I think the comparison between AT and martial arts is actually more apt than you suspect - but AT is like boxing - the principles are ridiculously simple (step and pivot for AT, jab-cross-hook for boxing), but the way they can be combined and how they work in motion are endlessly complex and can be the study of a lifetime. And you need at least some amount of time with somebody more experienced to get a rough idea of the gestalt of the whole thing. Mauricio Castro has tried to sum up the principles of what tang is in "Tango: The Structure of the Dance", which may be helpful to other people, but for myself it was not helpful - i understood the things i had already understood before, but i wasn't able to learn things that i hadn't understood before. Again - very much like martial arts books

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So, my short answer would be: If you just want to do something that vaguely looks like tango just imitate whatever video you like, but to actually dance tango you have to learn how to dance tango. And learning tango without feeling what a good leader/follower feels like is awfully hard - and for me i think it would be impossible. I once said that i really don't understand how leaders get the patience to learn tango - its like somebody tosses a salmon that is still alive and flopping into your lap, shows you a delicately cut piece of sashimi and tells you "see, that is what it should look like - go for it".
So, now that i have finished my rant let me be hypocrital and tell you what tango is like:
There are only three moves in tango: Stepping, Standing balanced on one foot, and pivoting on this one foot.
The followers role is to expect nothing, but if something happens she has to take this impulse and put her whole self into that one step, make it a universe, and then come to perfect rest and openness again.
The follower owns all the space between the impulses - she can do whatever adornment or variation she wants as long as she is ready to accept the next impulse and the way she shapes the couple is not breaking the connection with the leader (which often, but not always means that she has to end up at the spot the leader expects within the time that the leader expects her to get there).
The leader gives an impulse, watches her go and the followes her.
The best way to figure out if the leader is actually marking what he thinks he is marking is to dance without using the arms using just the chest lead if in close embrace or the follower watching his chest in open embrace. If he can't communicate something using only his torso he shouldn't communicate it any other way.
To rephrase korey ireland "tango is the dance of a followers obsession with a leaders shirtbuttons - she strives to always look at the buttons, be close to them, and she does whatever it takes to stay in front of them"
There are no tricks in tango - the proper lead makes a move inevitable. Anything that requires the leader to explain what the follower should do is probably not lead well (ok, this is very dogmatic - i haven't yet figured out how to lead a cross - a fearless beginner with good balance will be able to follow almost everything else, but the lead to the cross results for me in a sort of stumbling short ocho. But i think striving for this inevitability is a good idea)
All the moves (volcada, boleo,sacada, gancho, enganche) that don't look like walking are just walking, too. A gancho or an enganche is a walk interrupted by a fixed object. A sacada is a walk through a mobile object - like a saloons swinging doors. A volcada or a boleo is a walking step that is interrupted before the weight is shifted.
GSH