My quest for pleasure: unraveling the secrets of heavenly joy

Part 2

A bit of mathematical analysis

This is part 2 of a series of blog posts. Please read part 1 first.

Let's see if we can get some insights from the pleasure formulas using analysis:

The core equations are:

$$ P_1 = P^{prop}_1 + c_1 \cdot P^{soc}_1 $$

and

$$ P_2 = P^{prop}_2 + c_1 \cdot P^{soc}_2 $$

First we should simplify the equations a bit. We could for instance assume that the social pleasures $P^{soc}_i$ follow the pleasures $P_i$ very fast. This would mean:

$$ P^{soc}_1 \approx P_2 $$

and

$$ P^{soc}_2 \approx P_1 $$

If we assume equality, we get the following simplified equations:

I. $P_1 = P^{prop}_1 + c_1 \cdot P_2$

and

II. $P_2 = P^{prop}_2 + c_1 \cdot P_1$

These correspond in fact to two different computation steps. But once the algorithm has reached convergence, $P_1$ and $P_2$ should not change anymore.
Therefore we are allowed to insert the RHS from II into I, and we get an equation which contains only $P_1$. If we solve it for $P_1$, we get:

$$ P_1 = \dfrac{ P^{prop}_1 + c_1 \cdot P^{prop}_2 }{ 1 - c_1 \cdot c_2 } $$

We see that the pleasure of person 1 corresponds to its own proper pleasure plus the felt fraction of the proper pleasure of person 2. This is then multiplied by an amplifying factor A:

$$ A := \dfrac{ 1 }{ 1 - c_1 \cdot c_2 } $$

This factor is not bounded, because $c_1 \cdot c_2$ can become very close to 1 (for values of both $c_i$ close to 1, i.e. high mutual compassion)

This explains why very high values for the pleasure are possible.

As this amplifying factor is strictly positive (both $c_i$ < 1), we see that person 1 experiences (positive) pleasure exactly if

$$ P^{prop}_1 + c_1 \cdot P^{prop}_2 > 0 $$

$$ P^{prop}_2 > \dfrac{- P^{prop}_1}{c_1} $$

This means that a positive experience is possible even if $P^{prop}_1$ is negative (a high compassion $c_1$ and a large and positive proper pleasure $P^{prop}_2$ of person 2 are required). We could call this the masochistic case.

But because of

$$ P_2 = (P^{prop}_2 + c_2 \cdot P^{prop}_1) \cdot A $$

must $c_2$ (= compassion of person 2) in this case be low to keep the proper suffering $P^{prop}_1$ of person 1 away from person 2. But this keeps the amplifying factor A low as well. In the masochistic case the pleasure of both persons is therefore limited.

Please note that we are only talking about psychical pain here! Any exchange of physical pain does not appear in these equations! Such an exchange might therefore be compatible with a strong shared experience of pleasure.

Stay tuned (and please don't take all this too seriously)!

Image on top: DALLE-3

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