Some of you may have heard the phrase 'magical thinking' before. According to many people trained to think causally, magical thinking often involves treating a link of correlation (that is, a tendency to be associated) as a causal link: for instance, if we did a study that found that people with a greater body fat percentage tended to have more heart attacks than those who did not, and so we gave them a drug that had been administered in a study where it was found that the people who received the drug tended to have fewer heart attacks, we would have done purely magical thinking under this definition. After all, it's very likely that rather than having high body fat itself causing heart attacks, something that also contributes to body fat raises heart attack rates. And similarly, it may be somewhat likely that the people who received the drug in the second study were already less susceptible to heart attacks than those who did not. I'm not trying to fling verbal feces at the medical establishment; I'm just trying to show that, even if ritual and dance and ecstasy aren't involved like they are in some practices of magic, there's still a strong current of magical thinking manifest in our society.
I don't think this is a problem. As Ramsey Dukes points out, the technologies we create using science change society at a rate faster than science itself can keep up with. It's not necessarily a bad idea to avoid using prescription drugs or food additives that correlate with nasty side effects or poor health in order to avoid those maladies, particularly if more extensive research has yet to be performed.
In fact, this type of thinking can help avoid some of the pitfalls which science is subject to. For a long time, people were advised to avoid exposure to the sun due to harmful ultraviolet rays that can cause cancer. These rays are basically high-energy light that very occasionally will hit one of your at least 230 trillion chromosomes and may cause a genetic mutation, a small subset of which will cause cancer rather than simply the death of that cell or no impairment in function. Much more recently there has been a lot of news on the web about how important exposure to the sun is to health, with studies linking Vitamin D (which our body produces from sun exposure) to lower cancer rates, fewer allergies, and a variety of other health benefits.
This seems to be a case where one causal link that very seldom comes into play in normal situations (tanning beds are not a normal situation) received a disproportionate amount of attention because it was understood using analysis and causality, while the benefits of sunlight exposure had not been probed as extensively with those tools of understanding. This situation provides a synecdoche for why it's important not to put the entirety of our trust into any single system of knowing.
When we trust science and nothing else, we fixate on causal connections we understand. Often when we find a circle of causes (such as the water cycle, where evaporation causes cloud formation which causes precipitation), there is a tendency to write the rest of the matter off. The same thing occurs when we have limited instrumentation for looking at a complex system: for the better part of the 20th century, experimental psychologists refused to make reference to internal mental states simply because behavior was easier to objectively measure and quantify, even though it is obvious enough to anyone that your state of mind is one of the most pertinent things for psychology to address. Similarly, the idea of the body's electromagnetic field was only seriously considered long after the microscope's heyday, and biology is still riddled with problems that result from only being able to look at a great many tissues and cells when they are squished onto a slide rather than integrated into the system of the organism.
Science, and its basis, monological thinking, is very good at processing linear things. It may be indicative that science's ascendancy as we would recognize it today came after the invention of the printing press, which allowed people to send long, single-file chains of letters to each other. This makes science a very powerful tool, but it also makes it a limited one. As long as we require claims of truth to be of the form "A causes B" or vice versa, with no ambiguity, it is more difficult to accept synchronic orders as such, and much more difficult to understand retrocausation. In order to understand something science must force it to be a causal problem, and thus, for instance, we think of the water cycle as a closed loop rather than a set of processes that are simultaneously occurring in a way that allows each process to continue somewhere.
Alan Watts puts it very nicely: imagine a fence with a single post in it missing, so that you can see through to the other side in a limited area. Then imagine that a cat walks across the other side of the fence. You see the cat's head, then its torso, then its tail. Recognize that this perception of the space on the other side of the fence is just like our perception of time - just as we can only see a small slot of the neighbor's yard, we can only perceive a moment at a time. But we would not say that the head of the cat caused the tail of the cat. The two simply go with one another, neither causing its fellow. Perhaps, if we perceived time with fewer limitations, we would see that the birth and the death go with each other the same way. We might also understand larger patterns in human history and even in the behavior of quanta with an outlook on time that did not depend on causal statements to say anything at all.
If you feel that you have a hard time applying these ideas to your life, there's a way to fix that. The first step to thinking synchronically in a directly applicable manner involves interpreting coincidences. Think of the last time you experienced an uncanny coincidence. Odds are that you dismissed it after finding a possible, if not certain, way of explaining its occurrence. Next time you have one, don't try to explain to yourself why it happened in terms of causes. Instead, interpret it.
Now, be very careful about what you mean by not explaining it: if you take the coincidence as a message, interpreting it as a missive from a massive divinity, you ave explaining it and not interpreting it as soon as you stop thinking about the content of the message and start thinking about what could've sent it and why. Rather, think about what else is going on in your life that matches the coincidence in tone or content. In other words, rather than trying to cut to why the coincidence took place, find ways to see it as a bigger coincidence that the event happened to you specifically, and that it happened where and when it did.
This exercise will probably seem alien at first, but that's what opening your mind to a new way of thinking always feels like. I hope you give it a try; there may be a whole journey waiting for you behind this door.