Life as a function

Definition

In previous post we defined the Hypothesis, here I propose my thoughts about the function f. This is a set of actions a person performs. So let’s split this function by subfunctions in the following way:

f(t) = i = (1, n) fi (ai t)

Where

fi – some area of actions

ai ∈ [0, 1], i = (1, n) ai = 1

These limitations are obvious as we have limited time and we have control how to spend it. Also, we need to define t as the time span. For the first test I will use a week what is 24 x 7 = 168 hours. I don’t think we need to extract time when we’re sleeping or working as, for instance, with regular 8h sleep most of us performs much better than with 4h daily sleep. Work cannot be extracted as well, because as e.g. person can find side job and it will influence entire f(t) function.

My set of actions

The set of fi defines our success as we discussed above. For my test I selected following activities:

  • f1 – sleep
  • f2 – work
  • f3 – family
  • f4 – sport
  • f5 – education
  • f6 – business
  • f7 – friends
  • f8 – relax

Structure

Let’s dig into the structure of the functions. Probably functions are not linear and may have sigmoid e.g. structure – impact should mitigate overtime:

But as for simplification let’s assume these functions are linear in this case:

fi = bi t + ci

We got an optimization problem:

max( i = (1, n) bi ai t + ci ),

ai ∈ [0, 1], i = (1, n) ai = 1

This optimization problem reminds neural network equation but as we have ai limitation it can’t be solved with gradient descend. I’m planning to use stochastic search for few first weeks of testing the Hypothesis. But are ideas for optimization are welcome.

Another problem we have is the fuzziness of measurements. But this is discussion for further posts.

For coming week, I plan to try figure out the structure of these functions. Can we control bi? Is it measure of quality of our actions? E.g. doing sport, we can walk, or we can run; playing with kids we can either check phone or be fully dedicated; etc. Also, I will setup ai with my common sense and try to measure results.

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