What is the Mathematical Model for Desires and Eating Habits?

[Fat=laziness]

Homework Statement

A persons desire to eat is inversely porportional to a persons desire to not eat. The problem is I don't know how to write this down mathematically. Let's give a value to someone's desire to not eat after 3 days [40], that persons desire to not eat is going to be [-40]. Let x be the desire to eat, and -x is the desire to not eat, let -x = y. I can right down an equation for this:

Homework Equations

x = -y, 40x = -40y

The Attempt at a Solution

y = k / x, -40 = ?/40, I have no clue what I'm supposes to do.

 

[jedishrfu]

inversely proportional means:

desire to eat = x

desire not to eat = 1 / x

what is the rest of the problem?

 

[Fat=laziness]

inversely proportional means:

desire to eat = x

desire not to eat = 1 / x

what is the rest of the problem?

Does it make sense? Desire to eat [40], desire to not eat [1/40]? It doesn't make sense.

 

[Mark44]

Most of it doesn't make sense to me, starting with the basic premise that "A persons desire to eat is inversely porportional to a persons desire to not eat."

If we are to assume that this is reasonable, then what jedishrfu said is pretty close. Two quantities are inversely proportional if their product is some nonzero constant. If E(t) is the desire to eat at day t, and N(t) is the desire to not eat at day t, then we have E(t) * N(t) = k, with k being the constant.

Alternatively, E(t) = k/[N(t)].

The basic idea is that if you double E(t), then N(t) gets halved. If you triple E(t), then N(t) gets reduced to 1/3 of its former value.

For a more realistic example, if you have a rectangle whose area is constant, then the length and width are inversely proportional.

 

[Fat=laziness]

Most of it doesn't make sense to me, starting with the basic premise that "A persons desire to eat is inversely porportional to a persons desire to not eat."
.

I shouldn't have used the inverse relation. What I really meant was this: x = -y, 40x = -40y, how can I change this equation to make one go up in value while the other goes down? It's like when i spend more money I have less. Do you see what I mean? Is there an equation for that?

 

[Curious3141]

I shouldn't have used the inverse relation. What I really meant was this: x = -y, 40x = -40y, how can I change this equation to make one go up in value while the other goes down? It's like when i spend more money I have less. Do you see what I mean? Is there an equation for that?

It's as simple as $x + y = k$, where x is "desire to eat", y is "desire not to eat" and k is a constant (does not change), all the quantities being given in arbitrary units of your choosing.

Let's say k is set at 100. When x is 10, y is 90, but when x goes up to 30, y goes down to 70. And so forth.

 

[Fat=laziness]

It's as simple as $x + y = k$, where x is "desire to eat", y is "desire not to eat" and k is a constant (does not change), all the quantities being given in arbitrary units of your choosing.

Let's say k is set at 100. When x is 10, y is 90, but when x goes up to 30, y goes down to 70. And so forth.

X +y = k, * D + -D = action


D =Units of desire*

Faced with two options of actions, if the desires adds up a (-) then no action, if the desires add up to a (+), then action.

Is the math right?

 

[Curious3141]

X +y = k, * D + -D = action


D =Units of desire*

Faced with two options of actions, if the desires adds up a (-) then no action, if the desires add up to a (+), then action.

Is the math right?

You can set k to zero if you want x = -y.

It would help if we knew exactly what you were trying to accomplish. Is this homework? If so, post the *exact* question, verbatim.

 

[AGNuke]

Suppose that person is served a grand buffet. If he has desire to eat that day, he will take as much as it can take. But if he do not have desire, he will take as minimum as possible. (Fraction?) If you see, negative desire can mean that he has desire to "give" food, opposite to his desire mentioned in question.

And it is as simple as tossing coin. Chances of getting head is inversely proportional to chances of getting tail. Desire to eat is inversely proportional to desire not to eat. The more hungry you are, the less you will think to ditch the food, but you may think of eating less, this and that (desire not to eat). If you are on fast, you will ignore most of the food you are served. That is not stopping you to steal one grape. See, this is a reasoning I am making with myself. Mathematics takes account of reason.

 

[Fat=laziness]

You can set k to zero if you want x = -y.

It would help if we knew exactly what you were trying to accomplish. Is this homework? If so, post the *exact* question, verbatim.

This is not really homework it's just an idea of mine (it's still important for my math skills), but I'll explain anyways. Here's my premises: given all perceived option of choices a person will always choose the most desirable at that time. there are units of desires at given moments of time.

A persons desire to eat after 3 days fasting is [40] that means that persons desire to not eat is [-40]. If that persons desire to eat went up 2 points, then his desire not to eat would go down
-2 points, if the desire to eat would go up 5 points, then the desire to not eat would go down -5 points. My question is, is there an equation for this?

 

[Mentallic]

The only reason I don't like this problem is because I don't know what the units for "desire to eat" are measured in. If we use x+y=k, what are the units for k?

 

[Curious3141]

This is not really homework it's just an idea of mine (it's still important for my math skills), but I'll explain anyways. Here's my premises: given all perceived option of choices a person will always choose the most desirable at that time. there are units of desires at given moments of time.

A persons desire to eat after 3 days fasting is [40] that means that persons desire to not eat is [-40]. If that persons desire to eat went up 2 points, then his desire not to eat would go down
-2 points, if the desire to eat would go up 5 points, then the desire to not eat would go down -5 points. My question is, is there an equation for this?

First of all, if it's not homework, you might have been better off posting in the Gen Math forums, which would better accommodate more speculative topics like this.

Second, what I think you're trying to do is to construct a simple mathematical model governing motivation to eat. You're considering "desire to eat" as an independent variable, and this might be influenced by hunger, attraction to the particular food, smell and taste, etc. It is possible to introduce another variable like "desire to abstain from eating" as another independent variable, and this might be influenced by health considerations, cost of the food vs budget, etc.

It makes very little sense to link these two variables so directly as you did. For one thing, the desire to abstain from eating may be influenced by wholly different factors, as I mentioned. For another, making one simply the negative (additive inverse) of the other means that the two will always end up cancelling each other out, and you'll have no net effect. What would you accomplish by doing it this way?

 

[Curious3141]

The only reason I don't like this problem is because I don't know what the units for "desire to eat" are measured in. If we use x+y=k, what are the units for k?

That is not in and of itself a major objection, because there are plenty of subjective ordinal scales used in clinical practice - e.g. pain scores. It's not unreasonable to set up a "hunger score" for instance.

There are no real units to such an ordinal scale, so we don't really have to worry about dimensional consistency.

 

[Mentallic]

That is not in and of itself a major objection, because there are plenty of subjective ordinal scales used in clinical practice - e.g. pain scores. It's not unreasonable to set up a "hunger score" for instance.

There are no real units to such an ordinal scale, so we don't really have to worry about dimensional consistency.

These scores are rarely ever linear, and that's just the thing with this kind of problem: How do you devise a linearly ranked system to measure your hunger?

 

[Fat=laziness]

First of all, if it's not homework, you might have been better off posting in the Gen Math forums, which would better accommodate more speculative topics like this.

Second, what I think you're trying to do is to construct a simple mathematical model governing motivation to eat. You're considering "desire to eat" as an independent variable, and this might be influenced by hunger, attraction to the particular food, smell and taste, etc. It is possible to introduce another variable like "desire to abstain from eating" as another independent variable, and this might be influenced by health considerations, cost of the food vs budget, etc.

It makes very little sense to link these two variables so directly as you did. For one thing, the desire to abstain from eating may be influenced by wholly different factors, as I mentioned. For another, making one simply the negative (additive inverse) of the other means that the two will always end up cancelling each other out, and you'll have no net effect. What would you accomplish by doing it this way?

First of all I'm new to this forum so I apologize for putting it in the wrong section. I'm not looking for a precise mathematical model for our decisions, however I'm asking for, given that we know the persons desires, and given this premise that; of all perceived options of actions a person will always choose the most desirable to him at that time, and given that there's scales of desires, can we make a simple mathematical formula?

I know desires are caused by other factors, but I'm asking for, given that we know these factors, can we make a simple mathematical formula for this?

And lastly I know that I'm not very skilled in mathematics (that's why I made some dumb mistakes here). That's why I put it in the homework section, and asked for people's help.

 

[Curious3141]

These scores are rarely ever linear, and that's just the thing with this kind of problem: How do you devise a linearly ranked system to measure your hunger?

If you have "truly" quantitative measurements (usually called "interval variables" in statistics - like weight, height, temperature), then you can do lots of meaningful manipulations with them. However, you can have semi-quantitative variables called "ordinal variables" where the difference between numerical values is not meaningful, but the rank is - like pain scores and order of childbirth. These can still be manipulated in equations and used in nonparametric statistical tests, for example. Of course, it's not as robust as in the former case.

Anyway, we're digressing. It's better that the thread starter defines exactly what he wants his way, because it's his problem.

 

[Curious3141]

First of all I'm new to this forum so I apologize for putting it in the wrong section. I'm not looking for a precise mathematical model for our decisions, however I'm asking for, given that we know the persons desires, and given this premise that; of all perceived options of actions a person will always choose the most desirable to him at that time, and given that there's scales of desires, can we make a simple mathematical formula?

I know desires are caused by other factors, but I'm asking for, given that we know these factors, can we make a simple mathematical formula for this?

And lastly I know that I'm not very skilled in mathematics (that's why I made some dumb mistakes here). That's why I put it in the homework section, and asked for people's help.

You can conceivably do it like this:

Let's say there are four factors influencing the motivation of a person to act a certain way.

w and x measure factors favouring action, while y and z measure factors favouring inaction.

The threshold for action is A > 0, while the person doesn't act if A ≤ 0.

You can set up an equation like this:

$$k_1w + k_2x + k_3y + k_4z = A$$

where the respective "k"s are weighting constants that influence how important each variable is relative to the others. You can make $k_3$ and $k_4$ negative (while leaving the other two positive) in order to ascribe negative weights to y and z, as you require.

This is just a simple linear model, there's no single way to do this sort of thing.

 

[Fat=laziness]

You can conceivably do it like this:

Let's say there are four factors influencing the motivation of a person to act a certain way.

w and x measure factors favouring action, while y and z measure factors favouring inaction.

The threshold for action is A > 0, while the person doesn't act if A ≤ 0.

You can set up an equation like this:

$$k_1w + k_2x + k_3y + k_4z = A$$

where the respective "k"s are weighting constants that influence how important each variable is relative to the others. You can make $k_3$ and $k_4$ negative (while leaving the other two positive) in order to ascribe negative weights to y and z, as you require.

This is just a simple linear model, there's no single way to do this sort of thing.

Thanks, just one more point. Even if all desires are less than 0, a person will choose the one closest to 0.

 

[Curious3141]

Thanks, just one more point. Even if all desires are less than 0, a person will choose the one closest to 0.

This is not very clear at all.

 

[Fat=laziness]

This is not very clear at all.

I'll give you an example: a person faced with two options, kill himself [-40], and live a miserable life [-36] the person will choose to live a miserable life. A person will always choose the option that has th highest desire value, even if it's all negative. See what I mean?

 

[Curious3141]

I'll give you an example: a person faced with two options, kill himself [-40], and live a miserable life [-36] the person will choose to live a miserable life. A person will always choose the option that has th highest desire value, even if it's all negative. See what I mean?

If it's just a question of finding the greater value between two options, then just use the maximum function (max).

$$max(x,y) = \frac{1}{2}(x + y + |x - y|)$$

where |a| represents the absolute value of a (e.g. |3| = |-3| = 3).

In your example, max (-36,-40) = ½*(-36 - 40 + 4) = ½*(-72) = -36.

(You'll need to work out what you want to do when the values are tied, if ever).

The max function can be extended to a greater number of arguments by just pairing them up, then finding the maximum recursively.

But I thought you wanted to add individual values to find a net "action". At any rate, I don't think I can help you any further until you're able to state very clearly and rigorously what you want.

 

[Fat=laziness]

If it's just a question of finding the greater value between two options, then just use the maximum function (max).

$$max(x,y) = \frac{1}{2}(x + y + |x - y|)$$

where |a| represents the absolute value of a (e.g. |3| = |-3| = 3).

In your example, max (-36,-40) = ½*(-36 - 40 + 4) = ½*(-72) = -36.

(You'll need to work out what you want to do when the values are tied, if ever).

The max function can be extended to a greater number of arguments by just pairing them up, then finding the maximum recursively.

But I thought you wanted to add individual values to find a net "action". At any rate, I don't think I can help you any further until you're able to state very clearly and rigorously what you want.

There's two aspects to this theory, the desire value of the single option, and the desire values of many options and the maximum value gets selected.

I think your first equation works for the desire value for one option. And the second equation works for many options when compared.

 

[Curious3141]

There's two aspects to this theory, the desire value of the single option, and the desire values of many options and the maximum value gets selected.

I think your first equation works for the desire value for one option. And the second equation works for many options when compared.

So you should have a good starting point to try and formulate your model, hopefully.

 

[Fat=laziness]

So you should have a good starting point to try and formulate your model, hopefully.

Thank you, appreciate your help.