipedia maintains a list of song titles with a number in the title. Musical examples are John Lennon’s ‘Revolution 9’ and the fact that Beethoven wrote 9 symphonies. On the Divine 9 site, Gert Kramer gives examples of how the number 9 keeps showing up. Where it goes wrong is where the number 9 is lifted to a divine status. Interesting, but not that spectacular, since both nature and the Fibonacci sequence follow simple rules. Both the Fibonacci sequence and the related golden ratio (I’ll get into the details), really do show up in nature. In fact, this connection with nature is based on spirals, the Fibonacci sequence, and the golden ratio. If you take a look at the Divine 9 music site, you’ll read about the importance of the number 9 and how it should show up everywhere in nature. Now let me try to explain why the Divine 9 theory qualifies as pseudo-science. Pseudo-science just starts with a conclusion and tries to find facts supporting this conclusion, ignoring facts that don’t fit with the result. Scientists try to find counter-examples to disprove their own theory. The usual scientific principle is to start with the facts, and then trying to draw a conclusion. Let’s start with the pseudo-science part. In this post I’ll skip the musical part of the Divine 9 tuning, and will focus on the arguments about the divinity of the number 9. I’ve received a few questions about the details of the mathematics in my Divine 9 post, and why the Divine 9 theory qualifies as pseudo-science.
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