Principle - Can this principle be expressed mathematically?

[MathHelp]

Hi there,

When it comes to disputes, the more you engage in arguing/conflict the more complicated the argument becomes for a third party to try and resolve.

The sooner you take your conflict to your manager or a judge (litigation), the easier it is going to be for them to figure out what has happened and resolve things quickly.

Is there away to present this idea mathematically? Preferably in simple maths...

I was thinking something similar to:

Conflict with two facts to resolve: C = 1/2 x 1/2. (i.e. if there is two facts then each fact is one half of a whole).

Conflict with three facts to resolve: C = 1/3 x 1/3 x 1/3. (i.e. if there are three facts then each fact is one third of the whole conflict)

I am not very skilled in maths so any advice or suggestions would be really useful.

The equation does not need to be technically correct. I am looking for something that helps give people a general idea of how unnecessarily engaging in verbal conflict can turn a simple issue into a much more complex issue.

Edited October 6, 2023 by MathHelp

[OldChemE]

As an alternative, try expressing the situation as an oscillation (I say/he says/.......).  When there is too much feedback the oscillation amplitude increases.  The goal of conflict resolution is to reduce the amplitude of the oscillation until it approaches zero.  In therms of a classical electrical oscillator, this means damped oscillation.  The appropriate equations can be found in electrical textbooks.  The point of using the oscillator analogy is that an argument can be de-escalated by making small concessions that gradually reduce the amplitude of disagreement (i.e. by turning the out of control oscillation into damped oscillation).

[MathHelp]

What I was hoping to show is a bit different. I am not looking to show the benefits of de-escalation - in fact de-escalation would be counter to the point that I am trying to make. The point I am trying to make through mathematics (while lacking the mathematical skills to actual make it) is that any time you add to an argument (whether you add something positive or negative) it becomes more complicated for a third party to resolve because they get information overload and there are too many things to dispute.

I call it "The Maths of Muddying the Waters".

As an example:

Scenario 1:

1. Bob steals Gregs apple.
2. Greg goes straight to the police and shows them footage of Bob stealing the apple.
3. The police tell Bob to give Gregs apple back and give him a warning.
4. Issue resolved.

Scenario 2:

1. Bob steals Gregs apple.
2. Greg demands Bob return it.
3. Bob refuses.
4. Greg tries to make a concession and says that Bob can have the apple so long as he does not steal any more.
5. Bob refuses.
6. Because Bob refuses not to steal again Greg demands the apple be returned.
7. Bob says no because Greg already said that Bob can have the apple.
8. Greg disagrees and says he only said that conditional on Bob agreeing not to steal again.
9. Bod says he only heard Greg say he could have the apple and Greg only demanded that Bob not steal any more apples after he had given him the apple.
10. Greg tries to physically take the apple from Bob.
11. Bob pulls away and pushes Greg back causing Greg to fall over.
12. Greg now accuses Bob of assault. 
13. Bob claims Greg assaulted him and he was defending himself.
14. The issue ends up in court where the judge now has to decide:

1. Did Bob steal the apple?

2. Did Greg give Bob the apple?

3. Did Greg assault Bob?

4. Did Bob assault Greg?

5. Did Bob act in Self defence?

6. Was Greg defending property?

As you can see, engaging in argument turned a very simple problem into an unnecessarily complex situation which is going to cost Greg a lot of money, waste the courts time, and possibly result in Greg going to prison for assault. Even if he does not go to prison for assault, the proceedings can still be very stressful.

Note: I have given a really bad example, there are plenty of good examples in the Family Court system but it would take far too long to articulate the entire chain of events (which literally proves my point about the unnecessary complexity people create for themselves).

Edited November 4, 2023 by MathHelp

[MigL]

Chaos theory and diverging oscillations that OldChemE has mentioned.

[MathHelp]

Chao theory is beyond my comprehension and the suggestion by OldChemE does not actually cover what I am wanting to achieve.

Any chance you could explain in words (or very basic maths) how chaos theory can be used to illustrate the what I am trying to say? Remember:

1. This needs to be something simple for people without a maths background to understand.

2. It doesn't need to be 100% accurate. It just needs to be a way of giving a general understanding of the idea, even if the maths would breakdown under mild scrutiny. 

 

[swansont]

You don’t need to understand the math to use the result, so “people” don’t need to understand the math, but in order to create the model, you need to understand the math. You have to quantify the effects and have a formula that describes the various interactions and processes.

Or you can go with a boolean system, with a series of yes/no questions to be answered, which could be laid out in a flowchart. But you need to have a comprehensive list of questions and cover all of the possible situations.

It might be helpful to learn a little bit of game theory

[Sensei]

On 10/6/2023 at 8:30 AM, MathHelp said:

The sooner you take your conflict to your manager or a judge (litigation), the easier it is going to be for them to figure out what has happened and resolve things quickly.

Judges, especially in the U.S., twelve jurors, don't have that option, because they are ordinary people randomly selected from the crowd..

  

On 10/6/2023 at 8:30 AM, MathHelp said:

The equation does not need to be technically correct. I am looking for something that helps give people a general idea of how unnecessarily engaging in verbal conflict can turn a simple issue into a much more complex issue.

For such things, the simplest way is to run a computer program/script that will perform the most basic version of the equation in a loop.

Don't know the result? It doesn't matter, use a (pseudo) random number generator and repeat the procedure over and over to average the results.

 

 

Edited November 4, 2023 by Sensei

[studiot]

7 hours ago, MathHelp said:

Chao theory is beyond my comprehension and the suggestion by OldChemE does not actually cover what I am wanting to achieve.

Any chance you could explain in words (or very basic maths) how chaos theory can be used to illustrate the what I am trying to say? Remember:

1. This needs to be something simple for people without a maths background to understand.

2. It doesn't need to be 100% accurate. It just needs to be a way of giving a general understanding of the idea, even if the maths would breakdown under mild scrutiny. 

 

Is this homework ?

 

The mathematical model you seek is called a Markov process.

This is the process underlying what is popularly called artificial intelligence.

The good news is that the concept is very easy to understand.

The bad news is the quantity of data that needs to be collected and processed to achieve any reasonable sort of correspondence between the model and reality.

For AIs literally trillions of cases were examined to obtain realistic the required realistic processes.