In this video, I'd like to take a look at the Golden Ratio through science through a different lens. And here we have the study of metrology or measurement. And my proportion is open here to show that the kilometer is actually a golden ratio with respect to the mile. So here we have the world's two most popular systems, we have the system in the United States the mile or sometimes called the imperial system. And the kilometer part of the metric system are related in this golden ratio way, and it's 99.5% accurate, so it's not exact, but it nevertheless is very close to this relationship. Here we have a graphic showing the Earth and the Moon together and the measurements.

So it's really amazing. I think that the polar diameter of the Earth is 10,000 kilometers. times the square root of phi. And that's 99.97% accurate. Also, when you look at the combined polar diameters of Earth and Moon together, that's 10,000 kilometers times five, again, with the same astonishingly high degree of accuracy. Now, there's nothing in the metric system that would lead us to this conclusion.

The metric system was initially defined by a meridian running through Paris, that went around the entire Earth went through Paris through the North Pole through the South Pole, and then back through Paris again. And that was defined to be 40,000 kilometers Exactly. Since that time, the way the metric system has shifted, but essentially, they're the same meters. But there's nothing in that definition that would encode the golden ratio. As you see here, but nevertheless it does. And the reason that it does is because the Earth and the Moon have this proportional relationship with the golden ratio.

So if you take the size of the Earth as one, then the combined sizes of Earth and Moon together is the square root of phi. And that can be combined into what is called a Kepler triangle where the high pot news is equal to the golden ratio. I looked at the planet Saturn, when this beautiful image was coming back from NASA. And I hold I held up my golden ratio calipers to it and I was really blown away to see that the planet itself is in a golden ratio with respect to its rings. And there's nothing in physics that says this must be so And nevertheless it is so quite a beautiful geometry underlying the proportions. Perhaps the most beautiful planet after the earth in our system.

Here's the visible spectrum of light down below. And you can see that the three primary colors are in a golden ratio relationship with respect to one another. This was discovered by clay Taylor, and I've illustrated it here with my proportions. Here's the DNA molecule. This is a 3d model of the DNA molecule coiled up as much as possible. It shows that the major and minor grooves are in a golden relationship with one another.

And simultaneously and independently of that the pitch is in a golden relationship with the diameter. And the axial view shows a molecule with 10 parts symmetry. And when we have if you ask me to design a molecule based on the golden ratio, there's no way I could have or probably anyone could have come up with a better molecule It encodes the golden ratio in many different simultaneous ways. And here's a really big picture idea this, this is a cent. This is a logarithmic scale on the left, it shows the visible universe at the top. That's everything that we can see with any telescope, all the way down to the human scale, and then all the way down to the smallest thing of all the proton.

So the proton is really the smallest thing that can be measured. And that book ends one end of the scale. What's really amazing is the human scale happens to be right at the Golden Ratio with respect to all things. The human scale is 10 to the zero with power or approximately one meter. And remember, this is a scale logarithmic scale or orders of magnitude scale. So any creatures that are approximately one meter in size would fit the bill.

So it's I think it's really amazing that our experience of the universe happens to be at this golden ratio point. The Golden Ratio. It's just written throughout this entire mathematical universe.