It is common to think of alchemy as only being a superstitious fore-runner
of chemistry - a mistaken search for 'The Philosopher's Stone' that would
turn lead into gold.  But there is a long tradition of considering it as
a metaphor - a source of symbolism (like tarot, numerology and astrology) -
that can be used to help understand some basic human truths.

'BDSM' stands for safe, sane and consensual Bondage & Discipline,
Dominance & Submission and Sadism & Masochism.
A 'Top' is one who binds, dominates or inflicts pain.
A 'Bottom' is one who is bound, submits or accepts pain.

Such nice clear definitions aren't they?  How tempting to think that matters
can be simplified to "Everyone into BDSM is either a top or a bottom".
To think of BDSM as a zero sum game; the masochist loses pleasure and the
sadist gains it; the submissive loses power and the dominant gains it;
the person tied up loses freedom of action and the binder gains it.
So tempting, so mathematically precise and quantifiable, ... so wrong.

Which is not to say that BDSM can never be understood, just that humans
don't always fit the mathematical mold of 1 + 1 = 2.  This is where
alchemy comes in.  Long before the invention of alternative algebras,
magickians were investigating the idea of transmutation.  One way of
looking at Sex Magick (S&M) is as the transmutation into pleasure of pain.

The first step is to stop thinking in such a limited dualist way; all
black and white, no grey.  Some people like sadism but not bondage.
Some people are simultaneously masochistic and dominant.  Some people
like both sadism and masochism but with different people or at
different times.  Such people who are neither pure tops nor pure bottoms
have a name of their own to be proud of, 'switches'.

Pleasure is not a single quality.  There are many different sources of
pleasure.  If a sadist gains pleasure from inflicting pain, that doesn't
mean the masochist must lose pleasure from receiving it.  Pleasure and
pain are not opposites.  When pain is pleasurable (such as when a jogger
passes the pain barrier and gets a high from endorphins - the natural
opiates the body produces in response to pain) then the sum of the
two people's pleasure has increased.

Freedom is not a single quality.  There are many different actions
which you can be free to do.  Someone who has been tied up may lose
the freedom to move about, but gain the freedom to struggle as much
as they want without fear of consequences.  It can be though of as
a transmutation of one form of freedom to another form that may at
that point be more valuable (desirable) to the person wanting to be
tied up.  It can also be thought of as an exchange, where the bindee
offers up various freedoms, in return for which the binder accepts
the accompanying burdens of responsibility.

Power is not a single quality.  There are many different abilities
which contribute to your personal power.  The ability to take risks,
the ability to face unpleasant truths, self-assurance, strength of
will, self-control, the ability to accept with calm the things we
cannot change, many other things.  D&S can be used to transmute
(or exchange) different types of power, often increasing the total
amount.  For example, one sub with much strength of will but little
self-control might arrange themselves into a relationship where,
by keeping the willfulness under control, they have the opportunity
to strengthen their self-control.  Another sub who is self-controlled,
but cannot take even small risks, might find a way through d&s to
explore that risk taking aspect.

No one can give up their power to choose what to do - because at any time
they at least have the choice as whether to submit or resist, whether
to consent or not.  But in d&s, as a tool in increasing other powers,
their powers to choose can be narrowed down so that is the only choice
they have.  The reason for such a submission, for the consenting to
have extreme forces applied to reduce your choices, is important.
There is a difference between someone submitting to you, because you
will beat them otherwise, and someone freely submitting to you then
doing something you order because you will beat them otherwise.

If someone submits to you because you will beat them otherwise, then
you are a bully or an abuser, not a dominant.
If someone submits to you because you will give them a diamond if
they do, or will leave them if they don't, then you are a trader
or a manipulator, not a dominant.
But if someone submits to you because they wish to, for submission
itself and its intrinsic advantages, then you have found something
more precious than all the gold in the world.