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Good evening! I have been encouraged to ask my question on this forum, even though it might be perceived as a pure subjective and open-ended question, but I am 100% sure there is a perfectly acceptable solution to my equation.

I am a tango dancer, having been doing this for 5 years. Recently I have been asking myself if there would be a way to quantify this transcendental dance, in order to explain in a simple, yet elegant way why a few dances seem to offer a pure bliss, meditative-like 0 state.

I can offer a few constants which are common to all dancers:

  • The level of interest of the lead: IL
  • The level of interest of the follower: IF
  • The effect music has on the lead: M1
  • The effect music has on the follower: M2
  • Dance chemistry (dancing in sync, anticipation, beautifully executed moves, posture etc): c

Since I wanted to keep this simple and elegant, following the Yin and Yang principle, I decided to make the formula in the following way: ((IL * M1) + (IF * M2)) / 2 - c = 0. If both dancers enjoy the music and completely surrender themselves to each other, the result of the nominator is 2, therefore 1 - c = 0. If the chemistry is also perfect, then we have a perfect dance (dancers call it "tangasm").

However, there are a few problems with this. If there is no chemistry and none of the partners actually enjoy the music or dancing with each other, we might have a situation such as 0 - 0 = 0. This does not mean bliss, this is a complete waste of time.

Can you please suggest me a way to force the nominator to be different than 0 no matter what happens? And even so, we might still be in the weird situation of having a mediocre interest and chemistry, say 0.35, yet having 0.35 - 0.3 = 0 .05, which is close to a perfect experience, but in fact it's awkward.

Please forgive my limited vocabulary and math knowledge, I have not taken a math class in more than 7 years, but I hope someone might see the fun in such a question and provide an alteration or maybe turn it into a limit problem or inequality. I also hope the question does not violate the rules of the forum.

Thank you!

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closed as primarily opinion-based by Somos, Yanior Weg, Theo Bendit, Javi, José Carlos Santos May 2 at 20:53

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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A very interesting modeling problem! Not unlike prospect theory, except your model doesn't give the partners choices in the parameter values. Well, anyway...


First, I would suggest labeling the music effects with subscripts that relate to leader and follower: $M_{L}$ is the effect of music on the leader, $M_{F}$ on the follower. Similarly, the interests are $I_{L}, I_{F}$.

Questions:

*) Am I correct in surmising that each of the parameters you introduced varies continuously in the range from 0 to 1?

*) Why is it an equation, and not just an expression of (Q)uality of the tango experience: $$ Q = {I_L M_L + I_F M_F \over 2} - c \quad ? $$ (Unless your $2-c$ was the denominator; i.e., you meant to parenthesize it $(2-c)$.)

*) Is this expression a measure of "Badness" or "Goodness"? I.e., is $Q = 0$ the the worst case? If so, why do you consider $Q = 0.05$ close to a perfect experience? And if it is the best case, why do increased interest and music effect result in a worse experience?

*) Are chemistry and interest really independent variables? Can a partner sustain interest for a substantial time if there is no chemistry?

CONSIDERATIONS

If $Q$ measures how good the experience quality is (i.e., the higher the $Q$, the better), then $Q$ should increase with $c$ and with each $I$ and each $M$. The formula $$ {c + I_L M_L + I_F M_F \over 3} $$ will do the job. This formula has the following properties:

  • unless all five parameters are zero, the numerator is positive
  • if all five parameters are zero, then the formula gives a zero (an absolutely worst experience)
  • if all five parameters equal 1, then the formula gives a 1 (a perfect experience).

Are you troubled by the possibility that the numerator may be zero? Why?

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  • $\begingroup$ Thank you so much for your reply! I will try to answer your questions: *) Yes, the parameters vary from 0 to 1 just for the ease of computation, so that 1 is the best option. *) It may be an expression of quality as well, why not. *) I do not consider 0.05 a perfect experience in that case, which showed that my model was wrong. Since it was a subtraction, 0 would be the perfect case. But with Q, 1 is the best experience. This is why I was troubled of having the numerator 0. Chemistry and interest, indeed, might be related. Unless they dance perfectly, but they are simply tired. $\endgroup$ – Tango Apr 30 at 19:59
  • $\begingroup$ In my humble attempts at combining philosophy with math, for me, 0 meant a mindfulness state. But since they are 2 dancers, the result "1" might mean this is the way they become 1, no matter what intentions they have from the embrace. it is interesting to think what else might be added to the model as to keep it simple and beautiful. $\endgroup$ – Tango Apr 30 at 20:02
  • $\begingroup$ Yes, we can reconcile that: think of $Q$ as [1 - (total impurity)], rather than (total impurity). The perfect mindfulness is zero impurity, which corresponds to $Q=1$. Also, we can let chemistry affect interest by calling $I_{L}, I_{F}$ "primary interest" (i.e., before we factor in the chemistry), and correct them in the formula by using chemistry: $$ {c + {1 \over 2 - c} \left(I_L M_L + I_F M_F \right) \over 3}. $$ When all the parameters are zero, this expression is zero (complete impurity of mindfulness, worst experience). When all parameters are 1, the expression is 1. $\endgroup$ – avs Apr 30 at 20:07
  • $\begingroup$ Instead of interest (difficult to measure), you might want to call the $I$'s "involvement". This way, being tired doesn't mean less interest, but it does mean less involvement. $\endgroup$ – avs Apr 30 at 20:14
  • $\begingroup$ This is so amazing and beautiful... it proves that there is no need to force something to equate to 0. And even if we want, we can still change the signs to make 0 be the "Goodness" state. Thank you for your effort and enjoying this model. $\endgroup$ – Tango Apr 30 at 20:27

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