The dictionary definition of 'science' is: 

1. a systematic study of the nature and behaviour of the material and physical universe, based on observation, experiment and measurement, and the formulation of laws to describe these facts in general terms. 
2. the knowledge so obtained or the practice of obtaining it. 
3. any particular branch of this knowledge. 
4.  any body of knowledge organised in a systematic manner. 
5. skill or technique.  
6. Archaic knowledge. [C14 via Old French from Latin scientia knowledge, from scire to know]
           -  Collins New Edition English Dictionary

With this definition in place, it is impossible to understand how any of the esoteric or divinatory arts: astrology, tarot, runes, I Ching, dowsing, etc, cannot be classified as 'scientific'.

Taking astrology as an example, does the definition of 'science' fit?  Here is astrology applied to the dictionary definition of science:
1. a systematic study.....of the behaviour of the.....physical universe......based on observation, experiment and measurement, and the formulation of laws to describe these facts in general terms. 
2. the knowledge so obtained or the practice of obtaining it. 
3. any particular branch of this knowledge. 
4. any body of knowledge organised in a systematic manner. 
5. skill or technique.  
6. Archaic knowledge.

So how is it that astrology is branded 'unscientific'?

The answer to this goes back to the 15th Century, and the dawning of the age of 'measurement'....if you could weigh it, measure it, describe it, it was 'scientific', but if there was nothing which was apparently sufficiently consistent to measure, then it was 'random', inexplicable, or unscientific.

The first dictionary definition, above, states that science is 'based on observation, experiment and measurement', but does not determine how consistent or repeatable those 'observations, experiments or measurements' must be in order to qualify as 'scientific'.

Astrology is based on an immense amount of detailed information (observations), refined over centuries (experiments), but what about the measurements?

Do you read your horoscope? Do you understand or interpret it for yourself? Does what appears in your horoscope actually occur in some form in your life?   Horoscopes do not describe 'absolutes', but only tendencies and liklihoods.   Does this make horoscopes 'unscientific'?

The answer is 'no', for the same reason that Heisenberg's Uncertainty Principle is part of accepted main-stream science!  At any particular level, 'the formulation of laws to describe these facts in general terms' must, by its very nature, include an 'error' function, either to cover experimental inaccuracies, or to cover the inadequacies of the 'generalisation' necessary in formulating a 'law'.  Heisenberg could no more be absolute about the location of electrons orbiting the nucleus of an atom than you can be absolute about your interpretation of your horoscope, so why should your horoscope be labelled 'unscientific'?

Another example is 'dowsing'.....take your dowsing rods into a field and experiment.  Everyone can dowse, even though many have never tried.  Everyone who has tried and found how sensitive and reliable a method of divination it can be is genuinely surprised, but most don't want to talk about it, unless they are labelled 'odd' in some way.

Why would someone who can 'dowse' be labelled 'odd'?  American soldiers in Vietnam who used dowsing to locate mines and booby traps obviously thought it was a normal-enough way to preserve their lives in an environment where hostilities and atrocities were deemed to be 'normal'.

The answer is that 'science' cannot yet explain how we can dowse: measurements have been taken that show a nerve response in the Pineal Gland at the top of the spine, in the centre of the brain.  The problem is that there is nothing which explains how the nerve response is triggered in the first place!!  And of course, if you cant measure or explain it by a general rule, it cannot be scientific!!  Or can it?

Look at the 5th definition of science: skill or technique.  Dowsing is both a skill (it can be taught, or enhanced by training), and a technique.  So dowsing IS scientific!

It still doesn't alter the fact that 'science' cannot produce a generalised law to explain its occurrence, but just because it cannot be explained does NOT mean it is unscientific, or does  not happen!!

This last point is perhaps the most important!!

You will often hear that 'science says it cannot happen', or 'it is impossible', even though people have direct experiences of actual events!   The confusion, then, is actually in the minds of the scientists, generated by their inability to describe or define actual events and occurrences within the framework of the laws they have defined for themselves.

Oh, excuse me! This is scientific heresy: could a scientific law be inadequate in its ability to explain the actual experience of real beings within a universal context?  Is it that the events do not actually occur, or is it that they occur, but their occurrence doesn't fit the self-determined laws?

The principle of 'debate' is an attempt to expose all aspects of a situation in order to uncover the 'truth'.  That means starting from an hypothesis, exploring it, and then producing a counter proposal and exploring it, etc.   With that principle in mind, we should not start from a precept of 'science is right' unless we similarly start from the precept that 'experience is right'.  Back to the context of 'dowsing'......

Science says dowsing cannot happen because there is no satisfactory explanation for its operation.   Experience says it does actually happen.  Conclusion of debate: Dowsing does actually happen, but scientific theories have not progressed sufficiently far to be able to explain how and why.

Now apply the same questioning to all mysteries, experiences, perceptions, and belief systems......look at what a different result you get!!   Other topics to be covered in Bright New Science will include gravity, levitation, particle/wave duality, speed of light, etc.