Well I clearly arn't going to trade by it unless it can be proven/makes sense.
Even the pyramids which are said to be made with the golden ratio arn't. Giza is 756 feet high and 481 feet wide or 1.5717 ratio. I assume things have to actually be 1.618 and not just close to it.
One website claims this:
A DNA molecule measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral. In the Fibonacci series, 34 and 21 are successive numbers.
So what? It equals a ratio of 1.619...? When talking about the golden ratio appearing in our DNA, one would think you would have to be exact, not just pretty close. If DNA is wrong you end up a vegetable. Clearly it's not supposed to be 1.618 but rather 1.619. People do this with markets all the time. They make up fib levels that don't exist (50%) or are lax about the requirements i.e. "Ah well 1.70 is very close to 1.618, it must be reversing soon". If such inaccuracies are accepted then you can say that anything occurs at a fib level, especially when you make up new fib ratios!
Even if this is the case, it doesn't mean it can apply to human psychology. Perhaps the ratio is something that just works, like pi, but it doesn't mean groups of millions of people can as a herd gravitate towards this ratio in an infinitely complex market. Such a claim requires extraordinary evidence. By making such a claim you are saying that you don't believe markets move by supply/demand or that they only move via supply/demand up to certain points before they reverse. There may be a self-fulfilling prophecy somewhat though.