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